CFD Analysis of Cold Stage Centrifugal Pump for Cooling of Hot IsostaticPress with Validation Case Study

Shane Hereford

Master’s Thesis within Department of Mechanics

Academic Advisor: Dr. Stefan Wallin

Industry Advisors: Dr. Per Burstrom and Oscar Olovsson

August 9, 2017

AbstractHot isostatic pressing (HIPing) has been a growing material treatment process for performance part manu-facturing for over 50 years. This process of using an inert gas at high temperature and pressure to densifymaterials leads to vastly improved material properties by removing pores and other micro-flaws. Interest forHIP treatment has greatly increased in recent years due to the development of metal 3D printing technology.HIP treatment is very well suited for treating 3D printed and cast parts due to their relatively poor materialproperties.

An important part of any HIP cycle is the cooling phase. New uniform and rapid cooling technology hasvastly reduced HIP cycle times, but room for further improvement exists. This study aims to accurately andtrustfully evaluate the performance of one of a pair of centrifugal pumps used in a Quintus Technologies ABHIP cooling system. Computational fluid dynamics (CFD) software and techniques are used to achieve this.This paper is split into two main parts; the first of which is a validation case study, and the second is theperformance analysis of a Quintus HIP cold gas pump. The validation case study is conducted to supportthe accuracy and reliability of results obtained in the Quintus cold gas pump performance analysis.

The validation case study results show good agreement with experimental data and supports the accuracy ofCFD in the analysis of centrifugal pumps. Both detailed flow and macro flow characteristics are shown to beaccurately predicted. The pump curve generated for the Quintus Cold gas pump quantifies its performanceover a range of rotational speeds and mass flow rates. The work done here lays the groundwork for furtheranalysis and improvement of Quintus HIP cooling systems.

Keywords: CFD, HIP, Quintus Technologies, Centrifugal pump, pump curve

Acknowledgements

I would like to give my utmost gratitude to my supervisors at Quints Technologies AB, Dr. Per Burstom andOscar Olovsson, for their outstanding guidance during this thesis work. Their feedback on the report andpresentations was very much appreciated and helpful. I would also like to thank the rest of the employees atQuintus Technologies for providing a fun and challenging work environment where I always felt supported.

From the Royal Institute of Technology, KTH, I would like to thank my academic supervisor Dr. StefanWallin for his academic and administrative support. A large part of simulations for this thesis were performedon resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Centre forHigh Performance Computing (PDC-HPC). Dr. Wallin’s help with getting access to the KTH HPC-PDCcomputing cluster was critical to the completion of this project.

Nomenclature

Abbreviations

CAD Computed Aided Design

CFD Computational Fluid Dynamics

ERCOFTAC European Research Community on Flow, Turbulence, and Combustion

HIP Hot Isostatic Press

RANS Reynolds Averaged Navier-Stokes

RMS Root Mean Square

SST Shear Stress Transport

URC Uniform Rapid Cooling

URQ Uniform Rapid Quenching

Subscripts

0 at inlet

1 at impeller blade inlet

2 at impeller blade outlet

2D 2D value

3 at diffuser vane inlet

3D 3D value

4 at diffuser vane outlet

t Total value

u Usable value

Symbols

ψ Total Pressure rise coefficient -

1

ρ Density kgm3

A Area m2

b Blade span m

c Fluid velocity ms

Cp Coefficient of static pressure -

D Diameter m

g Gravitational acceleration ms2

Gi Impeller circumferential pitch rad

H Pump head m

h Average edge length m

N Number of elements -

P Power Js

p Static pressure Pa

Q Volumetric flow rate m3

s

q Dynamic pressure Pa

r Radius m

Ti Impeller blade passing period s

U Specific internal energy ms

ss

u Impeller blade tip velocity ms

V Volume m3

W Specific work m2

s2

yi Impeller circumferential coordinate rad

z Vertical distance coordinate m

zd Number of diffuser vanes -

zi Number of impeller blades -

2

Contents

1 Introduction 81.1 Hot Isostatic Pressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 Centrifugal Pumps and Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Quintus Cold Gas Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Aim of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5.1 ERCOFTAC Centrifugal Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.6 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6.1 Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.6.2 Pump Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Method 212.1 ERCOFTAC Validation Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.1 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1.2 2D Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.1.3 3D Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.1.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.1.5 Numerical Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.1.6 Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.7 2D Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.8 3D Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.9 Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Quintus Cold Gas Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.1 Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.2.3 Numerical Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2.4 Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2.5 Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2.6 Data Acquisition Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2.7 Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Results 383.1 ERCOFTAC Validation Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.1 2D Steady State Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 2D Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1.3 2D Steady State Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1.4 2D Transient Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.1.5 2D Transient Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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3.1.6 3D Steady State Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.1.7 3D Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.8 3D Steady State Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.1.9 3D Transient Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1.10 3D Transient Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2 Quintus Cold Gas Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.1 Steady State Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.2.2 Transient Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2.3 Mesh Independence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2.4 Pump Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Discussion 594.1 2D ERCOFTAC Validation Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.1.1 Steady State Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.2 Transient Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 3D ERCOFTAC Validation Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.1 Steady State Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.2.2 Transient Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3 Quintus Cold Gas Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4

List of Figures

1.1 Left: ASEA press used in 1953 to create some of the world’s first synthetic diamonds. Center:Sketch of how the dies were used to press synthetic diamons. Right: synthetic diamondscreated by Avure Technologies AB [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 HIP built by Avure Technologies circa 2012 [15]. . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Graph comparing conventional cooling during general HIP cycle to Quints Technolgoies’ URC

[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 A sketch of a typical centrifugal pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Sketches of Quintus HIP design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Photo of the ERCOFTAC centrifugal pump experimental set up. . . . . . . . . . . . . . . . . 141.7 Side view, left, and top view, right, of the ERCOFTAC centrifugal pump. All values are full

daimeter unless denoted by R for radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.8 A 2D illustration of how the Ansys CFX discretization algorithim creates finite volumes. . . . 18

2.1 Diagram of how the ERCOFTAC circumferential coordinate system is defined [11]. . . . . . . 222.2 Visualization of circumferential line along which measurements are taken and circumferential

coordinate system for the ERCOFTAC pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3 (a) Reconstructed experimental coefficient of static pressure, (b) normalized radial velocity,

and (c) normalized tangential velocity [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Comparison between reconstructed coefficient of static pressure. . . . . . . . . . . . . . . . . . 252.5 Modified reconstructed experimental coefficient of pressure plot [7]. . . . . . . . . . . . . . . . 252.6 (a) ERCOFTAC 2D flow domain and (b) a close up of the 2D mesh 3. . . . . . . . . . . . . . 272.7 (a) ERCOFTAC 3D flow domain and (b) the 3D mesh 3. . . . . . . . . . . . . . . . . . . . . 282.8 The geometry of the Quintus cold gas pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1 Plots used for determining convergence for the 2D ERCOFTAC medium mesh steady statesimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Total pressure rise coefficient versus average edge length for 2D mesh study. . . . . . . . . . . 403.3 Results of 2D ERCOFTAC steady state simulation. . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Plots used for determining convergence for the 2D ERCOFTAC transient simulation. . . . . . 433.5 Coefficient of static pressure results for the 2D ERCOFTAC transient simulation. . . . . . . . 443.6 Normalized radial velocity results for the 2D ERCOFTAC transient simulation. . . . . . . . . 453.7 Normalized tangential velocity results for the 2D ERCOFTAC transient simulation. . . . . . 463.8 Plots used for determining convergence for the 3D ERCOFTAC medium mesh steady state

simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.9 Total pressure rise coefficient plotted versus average edge length for 3D mesh independence

study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.10 Results of 3D ERCOFTAC steady state simulation. . . . . . . . . . . . . . . . . . . . . . . . . 493.11 Plots used for determining convergence for the 3D ERCOFTAC transient simulation. . . . . . 503.12 Coefficient of static pressure results for the 3D ERCOFTAC transient simulation. . . . . . . . 513.13 Normalized radial velocity results for the 3D ERCOFTAC transient simulation. . . . . . . . . 52

5

3.14 Normalized tangential velocity results for the 3D ERCOFTAC transient simulation. . . . . . 533.15 The plots used to determine convergence for the Quintus cold gas pump steady state solution. 553.16 The plots used to determine convergence for the Quintus cold gas pump transient solution. . 563.17 Total pressure rise coefficient plotted versus the average 3D edge length for various Quintus

cold gas pump meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.18 The pump curve for the Quintus cold gas pump. . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.1 Velocity contour of ERCOFTAC 2D steady state simulation. . . . . . . . . . . . . . . . . . . 654.2 Pressure contour of ERCOFTAC 2D steady state simulation. . . . . . . . . . . . . . . . . . . 664.3 Velocity contour of a cross section of the Quintus cold gas pump. Transient last time step,

600 RPM with 3kgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.4 Pressure contour of a cross section of the Quintus cold gas pump. Transient last time step,

600 RPM with 3kgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.5 Pressure contour on the rotor and stator blade regions of the Quintus cold gas pump. Transient

last time step, 600 RPM with kgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6

List of Tables

1.1 Geometric data and operating conditions of the ERCOFTAC centrifugal pump during Ubaldiet al. experiments in 1994 [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1 Boundary conditions for both 2D and 3D ERCOFTAC fan simulations . . . . . . . . . . . . . 282.2 Numerical settings for the ERCOFTAC pump simulations. . . . . . . . . . . . . . . . . . . . . 292.3 The locations of the three monitor points used for both 2D and 3D ERCOFTAC simulations. 302.4 2D and 3D computational mesh sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5 The gas properties of argon used for the Quintus cold gas pump simulation. . . . . . . . . . . 342.6 The boundary conditions for the Quintus cold gas pump. . . . . . . . . . . . . . . . . . . . . 342.7 Numerical settings for the Quintus cold gas pump simulations. See [12] for detailed explanations. 352.8 The locations of the three monitor points used for the Quintus cold gas pump simulations. . . 352.9 The number of elements and nodes in each of the meshes used in the mesh independence study

for the Quintus cold gas pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1 The maximum y+ values of each mesh generated for the mesh independence studies. . . . . . 403.2 The the average and maximum y+ values for the meshes used in the Quintus cold gas pump

mesh independence study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7

Chapter 1

Introduction

This chapter presents a short introduction to hot isostatic pressing (HIPing), its history, their cooling systems,and centrifugal pumps. An introduction to previous experimental and computational work is also presentedas it relates to this paper. The aim for this study, along with any limitations, and relevant theory is alsodiscussed.

1.1 Hot Isostatic Pressing

Hot isostatic pressing was first publicly documented in 1957 when researchers at an American company, theBattelle Memorial Institute, submitted a patent for ”a method for bonding” [1]. The process of using inertgases at high pressure and temperature to densify materials was called hot gas bonding until more widespreaduse of the technology appeared in the 1970s and it began to be referred to as hot isostatic pressing. Oneof the first applications of high pressure manufacturing technology, not only HIPing, was for the creationof synthetic diamonds. Almanna Svenska Elektriska Aktiebolaget (the General Swedish Electric Company),ASEA, independantly created some of the world’s first synthetic diamonds using a mechanical high pressuremachine in 1953. It had been done earlier in the 20th century with varying degrees of success, but therewas little to no cooperation between the researching parties. The top secret project to create these syntheticdiamonds was named Quintus, and the successes were not public record until the 1980s. The internal groupat ASEA that handled the Quintus project was called Avure, formed in the 1940s to research high pressuremanufacturing technology. In 1988 ASEA merged with a Swiss company and formed what is known as ABBtoday. Avure Technologies was sold off as an independent company for the first time in 1999, and changedit’s name to Quintus in 2015 as a tribute to its heritage. The work done by Avure Technologies, in all itsforms and ownership, developed high pressure technology and led the way for HIPing to become what it istoday.

8

Figure 1.1: Left: ASEA press used in 1953 to create some of the world’s first synthetic diamonds. Center:Sketch of how the dies were used to press synthetic diamons. Right: synthetic diamonds created by AvureTechnologies AB [15].

Before 1970, HIP machines were rarely found outside of laboratories, but technological improvements allowedfor larger working zones. Laboratory units had furnace areas rarely larger than 50 mm in diameter, but whenlarger units came to the market, with diameters up to 1200 mm, commercial and industrial opportunitiesarose [1]. Quintus Technologies was a huge part of this shift due to their innovative wire-bound pressurevessel technology [3].

Hot isostatic pressing works by increasing the temperature and pressure within a furnace zone up to 2500bar and 2000◦ C. This is achieved with inert gases, most commonly argon, and heating elements made fromkanthal, molybdenum, or graphite [2]. Materials within the working zone are compressed at high tempera-ture relieving and removing any porosity or other material flaws. The goal of this process is the achieve themaximum theoretical density for a given material, yielding the highest corrosion, impact, and wear perfor-mance possible. Its is very common for parts, especially when cast or 3D printed, to have a density lowerthan the material they are made from due to these flaws, making HIPing a highly sought after process amonghigh performance part manufacturers. HIPing has opened the door complex 3D printed performance parts.Previously, such parts were not feasible due to their complexity requiring 3D printing, which, in general,creates very poor material properties in the final product. HIPing allows for these properties to be improvedafter manufacturing.

Quintus Technologies has been a world leader in designing, building, and maintaining HIP machines sincethe 1980s (then part of ABB). Part of what put them ahead of the market was an innovative cooling processthat drastically reduced HIPing cycle times, called uniform rapid cooling (URC), first patented in the early1980s. Later, Quintus Technologies developed the uniform rapid quenching (URQ) system which could cooldown the working zone over ten times faster than URC [3]. The URQ system is currently being tested forheat treating and hardening applications. Quintus was also the first company in the world to design, build,and implement a HIP system with a working diameter of 2050 mm. This ’giga-HIP’ was ordered by MetalsTechnology Ltd. in Japan in 2009 [2]. Quintus Technologies has always been pushing the state of the art forHIP technology, striving always for bigger and more efficient HIP machines.

Figure 1.3 shows the temperature and pressure inside the working zone during a typical HIP cycle. It iseasy to see how URC drastically reduced HIP cycle time; by over a factor of two. This patented technologyled Quintus to be the industry leader in HIP technology, and an integral part of the URC system (in large

9

Figure 1.2: HIP built by Avure Technologies circa 2012 [15]. The working zone diameter in this press is 1250mm, notice the size. Large working areas require very large construction to contain the high pressure andtemperature, and Quintus Technologies has built and delivered presses with working zone diameters over2000 mm [2].

Figure 1.3: Graph comparing conventional cooling during general HIP cycle to Quints Technolgoies’ URC[2].

HIPs), are a pair of centrifugal pumps that circulate argon throughout the furnace and cooling channels.This paper investigates the performance of the cold side pump for this URC system.

1.2 Centrifugal Pumps and Fans

Centrifgual pumps are one type of turbomachine, which are devices that transfer mechanical energy to andfrom working fluids. Some turbomachines, known as turbines, take energy from a working fluid to gener-ate mechanical work. These are commonly found in dams, windmills, and jet engines. The other type ofturbomachine, known as pumps, fans, blowers, or compressors, impart mechanical energy from a motor toa working fluid. These are found in a very wide range of applications as well. Various configurations existwithin these two broad categories of turbomachines, and two of the most common are axial and centrifugalconfigurations. In an axially configured turbomachine, the working fluid enters and exits parallel to the axisof rotation within the machine. Imagine a propeller on a plane, a household fan, or the turbofan blades in a

10

Figure 1.4: A sketch of a typical centrifugal pump featuring radial impeller blades, forward swept diffuservanes, and a volute. On the left is a side view and on the right is a top down view of the pump [5]. Theshroud is the side of the pump where fluid enters, and the hub is the side at which the blades and vanes areattached.

typical Boeing 747 engine. Conversely, in centrifugally configured turbomachines, the working fluid generallyenters parallel to the axis of rotation, but then exits radially [6]. Generally, turbomachines working withgases are called fans or blowers, while those working with liquids are called pumps. They will be referred toas pumps in this study even though gases are the working fluids because of the high density of argon at thehigh pressure within a HIP.

There are many advantages and disadvantages to both axially and radially configured turbomachines, whichis why it is important for designers to thoroughly understand fluid dynamics when choosing a configurationfor a design. Centrifugal pump characteristics will be focused on in this section since the pumps analysed inthis study are centrifugally configured. The main advantage of centrifugal pumps is their ability to efficientlyincrease static pressure. The centrifugal acceleration developed through the rotating motion is what allowsfor this higher pressure gain, hence the name [4]. In essence, the centrifugal momentum of the fluid is utilizedwhich is why centrifugal pumps are common in liquid applications where the working fluid density is high.

The major parts of a centrifugal pump include the impeller or rotor, diffuser or stator, hub, shroud, blade,vane, and volute; see figure 1.4. The rotating part of a centrifugal pump is referred to as the impeller orrotor, and the blades are the parts that contact the working fluid. Various blade configurations exist, suchas forward swept, backward swept, or radial. Each of these have their own advantages depending on theapplication. The non-rotating part of a centrifugal pump can include the diffuser, stator, and volute. Adiffuser or stator is a series of blades, referred to commonly as vanes, that redirect the fluid. These vanesconvert kinteric energy of the fluid into a static pressure increase [4]. Both pumps in this study have diffuservanes. Centrifugal pumps can also have a volute, a snail-shell shaped casing that redirects the fluid to exita smaller radial area. Volutes can also contain diffuser vanes. Finally, the hub of a centrifugal pump is the”back”, or the side to which the blades and vanes are attached. On the other side, the shroud as it is called,is where the fluid enters and is usually one piece. The hub is usually divided into two parts since the innerpart must rotate as it is the backing of the impeller.

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The pumps analysed in this study are centrifugally configured. The ERCOFTAC pump, used for the valida-tion case, pumps air at atmospheric conditions with a classic centrifugal configuration; axial inlet and radialoutlet. The Quintus Technolgies AB pump uses argon gas at high pressure as its working fluid. The majordifference between these two pumps, aside from the working fluid and size, is that the Quintus Technologies’pump has a unique configuration. The working fluid both enters and exits this centrifugal pump parallelto the axis of rotation, contrary to the common definition of centrifugal pump configurations. However,the mechanical energy is transferred to the argon by way of a radial impeller, the defining characteristic ofcentrifugal pumps. The argon effectively sees five 90 degree turns as it travels through the Quintus pump,four more than a traditionally configured centrifugal pump.

1.3 Quintus Cold Gas Pump

The cooling system Quintus designs for large and medium series HIP machines, ones with working zonediameters over 450 mm, utilize two centrifugal pumps to circulate argon gas through the cooling zones.The first, cold side, pump is to be analysed in this study, see figure 1.5. The operating conditions for theQuintus cold side pump are quite intense. The cooling cycle operates at over 1500 bar, and the temper-ature of the argon at the cold side of this cycle is around 150◦C. Quintus Technologies has developed anin-house solver for an equation of state for argon at pressures and temperatures up to 2000 bar and 2000◦C.This solver is used to determine the density and dynamic viscosity of argon. The ideal gas model is usedduring simulations, but property values of argon at the reference conditions are input. The ideal gas modelis expected to hold within small variations from these defined properties calculated using the equation if state.

Figure 1.5: On the left is a cut away view of a typical Quintus Technolgies HIP showing how the internalworking area is encased in a heater, mantle, and a wire bound pressure vessel. On the right is a sketch ofhow the centrifugal pumps are placed in a Quintus HIP cooling system [2].

The Quintus Cold Gas pump is an interesting centrifugal pump because of its configuration. It is an axialinlet, axial outlet pump with radial impeller blades. Most centrifugal pumps are axial inlet and radial outlet,meaning that the fluid makes one 90 degree turn when going through the pump. In this case, the argonflowing through the Quintus pump makes five 90 degree turns since the impeller blades produce a radial flowand the stator vanes redirect the argon axially. Specifics on the pump geometry is presented in section 2.2.

12

1.4 Aim of Study

This paper aims to accurately and trustfully evaluate the performance of a proprietary centrifugal pumpdesigned and used by Quintus Technologies AB in the cooling system of a HIP. Specifically, this pump workson the cold side of the cooling system; used to pump the argon through the outer cooling channel bringingit down to the lowest temperature in the cycle. Before this pump is analysed, a validation case is conductedto evaluate the effectiveness and accuracy of CFD, and more specifically the Ansys CFX solver, for analysisof centrifugal pump. This validation case is also used to explore best meshing, simulating, and processingpractices when using CFX on centrifugal pumps.

The validation case aims to motivate and support simulation decisions used for analysis of the QuintusTechnologies AB cold gas pump. The ERCOFTAC centrifugal pump will be used for validation, as detailedexperimental measurements are provided by Ubaldi et al [7]. The results of the validation case will be usedto support the accuracy and trustworthiness of later CFD simulation settings and results for the Quintuspump. The main tasks for this study are outlined in bullet points below.

• Perform 2D CFD analysis on the ERCOFTAC centrifugal pump and compare results to experimentaldata.

• Perform 3D CFD analysis on the ERCOFTAC centrifugal pump and compare results to experimentaldata.

• Perform CFD analysis on Quintus cold gas pump using the same method as used in the validationcase.

• Extract pump performance data and generate pump curve.

• Evaluate reliability and support resulting performance characteristics using the validation case.

1.4.1 Limitations

The main limitation of this study, like many CFD analyses, is computational resources. The ERCOFTACvalidation study, both 2D and 3D cases, were carried out on a desktop workstation with 40 Gb of RAM andan Intel Xeon E5-2650 v2 with 8 cores running at 2.6 GHz. This was more than enough to carry out the2D cases along with the 3D ERCOFTAC steady state case. For the transient run, some compromises withboundary layer resolution had to be made in order to obtain a reasonable simulation time. This is shown tonot substantially affect the results.

For the Quintus cold gas pump performance study, computational resources were provided by the SwedishNational Infrastructure for Computing (SNIC) at PDC Centre for High Performance Computing (PDC-HPC). Due to the number of transient cases that are required, it would be impractical to perform thesesimulations on the local machine. Even with access to the PDC-HPC, the same reduction in boundary layerresolution as in the ERCOFTAC 3D case was done to reduce the computational time needed for each run.This change is expected to, and shown in the results of this study, to not substantially effect the Quintuscold gas pump performance curve results.

1.5 Previous Work

In 1994, Marina Ubaldi et al. from the University of Genova, in Genova, Italy, published an experimentalstudy of unsteadiness generated between an impeller and diffuser in a centrifugal fan. Titled ”An Experi-

13

mental Study of Stator Induced Unsteadiness on Centrifugal Impeller Outflow” [7], it became a very popularand influential paper in the turbomachinery field. Ubaldi et al. built a test rig centrifugal pump, now calledthe European Research Community On Flow, Turbulence, and Combustion pump (ERCOFTAC centrifugalpump) for the experiment. Pressure and velocity measurements were taken in the impeller-diffuser gap inorder to quantify the unsteadiness of the flow in this area. Further experimentation was conducted in 1996with the aim of acquiring more accurate velocity measurements between the outlet vanes using laser-Dopplervelocimeter.

Figure 1.6: Photo of the ERCOFTAC centrifugal pump experimental set up. Observe the taps where pressuretransducers were placed to measure the radial and circumferential pressure gradient [7].

In recent years a number of papers have used the ERCOFTAC centrifugal pump experiment as a validationcase [7, 8, 9, 11]. This experiment is very popular because of its detailed measurements which are well suitedfor validating CFD simulations. In 2009 Oliver Petit et al. conducted a case study on the ERCOFTACcentrifugal pump by simulating at 2D model and comparing simulation results to the experimental data[8]. Later, in 2010, Shasha Xie wrote a master’s thesis comparing OpenFOAM solver algorithms, advectionschemes, and turbulence models using the ERCOFTAC centrifugal pump experimental data for validation[11]. Most recently, in 2013 Oliver Petit et al. conducted a detailed 3D transient simulation of the ERCOF-TAC centrifugal pump model [9]. All of the aforementioned CFD publications have used OpenFOAM as thesolver, an open source CFD software. In contrast, this study is conducted using Ansys CFX. This paperwill compare results directly with the experimental results from Ubaldi et al. [7], but will refer to the morerecent CFD literature, that also used the ERCOFTAC centrifugal pump data, to motivate some decisions.These decisions include numerical settings such as turbulence models, advection schemes, transient schemes,and mesh size.

14

1.5.1 ERCOFTAC Centrifugal Pump

The ERCOFTAC centrifugal pump, built by Ubaldi et al. in 1994, consisted of a 420 mm diameter impellerwith seven backward swept blades. The diffuser is a total of 750 mm diameter with twelve forward sweptvanes. The diffuser is also able to be rotated about the impeller in order to investigate various impeller-diffuser relative positions. The impeller blade inlet had a diameter of 240 mm and the diffuser vane inlet hasa diameter of 444 mm and an outlet diameter of 664 mm. This provided a 6% vaneless radial gap betweenthe impeller blades and diffuser vanes. The fan also had a 1% gap between the blades and the shroud,namely 0.4 mm, but this is disregarded in the present analysed geometry. The ERCOFTAC centrifugalpump detailed geometry and operating conditions are presented in table 1.1 and figure 1.7.

Table 1.1: Geometric data and operating conditions of the ERCOFTAC centrifugal pump during Ubaldi etal. experiments in 1994 [7].

Impeller DiffuserInlet diameter D0 = 184 mm Inner diameter 434 mmOuter Diameter 434 mm Outlet diameter 750 mmBlade inlet diameter D1 = 240 mm Vane inlet diameter D3 = 444 mmBlade outlet diameter D2 = 420 mm Vane outlet diameter D4 = 664 mmBlade span b = 40 mm Vane span b = 40 mmNumber of blades zi = 7 Number of vanes zd = 12Inlet blade angle -65 deg Inlet vane angle -74 degOutlet blade angle -70 deg Outlet vane angle -68 deg

Operating Conditions Inlet air reference conditionsRotational speed ωi = 2000 rpm Temperature 298 K

Flow rate coefficient φ = 0.048 Density ρ = 1.2 kgm2

Total pressure rise coefficient ψ = 0.65 Static pressure p0 = 843 PaReynolds number 6.5e5

The experimental measurements carried out on the ERCOFTAC centrifugal pump consisted of both pressureand velocity measurements. The measurements were taken at a radius of 214.2mm, which correspondsto a diameter ratio of D

D2=1.095 [7], see figure 2.2. Velocity measurements were taken with a constant

temperature hot wire anemometer with single sensor probes at 17 span positions and 160 circumferentialpositions across two impeller gaps. Pressure measurements were taken at this same radius using a flushmounted semiconductor transducer, and the static pressure was measured using taps in the shroud and aBetz micromanometer [7].

15

Figure 1.7: Side view, left, and top view, right, of the ERCOFTAC centrifugal pump. All values are fulldaimeter unless denoted by R for radius.

1.6 Theory

In this section, theory relevant to this study is presented. Theory pertaining to the fundamentals of CFDand the basic quantification of centrifugal pump performance is discussed.

1.6.1 Computational Fluid Dynamics

Computational fluid dynamics, referred to as CFD, is a field of study that uses characteristic physical equa-tions to model fluid flow. The most basic form of these characteristic equations are called the Navier-Stokesequations. These equations are grouped into three categories; continuity, momentum, and energy equations.The continuity equation for fluid flow were developed using the fundamental law of conservation of mass.Likewise, the momentum and energy equations were developed from the fundamental law of conservationof momentum and conservation of energy. The set of momentum equations contains three different, butvery similar, equations for each spatial direction. Together, there are five Navier-Stokes equations; one forcontinuity (equation 1.1), three for momentum (equations 1.2, 1.3, and 1.4), and one for energy (equation1.5). These equations are solved simutainiously and interatviely in order to compute the fluid properties atany and all points in a flow field [16].

∂ρ

∂t+∇ • (ρV ) = 0 (1.1)

∂(ρu)

∂t+∇ • (ρuV ) = −∂p

∂x+∂τxx∂x

+∂τyx∂y

+∂τzx∂z

+ ρfy (1.2)

∂(ρv)

∂t+∇ • (ρvV ) = −∂p

∂y+∂τxy∂x

+∂τyy∂y

+∂τzy∂z

+ ρfy (1.3)

∂(ρw)

∂t+∇ • (ρwV ) = −∂p

∂z+∂τxz∂x

+∂τyz∂y

+∂τzz∂z

+ ρfz (1.4)

16

∂

∂t[ρ(e+

V 2

2)] +∇ • [ρ(e+

V 2

2)V ] = ρq +

∂

∂x(k∂T

∂x) +

∂

∂y(k∂T

∂y) +

∂

∂z(k∂T

∂z)

−∂(up)

∂x− ∂(vp)

∂y− ∂(wp)

∂z

+∂(uτxx)

∂x+∂(uτyx)

∂y+∂(uτzx)

∂z

+∂(vτxy)

∂x+∂(vτyy)

∂y+∂(vτzy)

∂z

+∂(wτxz)

∂x+∂(wτyz)

∂y+∂(wτzz)

∂z+ ρf • V

(1.5)

There are very few analytical solutions (to very specific cases) to the Navier-Stokes equations, meaning thatthey can only practically be solved using numerical methods. Additional equations are often included, alongwith the original five, to help model more complex fluid phenomena (turbulence or combustion to name two)[16]. This leads to a mathematical problem called the problem of closure. Most flow models introduce somesort of simplification in order to ’close’ the system of equations modelling the flow leading to a solution. Thisinvolves searching for a system of equations with the number of unknown dependant variables less than orequal to the number of governing equations used.

One of the most important, albeit complex, phenomena to model in CFD is turbulence. This chaotic mixingand rotation in a fluid can heavily impact flows. Theoretically, the Navier-Stokes equations can model bothlaminar and turbulent flows. The problem is that turbulence occurs at many different length and time scales,mostly at scales orders of magnitude smaller than that needed to model the bulk flow for a given case. Thismeans that to be able to properly capture the fluid motion within turbulent zones, a prohibitivly fine meshwould need to be used. One so fine that modern computing has recently gotten to the point to be able torun direct numerical simulations, i.e directly solve the Navier-Stokes equations, for turbulent fluid motion inrealtivly simple cases. The most common solution to this problem are statistical turbulence models. Usingtime averaging, it is possible to split a pricipal fluid property, such as velocity, into mean and fluctuatingvalues. This process is called Reynolds Averaging [12]. The Navier-Stokes equations are rewritten withthese mean and fluctuating values resulting in the Reynolds Averaged Navier-Stokes equations (RANS).These modified equations involve a statistical approach to include the effect of turbulence in fluid flow. Mostturbulence models also add two extra equations to the system of governing equations. Usually, these extraequations model the turbulent kinetic energy and dissipation rate. Together, these equations can adequatelymodel the influence of turbulence. The turbulence models used in this study are further discussed in section2.1.5

The solver used in this study, Ansys CFX, solves the RANS equations in their conservation form for sim-ulating flows [12]. Additionally, Ansys CFX discretizes the flow domain with the finite volume method,the most common discretiziation scheme in modern CFD [12]. In the finite volume method, the fluid fluxproperties entering and exiting a fixed (small) volume of fluid are used to determine the fluid properties atthe center of the finite volume. Ansys CFX accomplishes this by first dividing the flow domain into smallchunks, or a mesh. It then constructs the small volumes for the finite volume method about each mesh nodeby connecting adjacent mesh element center points, see figure 1.8. The fluid properties, or solutions to thegoverning equations, are then stored in the mesh nodes [12].

17

Figure 1.8: A 2D illustration of how the Ansys CFX discretization algorithim creates finite volumes. Theshaded area is the finite volume, constructed between the center points of all adjacent mesh elements. Atthe center of the finite volume is a mesh node at which the fluid properties are stored [12].

One of the most important, albeit complex, phenomena to model in CFD is turbulence. This chaotic mixingand rotation in a fluid can heavily impact results. Theoretically, the Navier-Stokes equations can model bothlaminar and turbulent flows. The problem is is that turbulence occurs at many different time scales, mostlyorders of magnitude smaller than that needed to model the general flow in a given case. This means that tobe able to properly capture the true fluid motion within turbulent zones, a prohibitivly fine mesh would needto be used. One so fine that modern computing is just getting to the point to be able to run direct numericalsimulations, i.e directly solve the Navier-Stokes equations, for turbulent fluid motion. The most commonsolution to this problem are statistical turbulence models. Using time averaging, it is possible to split apricipal fluid property, such as velocity, into mean and fluctuating values. This process is called ReynoldsAveraging [12]. The Navier-Stokes equations are rewritten with these mean and fluctuating values resultingin the Reynolds Averaged Navier-Stokes equations. These modified equations involve a statistical approachto include the effect of turbulence in fluid flow. Most turbulence models also add two extra equations tothe system of governing equations. Usually, these extra equations model the turbulent kinetic energy anddissipation. Together, these equations can adequately model the influence of turbulence. The turbulencemodels used in this study are further discussed in section 2.1.5.

1.6.2 Pump Curves

The most common way of quantifying the performance of a pump, compressor, or fan is to evaluate the totalpressure rise over the device. The total pressure rise, the difference in total pressure between the pump inletand outlet, is usually expressed in one of three ways; simply the total pressure difference, the total pressurerise coefficient ψ, equation 1.6, or the pump head H, equation 1.7 [5, 7].

18

ψ =2(pt4 − pt0)

ρu22(1.6)

H =(pt4 − pt0)

ρg(1.7)

Where pt is the total pressure, ρ the density, g acceleration of gravity, and u2 the impeller blade tip veloc-ity. The subscripts 0 and 4 denote the inlet and diffuser vane outlet locations, respectively. Head is mostcommonly used in hydraulic applications, but can be applied to any pump. Both of equation 1.6 and 1.7are valid only for isothermal level flows, i.e flows without heat transfer or significant elevation changes. Inorder to include all physical losses of energy, extra terms for changes in ineternal energy and elevation mustbe included. [5].

Any fluid flow can be evaluated using the difference in total enthalpy at two points. The total enthalpy isthe combination of internal energy, potential energy, static pressure energy, and dynamic pressure energywithin the flow, seen in equation 1.8 [5]. The numbered subscripts denote first and second positions along astreamline.

∆ht = (U2 − U1) +p2 − p1

ρ+c22 − c21

2+ g(z2 − z1) (1.8)

Here, ht is the total enthalpy, U the internal energy, c the fluid velocity, and z the height. This equationcomes from a combination of the law of conservation of energy and Bernoulli’s equation [5]. In an isothermallevel flow case, equation 1.8 simplifies to equation 1.9, also where the numbered subscripts denote first andsecond positions along a streamline. The simplification comes out of U2−U1 = 0 and z2− z1 = 0 due to theinternal energy staying constant (isothermal) and no change in elevation.

∆ht =p2 − p1

ρ+c22 − c21

2(1.9)

Thus, the change in total specific enthalpy is any and all energy change within the fluid (gained in the caseof a pump), so it can be considered also the specific work done on the fluid. The specific work, W , and pumphead can be related by combining equations 1.7 and 1.9 [5].

W = ∆ht = Hg =pt4 − pt0

ρ(1.10)

Pump curves can include various different curves, two of which are called the pump characteristic curve andpump efficiency curve [5]. In this study, both the pump characteristic curve and efficiency curve will beplotted versus varying mass flow rates at different rotational speeds. These two types of curves are veryuseful because they can easily be used to identify which pump is suitable for a given duty. The pumpefficiency can be found using equation 1.11, namely dividing the usable power transferred to the fluid (bythe impeller) by the shaft power.

η =PuP

=ρQW

P(1.11)

19

Where Q is the volumetric flow rate through the pump. Shaft power, P , can be found multiplying thetorque on the impeller blades by the rotational speed, equation 1.12. This is essentially evaluating howmuch mechanical energy is imparted to the fluid by the impeller blades. For a high efficiency pump, a higherfraction of this imparted mechanical energy is converted into increased pressure, i.e usable power Pu.

P = τiωi (1.12)

Where τ is torque, and ω is rotational speed. The pump efficiency, η, is plotted versus mass varying massflow rates to form pump efficiency curves, and the total pressure rise is plotted versus varying mass flowrates to form pump characteristic curves. Together, these curves make up a pump curve. Often, a systemcurve is also included in the pump curve. This line shows the amount of pressure required to drive a systemat varying mass flow rates. This system curve required pressure will increase with mass flow rate, whilea pump characteristic curve will generally decrease with increased mass flow rate. Where the system andcharacteristic curves intersect is one operating point of the pump. If this point is extended straight up tothe efficiency curve, the effectiveness of this pump at this operating condition can be found. The limited tono data available for the Quintus cold gas fan makes generating a pump curve for this fan a crucial step inperformance evaluation.

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Chapter 2

Method

This chapter presents the method for this study. This chapter is divided into two parts; first the validationcase and, second, the Quintus fan performance study. Great care is also taken to properly interpret thedata provided by the test case, namely Ubaldi et al., presented in section 2.1.1 [7]. The validation caseis conducted in order to explore Ansys CFX settings and meshing best practices for centrifugal fans. Theresults of the validation case will also be used to support results obtained in the Quintus pump performancestudy, lending to the accuracy and reliability of Ansys CFX when used for centrifugal fan analysis. Thesecond part of the method is the major aim for this study. The Quintus cold gas pump is analysed and apump curve is generated in order to quantify its performance.

Ansys Spaceclaim was used as the CAD software, Ansys Meshing as the meshing software, and Ansys CFXas the solver. MATLAB is used to generate the plots, and LATEX to write this paper.

2.1 ERCOFTAC Validation Case

As discussed in section 1.5, experimental data from the Ubaldi experiment in 1994 on the ERCOFTACcentrifugal pump [7] is used for validation of CFD simulations on the same centrifugal pump. The resultsof this validation study is used to support the reliability of results obtained from simulations of the Quintuscold gas pump. This section presents the method used for the validation case analysis of the ERCOFTACcentrifugal pump CFD analysis.

2.1.1 Data Reduction

The ERCOFTAC centrifugal pump experimental data is presented in a system of circumferential coordinatesnormalized by the impeller circumferential pitch; namely yi

Giwhere the impeller circumferential pitch is

Gi = 2πrzi

. Equation 2.1 and figure 2.1 show how this coordinate system is defined.

yi = ωrt+ rθk + (m− 1)2πr

zb(2.1)

The impeller circumferential coordinate, yi, is given as a function of the location of measuring point Pm;within the mth diffuser vane passage and with a diffuser counter clockwise rotation of θk degrees. This coor-dinate is also a function of the impeller angular velocity and radius of the measuring point. To reconstruct

21

Figure 2.1: Diagram of how the ERCOFTAC circumferential coordinate system is defined [11]. Measurementsare taken at points P1 and P2 within diffuser vane passage M at various diffuser positions θk

the experimental data into plots, it is assumed that t = 0 and that m = 1. This reduces the circumferentialcoordinate to just a circumferential distance in the anticlockwise direction from 0. This simplification canbe made because the measurements are only taken from the first two impeller passages.

Since Ubaldi et al. took measurements across two impeller blade passages, yi varies between 0 and 2 foreach measurement series. Each measurement series is then executed at 17 different blade span locations, asdiscussed in section 1.5.1. The line along which measurements are taken can be visualized in figure 2.2. Thisfigure shows the impeller-diffuser relative position and yi coordinate at t = 0. As a result, measurementstaken at later times, while the fan is running, the circumferential coordinate moves with the impeller bladesbecause it is defined with respect to the moving frame of the impeller.

Figure 2.2: Visualization of circumferential line along which measurements are taken and circumferentialcoordinate system for the ERCOFTAC pump.

The experimental measurements at different impeller-diffuser relative positions are recorded at increasing

22

time normalized by the impeller passing period; namely tTi

where the impeller passing period is Ti = 2πωzi

.

The coefficient of static pressure measurements are taken from tTi

= 0 to tTi

= 0.3 by steps of 0.1, corre-

sponding to 4.286e-4 seconds between each measurement. Velocity measurements are taken from tTi

= 0.126

to tTi

= 0.426 by steps of 0.1. The reconstructed experimental data at the midspan location ( zb = 0.5) ispresented in figures 2.3a, 2.3b, and 2.3c. Pressure measurements were normalized to a coefficient of staticpressure, defined in equation 2.2. Radial and tangential velocity measurements were normalized by dividingby the impeller blade tip velocity, u2 = 43.98ms .

Cp =2(p− p0)

ρu22(2.2)

Where p is static pressure and p0 the reference static pressure. In the Ubaldi experiment this referencepressure is measured in the suction tube before the pump inlet.

23

(a) (b)

(c)

Figure 2.3: (a) Reconstructed experimental coefficient of static pressure, (b) normalized radial velocity, and(c) normalized tangential velocity [7].

When the examining the recustructed experimental coefficient of static pressure, the circumferential coor-dinate seemed to be shifted slightly, seen in figure 2.4. Further investigation revealed that the providedexperimental data is shifted about -4.6 deg, corresponding to yi

Gi= −0.090. Shifting the reconstructed data

yeilds a better plot when compared to the original plot from Ubaldi et al. [7]. The reason for this is likelydue to a number of missing data points. In figure 2.4, the original plotted data includes more data pointsbetween about yi

Gi=0 and yi

Gi=0.25. This shifted reconstructed pressure data, in figure 2.1.1 will be used for

the rest of this paper. The reconstructed experimental velocity data is not changed.

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Figure 2.4: Comparison between reconstructed coefficient of static pressure, left, and original plot from [7],right.

Figure 2.5: Modified reconstructed experimental coefficient of pressure plot [7].

Another point of confusion in the reconstruction of the experimental data is the value of p0, defined byUbaldi et al. as the static pressure in the ’suction tube’. The experimental set up used by Ubaldi et al. in-cluded a tube that extended the inlet of the ERCOFTAC pump. This static pressure is used as the referencepressure when calculating the coefficient of static pressure at measuring points, see equation 2.2. However,this reference pressure is not given in any of the literature on the ERCOFTAC centrifugal pump. Therefore,

25

this reference pressure is calculated in the following way. A similar method is used by Xie [11].

The total pressure rise coefficient, ψ, is given as 0.65 (see equation 1.6) [7]. This yields in a total pressuredifference between the inlet and outlet of 770 Pa. The flow rate coefficient during operation is also given as0.048, defined in equation 2.3.

φ =4Q

u2πD22

(2.3)

Solving for the volumetric flow rate gives Q = 0.292m3

s . Dividing this by the inlet and outlet area givesthe flow velocity at the inlet and outlet; 10.98 m

s and 3.10 ms respectively. This yields dynamic pressures of

73.84 Pa and 5.89 Pa at the inlet and outlet, respectively. Finally, the static pressure at the inlet is solvedusing equation 2.6.

The total pressure difference between the outlet and inlet can be defined as the sum of static and dynamicpressures at the inlet and outlet. Setting this equal to 770 Pa we get the following.

pt4 − pt0 = (p+ q)4 − (p+ q)0 = 770 (2.4)

Where q is dynamic pressure. Substituting for what is known, namely the static pressure at outlet (atmo-spheric pressure), p4, and the dynamic pressure at the inlet and outlet,q0 and q4, results in the following.

(101325 + 5.89)− (p0 + 73.84) = 770 (2.5)

101325− p0 = 837.95 (2.6)

Finally, the gauge static pressure at the inlet is found to be -837.95 Pa. This is used as p0 for the rest ofthis paper.

2.1.2 2D Computational Domain

The ERCOFTAC centrifugal pump geometry is provided as an Ansys ICEM surface file. These surfaceswere exported as .stl files and then opened in Ansys Spaceclaim. The 2D geometry is then created in AnsysSpaceclaim by projecting the blade surface onto a 1mm thick disk with an outer radius that of the outletdiameter of the ERCOFTAC centrifugal pump. The flow domain had to be 3D because Ansys CFX cannotsolve a purely 2D domain, but the domain is meshed to have only 1 element in the thickness directionmimicking a 2D flow simulation. Great care is taken to ensure that the impeller-diffuser relative positionis correct for t = 0 using the impeller and diffuser blade positions provided by Ubaldi et al. The final 2Dflow domains and one mesh are presented in figures 2.6. The computational mesh is generated using AnsysMeshing and finally exported to Ansys CFX for solving.

26

(a) (b)

Figure 2.6: (a) ERCOFTAC 2D flow domain and (b) a close up of the 2D mesh 3.

The 2D geometry is split into two domains, the impeller and diffuser domains. The interface between thetwo is located at a radius of 217 mm as detailed by Ubaldi [7]. The impeller domain has a rotational velocityof -2000 RPM and a general grid interface (GGI) is used to model the interface between the two domains.The fluid modelled is air at standard temperature and pressure; 298 K and 1 atm. The reference pressure ofboth domains is set to 1 atm. Incompressible and isothermal flow is assumed. See figure 1.7 for a detaileddrawing of the ERCOFTAC fan.

2.1.3 3D Computational Domain

The 3D ERCOFTAC computational domain is created similarly to the 2D domain using Ansys Spaceclaim.The fluid region is extracted using the Volume Extraction Function in Ansys Spaceclaim. The 3D flow do-main and mesh can be seen in figure 2.7. The computational mesh is also generated using Ansys Spaceclaimthen exported to Ansys CFX for solving.

27

(a) (b)

Figure 2.7: (a) ERCOFTAC 3D flow domain and (b) the 3D mesh 3.

The 3D flow domain is also split into two domains, the impeller and diffuser domains. The interface betweenthe two is also modelled as a GGI, and the fluid used is air at standard conditions; 298 K and 1 atm. Thereference pressure for both domains is 1 atm. The flow as assumed to be incompressible and isothermal.

2.1.4 Boundary Conditions

The provided operation conditions, given in table 1.1, are used to produce the boundary conditions used inboth the 3D and 2D simulations. The boundary conditions are given in table 2.1. The inlet radial velocityfor the 2D simulation is slightly more than the axial inlet velocity for the 3D case because of the inletgeometry. For the 2D case, the inlet is in the same plane as the impeller and diffuser, so the inlet area is thecircumference of the inlet multiplied by the thickness of the fan. For the 3D case, the inlet is located in adifferent plane, but parallel to the impeller and diffuser planes, so the inlet area is the circular area of thisaxial inlet; namely the radius squared multiplied by π.

Table 2.1: Boundary conditions for both 2D and 3D ERCOFTAC fan simulations

2D Calculated Data 3D Calculated Data

Inlet Radius r0 = 0.092mm Inlet Radius r0 = 0.092mm

Thickness 1mm Thickness 40mm

Volumetric Flow Rate Q = φu2πD2

4 = 0.292m3

s Volumetric Flow Rate Q = φu2πD2

4 = 0.292m3

s

Inlet Radial Velocity c0 = Q2r0π.04

= 11.6ms Inlet Axial Velocity c0 = Qπr20

= 10.98ms

Impeller Rotational Velocity 2000 RPM Impeller Rotational Velocity 2000 RPM

2D Boundary Conditions 3D Boundary Conditions

Inlet Radial Velocity c0 Inlet Axial Velocity c0

Inlet Turbulence Intensity 5% Inlet Turbulence Intensity 5%

Outlet Static Gauge Pressure Average 0 Pa Outlet Static Gauge Pressure Average 0 Pa

28

2.1.5 Numerical Settings

The numerical settings for both 2D, 3D, steady state, and transient simulations were set to the high resolutionadvection schemes, high resolution tuburlence modelling for steady state simulations, and second ordertubulence modelling for transient simulations [12]. The turbulence model used is the two equation k−ω SSTmodel [17]. The standard k − ε model was also tested in some preliminary 2D simulations, but convergencewas difficult to obtain. For the rest of the study, the SST model is used because it demonstrated the bestagreement with experimental results in previous work, discussed in [8]. The flow is also modeled as isothermaland the air is considered incompressible and ideal. These assumptions are also used in the literature, andare reasonable due to the relatively light operating conditions of the ERCOFTAC pump.

The mesh connection used between the rotor and stator for the steady state simulations is called frozenrotor. This is a relatively new model, whereas the standard model is called the mixing-plane model. Thefrozen rotor model uses a multiple reference frame (MRF) algorithm to, in principle, model a snapshot ofthe flow with pseudo transient effects. The solver simulates rotation of the rotor domain by varying thereference frame. Pseudo transient effects such as vortex shedding, wake separation, and eddies are modelled,but not always physical. Their positions also do not change with the frozen rotor approach. In contrast,the mixing-plane model circumferentially averages the fluid flow about the mesh contact region, advectingthe flow through the rotating domain. The frozen rotor approach is also very dependant on the rotor-statorrelative position, while the mixing-plane model is more robust. For more physical results, and a better initialcondition for the transient simulations, the frozen rotor model is used in the steady state simulations. InCFX, the sliding grid model is called ’transient rotor-stator’ and is used for all transient simulations. Inthis model, the rotor domain is rotated each time step and the flow is calculated until convergence at eachstep. This approach yields the most realistic results with respect to turbulent and unsteady flow details. Forthe ERCOFTAC pump simulations, these flow details are important to capture since the aim of the originalexperiment is to investigate diffuser vane induced unsteadiness within the impeller-diffuser gap. The fullsettings are listed in table 2.2.

Table 2.2: Numerical settings for the ERCOFTAC pump simulations.

2D Simulations 3D Simulations

Steady State Transient Steady State Transient

Energy Equation Isothermal Isothermal Isothermal Isothermal

Ideal Gas Yes Yes Yes Yes

Turbulence Model k − ω SST k − ω SST k − ω SST k − ω SST

Advection Scheme High Res High Res High Res High Res

Turbulence Setting High Res High Res 2nd Order 2nd Order

Mesh Connection Frozen Rotor Frozen Rotor Sliding Grid Sliding Grid

A useful characteristic of the SST turbulence model is its automatic wall treatment; the abilty to switchbetween a scalable wall function and a low-Reynolds near wall formulation [12]. A scalable wall functionis used when the y+ value is greater than 11, so the boundary layer is not fully resolved because the firstelement is not within the viscous sublayer [13]. Scalable wall functions virtually insert a velocity and pressuregradient within this first element in order to properly model wall effects. If the y+ value is below 1, the firstmesh element is within the viscous sublayer and the boundary layer is fully resolved by the computationalmesh. In this case, the SST model uses a low-Reynolds near wall formulation to compute the fluid propertiesin this near-wall region.

29

2.1.6 Convergence Criteria

Three criteria checked for convergence during the ERCOFTAC pump simulations: RMS residuals, domainimbalance, and monitor point steadiness. For 2D simulations, a strict convergence accepted when the RMSresiduals reached below 10−6, mass imbalance within all domains is below 1%, and that both the velocityand pressure at three monitor points are stable. This same convergence criteria is used for 3D simulations,but the RMS residuals were accepted once below 10−5. Table 2.3 details the location of the monitor points.

Table 2.3: The locations of the three monitor points used for both 2D and 3D ERCOFTAC simulations.Velocity and pressure are monitored at each point as part of determining convergence.

x-Location y-Location z-Location (3D) DescriptionMonitor Point 1 0.1m 0m 0.02m InletMonitor Point 2 0.215m 0m 0.02m Rotor Blade OutletMonitor Point 3 0.370m 0m 0.02m Outlet

CFX adaptive time stepping is used for the transient simulations. The approach to observe convergence intransient simulations on the ERCOFTAC pump is to keep the RMS Courant number below 5, residuals below10−5, and to observe periodicity in velocity and pressure at all monitor points. After these conditions aremet, the data is extracted beginning at the first rotor-stator relative position at the same time step intervalsused in the Ubaldi experimental study. An RMS Courant number of 5 is chosen because the flow throughthe ERCOFTAC pump is expected to contain unsteady phenomena, but the steady state simulations havestrict convergence criteria. This strict convergence reduces the need to maintain a Courant number below1, since the flow will be steady and tightly converged before the transient simulations are run. A Courantnumber of 5 also yields a time step value at least 1

3 of the impeller passing period for the coarsest mesh usedin both the 2D and 3D ERCOFTAC cases. This means that there will be at least three time steps before oneimpeller blade passes one stator gap. This resolution is better with finer meshes since the time step valuewill be reduced with the Courant number held constant.

2.1.7 2D Mesh Independence Study

Mesh generation for the 2D ERCOFTAC flow domain focused on accurately and completely resolving theboundary layer. This is done by calculating the theoretical first element height when the y+ is kept to below1. The entire flow domain is filled with hexahedral elements, only one element thick in order to be usedin Ansys CFX while mimicking a 2D flow. An initial mesh is generated and used as the starting point forthe mesh independence study, then two coarser and two finer meshes are generated. The mesh sizes arepresented in table 2.4.

Initial simulations showed that additional mesh resolution is required at the leading and trailing edges of theblades and vanes. This is taken into account when creating the various meshes. With the coarser meshes,the boundary layer resolution is also decreased to investigate the effect of an increased y+ value.

To evaluate the ERCOFTAC 2D mesh independence, a method presented by Burstrom et al. is used [14].This method plots a global variable, in this case the total pressure rise coefficient (see equation 1.6), versusthe average edge length h. The average edge length value provides a convenient way of quantifying meshresolution. The average edge length, for a 2D mesh, is calculated using equation 2.7. A curve can then befit to the plotted data do extrapolate how fine a mesh must be to yield an adequately independent solution.

30

Table 2.4: 2D and 3D computational mesh sizes.

2D Mesh 3D MeshNumber of Elements Number of Nodes Number of Elements Number of Nodes

Mesh 1 52867 110448 1577827 545439Mesh 2 88635 183028 2244859 820815Mesh 3 134244 275924 4528522 1640768Mesh 4 174518 356158 8125489 2944017Mesh 5 427863 889955 15215715 5512940

h2D = [A2D

N]1/2 (2.7)

Where A2D is the area of the 2D mesh, N the number of mesh elements, and h the average edge length.After a number of meshes are run, the resulting total pressure rise coefficient is plotted versus the averageedge length for each mesh. A second degree polynomial is then fit to the data and the resulting curvevertex is centered on the y-axis, i.e the derivative is 0 at the y-intercept. The resulting y-intercept of thissecond degree fit function is, theoretically, the total pressure rise coefficient with an infinitesimally fine meshwhere the average edge length, h, is 0. A mesh is considered independent when it comes within 2% of thistheoretical total pressure rise coefficient.

2.1.8 3D Mesh Independence Study

The meshes generated for the 3D ERCOFTAC centrifugal pump flow domain are filled with tetrahedral ele-ments. Similar to the 2D mesh independence study, an initial mesh is generated using 4.5 million elements.Then two coarser and two finer mesh are then generated. Initially, the mesh is generated aiming for a y+ ofless than 1 in order to fully resolve the boundary layer. Early simulations showed difficulty converging, andthe problem areas with the highest residuals were located within the boundary layer at leading and trailingimpeller blade edges. For this reason, first cell height is increased to achieve a y+ of between 11 and 20 [13].This triggered the SST turbulence model to insert a scalable wall function within this first cell, reducingmesh size and helping convergence. The various mesh sizes are presented in table 2.4.

Similar to the 2D mesh independence study, the 3D mesh independence study also qauntifies a mesh thatprovides a mesh independent solution by use of the average edge length h (see equation 2.7). For a 3D mesh,the average edge length is calculated using equation 2.8.

h3D = [V3DN

]1/3 (2.8)

Where V3D is the area of the mesh domain. A second degree polynomial is fit to the data, and the vertexis set as the y-intercept. The mesh is considered solution independent if the total pressure rise coefficient iswithin 2% of the y-intercept.

2.1.9 Post Processing

The results of all ERCOFTAC simulations are presented just as the original article by Ubaldi et al. presenteddata, as discussed in section 2.1.1. The coefficient of static pressure, radial velocity, and tangential velocityare extracted along the measuring line, just past the impeller blade outlet at a radius of 214.2mm (see figure

31

2.2). The radial and tangential velocities are normalized by the impeller blade tip speed, u2, and all three ofthese fluid properties are plotted versus the circumferential coordinate yi

Gi. For the 3D case, the measuring

line is located at the mid blade span position zb = 0.5.

The data along the measuring line is extracted at 1 degree intervals, resulting in about 102 data pointsper simulation. Ubaldi et al. measured 160 data points across the same range, but data points at 1degree intervals provide enough resolution for a comparison between experimental and simulation data. Thereconstructed experimental data is plotted on the same graphs as the simulation results in order to evaluateagreement between the data.

Data is extracted from transient simulations after convergence is observed. The run is restarted with thetime steps at which the Ubaldi data is extracted after convergence is observed. For example, a transient runmay require a time step of 104 seconds to acheive convergence, but once the convergence criteria are met,the run is started over using the time step of t

Ti= 0.1 in order to extract data at the same instants as Ubaldi

et al.

2.2 Quintus Cold Gas Pump

This section details the method used to simulate the performance and extract a pump curve for the Quintuscold gas pump. The process includes a mesh independence study, convergence study, and a process ofsimulating various operating conditions in order to gather data points for a pump curve. The pump geometryis provided by Quintus Technologies AB and is a proprietary design.

2.2.1 Computational Domain

As mentioned in the introduction, the geometry of the Quintus cold gas pump is quite unique. It features anaxial inlet and outlet with a radial impeller. This configuration introduces four 90◦ turns in the flow path.With the control valves included in the computational domain, the argon will experience five 90◦ turns. Thepump is assumingly designed this way in order to make it as compact as possible, but it introduces somecomplexity when analysing the flow. Many of these turns have sharp geometries and sudden cross sectionalarea changes which can create flow separation, vortices, or other complex flow phenomena. The flow domainis shown in figures 2.8a, 2.8b, and 2.8c. The angled connections between some of the subdomains is done toallow for the connection of boundary layer inflation meshes to connect smoothly. The domain is extendedto include the inlet (flow control) valves after some preliminary calculations showed that they are a majorchoke point. The pressure losses over these valves, even when fully open, were expected to substantiallyaffect the flow through the rest of the pump assembly, so they are included in the computational domain.

32

(a) (b)

(c)

Figure 2.8: The geometry of the Quintus cold gas pump. 2.8a Full Quintus cold gas pump flow domain. 2.8bA cross section of the Quintus cold gas pump detailing the flow path. 2.8c The geometry of the Quintus coldgas pump rotor and stator blades with the walls removed.

As in the ERCOFTAC validation case, the flow domain for the Quintus cold gas pump is extracted using the’extract volume’ tool in Ansys Spaceclaim. The original CAD model of the fan module, where the cold gaspump is located, is provided by Quintus Technologies. Before extracting the flow domain, any small featuressuch as screw heads, screw holes, and small tolerance gaps are removed. Other small features such as thesprings in the valve stems are also removed. These small features would not affect the flow significantly, but

33

Table 2.5: The gas properties of argon used for the Quintus cold gas pump simulation.

Property Value at 150◦ and 1500 bar

Density ρ = 910.1 kgm3

Dynamic Viscosity µ = 7.75e− 5 kgms

Specific Heat at Constant Pressure Cp = 676 Jkg◦C

would introduce unnecessary complexity when meshing. The domain is filled with tetrahedral elements.

The fluid in the Quintus cold gas pump is argon pressurized to 1500 bar and operates at 150◦C. This is usedas the reference pressure for the entire domain. An in-house calculator is used to determine the density,dynamic viscosity, and specific heat of argon at 150◦C and 1500 bar. The argon properties used are presentedin table 2.5.

Because the goal of this study is to generate a pump curve, and therefore determine the overall pressurerise at varying mass flow rates, the working fluid is modelled as a constant property fluid with isothermalflow. The pressure changes within the pump flow domain are negligible when compared to the pressure thatthe entire system is pressurised to, so the flow is modelled as incompressible. Also, the expected maximumvelocities (considering the rotor blade tip velocity) is not expected to get anywhere near a compressibleregime. Furthermore, the temperature of the argon through this pump stays relatively constant and thecooling over the pump is negligible, so the flow is also modelled as isothermal. These simplifications aremade to reduce computational time while keeping in mind the goal of the study since many cases need tobe run in order to collect enough data points.

2.2.2 Boundary Conditions

The boundary conditions used for simulation of the Quintus cold gas pump simulations are presented in table2.6. One of the challenges of analysing this pump is the limited about of data available on the operatingconditions. Quintus designs each HIP to fulfil a client’s production cycle requirements, i.e the temperatureand pressure required within the furnace to attain the desired material properties for what the client willuse the HIP for. The pressure losses through the inner furnace area, the outer or inner cooling channels,or the pressure gains over the two pumps are not known. The exact flow rate through the system is alsonot known. The HIPs cooling cycles are driven by varying the pump RPM, between a few pre-set speeds,and opening and closing inlet valves. For this reason, the known total pressure at which the entire systemis pressurized is set as the inlet pressure (1500 bar). The approximate mass flow rate through the system iscalculated through hand calculations by knowing the temperature of the furnace area throughout a coolingcycle and knowing the thermal energy extracted during the cooling cycle. With the approximate mass flowrate during cooling found to be between 0 and 5 kg

s , values within this range are used as outlet boundaryconditions when generating the pump curve. The operating rotor rotational speeds are also known to varybetween 0 and 900 RPM, so three values commonly operated at are used for the pump curve.

Table 2.6: The boundary conditions for the Quintus cold gas pump. Five different mass flow rates were runat three different rotor speeds to generate a pump curve.

Rotor Speeds 300 RPM 600 RPM 900 RPM

Outlet Mass Flow0.25, 0.5, 0.75, 0.25, 0.5, 1, 1.25, 1.5, 0.5, 1, 1.5, 2, 2.5,

1, 1.5, 2 kgs 2, 2.5, 3, 3.5, 4 kg

s 3, 3.5, 4, 4.5, 5 kgs

Inlet Average Total Pressure 0 Pa 0 Pa 0 Pa

34

2.2.3 Numerical Settings

The solver numerical settings are shown in table 2.7. The flow is set as isothermal and the argon fluidproperties are input as a custom fluid using the in-house equation of state to solve for the properties ofargon at 1500 bar and 150◦C. The gas is set as a constant property gas because the pressure and velocityvariations within the pump are not large enough to cause any compressibility effects, especially when com-pared to the pressure at which the entire system is pressurized. The k − ω SST turbulence model is usedhere again due to its documented success in turbomachinery applications and to keep consistent with theERCOFTAC validation case [9]. Also, the turbulence numerics are set to first order resolution rather thansecond order resolution. This is done in order to help convergence, because in preliminary runs with secondorder turbulence resolution the highly unsteady nature of the flow through this pump lead to numericaldiversions. In order to fix this, higher resolution meshing would need to be used, but this is not possible dueto the computational resources available. Similar to the EROFTAC validation case, the frozen rotor meshconnection is used for steady state simulations, and the sliding grid is used for transient runs.

Table 2.7: Numerical settings for the Quintus cold gas pump simulations. See [12] for detailed explanations.

Steady State Transient

Energy Equation Isothermal Isothermal

Equation of State Constant Gas Constant Gas

Turbulence Model k − ω SST k − ω SST

Advection Scheme High Res High Res

Turbulence Setting First Order First Order

Mesh Connection Frozen Rotor Sliding Grid

2.2.4 Convergence Criteria

The convergence criteria for the Quintus cold gas pump, like the ERCOFTAC validation case, will examineRMS residual values, monitor point pressures and velocities, and domain imbalances. Due to the high degreeof unsteadiness expected, and found in preliminary simulations, heavier focus will be placed on the monitorpoints rather than the residual values. Therefore, the residuals will be accepted once below 10−3. Also,due to the highly unsteady flow, a steady state solution could not be found, requiring a transient simulationto reach a converged solution. The location of the three monitor points in shown in table 2.8. Transientconvergence is accepted when all domain imbalances are steadily below 1%, RMS residuals are maintainedbelow 10−3, and monitor point values are periodic.

Table 2.8: The locations of the three monitor points used for the Quintus cold gas pump simulations. Velocityand pressure is monitored at each point as part of determining convergence.

x-Location y-Location z-Location DescriptionMonitor Point 1 0m 0.22m 0.1m Just inside inletMonitor Point 2 -0.0105m 0.107m 0.25m Between two stator bladesMonitor Point 3 0m 0.045m 0.49m Just before outlet

Each mesh independence study simulation is first run as steady state for 300 iterations in order to get closeto the converged solution before running transient. This steady state solution is then used as the initialcondition for a transient simulation. It was found that the simulation had to run for over 5 seconds in orderto reach a converged solution where all pressure and velocity monitors were periodic. This procedure isrepeated for each mesh of the mesh independence study. When gathering data points for the pump curve,

35

the transient runs are only run for 0.3 seconds with the previous operating condition used as the initialcondition, without any steady state runs. This allows for the simulation to converge while not requiring asmany computational resources.

CFX adaptive time stepping is again used for the transient simulations. A Courant number of 100 ismaintained and 5 coefficient loops are allowed for each time step. These settings are the result of balancingthe available computational resources, target maintained residuals, and required rotational resolution. Usingthe steady state solution as a starting point, each time step’s residuals reached below 10−3 in 5 coefficientloops. A Courant number of 100 is chosen because it allowed for a time step large enough that is manageablewith the available computational resources while maintaining a frequency 3x that of the rotor blade passingfrequency. This means that the flow is calculated three times while a rotor blade is passing between twostator blades. This will allow for the rotor passing frequency to be observed in the stator monitor point.

2.2.5 Mesh Independence Study

The mesh independence study carried out on the Quintus cold gas pump will follow the same methodologyas in the ERCOFTAC validation case. The process begins with the creation of four meshes. The targetaverage y+ value for these initial medium mesh is one above 11. For areas where large velocity gradients orcomplex flows are expected, such as around the rotor blades and stator vanes, the boundary layer inflationresolution is increased. For areas where the flow is aligned well with the wall the boundary layer meshresolution is decreased. With a y+>11, the SST turbulence model will input a scalable wall function in mostareas and reduce computational complexity. This is done bearing in mind the decision to do the same forthe 3D ERCOFTAC case. The boundary layer inflation mesh resolution is also altered between meshes.

Table 2.9: The number of elements and nodes in each of the meshes used in the mesh independence studyfor the Quintus cold gas pump.

Number of Elements Number of NodesMesh 1 5087853 1897234Mesh 2 7832096 3033154Mesh 3 9145682 3582905Mesh 4 14532469 6040085

These four meshes are then solved and the average total pressure rise over the pump is extracted. The totalpressure rise coefficient for each case is calculated using equation 1.6 and is plotted against the average threedimensional edge length, found using equation 2.7. A 2nd degree polynomial is then fit to the resulting datapoints, and the vertex of the curve is set as the y-intercept. This will show the theoretical total pressure risecoefficient for an infinitesimally fine mesh. From this value, a 2% envelope is formed, and any mesh datapoints within this envelope are considered independent.

2.2.6 Data Acquisition Procedure

The mesh independence study results in one converged transient solution for a rotational speed of 600 RPMand an outlet mass flow rate of 3 kg

s . This solution is then used as the initial condition for a transient run at

both 2.5 kgs and 3.5 kg

s . Further transient runs up to 4 kgs and down to 0.25 kg

s are run using the preceding

solution as the initial condition. Next, the solution for 600 RPM and 0.25 kgs is used as the intitial condition

for a transient run at 300 RPM and 0.25 kgs . Further runs at 300 RPM are done, again using the preceding

solution as the intitial condition up to an outlet mass flow rate of 2 kgs . Finally, the 600 RPM and 0.5 kg

s

36

is used as the initial condition for a run at 900 RPM and 0.5 kgs . Further runs at 900 RPM are done using

preceding solutions as initial conditions up to an outlet mass flow rate of 5 kgs .

Ansys CFX transient statistics is used to extract the average outlet total pressure and average torque onthe impeller blades during the periodic portion of each simulation. The average total pressure is plottedversus the outlet mass flow rate for each rotational speed to form pump characteristic curves. Then theshaft power of the pump, using equation 1.12, is evaluated using the average torque on the impeller bladesfor each simulation. This is used to calculate the efficiency for each simulation, using equation 1.11, andplotted versus the outlet mass flow rate to form pump efficiency curves for each rotational speed. Finally,second degree polynomials are fit to each data set, forming a pump curve graph that includes six lines; onepump characteristic curve and one efficiency curve for each pump rotational speed.

2.2.7 Post Processing

The desired pump curve to be generated for the Quintus cold gas pump will include six lines; one pumpcharacteristic curve and one pump efficiency curve for each rotational speed. Ansys CFX transient statisticsis used to extract the average outlet total pressure and average torque on the impeller blades during theperiodic portion of each simulation. The average total pressure is plotted versus the outlet mass flow ratefor each rotational speed to form pump characteristic curves. Then the shaft power of the pump, usingequation 1.12, is evaluated using the average torque on the impeller blades for each simulation. This is usedto calculate the efficiency for each simulation, using equation 1.11, and plotted versus the outlet mass flowrate to form pump efficiency curves for each rotational speed. Finally, second degree polynomials are fit toeach data set, forming a pump curve graph that includes six lines.

37

Chapter 3

Results

This chapter presents results in two different sections. The first section contains the validation case usingERCOFTAC centrifugal pump data, and the second contains the performance analysis of the Quintus Coldgas pump. The ERCOFTAC validation case is compared directly to experimental results obtained fromUbaldi et al. [7]. The results from the Quintus Cold gas pump analysis are used to generate a pump curvethat quantifies its performance over a range of mass flow rates and RPM.

3.1 ERCOFTAC Validation Case

The following section presents the results of the ERCOFTAC centrifugal pump validation case. This valida-tion study includes a mesh independence study and both steady state and transient simulations for both a2D and 3D model of the ERCOFTAC centrifugal pump. The results show good agreement with experimentaldata provided by Ubaldi et al. [7] and therefore lends to the accuracy and reliability of results obtained forthe Quintus Cold gas pump, which uses the same method.

3.1.1 2D Steady State Convergence Study

Figures 3.1a, 3.1b, 3.1c, and 3.1d show the plots used to determine convergence for the ERCOFTAC 2Dsimulation. About 800 iterations are required to meet the convergence criteria outlined in 2.1.6. The monitorpoint values and domain imbalances meet the convergence criteria well before 800 iterations, but for strictconvergence the simulation is run until the residuals are below 10−6.

38

(a) (b)

(c) (d)

Figure 3.1: Plots used for determining convergence for the 2D ERCOFTAC medium mesh steady statesimulation. (a) Residual values during the simulation. (b) Monitor point gauge static pressure values duringthe simulation. (c) Monitor point velocity values during simulation. (d) Domain imbalances during thesimulation.

3.1.2 2D Mesh Independence Study

The total pressure rise coefficient for five different 2D meshes can be seen in figure 3.2. The smaller theaverage edge length h, on the horizontal axis, the higher resolution the mesh is. The number of elements and

39

Table 3.1: The maximum y+ values of each mesh generated for the mesh independence studies. The 2Dsimulations aimed to fully resolve the boundary layer, so the desired y+ are between 0.1 and 5. The 3Dsimulations used the scalable wall functions as part of the k − ω SST turbulence model, so the desired y+values are between 11 and 20.

2D Meshes 3D MeshesMaximum y+ Average y+ Maximum y+ Average y+

Mesh 1 16.5 10.3 19.5 16.3Mesh 2 13.2 6.48 16.6 15.4Mesh 3 3.10 1.23 16.2 14.8Mesh 4 2.00 0.68 16.0 14.2Mesh 5 0.780 0.24 13.3 12.6

nodes in each mesh are presented in table 2.4. The maximum y+ value for each mesh is also given, in table 3.1.

Figure 3.2: Total pressure rise coefficient versus average edge length for 2D mesh study. The equation for thesecond degree polynomial fit curve is included, along with the r-squared value. The 2% envelope indicates a2% range from the estimated theoretical total pressure rise coefficient optained using an infinitesimally finemesh. Meshes 4 and 5 are considered independent because they fall within this envelope.

From these results, it can be concluded that a 2D mesh with an average edge length of about 0.0015m, whichcorresponds to about 140000 elements, is solution independent. The total pressure rise coefficient for meshes4 and 5 also varies less than 2% from the theoretical value when using a infinitesimally fine mesh. Also,the y+ values for meshes 4 and 5 are very close to the required value of 1 in order to resolve the viscoussublayer. Therefore, mesh 4 is deemed solution independent, and is used for the rest of this paper for theERCOFTAC pump 2D simulations.

40

3.1.3 2D Steady State Simulation

The results from the 2D steady state simulation of the ERCOFTAC centrifugal pump are presented in figures3.3a through 3.3c. The coefficient of static pressure, radial, and tangential velocities are plotted versus thenormalized circumferential coordinate along a measuring line at a radius of 214.2mm (for details see figure2.2). The black squares denote diffuser vane position and the triangles denote impeller blade position.

(a) (b)

(c)

Figure 3.3: Results of 2D ERCOFTAC steady state simulation. (a) Coefficient of static pressure, (b)normalized radial velocity, (c) and normalized tangential velocity.

41

3.1.4 2D Transient Convergence Study

Figure 3.4 presents the plots used to determine convergence for the ERCOFTAC 2D transient simulation.About 2200 iterations were required to obtain convergence. As can be seen, most convergence criteria aremet well before 2200 iterations, but the outlet velocity too much longer to become steadily periodic. Thedomain imbalance plot is not included because an imbalance of well below 1% is maintained from the steadystate case. Velocity and pressure contours are shown in the appendix.

42

(a) (b)

(c)

Figure 3.4: Plots used for determining convergence for the 2D ERCOFTAC transient simulation. (a) Residualvalues during the simulation. (b) Monitor point gauge static pressure values during the simulation. (c)Monitor point velocity values during simulation.

3.1.5 2D Transient Simulation

The ERCOFTAC centrifugal pump 2D transient simulation results are presented in figures 3.5, 3.6, and3.7. As in the 2D steady state results, the transient simulation results are plotted versus the circumferentialcoordinate yi

Gi. The successive plots in each figure are increasing time steps (see section 2.1.1); ranging

43

from tTi

= 0 to tTi

= 0.3 for the pressure measurements, and tTi

= 0.126 to tTi

= 0.426 for the velocity

measurements. tTi

is the time, from start, normalized by the impeller passing period. The squares denotediffuser vane position, and triangles the impeller blade position.

(a) (b)

(c) (d)

Figure 3.5: Coefficient of static pressure results for the 2D ERCOFTAC transient simulation. Each successiveplot are successive timesteps, beginning at t

Ti= 0 through t

Ti= 0.3 by steps of 0.1. On the x-axis is the

circumferential coordinate yiGi

.

44

(a) (b)

(c) (d)

Figure 3.6: Normalized radial velocity results for the 2D ERCOFTAC transient simulation. Each successiveplot are successive timesteps, beginning at t

Ti= 0.126 through t

Ti= 0.426 by steps of 0.1. On the x-axis is

the circumferential coordinate yiGi

.

45

(a) (b)

(c) (d)

Figure 3.7: Normalized tangential velocity results for the 2D ERCOFTAC transient simulation. Each suc-cessive plot are successive timesteps, beginning at t

Ti= 0.126 through t

Ti= 0.426 by steps of 0.1. On the

x-axis is the circumferential coordinate yiGi

.

3.1.6 3D Steady State Convergence Study

Figure 3.8 shows the plots used to determine convergence for the 3D ERCOFTAC steady state simulation.Similar to the 2D steady state case, about 800 iterations are required to meet the convergence critera. Alsosimilarly, the monitor point values and domain imbalances meet the convergence criteria well before 800interations, but for strict convergence the simulation is continued until the RMS residual values reach below

46

10−5.

(a) (b)

(c) (d)

Figure 3.8: Plots used for determining convergence for the 3D ERCOFTAC medium mesh steady statesimulation. (a) Residual values during the simulation. (b) Monitor point gauge static pressure values duringthe simulation. (c) Monitor point velocity values during simulation. (d) Domain imbalances during thesimulation.

3.1.7 3D Mesh Independence Study

The results of the 3D ERCOFTAC mesh independence study is presented in figure 3.9. The various mesh sizescan be viewed in table 2.4. The results show that mesh 5, with about 15 million elements, is independent. The

47

total pressure rise coefficient at this mesh resolution is within 2% of the theoretical value for an infinitesimallyfine mesh (h3D = 0). Further mesh refinement is not possible past 15 million elements due to computationalresources and time available.

Figure 3.9: Total pressure rise coefficient plotted versus average edge length for 3D mesh independence study.The equation for the second degree polynomail fit curve is included, along with the r-squared value.

The y+ values for the ERCOFTAC 3D meshes are presented in table 3.1. As discussed in section 2.1.8,initial simulations had difficulty converging with a small first wall element height aimed at capturing theviscous sublayer. The decision is made to utilize a scalable wall function by increasing the height of thefirst element enough for a y+ value between 11 and 20. This proved to improve convergence and ensure anaccurate solution.

3.1.8 3D Steady State Simulation

The results from the 3D steady state simulation on the ERCOFTAC pump are presented in figures 3.10ato 3.10c. The coefficient of static pressure, radial velocity, and tangential velocity are extracted and plottedalong the measuring line (see figure 2.2). The x-axis is the circumferential coordinate system, spanninganticlockwise from yi

Gi= 0 to yi

Gi= 2, i.e 0 degrees to about 102 degrees.

48

(a) (b)

(c)

Figure 3.10: Results of 3D ERCOFTAC steady state simulation. Coefficient of static pressure (a), normalizedradial velocity (b), and normalized tangential velocity (c) are all plotted versus the circumferential coordinateyiGi

.

3.1.9 3D Transient Convergence Study

Figure 3.11 presents the plots used to determine convergence for the ERCOFTAC 3D transient simulation.Nearly 2000 iterations are required to meet the convergence criteria for this simulation. Similar to the2D transient simulation, most of the monitor point values and all RMS residual values fulfill the conver-gence criteria well before 2000 iterations, but the outlet velocity monitor did not level out until about 1800iterations.

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(a) (b)

(c)

Figure 3.11: Plots used for determining convergence for the 3D ERCOFTAC transient simulation. (a)Residual values during the simulation. (b) Monitor point gauge static pressure values during the simulation.(c) Monitor point velocity values during simulation.

3.1.10 3D Transient Simulation

The results from the ERCOFTAC pump 3D transient simulations are presented in figures 3.12, 3.13, and3.14. Each figure includes four different plots; each corresponds to a successive time step. The time stepsare expressed as time normalized by the impeller passing period, t

Ti(see section 2.1.1).

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(a) (b)

(c) (d)

Figure 3.12: Coefficient of static pressure results for the 3D ERCOFTAC transient simulation. Each succes-sive plot are successive timesteps, beginning at t

Ti= 0 through t

Ti= 0.3 by steps of 0.1. On the x-axis is the

circumferential coordinate yiGi

.

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(a) (b)

(c) (d)

Figure 3.13: Normalized radial velocity results for the 3D ERCOFTAC transient simulation. Each successiveplot are successive timesteps, beginning at t

Ti= 0.126 through t

Ti= 0.426 by steps of 0.1. On the x-axis is

the circumferential coordinate yiGi

.

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(a) (b)

(c) (d)

Figure 3.14: Normalized tangential velocity results for the 3D ERCOFTAC transient simulation. Eachsuccessive plot are successive timesteps, beginning at t

Ti= 0.126 through t

Ti= 0.426 by steps of 0.1. On the

x-axis is the circumferential coordinate yiGi

.

3.2 Quintus Cold Gas Pump

This section presents the results of the CFD analysis done on the Quintus Cold Gas pump. The goal ofthe analysis is to quantify the pump performance by generating a pump curve, which one includes pumpcharacteristic curve and one pump efficiency curve for each rotational speed. Before this is done, meshindependence and convergence studies were carried out to support the reliability of the results. The workdone here will lay the groundwork for future work in the improvement of Quintus Technologies’ URC and

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URQ systems.

3.2.1 Steady State Convergence Study

The plots used to determine convergence for the Quintus cold gas pump mesh 3 steady state simulation areshown in figures 3.15a, 3.15b, 3.15c, and 3.15d. The settings for all runs for the mesh independence studyare a rotational speed of 600 RPM and an outlet mass flow rate of 3 kg

s . From these plots it is determinedthat a steady state solution does not exist. The convergence criterion of domain imbalance less than 1%and all monitor pressures and velocities stable are not met. The high degree of instability can be seenin the monitor point 2 velocity. Because of this, transient simulations were expected to be required for aconverged solution. The change in these plots at about interation 2500 is a change in time step factor. AnsysCFX uses a pseudo-transient method for steady state simulations, so changing the time step factor can helpconvergence [12]. In this case, it did not.

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(a) (b)

(c) (d)

Figure 3.15: The plots used to determine convergence for the Quintus cold gas pump steady state solution.These are from mesh 3. (a) RMS residuals, (b) gauge pressure at the monitor points, (c) velocity at themonitor points, and (d) the domain imbalance % during the simulation.

3.2.2 Transient Convergence Study

The plots in figure 3.16 are used to determine convergence for the Quintus cold gas pump transient simu-lations. The mesh used here is mesh 3, with a rotational speed of 600 RPM and an outlet mass flow rateof 3 kg

s . These plots show that all convergence criterion from section 2.2.4 are met. RMS residuals aremaintained below 10−3, domain imbalance is less than 1%, and all monitor point values are periodic.

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(a) (b)

(c) (d)

Figure 3.16: The plots used to determine convergence for the Quintus cold gas pump transient solution.These are from mesh 3. (a) RMS residuals, (b) gauge pressure at the monitor points, (c) velocity at themonitor points, and (d) the domain imbalance % during the simulation.

3.2.3 Mesh Independence Study

The results mesh independence study carried out on the Quintus cold gas pump are presented here. Fourdifferent meshes were generated. The element and node count of these meshes is presented in table 2.9.Using the same method of determining mesh independence as in the ERCOFTAC validation case, the totalpressure rise coefficient is plotted versus the average 3D edge length; seen in figure 3.17. Here, the RMSresidual values are accepted once below 10−3. As discussed in the previous two sections, no steady statesolution was found, so transient runs were carried out for this mesh independence study.

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Figure 3.17: Total pressure rise coefficient plotted versus the average 3D edge length for various Quintuscold gas pump meshes. A 2nd degree polynomial fit curve, its equation and R-squared value, along withtwo horizontal lines, which form a 2% envelope from the theoretical total pressure rise coefficient using aninfinitesimally fine mesh (h=0), are included.

Table 3.2: The the average and maximum y+ values for the meshes used in the Quintus cold gas pump meshindependence study.

Average y+ Max y+

Mesh 1 73.8 489Mesh 2 44.7 312Mesh 3 18.9 240Mesh 4 17.4 140

From the results in figure 3.17, meshes 3 and 4 are considered independent. Mesh 3 will be used for the restof this study. The resulting y+ values are presented in table 3.2.

3.2.4 Pump Performance

The resulting pump curve quantifying the Quintus cold gas pump performance is shown in figure 3.18. Thetrends follow the classic pattern for hydraulic pumps; the pump characteristic curve decreases with highermass flow rate and the efficiency first increases then decreases. The pattern in figure 3.18 indicates that apump characteristic curve for any rotational speed between 0 and 900 can be generated. This could be doneusing the same equation of fit resulting from the three lines presented here, just with a different y-intercept.Pressure and velocity contours for a cross section along with a 3D pressure contour of the stator and rotorregions can be viewed in the appendix.

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Figure 3.18: The pump curve for the Quintus cold gas pump. Includes pump characterisitic and efficiencycurves. The solid lines are fit to the circle data points which are the total pressure rises for each run(left y-axis). The dotted lines are the pump efficiency curves fit to the X data points (right y-axis). Bluecorresponds to 300 RPM data, green to 600 RPM data, and red to 900 RPM data.

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Chapter 4

Discussion

This chapter presents a discussion of the results obtained in both the ERCOFTAC validation case and theQuintus cold gas pump performance study. The accuracy and reliability of the results and what can beconcluded is discussed.

4.1 2D ERCOFTAC Validation Case

The 2D ERCOTAC validation case proved that CFD, and specifically Ansys CFX, can be used to accu-rately predict macro flow characteristics and can predict reasonably well detailed flow characteristics withincentrifugal pumps. The total pressure rise coefficient from the mesh independence study results shows veryclose agreement with the experimental total pressure rise coefficient. The mesh study showed that with ainfinitesimally fine mesh, the theoretical pressure rise coefficient would be 0.668, see figure 3.2. Comparingthis to the reported total pressure rise coefficient during the ERCOFTAC experiments of 0.65, the accuracyof this method for predicting the total pressure rise over a centrifugal pump is supported.

The small increase of the total pressure rise coefficient in the ERCOFTAC simulations is likely due to thevarious simplifications made in the computational domain. The largest simplification is not including the1% gap between the rotor blades and the shroud. For real world operation, this gap is required for smoothoperation, but it creates leakage flow between the suction and pressure sides of impeller blades which canreduce efficiency. This can account for why the total pressure rise coeffcient found during simulations isslightly higher than that of the experiments. Previous numerical studies using the ERCOFTAC case forvalidation did not include this gap either in order to reduce meshing complexity [8, 9, 11]. Even with thissimplification, the results found here strongly agree with the ERCOFTAC experimental results, lendingfurther reliability to this computational method also used on the Quintus cold gas pump.

4.1.1 Steady State Simulations

Good agreement can be seen between the simulations and experimental data. However, it is clear the the2D steady state simulation is unable to capture all fluctuations in pressure or velocity at the measuringline, see figures 3.3a, 3.3b, and 3.3c. The simulation is especially not good at capturing the magnitude ofpressure drops, but the location of peaks and valleys can be sufficiently extracted. A slight phase shift in thetangential velocity plot can also be observed. Some variation from the experimental results is to be expectedin this steady state simulation because the region between the impeller blade outlet and diffuser vane inletis highly unstable. Steady state simulations will not be able to accurately resolve this unsteadiness, and

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is unable to properly advect any impeller blade wake phenomena through the grid interface and into thediffuser vane passages [11]. It is important to note that the impeller-diffuser interface is modelled using thefrozen rotor model in Ansys CFX, a new model that is better at predicting transient flow phenomena insteady state simulations than the standard mixing plane model [12]. Even so, they do not move or change,meaning they can be unrealistic.

The results obtained in the previous 2D ERCOFTAC computational studies agree very well with the resultspresented here [8, 9, 11]. This further supports that steady state simulations are not sufficient for capturingdetailed flow characteristics within impeller-diffuser gaps. However, general flow characteristics are suffi-ciently captured such as the location of large pressure or velocity fluctuations and the total pressure riseover the pump, seen in the mesh study results, figure 3.2.

It should be noted that the strict convergence criteria imposed on this 2D steady state case were notcompletely necessary. Seen in figures 3.1a to 3.1d, it can be seen that all monitor points and domainimbalances fulfill the convergence criteria at about 250 iterations. At this point, the RMS residuals havereached 10−5, one order of magnitude more than the prescribed convergence criteria of 10−6. The simulationtime, for this case, could be reduced by about 75% if a less strict RMS residual convergence criterion is set,but keeping the other criteria the same.

4.1.2 Transient Simulations

The 2D ERCOFTAC transient simulation yields results that agree better with the experimental results thanthe steady state run. Contrary to the steady state simulations, the transient results predict the locationpressure changes well and the magnitude of pressure changes better than the steady state simulations, seenin figures 3.5, 3.6, and 3.7. The same holds for the velocity results; however, the velocity results are still notcompletely predicting the magnitude of fluctuations. The velocity results still give good predictions of theaverage changes in velocity across impeller gaps.

The computational results from previous 3D ERCOFTAC computational studies also agree very well withthe results presented here [8, 9, 11]. This points to the idea that these 2D transient simulations are as goodagreement with the experimental results that CFD can provide (using a standard RANS equation solver andnot a computationally expensive LES or DES simulation). Knowing that this may be as good as CFD canget for this case, the question surfaces whether the CFD results or experimetal results are what actuallyhappens in the ERCOFTAC pump. The measuring devices and techniques used by Ubaldi et al. [7] couldhave disturbed the flow in this small region, leading to inaccurate readings. Essentially, these CFD resultscould be showing how the flow actually behaves in this region, while the experimental results include someerror due to the measuring tools.

4.2 3D ERCOFTAC Validation Case

Adding another dimension the ERCOFTAC validation case made for a great way to support the reliability ofresults obtained in the Quintus cold gas pump study since it will also be a 3D simulation. An important partof the 3D ERCOFTAC simulations is the use of a higher average y+ value in order to reduce computationalresources required by inducing the SST turbulence model to insert a scalable wall function. Even with thissimplification, the 3D mesh independence study results yield a theoretical total pressure rise coefficient, withan infinitesimally fine mesh, very close to that of the 2D mesh study results. This adds further support forthis method of predicting the total pressure rise over centrifugal pumps.

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This result supports that a y+ small enough to capture the laminar sublayer versus a larger y+ with ascalable wall function does not substantially affect global variables such as the total pressure rise coefficient.This is important because this same method of using a higher y+ is used for the Quintus cold gas pumpperformance study where the main focus is on the total pressure rise coefficient. Also, similar to the 2DERCOFTAC case, the 1% impeller blade-shroud gap is not included here either. This likely causes thesmall increase in total pressure rise coefficient here compared to the experimental one, just like in the 2DERCOFTAC simulation.

4.2.1 Steady State Simulations

The results of the 3D ERCOFTAC steady state simulation echo the results found in the 2D ERCOFTACsimulation. Similar variance in the coefficient of pressure can be seen, along with the radial and tangentialvelocities failing to capture faster fluctuations, see figures 3.10a, 3.10b, and 3.10c. A slight phase shift in thetangential velocity plot can also be observed, similar to the 2D case. However, the average velocity resultshere agree better than the 2D cases with the experimental data while not fully capturing fluctuations. Again,a steady state simulation is expected to not fully capture these small flow details, even when using the moreadvanced frozen rotor interface model, so the results are consistent with expectations. However, as discussedabove, this does not seem to substantially affect global flow variables since the total pressure rise coefficientfound in the mesh independence study agreed very well with both the 2D mesh independence study and theERCOFTAC experiment.

Making a similar observation as in the 2D steady state case, the convergence criteria set here could beloosened as well. Looking at figures 3.8a to 3.8d, the monitor point and domain imbalance convergencecriteria are met at about iteration 300. At this iteration, the RMS residual values are at about 2 ·10−4, morethan one magnitude higher than the prescribed convergence criterion of 10−5. Simulation time could havebeen heavily reduced here, as well, had the RMS residual convergence criterion been relaxed while keepingthe other convergence criteria the same.

4.2.2 Transient Simulations

The results from the ERCOFTAC 3D transient simulation provides the best agreement with experimentaldata. Seen in figure 3.12, the pressure data agrees well with the experimental data. Compared to the 2Dresults, these simulations provide better prediction of pressure fluctuation position and magnitude. The radialvelocity results, from figure 3.13, are slightly better than the 2D results, providing better prediction of smallerfluctuation magnitudes and a more accurate average when compared to the experimental data. Finally, thetangential velocity, in figure 3.14, simulation results provide the best agreement with the experimental data.Fluctuation magnitude is predicted well, with some smaller fluctuations not captured. For capturing fineflow details, this method of simulation will provide accurate and reliable results. Further mesh refinementcould be done to hone in even closer to experimental data, but the accuracy shown here is proven to besufficient for predicting macro flow characteristics such as the total pressure rise over a centrifugal pump.

4.3 Quintus Cold Gas Fan

Given the results from the ERCOFTAC validation case discussed above, the results of the Quintus cold gaspump performance analysis can be considered accurate and reliable. The ERCOFTAC 2D and 3D meshstudy results support the accuracy of the simulation methodology used in this study for predicting the totalpressure rise over a centrifugal pump. One important thing to consider is the use of the SST turbulencemodel scalable wall functions. The ERCOFTAC 2D case fully resolved the boundary layer with low y+values while the 3D case opted for a higher y+ in order to insert scalable wall functions and reduce mesh

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element count. Due to the great agreement between the ERCOFTAC 3D and 2D total pressure rise, theeffect of using higher y+ values and scalable wall functions does not substantially effect macro flow results.This supports results obtained during the Quintus cold gas pump performance study since scalable wallfunctions were used there as well.

Given the strict convergence criteria, and that they may have been more strict that needed for the ERCOF-TAC cases, discussed above, it can be argued that the loose RMS residual convergence criterion used in theQuintus cold gas pump analysis is sufficient. The convergence criteria for the Quintus cold gas pump analysisfocused more heavily on monitor points and domain imbalances, rather than the RMS residual values. Thesteadiness of the monitor points and domain imbalances well before the strict RMS residual target set duringthe ERCOFTAC simulations supports the use of a looser RMS residual target during the Quintus pumpanalysis.

The second degree polynomial fit curves used in figure 3.18 are very closely correlated to the pressure risedata, but not so well correlated for the efficiency data. This means that one could confidently generatefurther pump characteristic curves for any rotational speed using the same fit equation from the data shownhere. This cannot be done for the efficiency curves. Adding a system curve to this graph will complete theperformance picture, predicting the performance at any given operating condition.

In reality, this cold gas pump operates in tandem with the hot gas pump during a cooling cycle. In order tofully realize the effectiveness of the pumping system used in the cooling cycle, the hot gas pump performancewill also need to be evaluated. The pump curve for both pumps working together can be used to determineoptimal operating speeds, pressures, and flow rates during cooling cycles. Once the pump characteristic andefficiency curves are generated, tests will need to be conducted to form a system curve. This curve will showhow the required pressure to drive the cooling cycle increases as the mass flow rate increases. The intersectionof this system curve and the pump characteristic curve is the operating point of the pumps working together,and extending this point up to the efficiency curve will predict the efficiency of this pumping system at thisoperating condition.

4.4 Conclusion

The conclusions drawn from the work presented in this paper will lay the foundation for further analysis andimprovement of the Quintus HIP cooling systems. The main aims of this study are repeated below.

• Perform 2D CFD analysis on the ERCOFTAC centrifugal pump and compare results to experimentaldata.

• Perform 3D CFD analysis on the ERCOFTAC centrifugal pump and compare results to experimentaldata.

• Perform CFD analysis on Quintus cold gas pump using the same method as used in the validationcase.

• Extract pump performance data and generate pump curve.

• Evaluate reliability and support resulting performance characteristics using the validation case.

The ERCOFTAC 2D and 3D CFD analysis resulted in good agreement with experimental results. Betteragreement is obtained when running transient simulations. Agreement with experimental results can be seenin both detailed and macro flow characteristics. Comparing simulation data collected along the measuringline, same as in the experiment, reveals that transient simulations predict well the pressure and velocityfluctuations in very small regions. This supports the accuracy of CFD analysis in predicting detailed flowcharacteristics. The mesh independence studies, for both 2D and 3D ERCOFTAC, show that CFD is alsovery well suited for predicting macro flow characteristics, such as the total pressure rise. The predicted ’real’

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(with an infinitesimally fine mesh) total pressure rise, in both the 2D and 3D ERCOFTAC cases, is 0.668.Comparing this to the experimental value of 0.65 shows less than a 3% difference.

With the accuracy of CFD in predicting both detailed and macro flow characteristics supported by theERCOFTAC validation case results, it can be said that the Quintus cold gas pump performance analysisis reliable. The best support for the Quintus pump results is the accuracy of the predicted total pressurerise from the ERCOFTAC case mesh independence studies. The predicted total pressure rise is very closeto that of the experiment, lending support for the same method used when analyzing the Quintus pump.

4.5 Future Work

Future work building on the work done in this study can be to explore design optimization of the Quintuscold gas pump, evaluation of the entire pumping system efficiency, and evaluation of HIP cooling cycleefficiency. The results of this study show that there is a lot of room for the Quintus cold gas pump tobe improved. The maximum efficiency seen is about 27%, but it is important to keep in mind that thisnumber is including the inlet valves which contribute a substantial pressure loss. Other similar centrifugalpumps, used in hydraulic applications, can reach an efficiency of 80%, albeit this is only taking the rotorand stator stages into account. Given the lack of space in a HIP fan module, requiring the pumps to makenumerous turns in the flow path, a conservative estimate could yield an increased efficiency of 10%. Thiswould include varying rotor blade and stator vane geometry, inlet valve design, and improvement of the flowpath. Increasing the efficiency could also be used to downsize the pumps in order to reduce the overall sizeof a HIP. Having the same performance in a smaller package is always better.

Including the hot gas pump into the performance evaluation and pump curve will provide the whole pumpingperformance picture. With a pump curve that includes both pumps, the efficiency of the entire cooling cyclepumping system can be evaluated. However, a system curve must also be generated that shows the pressurerequired to drive the cooling cycle. With all of this data, the operating condition during a cooling cycleand the corresponding efficiency can be extracted. This data could also indicate possible performanceimprovements for both pumps if increased efficiency is required. This would also show which mass flow ratesand rotational speeds provide the highest pumping efficiency.

With the performance of both pumps working together evaluated, this data can be input into a model forsimulating the cooling within the furnace area of a HIP under varying thermal loads. With more accuratepressure increase and mass flow rate data, a more accurate full cooling cycle model can be built. Balancingand matching the best efficiency points of the pumping system and furnace cooling flow will be crucial forfurther reduction of HIP cooling cycle times.

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Bibliography

[1] Bowles, A.G and D.E Witkin. ”Hot Isostatic Pressing”. High-Pressure Science and Technology. SpringerUS, 1979.

[2] ”Recent Trends in Hot Isostatic Pressing (HIP) Technology: Part 1 - Equipment”. Powder MetallurgyReview. www.ipmd.com June, 2012.

[3] ”The Ultimate Heat Treatment Solution”. Quintus Technologies. www.quintustechnologies.com, 2017.

[4] Schobeiri, Meinhard T. ”Turbomachinery Flow Physics and Dynamic Performance”. Second Edition.Springer US, 2012

[5] Gulich, Johann F. ”Centrifugal Pumps”. Third Edition. Springer, 2014.

[6] Korpela, Seppo A. ”Principles of Turbomachinery”. First Edition. Wiley US, 2011.

[7] Ubaldi, Marina et al. ”An Experimental Investigation of Stator Induced Unsteadiness on CentrifugalImpeller Outflow”. Journal of Turbomachinery, vol 118. ASME, 1994.

[8] Petit, Oliver and Hkan Nilsson. ”Numerical Investigations of Unsteady Flow in a Centrifugal Pump witha Vaned Diffuser”. International Journal of Rotating Machinery, vol 2013. Hindawi Publishing Corp.,2013.

[9] Petit, Oliver et al. ”The ERCOFTAC centrifugal pump OpenFOAM case-study”. 3rd IAHR Interna-tional Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery andSystems. Brno, Czech Republic, October 2009.

[10] Petit, Oliver et al. ”The ERCOFTAC centrifugal pump OpenFOAM case-study”. (Power Point Slides).4th OpenFOAM workshop. Montreal, Canada, June 2009.

[11] Xie, Shasha. ”Studies of the ERCOFTAC Centrifugal Pump with OpenFOAM”. Master’s Thesis inFluid Dynamics. Chalmers University of Technology, Gteborg, Sweden, 2010.

[12] Inc ANSYS. ”Ansys Theory Guide 17.0”. 2016.

[13] LEAP CFD Team. ”Tips & Tricks: Estimating First Cell Height for correct Y+”. LEAP Australia:CFD Blog. Australia, July 1, 2013.

[14] E.C. Burstrom, Per et al. ”Modelling heat transfer during flow through a random packed bed of spheres”.Manuscript. 2015.

[15] Eklund, Anders. ”Avure Technologies PM-DK Temadag”. Avure Technologies AB. November 1, 2012.

[16] Anderson, John D. ”Computational Fluid Dynamics: The Basics with Applications”. InternationalEdition. McGraw-Hill Book Co., 1995.

[17] Menter, F.R. ”Zonal Two Equation k- Turbulence Models for Aerodynamic Flows”. AIAA Paper 93-2906. 1993

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Appendix

Figure 4.1: Velocity contour of ERCOFTAC 2D steady state simulation.

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Figure 4.2: Pressure contour of ERCOFTAC 2D steady state simulation.

Figure 4.3: Velocity contour of a cross section of the Quintus cold gas pump. Transient last time step, 600RPM with 3kgs .

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Figure 4.4: Pressure contour of a cross section of the Quintus cold gas pump. Transient last time step, 600RPM with 3kgs .

Figure 4.5: Pressure contour on the rotor and stator blade regions of the Quintus cold gas pump. Transientlast time step, 600 RPM with kg

s .

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