Numerical Analysis of Roughness Effects on Rankine Viscosity

Measurement

Hila Hashemi, University of California, Berkeley

Jinquan Xu, Mentor, Florida State University

Objective

Collecting research experience on computational science and applied mathematics, including defining a problem, formulating solution strategies, implementing the strategies, and anglicizing the results

Overview

Roughness effects on the pressure loss of micro-scale Rankine Viscometer tubes are numerically investigated;

Surface roughness is explicitly modeled through a set of generated peaks along an ideal smooth surface;

A parametric study is carried out to study the relationship between the roughness and pressure loss quantitatively.

Introduction

Rankine Viscometer; Hagen-Poiseuille law;

Newtonian fluid through a cylindrical tube with an ideal SMOOTH surface;

LQrP

8

4

where vrQ 2 zgP and

0

z

z1

z2

L

g

R

r

p0

p0

p1

p2

R

L = 933.5 mm r = 165.8 m, Re 15.0

Fig. 1 Schematic of a Rankine Viscometer

Introduction (cont.)Rough tube, with roughness

ranging from 0.0~5.0% (Roughness defined as the ratio between the average of the peak heights and the hydraulic diameter.

Fig. 2 Cross-section of a rough micro tube. (Picture courtesy:

Microgroup, Inc.)

Problem Formulation

• Numerical simulation of Newtonian fluid through a cylindrical tube with a rough surface;• Study of the relationship between tube length and pressure loss;• Generic modeling of flow in a short tube.

Fig. 3 A portion of the computational domain and mesh

Boundary Conditions• Inlet: a specified velocity;• Outlet: zero normal gradient;• Rough walls: non-slip BC.

Problem Formulation (cont.)

0 u

uu 2 PDtD

Governing Equations

Solution Technique

Gambit is used for meshing;

The flow equations are solved using the semi-implicit method for pressure-linked equation algorithm implemented in Fluent

Numerical Results And Discussions

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.2 0.4 0.6 0.8 1

Relative length

Pre

ss

ure

dro

p (

Pa

sc

al)

1. The pressure drop is linearly dependant to the relative length of tube which is normalized by a factor of 0.01658 meter;

2. We can study a short tube instead of a long one for expeditious computation.

The relation between tube length and pressure loss

Fig. 4 The relation between thetube length and pressure drop

Smooth tube, Liquid O2, Re= 15, r= 165 μm

Numerical Results And Discussions (cont.)

Fig. 5 The pressure contour of different roughness tube

Liquid O2,

r = 165.8 μm, Re= 15

Influence of roughness on pressure drop and velocity

Numerical Results And Discussions (cont.)

0

0.000005

0.00001

0.000015

0.00002

0.000025

0.00003

0 1 2 3 4 5 6

Roughness (%)

Pre

ss

ure

dro

p (

Pa

sc

al)

Liquid O2,

r = 165.8 μm, Re= 15

Fig. 6 The influence of roughness on pressure drop

Numerical Results And Discussions (cont.)

Liquid O2, r = 165.8 μm, Re= 15

Fig. 7 The velocity vector of different roughness tube

Numerical Results And Discussions (cont.)

5% roughnessLiquid O2, r = 165.8 μm

Fig. 8 The influence of flow velocity on pressure drop

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.20E-04

Velocity (m/s)

Pre

ss

ure

dro

p (

Pa

sc

al)

Conclusions

• The pressure loss is a linear function of the tube length;

• The roughness affects on the pressure loss in a non-trivial way; The rougher a tube is, the more the fluid pressure drops through the tube;

• It is feasibility to correct the Rankine viscometer measured data through numerical analysis;

• Mesh refinements are needed along the rough boundary.

Reference

1. Patankar SV, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, 1980.

2. Judy J, Maynes D, Webb BW, “Characterization of Frictional Pressure Drop for Liquid Flows through Microchannels,” International Journal of Heat and Mass Transfer, Vol. 45, pp. 3477-89, 2002.

3. Bird RB, Stewart WE, and Lightfoot EN, Transfer Phenomena, 2nd edition. John Wiley and Sons, Inc., 2002.

4. Croce C and D’Agaro P, “Numerical Analysis of Roughness Effect on Microtube Heat Transfer,” Superlattices and Microstructures. 2004. (In press)