“Virtual CFD test bench for heat exchangers performance prediction”somim.org.mx/memorias/memorias2018/articulos/A4_99.pdf · 2020. 1. 14. · “Virtual CFD test bench for heat

MEMORIAS DEL XXIV CONGRESO INTERNACIONAL ANUAL DE LA SOMIM 19 al 21 DE SEPTIEMBRE DE 2018 CAMPECHE, CAMPECHE, MÉXICO

Tema A4 Termofluidos: Dinámica de Fluidos Computacional

“Virtual CFD test bench for heat exchangers performance prediction”

Oscar Alcocer Escamilla1,a

, Youssef Beddadi2, Ricardo Romero Méndez

1

1Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava, Col. Zona Universitaria Poniente, San Luis Potosí, S.L.P., C.p. 78290, México 2 Valeo SystemesThermiques, 8 Rue Louis Lormand, La Verrière, C.p. 78321 France aAutor de contacto: [email protected]/[email protected]

A B S T R A C T

The aim of the present investigation is to propose numerical simulation strategies using available commercial software,

to guarantee that the numerical simulation is fast, precise and fits well with experimental evidence. The products

analyzed in this project are three automotive radiators, two with dimpled tube and one smooth tube technology. The

current proposal is to get an accurate steady state isothermal simulation to reproduce the coolant pressure drop of the

experimental test, using a periodic tube simulation to estimate the porous media coefficients and considering the humid

surfaces without geometrical assumption. A priori, the porous media approach is less accurate around ~±15%.

Comparing the complete mesh methodology vs. test, it was obtained a difference in results of ~±3% with dimpled tube;

however it was found that the accuracy is reduced with the smooth tube technology. Keywords: Numerical simulation, Turbulence, Radiator, Heat Exchanger, Simulation

R E S U M E N

El objetivo de la presente investigación es proponer estrategias de simulación usando un software comercial disponible,

para garantizar que la simulación es rápida, precisa y consistente con la evidencia experimental. Los productos

analizados en este proyecto son tres radiadores: dos con turbuladores y uno con tubo liso. Las propuesta es obtener una

simulación isotérmica precisa en estado estacionario para reproducir la caída de presión de la prueba experimental,

usando una simulación periódica de un tubo para estimar los coeficientes del medio poroso y considerar la superficie

humeda sin ninguna suposición geométrica. A priorí, la aproximación del medio poroso es menos precisa, obteniendo

una diferencia ~ ± 15%.Comparando la estrategia con malla completa contra experimento, se obtuvo una diferencia en

resultados de ~ ± 3%; sin embargo se encontró que la precisión en la predicción se reduce con la tecnología de tubo

liso. Palabras Clave: CFD, Simulación Númerica, Turbulencia, Radiador, Intercambiador de Calor

1. Introducción

The automotive standards demand a reduction in design time, production and manufacturing; this is one of the reasons why engineering, design and simulation teams are looking for improvement areas to reduce time from concept to launch of new products. Nowadays the challenge of the automotive industry is to maintain a high level of research and innovation, to keep this high level it is necessary to build prototypes and to develop some tests to validate the operation and performance of such products. The aim of the present investigation is to contribute to this objective by proposing numerical simulations strategies using available CFD commercial software Star CCM+™ by Siemens, to guarantee that the numerical simulation is fast, precise and fits well with experimental evidence. The use of standard computational techniques does not guarantee to achieve a good fit with experiments, which is why it is necessary to perform studies (mesh sensibility, initial

surface geometry, surface quality, experimental statistical studies, etc.) that will be described later in this document. Nowadays, virtual development and simulations are the first step between the customers and the design centers, and it is well-known that a design process is a challenging task. As it was mentioned, the design centers must reduce design conception times. To develop a product, it is mandatory to validate the operation and feasibility through tests and simulations. Knowing that the project will be developed for the Thermal Branch, it is necessary to run fluid flow and thermal simulations; Valeo Thermal Systems use CFD to validate the satisfactory performance of the products. The use of CFD has been extended to model particularly complicated problems. It is well known that for many of the governing fluid mechanics equations, analytical solutions are limited or complicated to obtain [1]. Computational fluid dynamics offers the opportunity to solve complex systems of partial differential equations by replacing them with simple algebraic equations, which have a relatively simple solution [2]. Considering the

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radiator as the domain and turbulent flow regime as the physics, it is almost impossible to find an analytic solution, which justifies the use of 3D CFD numerical simulations to predict the governing equations.

The project is a collaboration between U.A.S.L.P. (Universidad Autónoma de San Luis Potosí) and V.T.S. (Valeo Thermal Systems). It arises from Valeo’s requirement to develop a solution for certain issues, with innovation and finding of new research areas. Formerly, Valeo developed multiple test benches, making use of the CFD approach, in order to reach the objective mentioned above; this virtual test benches were developed for blowers, fans, alternators by including a wind tunnel as a computational domain and thermal camera mappings, for which good results have been obtained [3][4] .

The completion of this project verifies that numerical set-ups are able to predict with good accuracy the results of experimental tests. It is important to mention that numerical simulations do not substitute the real test bench, but give a first approximation which permits to know if the design goes in the proper direction. The product analyzed in this project was the automotive radiator. The radiator (heat exchanger) is a product located on the coolant circuit of the vehicle; this circuit comprises two parts: engine-coolant & coolant-environment, (air forced through the grid when the vehicle reaches high velocity or by the fan system at low vehicle speed) the radiator is an equipment of the engine cooling loop circuit. The heat exchanger includes four parts: inlet tank, outlet tank, fins, and tubes. The main challenge of this project is to get highly accurate 3D CFD simulations in order to predict the coolant pressure drop between the inlet and the outlet of the system. 1.1. Radiator: Automotive Heat Exchanger

Broadly speaking, a heat exchanger is a device used for transferring the internal thermal [U] energy between two or more fluids at different temperatures [5], referring to the thermodynamics fundamental that the higher temperature body transfers heat (via the heat transfer mechanisms) to the lower temperature body, examples of the applications of these devices are radiators, condensers, evaporators, air pre-heaters and oil coolers. The product analyzed in this project is the radiator, according to Kuppan [5] the radiator is a device considered as a compact liquid to gas heat exchanger widely used in automotive vehicles. The construction includes two parts: the heat exchanging elements, such as flat or dimpled arrays of brazed or mechanical tubes with a continuous aluminum fin array, and the fluid distribution elements, such as the tanks, headers, inlet and outlet nozzles or pipes [5]. The devices construction considers an inlet tank, header, core (tube and fins), outlet header and outlet tank.

1.2. Fluid Mechanic Fundamentals

The fluid mechanics approach used in this project is the continuum method, the continuum refers to a particle set which form a region to be studied in a macroscopic scale, without considering the existing discontinuities in microscopic level (molecular or atomic). It is supposed that there are no discontinuities between the particles and the mathematical formulation of this media and all the properties are continuous functions of space and time [6].

Using continuum mechanics approach for fluid

dynamics yields the following equations: continuity equation, momentum equations and energy equation, concentrating in the momentum and continuity equation for now, the equations are:

∇ ∙ �⃗� = 0 (1)

𝜌 [𝜕�⃗⃗�

𝜕𝑡+ �⃗� (∇ ∙ �⃗� )] = −∇�⃗� + 𝜇(∇2�⃗� ) + 𝜌𝑓 (2)

Where �⃗� is the velocity vector, 𝑃 is pressure, 𝜌 is

density and 𝜇 is absolute viscosity. (2) will be modified in further sections in order to yield the turbulent Navier-Stokes equations, since (1) and (2) are valid only for the laminar flow regime.

1.3. Turbulence Mathematical Models

Since 3D CFD numerical simulation is used to predict the behavior of the heat exchanger, it is fundamental to know the governing physics that needs to be solved by the software. As it was mentioned in the abstract the use of RANS Steady State model coupled to the 𝑘 − 휀 Realizable turbulence model is a mathematical way to predict the physics of the domain (heat exchanger). The RANS model is a set of algebraic equations which use the assumption of the integral velocity (or mean velocity) [7] to represent the behavior of the turbulent flow regime considering an incompressible and Newtonian fluid, the RANS is given by:

𝜌𝑈𝑗𝜕�̅�𝑖

𝜕𝑥𝑗= 𝜌𝑓�̅� +

𝜕

𝜕𝑥𝑗[−�̅�𝛿𝑖𝑗 + 𝜇 (

𝜕𝑈𝑖

𝜕𝑥𝑗+

𝜕𝑈𝑗

𝜕𝑥𝑖) − 𝜌𝑢𝑖

′𝑢𝑗′̅̅ ̅̅ ̅̅ ] (3)

Where, 𝑈𝑗 is the mean flow time average velocity given by:

�̅� ≡ 𝑈 = lim𝑡→∞ ∫ (𝑈𝑗 + 𝑢𝑗′)𝑑𝑡

𝑡

𝑡0 (4)

𝑢 = 𝑈𝑗 + 𝑢𝑗

′ (5)

𝑈𝑗 is the mean velocity, 𝑢𝑗′ is the fluctuations velocity,

𝑢 real value of the velocity in time, �̅� ≡ 𝑈 is the time average velocity [7], −𝜌𝑢𝑖

′𝑢𝑗′̅̅ ̅̅ ̅ is the Reynolds Stress tensor.

Coupled to this equations, is the 𝑘 − 휀 turbulence model, widely known and used in the industrial numerical simulations, being a two equations model, this means that include two more equations to represent the behavior to



solve two more variables, the turbulent kinetic energy 𝑘 and the turbulent dissipation rate 휀 , adding to, turbulent viscosity, production of 𝑘 , effect of buoyancy and other constants [8]. The following expressions are for 𝑘 and 휀 , since the simulations establish steady state the equations yield:

𝜕

𝜕𝑥𝑖(𝜌𝑘𝑢𝑖) =

𝜕

𝜕𝑥𝑗[(𝜇 +

𝜇𝑡

𝜎𝑘)

𝜕𝑘

𝜕𝑥𝑗] + 𝑃𝑘 + 𝑃𝑏

−𝜌휀 − 𝑌𝑚 + 𝑆𝑘 (6)

𝜕

𝜕𝑥𝑖

(𝜌휀𝑢𝑖) =𝜕

𝜕𝑥𝑗

[(𝜇 +𝜇𝑡

𝜎𝜀

)𝜕휀

𝜕𝑥𝑗

] + 𝜌𝐶1𝑆휀

−𝜌𝐶2𝜀2

𝑘+√𝜈𝜀+ 𝐶1𝜀

𝜀

𝑘𝐶3𝜀𝑃𝑏 + 𝑆𝜀 (7)

Where 𝜌 is density, 𝑘 is the turbulent kinetic energy 𝑢𝑖 is the velocity component, 𝜇 is the absolute viscosity, 𝜇𝑡 is the turbulent viscosity, 𝑃𝑘 is the generation of turbulent kinetic energy, 𝑃𝑏 turbulent buoyancy equation, 𝑆𝑘 is the stress tensor for 𝑘 , 𝑆𝜀 is the stress tensor for 휀 , 휀 is the turbulence dissipation rate, 𝜎𝑘 , 𝜎𝜀 , 𝐶1, 𝐶2, 𝐶1𝜀 , 𝐶3𝜀 , 𝑌𝑚 are turbulent constants given by the literature.

1.4. Porous Media Mathematical Model

Currently, meshing the product components is not possible; it requires a great mesh effort. Considering the values specified in the Table 1, the mesh grows up to 40 billion cells, this value is not acceptable for the industrial standards. The porous media offers the option to mesh with fewer elements, giving an acceptable approach to thermal and flow simulation.

Table 1 – Complete Radiator Mesh

Component Number of Cells

Tanks ~ 8 Mo (x2) Coolant ~ 6 Mo (x2) Fin ~ 2 Mo per fin (x 20,000) Tube ~ 20 Mo per tube (x 91)

The porous media models are physics that contain fluid

and fine-scale solid structures, for example: packed beds, chemical reactors, filters, radiators, honeycomb structures, perforated plates, flow distributions & tube banks [9],[10], these structures are too fine to be individually meshed and fully resolved by a computational grid [10]. The assumption used for the porous media model for single phase and multiphase flows is the Superficial Velocity Porous Formulation introducing momentum drop into the governing equations [9][11]. The superficial velocity is considered as a hypothetical velocity expressed by:

𝑈𝑠 =𝑄

𝑎 (8)

Where: 𝑈𝑠 superficial velocity, 𝑄 volumetric flow, 𝑎 is the cross-sectional area. The porous media are modeled according to the STAR-CCM+™, by the addition of a momentum drop term to the governing equation [11], as is shown below:

𝜕

𝜕𝑡(∫ 𝜌𝑣𝑠𝑉

) 𝑑𝑉 + ∮ 𝜌𝑣𝑠 ⊗ 𝑣𝑠𝐴∙ 𝑑𝑎

= −∮ 𝑝𝐼 ∙ 𝑑𝑎𝐴

+ ∮ 𝑇 ∙ 𝑑𝑎𝐴

+ ∫ 𝑓𝑏𝑑𝑉𝑉

+∫ 𝑓𝑝𝑑𝑉𝑉

(9) Where 𝑓𝑏 is the body force, 𝐼 is the identity matrix and

𝑓𝑝 is the porous tensor given by [11]:

𝑓𝑝 = −𝑃 ∙ 𝑣𝑠 (10)

And the porous resistance tensor consists of [11]:

𝑃 = 𝑃𝑣 + 𝑃𝑖|𝑣𝑠| (11)

Being 𝑃𝑣 , the viscous losses term (Linear) and 𝑃𝑖 the inertial losses term (quadratic), contributing with a pressure gradient in the porous media, creating a pressure drop that is proportional to the fluid velocity in each cell[9]. Both coefficients are function of other variables. 𝑃𝑣 is a function of the viscosity (𝜇) and the roughness (𝛼) and 𝑃𝑖 is a function of the density and the constant 𝐶2, yields [9]:

𝑆𝑖𝑗 = −[𝑃𝑣(𝜇, 𝛼)𝑣𝑖 + 𝑃𝑖(𝜌, 𝐶2)|𝑣|𝑣𝑗] (12)

This is true since the mathematical and dimensional

analysis shows that the units are coherent, and demonstrate that the pressure drop 𝑆𝑖𝑗 actually is a force per unit volume.

The background explained in this section is useful to

carry out the coolant pressure drop estimation in the core, being the way to calculate the inertial and viscous coefficients for (12), making possible the introduction of a momentum sink in the momentum equation. This assumption allows reducing the mesh size, Darcy law adopts a laminar behavior in the tube just adding the momentum sink as a velocity function, considering the inlet velocity and the velocity profile in each cell of the domain known as core.

1.5. Wall Treatment y+

vs u+

According to the law of the wall, published by von Kárman [12], it is define as behavior near to wall of the flow as function of the distance and the average velocity of the turbulent flow given by the following equation:

𝑢+ =

1

𝑘ln 𝑦+ + 𝐶+ (13)



Where 𝑢+ is a dimensional velocity, 𝑦+ dimensional

velocity is a function of the frictional velocity 𝑢∗ and the kinematic viscosity 𝜈, 𝐶+ is a smooth wall constant and 𝑘 is the von Kárman constant. Being important to the simulations because it sought a low Reynolds approach where 𝑦+ = 1 near to the wall as it is shown in the Figure 1. All the simulations were carried out with this assumption, and looking for the desire behavior.

2. Numerical and Experimental Methodologies

2.1. Experimental Methodology

Valeo standard is based on JIS norm (Japanese Industrial Standard): “Radiators or automobiles – Test Method of heat dissipation norm”. This norm specifies the test method of heat dissipation of radiators for cooling of engine to be used for water cooling engines of automobiles. The test bench is divided in two circuits: the hydraulic circuit (focus of this research) and the air circuit; the hydraulic circuit consists of equipment like pumps, tubes, pipe connectors, flow measurement instruments, pressure meters, etc. and the air circuit includes a blower, venture pipes, pressure meter, etc.; all the equipment is necessary to carry out the test. The test is carried out after the stabilization of the system; once the test reaches this point the test can be performed.

2.2. Measurement equipment

The test rig consists of a variety of measurement equipment, such as Venturi pipes, flow meters, differential pressure sensors, differential temperature sensors, temperature sensor, manometers, etc. The first measurement point is located at the air intake and is a differential pressure sensor. Two more measurement points, which are a differential pressure and differential temperature sensors, are situated in the heat exchanger test area; these sensors will measure the pressure and temperature at the inlet and outlet points.

2.3. Test Procedure

The test must be carried out considering some environment variables, such as relative humidity, bulk pressure, bulk temperature; other important parameters are: geometry constraints (header to header distance, number of tubes, tube spacing, test area (core), pitch, and percent of glycol in the coolant. The test begins with the heat exchanger preparation: the radiator is mounted in a wooden table with the same constraints as the core in order to produce the air flow through it, after this assembly, the wooden table with the radiator is mounted on the test rig. The next steps are to measure the environment variables, to introduce the geometrical parameters to the console and to proceed with the test. The test must reach a steady state condition in order to acquire measurement points, these points are variable, and can be taken from 5 iterations to 20 iterations depending on the customer and Valeo standards. After this point all the data collected is processed by an excel macro.

2.4. Periodic Domain Porous Media Methodology

It was proposed a CFD approach that computes a

periodic pattern of the tube that could replicate the behavior of the turbulence development zone and the boundary layer effects in a small domain, yielding an accurate porous media approximation, which is called “Periodic Domain”. The methodology described in this section allows to perform the same study, making a great effort in the mesh and not in the computation itself, by considering a minimal length and periodic boundary conditions, Priya and Rani [13], proposed the same methodology to flow and heat transfer simulation. The mesh parameters are specified in Table 2 and physics setup for the case was listed below: 3D Simulation RANS (Reynolds Average Navier-Stokes) Model 𝑘 − 휀 Realizable turbulence two layer Water: depends on the coolant glycol percent All 𝑦+ treatment Isothermal Steady Model Polynomial density and viscosity Segregated flow % Glycol

Table 2 – Mesh size for periodic approach

Product Polyhedral

Cells

Radiator 1 (Dimpled) ~100 k Radiator 2 (Dimpled) ~100 k Radiator 3 (Smooth) ~50 k

The boundary conditions are: inlet mass flow, adiabatic

wall and outlet pressure reference. The mass flow is given by:

0

5

10

15

1 2,7 7,29 19,683

u+

y+

u+ vs y+

Figure 1 – Law of the wall for Periodic Domain



�̇� =𝑄 𝜌(𝑇)

3.6𝑥106 ∙1

𝑁𝑡 𝑁𝑑 [

𝑘𝑔

𝑠] (14)

Where 𝑄 is the flow given by the test, 𝑁𝑡 is the number

of tubes in the core and 𝑁𝑑 is the number of divisions of the tube. It was necessary to create a two part code which introduces all the setups needed. The code is designed to import a CAD (Computer Aided Design) part, set the physics, set the mesh parameters, mesh the CAD part, add a post-processing of figures, text files, run and save the simulation file. The simulation was carried out by the standard form and running in the local workstation in order to validate the process and ensure the good results. Table 3 shows the values of the inertial and viscous coefficients for each product. The coefficients have been normalized using the maximum pressure drop and the maximum velocity.

Table 3 – Periodic Domain coefficients for porous media

Product 𝑷𝒊𝒖𝟐 𝑷𝒗𝒖 𝑹𝟐

Radiator 1 (Dimpled) 0.7503 0.2575 0.9997 Radiator 2 (Dimpled) 0.6743 0.32758 1 Radiator 3 (Smooth) 0.348 0.6418 0.9989

*Normalized coefficients.

Figure 2 - Core pressure drop: (a) Radiator 1, (b) Radiator 2 and (c)

Radiator 3, obtained by Periodic Domain approach

The behavior of the technologies presented are shown in Figure 2, each curve represent the pressure drop of the core and the impact of the geometry in the pressure value, it is appear that in the smooth tube the curve tends to the linear behavior instead the other products. The Figures 2(a) and (b) show the radiators with dimpled tubes, and as shown in Table 3, it appears that the coefficients of radiators 1 and 2 are not quite different than the coefficients obtained for the radiator with smooth tubes where the viscous coefficient is higher than that of other radiators. 2.5. Radiator Simulation Methodology

Once the coefficients were determined from periodic

approach, the simulation was carried out, adding a porous region instead of the core detailed tubes geometry with the following physics:

Polynomial Density Cell Quality Remediation Two Layer All y+ Wall treatment K-ε Turbulence and Realizable K-ε Two-layer Reynolds Averaged Navier Stokes Turbulent Regime Gradients Segregated Flow and Fluid Temperature Steady State Liquid and three Dimensional

The surfaces must be prepared; these cases include inlet and outlet tank, inlet and outlet port surface, core in and core out ports, excluding the core itself. The core is represented with extrusion from header to header as its shown in the Figure 3(a), yielding a smooth surface where the porous coefficients were going to be added. Extrusion at inlet and outlet 10 times the hydraulic diameter to ensure the numerical convergence and the fully developed boundary layer. Figure 3(b) shows how the mesh is built; use of the turbulence model proposed allows to compute

y = 0,348x2 + 0,6418x R² = 0,9989

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1 1,2

Dp

/L

Tube Inlet Velocity

Periodic DomainApproach

y = 0,7503x2 + 0,2575x R² = 0,9997

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1 1,2

DP

/L

Tube Inlet Velocity


(a)

(b)

(c)

y = 0,6743x2 + 0,3275x R² = 1

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1 1,2

Dp

/L

Tube Inlet Velocity




the boundary layer using only one layer near to the wall, applying a high Reynolds number approach near the wall, in order to compute the boundary layer development.

Table 4 - Mesh parameters for 3D Radiator domain

Product Polyhedral

Cells

Radiator 1 (Dimpled) ~9 Mo Radiator 2 (Dimpled) ~9 Mo Radiator 3 (Smooth) ~9 Mo

The porous media coefficients inertial and viscous will

be set with data from periodic domain inside the same radiator simulation. The conditions in the simulation are the same as those in the test, in terms of flows and temperatures. Using Gauss-Seidel Method (GSM) as solver and triggering the Conjugated Gradient Convergence Accelerator method [14][15][16][17]. The convergence stability was ensured in order to get a low level of residuals of pressure values, the simulation was stopped with a convergence criteria on the pressure values at ±5 𝑃𝑎.

2.6. Complete System Methodology

The complete system methodology was developed in

order to get a better geometrical assumption, considering the full model without fins (isothermal simulation). This methodology excludes the physical assumption as porous media and gets a more realistic approach. The methodology considers three boundary regions: inlet, wall, and outlet, simplifying the simulation and the mesh setups. The simulation does not consider heat transfer between the coolant and the ambient. The boundary conditions used for this kind of simulation are: mass flow at the inlet, adiabatic wall at the surface region and pressure reference at the outlet. The surface preparation includes inlet and outlet tank, inlet and outlet port surface and one complete tube with geometrical detail that includes the dimples. It was developed a macro that allows to automate the simulation workflow to avoid user error, similar to the periodic domain. The code is capable to import a CAD part, import the tubes with all the geometrical settings, carry out the tube array, which includes the duplication and translation

of the complete tube, set the physics (available to change: 𝑘 − 𝜔 and laminar physics model), set the mesh parameters, mesh the CAD part, add a post-processing of figures, text files, run and save the simulation file. The physics setups are the same as the periodic domain. The mesh setups are specified in Table 5. The simulations were carried out using the same setups as the past section.

Table 5 – Mesh parameters for complete system

Product Polyhedral

Cells

Radiator 1 (Dimpled) ~21 Mo Radiator 2 (Dimpled) ~21 Mo Radiator 3 (Smooth) ~12 Mo

Figure 4 shows the dimple representation using the

mesh size proposed for this methodology; a good representation of these structures allow acquiring the governing physics properly. This representation is important since the dimple is the structure which allows the creation and maintenance of turbulence.

2.7. Uncertainty Quantification

The uncertainty quantification was carried out based on [18], using the following equation:

𝑢𝑐 = √𝑢𝑟2 + 𝑢𝑖

2 + 𝑢𝐴2 (14)

Being the combined uncertainty given by the square

sum of the resolution uncertainty, calibration reports uncertainty and the variability uncertainty, all these given by:

𝑢𝑟 =𝑟

√12 (15)

𝑢𝑖 = 2% (16) 𝑢𝐴 =

𝑠

√𝑛 (17)

Figure 3 – (a) 3D Volume mesh for a radiator using the current

methodology, (b) 1 Prism Layer to compute the boundary layer

(a) (b)

Figure 4 – 3D Volume mesh for a radiator using the complete

system methodology



Where 𝑟 is the equipment resolution, 12 is the rectangular distribution factor, 𝑠 is the standard deviation, 𝑛 is the number of test points.

Table 6 – Uncertainty Results

Product Q1 Q2 Q3 Q4 Q5 Q6

Radiator 1 0.76 0.38 0.22 - - - Radiator 2 0.16 0.11 0.12 - - - Radiator 3 0.14 0.11 0.09 0.07 0.065 0.06

This uncertainty quantification shows the deviation due

to the test itself, as it can see the Radiator 2 and Radiator 3 have the lower values as result of the test data, Radiator 2 has 15 points per flow and Radiator 3 has 36 points per flow, reducing the variability uncertainty, it is not the case for Radiator 1 having 3 points per flow, increasing the variability uncertainty almost 75%, this is due to the test specification.

3. Radiator simulation Results

The figures 5, 6 and 7 show the comparison between each methodology detailed above. Each figure has three curves, the average test data and the uncertainty values. The purpose of these figures is to show the pressure drop values or the radiator and the difference of results obtained by each methodology. The pressure drop and the volumetric flows values were normalized with the maximum pressure drop and the maximum volumetric flow, in order to get a range of values between zero and one.

4. Discussion

The periodic domain methodology has comparatively a shorter queue time, mesh effort, better prediction of the behavior of the boundary layer and the law wall, overall more accurate and consisting results. As periodic methodology tends to overestimate the pressure drop for some cases and for others to underestimate the pressure drop as it is shown in Table 7.

Table 7 - CFD + Periodic Domain vs Test Deviation


Radiator 1 -6% 8% 10% - - - Radiator 2 -8% -10% -15% - - - Radiator 3 8% 11% 11% 7% ~0% -4.5%

*Being Q1 the higher flow and Q6 the lower flow The complete system methodology was initially used to

validate the periodic domain methodology. It was supposed that a complete simulation would allow determining if the Periodic domain was correct. Once the first simulation results were obtained and compared with the other pressure drops and the test, it showed to be a better alternative to have a predictive simulation, the computational cost is higher than the other methodologies but guarantee better fitting of the test results. The mesh has more elements than the other meshes, the mesh parameters are higher increasing the min size and the max size of the element, this allows us to acquire the physics with a coarse representation of the entire product, and to reproduce the real cases without geometrical assumptions, yielding the results shown in Table 8.

Table 8 – Complete System vs Test Deviation

Figure 6 - Results obtained by periodic domain methodology and

Complete system methodology for Radiator 2





0

0,2

0,4

0,6

0,8

1

1,2

0,20 0,40 0,60 0,80 1,00 1,20

Press

ure D

ro

p

Volumetric Flow

Periodic SimulationComplete SystemTest

0

0,2

0,4

0,6

0,8

1

1,2

0,4 0,6 0,8 1 1,2

Press

ure D

ro

p

Volumetric Flow


0

0,2

0,4

0,6

0,8

1

1,2

0,0 0,2 0,4 0,6 0,8 1,0 1,2

Press

ure D

ro

p

Volumetric Flow





Radiator 1 ~0% ~0% ~0% - - - Radiator 2 ~0% 1.6% 3% - - - Radiator 3 8% 10% 7% ~0% -7% -17%

*Being Q1 the higher flow and Q6 the lower flow Comparing Tables 7 and 8, An improvement was seen

in the deviation values simulation vs test (the improvement in Radiator 1 and Radiator 2 is notorious, since the values decrease to almost 0% from the test), but not for all cases, as the case of Radiator 3 with smooth tubes. Radiator 3 is accurate enough at high flow rate from Q1 to Q5. At low flow rate, Q6, the prediction is not accurate enough. This shows a research area to investigate in the future.

Regarding the mesh, it was seen that the mesh grows

when the complexity of the product is higher, for radiators this means number of tubes and tube definition, Radiator 3 is a product with a smooth tube and the mesh does not grow much as the other products, being 9 million of cells to 12 million of cells, for the Radiator 1 and Radiator 2, the mesh grows almost twice from the standard mesh, since the tube has dimples, this mesh size is acceptable for industrial application. The mesh parameters for the complete system methodology allow reproducing a good geometry of the dimple without losing the physical phenomena when the domain is discretized. Table 9 shows the comparison between the mesh for each methodology:

Table 9 – Mesh Comparison

Product Periodic

domain

Complete

System

Radiator 1 (Dimpled)

~9 Mo ~21 Mo

Radiator 2 (Dimpled)

~9 Mo ~21 Mo

Radiator 3

(Smooth) ~9 Mo ~12 Mo

Regarding the porous media approach, It was supposed

the difference between the Complete System and the Periodic Domain approach is a result of the turbulence boundary layer development inside of the tube since the tube height is smaller than the tube length, considering this fact Periodic Domain approach does not consider this transition between laminar an turbulent regime due the length in comparison with the Complete System. However, the Periodic domain since it considers a smaller length, It cannot be sure of the correct turbulence boundary layer development.

4. Conclusion

This project shows the different strategies to achieve a predictive simulation capable to duplicate a real test. The main objective of the comparison between methodologies

presented in this paper is to show how the simulations were carried out, the different methodologies used to obtain the porous media approach and how each impact in the complete pressure drop calculation and the complete system methodology developed to reduce the gap between the test and the simulation. The porous media estimation aims to be a good approach to reproduce the real pressure drop, but it needs more research in the topic, since the turbulence behavior in the tube has not been studied at all. The complete system methodology got the better results, so it produces an accurate enough strategy which could replicate real time tests, having a good compromise between computational cost and accuracy of prediction. The methodologies need to be compared to other turbulence models, such as the 𝑘 − 𝜔 . Since all the simulations were performed as isothermal, a methodology that introduces the thermal simulation may be needed. Under current computational restrictions, meshing the radiator fins and separators is a difficult task, because this may require up to 40 billion cells for the larger product, making not possible to carry out a complete thermal system simulation at this point. However the isothermal simulations were able to reproduce the behavior of the thermal test.

The results obtained using both methodologies tends to

be an alternative to get a predictive simulation capable to substitute the test in real time, in order to get results faster than other methods. The discrepancy obtained with the complete mesh methodology compared with the test, shows that the simulation could be applied to the industrial standard to reduce the design costs and time. The acceptable range for each product was proposed by Valeo. The results are accurate enough to conclude that the methodologies developed are the future step for the simulation workflow; however the methodologies will be in constant development to get better results.

The main advantages of the porous media approach is to allow predicting the behavior of the smooth tube at low flow rate obtaining a difference with the test of 𝟒. 𝟓% during the simulation process, instead of his counterpart which has a difference of 𝟏𝟕%, this since the porous media approach does not solve the turbulence equations inside the porous media region, being its main disadvantage because the Reynolds stress tensor is deactivated and does not consider the turbulent structures that could be created during the coolant flow inside the tube, decreasing the accuracy at high flow rates. The main issue of the complete system methodology lies in the treatment of the boundary layer and the transition to turbulent regime, referring to the Tables 7 and 8 and comparing the smooth tube technology, shows and improvement at high flow rates, where Q1 is equal, Q2 and Q3 gain around 𝟑% − 𝟒%, Q4 gain almost 𝟕%, but at the limit for the low flow rates, Q5 and Q6, the accuracy decreases. This is not the case for radiator 1 and radiator 2



where the accuracy increases when the methodology is switched. It can be concluded that the methodology is not ready but allows to investigate the behavior of the flow near the wall. It is expected that both methodologies could be extended to other product families in order to replicate the results obtained in this project, considering the proper governing physics and mesh parameters. It appears that the results shown in this project will reduce the mock-up construction since the simulation is accurate enough to give a first approach to the costumer.

Acknowledgements

The present research is supported by Universidad Autónoma de San Luis Potosí (UASLP) and Valeo Thermal Systems, The authors thank all people involved in this project, particularly the Valeo CFD team (Nicolas-Yoan Francois, Jonatan Vargas and Jonathan Oropeza), and the Valeo CAD Team.

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“Virtual CFD test bench for heat exchangers performance prediction”somim.org.mx/memorias/memorias2018/articulos/A4_99.pdf · 2020. 1. 14. · “Virtual CFD test bench for heat