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 microscale 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;
P  r 4

8LQ
where

Q  r v
2
and P  gz
Fig. 1 Schematic
of a Rankine
Viscometer
L = 933.5 mm
r = 165.8 m, Re
15.0
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
Problem Formulation (cont.)

Boundary Conditions
•
Inlet: a specified velocity;
•
Outlet: zero normal gradient;
•
Rough walls: non-slip BC.
 u  0
Du

 P   2u
Dt

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

The relation between tube length and pressure loss
0.00025
1. The pressure drop is
linearly dependant to the
relative length of tube which
is normalized by a factor of
0.01658 meter;
Pressure drop (Pascal)
0.0002
0.00015
0.0001
2. We can study a short
tube instead of a long one
for expeditious computation.
0.00005
0
0.2
0.4
0.6
0.8
Relative length
Fig. 4 The relation between the
tube length and pressure drop
1
Smooth tube, Liquid O2,
Re= 15, r= 165 μm
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
Numerical Results And Discussions (cont.)
0.00003
Pressure drop (Pascal)
0.000025
0.00002
0.000015
Liquid O2,
0.00001
r = 165.8 μm,
Re= 15
0.000005
0
0
1
2
3
4
5
6
Roughness (%)
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.)
5.00E-05
Pressure drop (Pascal)
4.00E-05
5% roughness
Liquid O2,
r = 165.8 μm
3.00E-05
2.00E-05
1.00E-05
0.00E+00
4.00E-05
6.00E-05
8.00E-05
1.00E-04
1.20E-04
Velocity (m/s)
Fig. 8 The influence of flow velocity on pressure drop
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.
2.
3.
4.
Patankar SV, Numerical Heat Transfer and Fluid Flow,
Hemisphere Publishing Corporation, 1980.
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.
Bird RB, Stewart WE, and Lightfoot EN, Transfer
Phenomena, 2nd edition. John Wiley and Sons, Inc., 2002.
Croce C and D’Agaro P, “Numerical Analysis of Roughness
Effect on Microtube Heat Transfer,” Superlattices and
Microstructures. 2004. (In press)