Turbulent Thermal Boundary Layer Research Articles

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.

The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer

Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ′+ and the Reynolds shear stress, u′v′¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50≤y+≤170). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u′2¯+ and v′θ′¯+ change little with the strength of acceleration, while v′+, w′+, and u′v′¯+ continue to decay in the flow direction. Furthermore, θ′+ and u′θ′¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for “transient growth” generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, “Coherent structure generation near-wall turbulence,” J. Fluid Mech. 453, 57–108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.

수직벽 화재 자연대류에 의한 난류 경계층 열유동 특성 해석

The analysis of characteristics of turbulent flow and thermal boundary layer for natural convection caused by fire along vertical wall is performed. The 4m-high vertical copper plate is heated and kept at a uniform surface temperature of <TEX>$60^{\circ}C$</TEX> and the surrounding fluid (air) is kept at <TEX>$16.5^{\circ}C$</TEX>. The flow and temperature is solved by large eddy simulation(LES) of FDS code(Ver.6), in which the viscous-sublayer flow is calculated by Werner-Wengle wall function. The whole analyzed domain is assumed as turbulent region to apply wall function even through the laminar flow is transient to the turbulent flow between <TEX>$10^9$</TEX><<TEX>$Gr_z$</TEX><<TEX>$10^{10}$</TEX> in experiments. The various grids from <TEX>$7{\times}7{\times}128$</TEX> to <TEX>$18{\times}18{\times}128$</TEX> are applied to investigate the sensitivity of wall function to <TEX>$x^+$</TEX> value in LES simulation. The mean velocity and temperature profiles in the turbulent boundary layer are compared with experimental data by Tsuji & Nagano and the results from other LES simulation in which the viscous-sublayer flow is directly solved with many grids. The relationship between heat transfer rate(<TEX>$Nu_z$</TEX>) and <TEX>$Gr_zPr$</TEX> is investigated and calculated heat transfer rates are compared with theoretical equation and experimental data.

Direct numerical simulation of heat transfer in a spatially developing turbulent boundary layer

Direct numerical simulation has been performed to investigate heat transfer in a zero-pressure-gradient spatially developing turbulent boundary layer with realistic thermal inflow boundary conditions. The temperature is considered as a passive scalar and the molecular Prandtl number is set to be 0.71. The turbulence statistics for both the velocity and temperature fields show good agreement with previous numerical and experimental data in the literature. The present study provides a valuable database for the spatially developing turbulent thermal boundary layer over a wide range of Reynolds numbers from Reθ = 1100 to 1940. The simulation results indicate that both the peak value and peak location of the streamwise velocity fluctuation grow slightly with increasing Reynolds number, same as those of the temperature fluctuation. The relationship between the streamwise velocity and temperature fluctuations has been examined and a strong correlation is observed in the vicinity of the wall. With increasing distance from the wall, however, the degree of correlation significantly decreases. In addition, the difference between the turbulent velocity and temperature fields is also analysed by investigating the mechanisms of heat and momentum transport in boundary layer flow.

The Reynolds analogy and a new formulation of the temperature-defect law for a turbulent boundary layer on a plate

A rational asymptotic theory describing the dynamic and thermal turbulent boundary layer on a plate at zero pressure gradient is proposed. The fact that the flow depends on a finite number of governing parameters makes it possible to formulate algebraic closure conditions, which relate the turbulent shear stress and heat flux to mean velocity and temperature gradients. As a result of an exact asymptotic solution of the boundary-layer equations, the known laws of the wall for the velocity and temperature and the velocity and temperature defect laws as well as the expression for the skin-friction coefficient, the Stanton number, and the Reynolds-analogy factor are obtained. The latter implies two new formulations of the temperature-defect law, one of which is completely similar to the velocity-defect law and does not contain the Stanton number and the turbulent Prandtl number, and the other does not contain the skin-friction coefficient. A heat-transfer law that relates only thermal quantities is also obtained. The conclusions of the theory agree well with experimental data.

303 サブミクロン冷線を用いた平板乱流温度境界層の速度と温度の高精度同時測定(OS4-1 熱および物質輸送現象の基礎と応用(1),OS4 熱および物質輸送現象の基礎と応用)

303 サブミクロン冷線を用いた平板乱流温度境界層の速度と温度の高精度同時測定(OS4-1 熱および物質輸送現象の基礎と応用(1),OS4 熱および物質輸送現象の基礎と応用)

J0550201 非一様加熱条件下で発達する平板乱流温度境界層の熱輸送機構と時空間相関構造

We have investigated experimentally the spatio-temporal characteristics of turbulent thermal boundary layers developing over a heated flat plate with various thermal boundary conditions. A ladder-structured temperature probe consisting of 10 cold-wires 3 μm in diameter has been used to measure temperature fluctuations simultaneously at the representative points - from the immediate vicinity of the wall to the outer region - in the thermal boundary layer. The present measurement technique enables us to investigate the effects of the wall thermal boundary condition on the spatio-temporal behaviors of the turbulence quantities of the thermal field. From the conditional sampling and averaging based on the VITA method with the temperature slope criterion, it is found that the spatio-temporal characteristics of temperature fields are strongly affected by the thermal boundary conditions.

Direct numerical simulations of turbulent thermal boundary layers subjected to adverse streamwise pressure gradients

An innovative method for prescribing turbulent thermal inflow information in spatially developing boundary layers under streamwise pressure gradients is introduced for attached flows. The approach is tested and validated in a suite of Direct Numerical Simulations (DNS) of thermal boundary layers for zero (ZPG) and adverse (APG) pressure gradients with momentum thickness Reynolds numbers (Reθ) up to 3000. The turbulent thermal data are generated based on the dynamic multi-scale approach proposed by Araya et al. [“A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially evolving flows,” J. Fluid Mech. 670, 581–605 (2011)], which is extended to include thermal field simulations in the present article. The approach is based on the original rescaling-recycling method developed by Lund, Wu, and Squires [“Generation of turbulent inflow data for spatially developing boundary layer simulations,” J. Comput. Phys. 140, 233–258 (1998)] for ZPG flows. Isothermal walls are considered for the thermal field and the molecular Prandtl number is 0.71. In addition, only inlet momentum/thermal boundary layer thicknesses must be prescribed while other flow parameters such as the inlet friction velocity, uτ, and friction temperature, Θτ, are computed dynamically based on the flow solution obtained downstream by means of a test plane. This plane is located between the inlet and recycle stations. Based on the unique and extensive DNS results of heat transfer obtained in this investigation, the effects of Reynolds numbers and adverse pressure gradients on the flow and thermal parameters are also explored and visualized. The principal outcome of adverse pressure gradient on the flow parameters has been determined as a secondary peak, particularly on the streamwise velocity fluctuations in the outer region, which shows clear evidence of energy production in the outer flow and not only in the buffer layer as traditionally known. Nevertheless, this peak is not so obvious on the thermal fluctuations but it is hypothesized that the reason is mainly attributed to the absence of a freestream thermal gradient, as imposed in the velocity field. Furthermore, the high-speed streaks in the buffer layer are observed to be notably shorter and wider in a Strong APG than in the ZPG case. Finally, a significant decrease of the turbulent Prandtl number is attributed to the presence of a Strong APG.

DNS of turbulent thermal boundary layers up to Reθ = 2300

A technique, based on the Lund et al. (1998) [1] approach, is introduced in order to numerically prescribe time-dependent turbulent inflow conditions in spatially-developing thermal boundary layers. A major difference with Lund’s approach is that the new multi-scale approach considers different scaling laws for the inner and outer parts of the boundary layer. Direct numerical simulations (DNS) are performed for incompressible zero (ZPG) and adverse (APG) pressure gradient flows. To the best of our knowledge, the present DNS in ZPG flows at a momentum thickness Reynolds numbers (Reθ) of 2300 represents the evolving thermal boundary layer simulations at the highest Reθ in the turbulence community. The temperature is treated as a passive scalar with isothermal walls as a boundary condition and a molecular Prandtl number of 0.71. The predicted Stanton number shows fairly good agreement with empirical correlations, and experimental and numerical data from the literature. Moreover, the influences of the Reynolds number and the APG strength on thermal parameters are also examined. Furthermore, the budget of the temperature variance shows a significant increase of production, turbulent diffusion, and dissipation in the buffer layer at higher Reynolds numbers. The main effects of adverse pressure gradients on the temperature field are manifested by a decreasing trend of thermal fluctuations but an increasing trend of the wall-normal turbulent heat fluxes when normalized by wall units as the APG strength is augmented.

Inflow turbulence generation for large eddy simulation in non-isothermal boundary layers

Many studies have presented the importance of turbulent inflow data for large eddy simulation, and several techniques have been proposed for generating inflow fluctuations for LES in a neutral boundary layer, but few studies have considered non-isothermal cases. In this study, first wind tunnel experiments were conducted to generate both unstable and stable turbulent thermal boundary layers in a thermally stratified wind tunnel at Tokyo Polytechnic University. The decrease of turbulence due to the effect of buoyancy was clearly observed in a stable boundary layer. Then a precursor method using a long domain and a recycling procedure using a short domain to generate the turbulence statistics corresponding to the experimental data were investigated for both unstable and stable conditions. The characteristics of the generated flow (mean profiles and fluctuation profiles) by both methods agreed relatively well with those of the wind tunnel experimental data. When a recycling procedure was adopted to generate turbulence statistics in a stable boundary layer, large damping was necessary to decrease the turbulence level. For the temperature field, giving only a mean profile (no temperature fluctuation) as an inflow boundary condition of the driver region was the simplest way. Even if the inflow temperature fluctuation was not given, temperature fluctuation gradually developed in the downstream direction with velocity fluctuation in the turbulent boundary layer.

Study of the blowing impact on a hot turbulent boundary layer using Thermal Large Eddy Simulation

We investigate Thermal Large Eddy Simulation in a complex case using Trio U. We develop a thermal turbulent inflow condition based on parallel flows in order to simulate a turbulent thermal boundary layer. This inflow condition is tested with a turbulent channel flow. We show that it produces fine profiles for velocity and temperature. Later, this inlet condition is used in the case of blowing through a porous plate. Two different blowing regimes are studied: the classical turbulent boundary layer and the blown off boundary layer. Comparisons show that we obtain similar experimental and numerical profiles (Brillant, G., Husson, S., Bataille, F., 2008. Experimental study of the blowing impact on a hot turbulent boundary layer. International Journal of Heat and Mass Transfer 51 (7–8), 1996–2005.). We finish with additional results obtained only through numerical simulations.

UNSTEADY HYDRODYNAMIC AND THERMAL BOUNDARY LAYERS OVER A FLAT PLATE WITH UNIFORM INJECTION OR SUCTION

A computational algorithm for calculating the unsteady compressible and turbulent hydrodynamic and thermal boundary layers over a porous flat plate with uniform suction or injection is developed in the present work. The mathematical modeling involves the derivation of the governing partial differential equations of the problem. These are the continuity, the momentum, the ( κ −ε ) turbulence model and the energy equations. Besides, the perfect gas law and the Sutherland' s law of molecular viscosity are also used. A proper initial and boundary conditions are specified to be used in the solution of the governing equations. A numerical solution of the governing equations is made by using the control volume approach, with non-staggered grid technique and modified SIMPLE algorithm. The numerical solution is capable of calculating the velocity and temperature distributions of the calculation domain, the kinetic energy and dissipation of turbulence, the local and average skin-friction and heat transfer coefficients and Nusselt number, and the hydrodynamic and thermal boundary layers thicknesses. All these parameters are calculated at the transient and steady states. The numerical results show that the developed algorithm is capable of calculating the flow field, properly and accurately. The results show that injection causess light decrease in the temperature inside the thermal boundary layer, a decrease in skin – friction coefficient, a slight increase in the Nusselt number, a decrease in hydrodynamic boundary layer thickness, an increase in thermal boundary layer thickness and an increase in the time required to reach the steady state. Suction almost causes reverse effects.

502 様々な熱的境界条件下における前向きステップ乱流温度境界層のDNS(OS6.各種スケールにおける熱流動現象(1),オーガナイズドセッション)

502 様々な熱的境界条件下における前向きステップ乱流温度境界層のDNS(OS6.各種スケールにおける熱流動現象(1),オーガナイズドセッション)

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.

Study on Process of Planing Forming of Plate Fin Heat Sinks

Primary heat dissipation method of IC Chip is still air-cooling at present. This paper presents a new machining method of air-cooled plate fin heat sinks, namely orthogonal planing. The surface of plate fins machined by this method are rough enough to augment its specific surface area; the rough surface can also disturb laminar sub-layer of turbulent thermal boundary layer, thus the thermal resistances of thermal boundary layer are reduced. Therefore, heat dissipation efficiency of heat sink can be enhanced further. The focus of plate fin heat sinks forming by orthogonal planing is how to machine flat chips. A new pattern of chip curl that is called down-curl can be observed when rake angle of tool is rather large and cutting thickness is very thin. As cutting thickness increases, down-curl chips become flat and then up-curling. There is a transition area that chips are not curled between down- and up-curl. The conditions that chips are not curled are obtained through investigating influences of rake angle and cutting thickness on chip curl, and flat plate fins with rough surface are produced.

Heat-transfer and temperature-defect laws in a turbulent boundary layer on a plate with injection

For a thermal turbulent boundary layer on a permeable flat plate, similarity laws for the heat flux at the wall and flow temperature are established. According to the universal temperature-defect law, the profiles of this quantity for any injection and sufficiently large Reynolds numbers everywhere outside the viscous sublayer may be described by a single curve, which is known from experimental data for an impermeable plate. The universal heat-transfer law in the form of the generalized Reynolds analogy allows one to represent the heat flux distributions that correspond to various Reynolds numbers and various injection velocities as a function of one variable. The results are obtained without the formulation of special closure hypotheses. 1. We consider an incompressible heat-conducting turbulent boundary layer flow over a smooth flat plate in a uniform stream with constant velocity U e and temperature θ e . The transpiration (injection or suction) velocity v w directed along the normal to the surface and the temperature on the wall θ w are also considered to be constant. The turbulent flow is assumed to develop directly from the leading edge of the plate. We also assume that the level of velocity and temperature fluctuation in the free stream is negligibly small and does not affect the flow and heat transfer in the boundary layer. Temperature is treated as a passive contaminant exerting no influence on the liquid motion.

625 強安定成層下にある乱流温度場境界層のDNS(乱流の数値シミュレーション,OS26 乱流の数値シミュレーション)

This paper presents a direct numerical simulation (DNS) of turbulent thermal boundary layers under strong stable stratification. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and/or unstable stratification exists, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban-space. Thus, in order to investigate a buoyancy-affected boundary layer, we have carried out spatially-developing DNS of a storongly-stratified stable boudary layer. In the DNS results, fundamental turbulent statistics of the storongly-stratified stable boudary layer are shown, and near-wall variation of turbulent quantities, which are difficult to obtain experimentally, are presented in detail, and then discussed. Especially in the results, pronounced counter-gradient diffusions are observed in the turbulent momentum and heat transfer, i.e., in the distributions of the Reynolds shear stress and the wall-normal turbulent heat-flux.

Dissimilarity between the velocity and temperature fields in a perturbed turbulent thermal boundary layer

Dissimilarity between the streamwise velocity and temperature fields is investigated in a perturbed turbulent thermal boundary layer using direct numerical simulation. Perturbations are provided into a turbulent boundary layer by uniform blowing or suction from a spanwise slot. The skin-friction coefficient and Stanton number are significantly changed due to blowing and suction. The streamwise evolution of the Stanton number is very different from that of the skin-friction coefficient because the pressure gradient induced by blowing or suction plays an important role in the momentum transport. Before the slot, the mean streamwise velocity changes smoothly, as compared to the mean temperature, due to the pressure gradient, and a similar behavior is also observed in the variations of the streamwise velocity and temperature fluctuations. Above the slot, the change in the mean streamwise velocity is smaller than that in the mean temperature, and after the slot the mean streamwise velocity recovers slowly to the unperturbed flow as compared to the mean temperature. By investigating each term in the mean streamwise velocity and temperature budgets, it is concluded that the mean pressure gradient is the main source of dissimilarity between the mean streamwise velocity and temperature fields. The budgets for the variances of the streamwise velocity and temperature fluctuations show that the difference between the production terms in both budget equations, which results from the existence of the mean pressure gradient, is the primary source of dissimilarity between the streamwise velocity and temperature fields above the slot, whereas downstream of the slot, the velocity pressure-gradient term (i.e., pressure gradient fluctuation) is another important source of dissimilarity. Dissimilarity between the streamwise velocity and temperature fluctuations caused by blowing persists longer in the streamwise direction than that by suction.

Direct numerical simulation of turbulent thermal boundary layers

In this paper, a method of generating realistic turbulent temperature fluctuations at a computational inlet is proposed and direct numerical simulations of turbulent thermal boundary layers developing on a flat plate with isothermal and isoflux wall boundary conditions are carried out. Governing equations are integrated using a fully implicit fractional-step method with 352×64×128 grids for the Reynolds number of 300, based on the free-stream velocity and the inlet momentum thickness, and the Prandtl number of 0.71. The computed Stanton numbers for the isothermal and isoflux walls are in good agreement with power-law relations without transient region from the inlet. The mean statistical quantities including root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and skewness and flatness of temperature fluctuations agree well with existing experimental and numerical data. A quadrant analysis is performed to investigate the coherence between the velocity and temperature fluctuations. It is shown that the behavior of the wall-normal heat flux is similar to that of the Reynolds shear stress, indicating close correlation between the streamwise velocity and temperature. The effect of different thermal boundary conditions at the wall on the near-wall turbulence statistics is also discussed.

Turbulent heat and momentum transport on a rotating disk

Measurements in the turbulent momentum and thermal boundary layers on a rotating disk with a uniform heat flux surface are described for Reynolds numbers up to 106. Measurements include mean velocities and temperatures, all six Reynolds stresses, turbulent temperature fluctuations, and three turbulent heat fluxes. The mean velocity profiles have no wake region, but the mean temperature profiles do. The turbulent temperature fluctuations have a large peak in the outer layer, and there is a third turbulent heat flux in the cross-flow direction. Correlation coefficients and structure parameters are not constant across the boundary layer as they are in two-dimensional boundary layers (2DBLs), and their values are lower. The turbulent Prandtl number agrees with 2DBL values in the lower part of the outer region but is reduced from the 2DBL values higher in the boundary layer. In the outer region of the boundary layer, the transport processes differ significantly from what is observed in two-dimensional turbulent boundary layers: ejections dominate the transport of momentum while both ejections and sweeps contribute to the transport of the passive scalar.