Numerical Analysis of Roughness Effects on Rankine Viscosity Measurement

1
Numerical Analysis of Roughness Effects on
Rankine Viscosity Measurement

• Hila Hashemi, University of California, Berkeley
• Jinquan Xu, Mentor, Florida State University

2
Objective

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

3
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.

4
Introduction

• Rankine Viscometer
• Hagen-Poiseuille law Newtonian fluid through a
  cylindrical tube with an ideal SMOOTH surface

and
where
5
Introduction (cont.)

• Rough tube, with roughness ranging from 0.05.0
  (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.)
6
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.

7
Problem Formulation (cont.)

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

• Governing Equations

8
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
9
Numerical Results And Discussions

• The relation between tube length and pressure loss

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.
Smooth tube, Liquid O2, Re 15, r 165 µm
Fig. 4 The relation between the tube length and
pressure drop
10
Numerical Results And Discussions (cont.)

• Influence of roughness on pressure drop
  and velocity

Liquid O2, r 165.8 µm, Re 15
Fig. 5 The pressure contour of different
roughness tube
11
Numerical Results And Discussions (cont.)
Liquid O2, r 165.8 µm, Re 15
Fig. 6 The influence of roughness on pressure drop
12
Numerical Results And Discussions (cont.)
Liquid O2, r 165.8 µm, Re 15
Fig. 7 The velocity vector of different roughness
tube
13
Numerical Results And Discussions (cont.)
5 roughness Liquid O2, r 165.8 µm
Fig. 8 The influence of flow velocity on pressure
drop
14
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.

15
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 DAgaro P, Numerical Analysis of
   Roughness Effect on Microtube Heat Transfer,
   Superlattices and Microstructures. 2004. (In
   press)