Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

Die turbulente Grenzschicht an einer stark geheizten ebenen Platte bei Unterschallströmung

Experiments for air flowing over a flat plate heated up to 250°C with velocities of 10 to 30 m/s, which have been made at the DFVLR-AVA, are briefly reviewed and a new analysis of the data is given. The analysis is based on an analytical representation of the velocity and temperature profiles. Close to the wall, a law of the wall approximation is used, which includes the effect of density and viscosity variation. The whole velocity profile is constructed by adding Coles' law of the wake to the law of the wall. In a similar way, the temperature profile is obtained from the law of the wall and an auxiliary distribution. The integrals of momentum and heat flux for two-dimensional flow are used in conjunction with a similarity assumption, to derive a relation between rate of heat transfer from the plate and skin friction. A maximum likelihood procedure has been applied to determine skin friction and rate of heat transfer from the measured dynamic pressure profiles.—The analytical velocity and temperature profiles are found in good agreement with the experimental data, except for the stations near the leading edge of plate. The skin friction coefficients and the Stanton numbers decrease slightly in downstream direction as a consequence of growing local Reynolds number, and decrease with increasing ratio of plate to free stream temperature. The latter fact is in qualitative agreement with the behavior of turbulent boundary layers in supersonic flow. The ratio of Stanton number to half of skin friction coefficient (Reynolds analogy factor) varies with increasing local boundary layer Reynolds number from 1.23 to 1.16.     

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

Forced convection heat transfer and pressure drop characteristics of air flow inside a horizontal semi-circular duct are investigated experimentally. The experiments are carried out on a semi-circular duct of 23 mm inner radius, 2 mm thickness, and 2,000 mm length within a range of Reynolds number (8,242 ≤ Re ≤ 57,794)., under uniform wall heat flux conditions. The friction factor is determined by measuring the axial static pressure at different selected axial stations along the semi-circular duct. The variations of surface and mean air temperatures, local heat transfer coefficient, local Nusselt number, and the friction factor with the axial dimensionless distance are presented. It is observed that, for a given value of Reynolds number, each of the local heat transfer coefficient and the friction factor has a relatively high value near the entrance of the semi-circular duct then it decreases with increasing the dimensionless axial distance until it approaches a nearly constant value at the fully developed region. Also, it is found that, with increasing the Reynolds number the average heat transfer coefficient is increased and the friction factor is decreased. Moreover, empirical correlations for the heat transfer coefficient and friction factor as a function of the Reynolds number are obtained.     

Investigation of the heat transfer and Reynolds analogy in a turbulent boundary layer at a high freestream turbulence level

The results of a systematic experimental study of the flow turbulence level effect on the heat transfer and Reynolds analogy coefficients over a wide range of the relevant parameters (the turbulence intensity and scale and the Reynolds number) are presented. The notion of the equivalent flow turbulence, which unifies the above-mentioned parameters, is introduced. It is established that the skin friction and heat transfer coefficients increase with the equivalent turbulence, while the Reynolds analogy coefficient remains unchanged. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 61–71, January–February, 2000.     

Heat transfer and skin-friction in a turbulent boundary layer under a non-equilibrium longitudinal adverse pressure gradient

The experimental data on the effect of weak and moderate non-equilibrium adverse pressure gradients (APG) on the parameters of dynamic and thermal boundary layers are presented. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re^** = 5500. The APG region was a slot channel with upper wall expansion angles from 0 to 14°. The profiles of the mean and fluctuation velocity components were measured using a single-component hot-wire anemometer. The friction coefficients were determined using two methods, namely, the indirect Clauser method and the direct method of weighting the lower wall region on a single-component strain-gage balance. The heat transfer coefficients were determined by a transient method using an IR camera. It is noticed that in the pressure gradient range realized the universal logarithmic region in the boundary layer profile is conserved. The values of the relative (divided by the parameters in zero gradient flow at the same value of Re^**) friction and heat transfer coefficients, together with the Reynolds analogy factor, are determined as functions of the longitudinal pressure gradient. The values of the relative friction coefficient reduced to c_f/c_f0 = 0.7 and those of the heat transfer to St/St₀ = 0.9. A maximum value of the Reynolds analogy factor (St/St₀)/(c_f/c_f0) = 1.16 was reached for the pressure gradient parameter β = 2.9.     

Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

Turbulent thermal boundary layer on a plate. Reynolds analogy and heat transfer law over the entire range of prandtl numbers

Arational asymptotic theory is proposed,which describes the turbulent dynamic and thermal boundary layer on a flat plate under zero pressure gradient. The fact that the flow depends on a finite number of governing parameters makes it possible to formulate algebraic closure conditions relating the turbulent shear stress and heat flux with the gradients of the averaged velocity and temperature. As a result of constructing an exact asymptotic solution of the boundary layer equations, the known laws of the wall for velocity and temperature, the velocity and temperature defect laws, and the expressions for the skin friction coefficient, Stanton number, and Reynolds analogy factor are obtained. The latter makes it possible to give two new formulations of the temperature defect law, one of which is identical to the velocity defect law and contains neither the Stanton number nor the turbulent Prandtl number, and the second formulation does not contain the skin friction coefficient. The heat transfer law is first obtained in the form of a universal functional relationship between three parameters: the Stanton number, the Reynolds number, and the molecular Prandtl number. The conclusions of the theory agree well with the known experimental data.     

Air-side performance of louver-finned flat aluminum heat exchangers at a low velocity region

The heat transfer and pressure drop characteristics of heat exchangers having louver fins were experimentally investigated. The samples had small fin pitches (1.0–1.4 mm), and experiments were conducted up to a very low frontal air velocity (as low as 0.3 m/s). Below a certain Reynolds number (critical Reynolds number), the fall-off of the heat transfer coefficient curve was observed. The critical Reynolds number was insensitive to the louver angle, and decreased as the louver pitch to fin pitch ratio (L _p /F _p ) decreased. Existing correlations on the critical Reynolds number did not adequately predict the data. The heat transfer coefficient curves crossed over as the Reynolds number decreased. Possible explanation is provided considering the louver pattern between neighboring rows. Different from the heat transfer coefficient, the friction factor did not show the fall-off characteristic. The reason was attributed to the form drag by louvers, which offsets the decreased skin friction at low Reynolds numbers. The friction factor increased as the fin pitch decreased and the louver angle increased. A new correlation predicted 92% of the heat transfer coefficient and 94% of the friction factor within ±10%.     

Effect of local forcing on a turbulent boundary layer

An experimental study is performed to analyze flow structures behind local suction and blowing in a flat-plate turbulent boundary layer. The local forcing is given to the boundary layer flow by means of a sinusoidally oscillating jet issuing from a thin spanwise slot at the wall. The Reynolds number based on the momentum thickness is about Re _θ =1700. The effects of local forcing are scrutinized by altering the forcing frequency (0.011 ≤ f ⁺≤ 0.044). The forcing amplitude is fixed at A ₀=0.4. It is found that a small local forcing reduces the skin friction and the skin friction reduction increases with the forcing frequency. A phase-averaging technique is employed to capture the large-scale vortex evolution. An organized spanwise vortical structure is generated by the local forcing. The cross-sectional area of vortex and the time fraction of vortex are examined by changing the forcing frequency. An investigation of the random fluctuation components reveals that turbulent energy is concentrated near the center of vortical structures. Received: 17 March 2000/Accepted: 3 April 2001     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Reynolds analogy in a dusty laminar boundary layer

The nonisothermal Blasius problem for a gas suspension is considered on the basis of the equations of a quasiequilibrium two-phase laminar boundary layer [1–3]. Approximate analytical expressions are obtained for the friction and heat transfer coefficients and their region of applicability is estimated; the Reynolds analogy between friction and convective heat transfer processes [4] is extended to the case of a dusty quasiequilibrium laminar boundary layer. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–162, November–December, 1986.     

Heat transfer and interfacial drag in countercurrent steam-water stratified flow

Local condensation heat transfer coefficients and interfacial shear stresses have been measured for countercurrent stratified flow of steam and subcooled water in rectangular channels over a wide range of inclination angles (4–87°) at two aspect ratios. Dimensionless correlations for the interfacial friction factor have been developed that show that it is a function of the liquid Reynolds number only. Empirical correlations of the heat transfer coefficient, based upon the bulk flow properties, have also been set up for the whole body of data encompassing the different inclination angles and aspect ratios. These indicate that the Froude number as a dimensionless gas velocity is a better correlating parameter than the gas Reynolds number. As an alternative approach, a simple dimensionless relationship for the beat transfer coefficient was obtained by analogy between heat and momentum transfer through the interface. Finally, a turbulence-centered model has been modified by using measured interfacial parameters for the turbulent velocity and length scales, resulting in good agreement with the data.     

钝头体中的广义雷诺比拟关系

钝头体壁面的摩阻和热流分布规律不同,平板流动中的雷诺比拟关系在钝头体壁面失效. 文章在前期高超声速广义雷诺比拟理论研究工作的基础上,利用数值仿真的方法对不同外形和来流参数条件下的钝头体广义雷诺比拟关系开展进一步研究. 通过建立钝头体绕流边界层的理论分析模型,得到了钝头体壁面雷诺比拟系数的线性分布预示公式. 采用数值求解 N-S 方程的方法,计算了圆柱和幂次体壁面的摩阻和热流以及二者之间的比拟系数. 通过与前期数值和理论结果对比,以及计算收敛性和网格无关性检验,对数值方法进行了验证. 通过在不同雷诺数 ($Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$) 和马赫数 ($M_\infty = 3\sim 12$) 条件下的计算结果对比分析雷诺比拟系数的分布,总结了钝头体中广义雷诺比拟关系受外形和来流条件的影响,评估了广义雷诺比拟理论的适用性. 研究发现,在较高雷诺数条件下,离驻点较远的下游 ($\theta > 60^\circ$) 部位,雷诺比拟系数的分布不同程度地偏离理论预示的线性规律. 相比于圆柱外形,幂次体壁面的雷诺比拟系数分布的线性规律相对较好,其分布斜率略低于圆柱壁面的结果. 研究表明,如果针对实际外形和雷诺数进行适当修正,可以提高广义雷诺比拟关系的预示精度.      

Mixed convection heat transfer in open ended channels with protruding heaters

Mixed convection heat transfer has been studied in vertical channels, open at the bottom and top, with protruding discrete heaters installed on one side. The flow is assumed to be steady, laminar and two-dimensional. The Boussinesq approximation is used to account for the density variation. Non-dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using the SIMPLER method. Heat transfer through the top and the right are calculated as functions of the Rayleigh number (0≤Ra≤10⁷), the Reynolds number (0≤Re≤200), various aspect ratios (1≤A≤6). The effect of the entrance and exit lengths and that of the position of the electronic components in the channel are also examined. Flow and temperature fields for various cases are produced, and the temperature variations in the electronic components are calculated. Received on 2 March 1998     

GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES$^{\bf 1)}$

钝头体壁面的摩阻和热流分布规律不同,平板流动中的雷诺比拟关系在钝头体壁面失效. 文章在前期高超声速广义雷诺比拟理论研究工作的基础上,利用数值仿真的方法对不同外形和来流参数条件下的钝头体广义雷诺比拟关系开展进一步研究. 通过建立钝头体绕流边界层的理论分析模型,得到了钝头体壁面雷诺比拟系数的线性分布预示公式. 采用数值求解 N-S 方程的方法,计算了圆柱和幂次体壁面的摩阻和热流以及二者之间的比拟系数. 通过与前期数值和理论结果对比,以及计算收敛性和网格无关性检验,对数值方法进行了验证. 通过在不同雷诺数 ($Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$) 和马赫数 ($M_\infty = 3\sim 12$) 条件下的计算结果对比分析雷诺比拟系数的分布,总结了钝头体中广义雷诺比拟关系受外形和来流条件的影响,评估了广义雷诺比拟理论的适用性. 研究发现,在较高雷诺数条件下,离驻点较远的下游 ($\theta > 60^\circ$) 部位,雷诺比拟系数的分布不同程度地偏离理论预示的线性规律. 相比于圆柱外形,幂次体壁面的雷诺比拟系数分布的线性规律相对较好,其分布斜率略低于圆柱壁面的结果. 研究表明,如果针对实际外形和雷诺数进行适当修正,可以提高广义雷诺比拟关系的预示精度.     

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Evaluation of flush mounted hot-film sensors for skin friction reduction measurements in viscoelastic polymer solutions

The purpose of this investigation was to evaluate the performance of flush mounted hot-film sensors for mean wall shear stress measurement in turbulent flows of dilute drag reducing polymer solution. A series of pipe flow expriments were conducted over a range of Reynolds numbers and polymer solution concentrations to compare the level of skin friction drag reduction measured by hot-film sensors with values calculated from pipe pressure drop. It is shown that water calibrated hot-film sensors consistently underestimate the wall shear stress suggesting that Reynolds analogy is not valid in dilute polymer solutions. The Newtonian form of the relationship between the wall shear stress and the heat transfer remains valid in dilute polymer solutions. However, multiplicative and additive factors in the relationship are shown to increase linearly with the logarithm of the polymer concentration.     

Jet impingement onto a tapered hole: Influence of jet velocity and hole wall velocities on heat transfer and skin friction

Jet impingement onto a hole with elevated wall temperature can be associated with the high‐temperature thermal drilling, where the gas jet is used for shielding the hole wall from the high‐temperature oxidation reactions as observed in the case of laser drilling. In laser processing, the molten flow from the hole wall occurs; and in the model study, the hole wall velocity resembling the molten flow should be accounted for. In the present study, gas jet impingement onto tapered hole with elevated temperature is considered and the heat transfer rates as well as skin friction at the hole wall surface are predicted. The velocity of molten flow from the hole wall determined from the previous study is adopted in the simulations and the effect of hole wall velocity on the heat transfer rates and skin friction is also examined. It is found that the Nusselt number and skin friction at the hole wall in the regions of hole inlet and exit attain high values. The influence of hole wall velocity on the Nusselt number and skin friction is found not to be very significant. Copyright © 2008 John Wiley & Sons, Ltd.     

Combined heat and mass transfer along a vertical moving cylinder with a free stream

The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u _w/(u _w + u _∞), where u _w and u _∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases. Received on 17 May 1999