Effect of Heat Flux Ratio from Both Side-walls on Thermal- Fluid Flow in Channel

Numerical analysis is performed to investigate transport phenomena in channel flows under uniform heating from both side-walls. Emphasis is placed on an effect of heat flux ratio from both sides on the velocity and thermal fields. The twoequation heat-transfer model is employed to determine thermal eddy diffusivity. It is found that (i) under strong heating from both walls, laminarization, i.e., a substantial deterioration in heat transfer performance occurs as in the circular tube flow case, (ii) during the laminarization process, both the velocity and temperature gradients in the vicinity of the heated walls decrease along the flow, resulting in a substantial attenuation in both the turbulent kinetic energy and the temperature variance over the entire channel cross section and (iii) in contrast, laminarization is suppressed in the presence of oneside-heating, because turbulent kinetic energy is produced in the vicinity of the other insulated wall. Therefore, an occurrence of laminarization in the channel is affected by the ratio of heat flux from both side-walls. NOMENCLATURE cp specific heat at constant pressure, J/(kgK) Cμ, C1, C2 empirical constants of k-ε model Cλ, CP1, CP2 turbulence model constants for temperature field CD1, CD2 turbulence model constants for temperature field h heat transfer coefficient, W/m2K H channel height, m f friction coefficient fμ, f1, f2 model functions of k-ε model fλ, fP1, fP2 turbulence model functions of temperature field fD1, fD2 turbulence model functions of temperature field g acceleration of gravity, m/s2 G mass flux of gas flow, kg/(m2s) Gr Grashof number, gqwH4/(ν2λT)in H channel height, m k turbulent kinetic energy, m2/s2 ML the number of mesh N heat flux ratio, qw2/qw1 Nu Nusselt number, 2Hh/λ P time-averaged pressure, Pa Pr Prandtl number Prt turbulent Prandtl number qw1, qw2 heat fluxes at y=0 and H, respectively, W/m2 q+w dimensionless heat flux parameter, Eq. (14) 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference 24-26 June 2002, St. Louis, Missouri AIAA 2002-2873 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. American Institute of Aeronautics and Astronautics 2 Re Reynolds number, 2umH/ν Rt turbulent Reynolds number, k2/(εν) Rτ dimensionless distance, y+ St Stanton number, qw/(ρcpum(Tw-Tb)) T time-averaged temperature, K t fluctuating temperature component, K t* friction temperature, qw/(ρcpu*), K t 2 temperature variance, K2 U, V time-averaged velocity components in axial, and normal-wall direction, respectively, m/s Ui, ui time-averaged and fluctuating velocity components in the xi directions, m/s um mean velocity over channel cross section, m/s u, v, w fluctuating velocity components in axial, wall-normal and tangential directions, respectively, m/s u* friction velocity, m/s u+ dimensionless velocity, U/u* − i j u u Reynolds stress, m/s i u t turbulent heat flux, mK/s x axial coordinate, m xi coordinates, m y wall-normal coordinate, m y+ dimensionless distance, u*δ/ν Greek Letters α thermal diffusivity, m2/s ρ density, kg/m3 δ distance from wall, m ε turbulent energy dissipation rate, m2/s3 εt dissipation rate of t 2 , K/s2 λ, λt molecular and turbulent thermal conductivities, respectively, W/(Km) μ, μt molecular and turbulent viscosities, respectively, Pa sec ν fluid kinematic viscosity, m2/s σk, σε, σh, σφ turbulence model constants for diffusion of k, ε, t 2 and εt, respectively θ tangential direction θ+ dimensionless temperature, + = − − θ T T T T c w c Subscripts c minimum or insulated wall inlet inlet max maximum w wall Superscripts time-averaged value INTRODUCTION When a gas in a circular pipe is heated with extremely high heat flux, the flow may be laminarized; that is, a transition from turbulent to laminar flows occurs at a higher Reynolds number than the usual critical value, i.e., Re=2,300. This phenomenon is referred to as laminarization. Both the criteria for its occurrence and its heat transfer characteristics have been reported by several investigators [1-6]. In order to investigate an effect of passage geometry on an occurrence of the laminarizing gas flow, Torii et al. [7] and Fujii et al. [8] deal with the thermal-fluid transport phenomena in concentric annuli under high heat flux heating. They disclosed that (i) when the gas flow is strongly heated with the same heat flux level from inner and outer tube walls, the local heat transfer coefficients on both walls approach the laminar values along the flow; that is, the laminarization takes place; (ii) the existing criteria of laminarization for circular tube flows can be applied to annular flows as well if the occurrence of laminarization is estimated using a dimensionless heat flux parameter q+w; but (iii) annular flows heated strongly from only one side are less vulnerable to laminarization even if the usual criteria are satisfied. The purpose of the present study is to investigate thermalfluid flow transport phenomena in a channel in which both walls are individually heated with different heat fluxes. The t 2 -εt heat transfer model proposed by Torii and Yang [9] and the k-ε turbulence model of Torii et al. [10] are employed to reveal the mechanism of heat transport phenomena. The turbulent thermal conductivity λt is determined using the temperature variance t 2 and the dissipation rate of temperature fluctuations εt, together with k and ε. Emphasis is placed on the effect of heat flux ratio from both sides on the velocity and thermal fields, based on the numerical results, i.e., the turbulent kinetic energy, temperature variance, velocity, and temperature profiles.