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 R Rankine Viscometer; Hagen-Poiseuille law; Newtonian fluid through a cylindrical tube with an ideal SMOOTH surface; P r 8LQ where
p0 z1 g R z p0 z2 4 0 p1 Q r v 2
and P gz L p2 r 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 mm Numerical Results And Discussions (cont.) Influence of roughness on pressure drop and velocity Liquid O2, r = 165.8 mm, 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 mm, 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 mm, 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 mm 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 DAgaro P, Numerical Analysis of Roughness Effect on Microtube Heat Transfer, Superlattices and Microstructures. 2004. (In press)