A near-wall two-equation model for turbulent heat fluxes

A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.     

柴油机缸内近气缸盖壁面边界层预测模型的研究

分析了缸内壁面速度边界层和热边界层的形成过程,建立了缸内近气缸盖壁面面湍流速度壁面函数和温度壁面函数,研究了边界层内的速度分布、温度分布及速度边界层厚度和热边界层厚度,并将预测结果与拖动发动机的实测值进行了比较,发现两的趋势是一致的。研究结果表明,缸内近气缸盖壁面有边界层形成,同一位置的速度边界层与热边界层的厚度很接近,不同位置的边界层厚度不同,大约在2mm-4mm左右。     

NUMERICAL INVESTIGATION OF AN INTERNAL LAYER IN TURBULENT FLOW OVER A CURVED HILL

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulent flow equations are solved by a control volume based, finite-difference method. The turbulence is described by a multiple-time-scale turbulence model. Computational results show that the internal layer is a strong turbulence field that develops beneath the external boundary layer and is located very close to the wall. The turbulence field of the boundary layer flow over the curved kill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of a strongly curved surface on the turbulence field. The turbulence structure in the near-wall region of the curved hill is almost the same as that of the airfoil in most of the curved region even though the approaching external flows are quite different. Results show that the development of the wall shearing stress and separation of the boundary layer at the rear of the curved hill depend mostly on the streamline curvature and are only slightly influenced by the external boundary layer flow.     

Transient Free Convection and Thermal Stratification in Uniformly—Heated Partially—Filled Horizontal Cylindrical and Spherical Vessels

An integral approach has been used to analyze the development of the free convection boundary layer on heatedconcave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar andturbulent velocity and temperature profiles closed form expressions for the boundary layer thickness,velocityscale as well as the boundary layer commencement after the point of instability are obtained.In addition,themass flowrate to the thermal stratified region is given.     

Interaction between near-wall turbulence structure and immiscible droplets falling with wobbling motion in upward water flow

Flow visualization and image processing have been carried out for turbulent upward water flow with falling immiscible droplets of perfluorocarbon or hydrofluoroether in a pipe. It is found that the decreases of the mean velocity and the increases of the turbulence intensities are caused by the droplet wake flow. The droplets of FC-72 fall near the axis with small-amplitude wobbling motion. On the other hand, the droplets of HFE-7200 fall near the pipe wall with noticeable wobbling motion. The near-wall turbulence structure is modified by the wake flow of the wobbling droplets. Also, direct numerical simulation has been carried out for understanding the modification of near-wall heat transfer by the droplet. It is found that the outward flow in the wake carries hot fluid into the central region and that the wallward flow induced by the main flow impingement onto the cap of droplet carries cool fluid into the near-wall region. These cause near-wall heat transfer enhancement. The ratio of the energy associated with the droplet and that of the equivalent fluid lump is effective for discussing the wobble motion and the wake flow of the droplets.     

The transpired turbulent boundary layer in an adverse pressure gradient

An experimental program was carried out to study the effect of transpiration on a turbulent boundary layer in an adverse pressure gradient. A wind tunnel with a porous test wall was designed so that the blowing velocity and the strength of the pressure gradient could be varied in the course of the experiments. The effect of transpiration on the location of the separation point was observed. Measurements of mean velocity profiles and heat transfer rates were compared with predictions of a boundary layer calculation method based on an effective viscosity model. Predictions of skin friction were satisfactory, but there was noticeable error in the predicted velocity profile shapes near separation. It was also found that a form of the law of the wake provides a good representation of velocity profiles with blowing and could be used as the basis tor an integral method of prediction.     

Wall-Resolved LES and Zonal LES of Round Jet Impingement Heat Transfer on a Flat Plate

Numerical large-eddy simulation (NLES) is performed for a round jet impinging on a flat surface at a Reynolds number of Re = 23,000 for nozzle-to-plate spacings of H/D = 6 and 2, where H is the distance from the nozzle to the plate and D is the jet diameter. The Reynolds number has been set to match the experiments of Cooper et al. (Int J. Heat Mass Transfer, vol. 36, pp. 2675–2684, 1993). Two numerical large-eddy simulation approaches are examined. The first quasi-direct numerical simulation (DNS) approach resolves streaklike structures using fine near-wall grids; the second is the zonal approach of Tucker (Int J. Heat Fluid Flow, vol. 25, pp. 625–635, 2004), which uses the Wolfshtein k–l (Int J. Heat Mass Transfer, vol. 12, pp. 301–318, 1969) Reynolds-averaged Navier-Stokes (RANS) model near the walls and NLES elsewhere. A Hamilton-Jacobi equation is used to match the RANS region to the NLES zone. The use of a Spalart-Allmaras model leads to low levels of turbulent viscosity in the near-wall region. This is also observed when using detached-eddy (DES) when using a volume-based filter. The use of the standard DES filter based on maximum grid spacing prevents jet shear-layer transition. The k–l near-wall model maintains RANS levels of turbulent viscosity in the boundary layer. The results of both the near-wall quasi-DNS and hybrid RANS-NLES methods are generally encouraging.     

Hall and ion-slip effects on MHD free convection flow of rotating Jeffrey fluid over an infinite vertical porous surface

An attempt has been made to explore Hall and ion-slip effects on an unsteady magnetohydrodynamic rotating flow of an electrically conducting, viscous, incompressible, and optically thick radiating Jeffrey fluid past an impulsively vertical moving porous plate. Analytical solutions of the governing equations are obtained by Laplace transform technique. The analytical expressions for skin friction, Nusselt number, and Sherwood number are also evaluated. The velocity, temperature, and concentration distributions are displayed graphically in detail. From engineering point of view, the changes in skin friction, Nusselt number, and Sherwood number are observed with the computational results presented in a tabular manner. It is observed that the effects of rotation and Hall current tend to accelerate secondary velocity and decelerate primary velocity throughout the boundary layer region. Thermal and concentration buoyancy forces tend to accelerate both velocity components. Thermal radiation and thermal diffusion tend to enhance fluid temperature throughout the boundary layer region. Rotation and Jeffrey fluid parameters tend to enhance both stress components.     

An improved flamelet/progress variable modeling for supersonic combustion

In order to dynamically describe the transition of the scalar dissipation rate of the mixture fraction variance from near-wall regions to mainstream in near-wall combustion, the traditional flamelet/progress variable (FPV) model, which can be used either within the Reynolds Averaged Navier Stokes (RANS) framework or the large-eddy simulation (LES) framework, is modified to form an improved FPV model within the framework of the improved delayed detached eddy simulation (IDDES). The model blends respective expressions of the scalar dissipation rate within the RANS and LES frameworks into a unified form with an employment of the IDDES concept. It also adopts an analogy between the mixture fraction variance and turbulent kinetic energy. A hydrogen-fueled near-wall combustion is simulated to validate this model. Large-scale turbulent structures, which can either locally enhance combustion or cause local extinction in the reacting zone, are reproduced. Due to the blockage to lateral extents of spanwise turbulent structures, a three-dimensional effect, that the low temperature fluid at lower corners of flow passage is forced to move away from sidewalls, is also reproduced. The results show that the improved FPV model can avoid the scalar over-mixing effect of the traditional FPV model by delaying and mitigating the development of the mixture fraction variance at the near-wall regions. Therefore, the starting point of the high temperature zone predicted by the improved FPV model is downstream of that predicted by the traditional FPV model. It is indicated that the improved FPV model tends to delay combustion. This tendency is also demonstrated by the less combustion efficiency in the upstream region predicted by the improved FPV model. As a result, it can generate a moderate growth of the mixing and reacting zone in the longitudinal direction, which therefore improves the predictions of the species concentrations. In contrast, the traditional FPV model thickens the mixing and reacting zone, which is negative to the combustion efficiency in the downstream region. It is implied that a reasonable development of the mixture fraction variance at near-wall regions is essentially required for near-wall combustion simulation using the FPV model within the IDDES framework.     

Numerical Investigation of Nanofluid Flow and Heat Transfer Around a Calabash-Shaped Body

Numerical simulation on unsteady flow and heat transfer of alumina–water nanofluids around a calabash-shaped body was performed in the present study. Improved models of drag force and Brownian force were introduced. As the reaction time of the particle perturbation is short, fluctuation in vorticity is more intense than that in temperature, and many extreme values are found. The streamline is uplifted near the separation point due to the contribution of the particle inertia, which increases the recirculation zone of the quasi-steady vortex. Fewer particles enter the vortex near the waist portion from the separation region, and relatively more particles enter the recirculation region from the reattachment zone. The local streamline is straightened and flow heat transfer is enhanced. It is shown that the variation in the Nusselt number is strongly related to the critical points along the wall.     

Effects of free stream turbulence on turbulent boundary layer on a flat plate with zero pressure gradient (part V: The calculation of heat transfer)

The effects of free stream turbulence on turbulent heat transfer were calculated by using a two-equation model for heat transfer. The calculations were performed with respect to turbulent boundary layers along a flat plate with a uniform wall heat flux. From the measured values of near-wall thermal turbulence, an improvement on turbulence model function has been made in the turbulent heat flux equation. The results for the heat transfer rate, logarithmic temperature profile distribution, the eddy diffusivity of heat, and the turbulent Prandtl number agreed comparatively well with the experimental values. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 97–106, 1997     

Modeling of the microconvective contribution to wall heat transfer in subcooled boiling flow

In the present work, the two-phase turbulent boundary layer in subcooled boiling flow is investigated. The bubbles in the near-wall region have a significant effect on the dynamics of the underlying liquid flow, as well as on the heat transfer. The present work develops a single-fluid model capable of accounting for the interactions between the bubbles and the liquid phase, such that the two-phase convective contribution to the total wall heat transfer can be described appropriately even in the framework of single-fluid modeling. To this end, subcooled boiling channel flow was experimentally investigated using a laser-Doppler anemometer to gain insight into the bubble-laden near-wall velocity field. It was generally observed that the streamwise velocity component was considerably reduced compared to the single-phase case, while the near-wall turbulence was increased due to the presence of the bubbles. Since the experimentally observed characteristics of the liquid velocity field turned out to be very similar to turbulent flows along rough surfaces, it is proposed to model the near-wall effect of the bubbles on the liquid flow analogously to the effect of a surface roughness. Incorporating the proposed approach as a dynamic boundary condition into a well-established mechanistic flow boiling model makes it possible to reflect adequately the contribution of the microconvection to the total wall heat transfer. A comparison against the experimental data shows good agreement for the predicted wall shear stress as well as for the wall heat flux for a wide range of wall temperatures and Reynolds numbers.     

Dynamics of ignition of stoichiometric hydrogen-air mixtures by moving heated particles

Studying thermal ignition mechanisms is a key step for evaluating many ignition hazards. In the present work, two-dimensional simulations with detailed chemistry are used to study the reaction pathways of the transient flow and ignition of a stoichiometric hydrogen/air mixture by moving hot spheres. For temperatures above the ignition threshold, ignition takes place after a short time between the front stagnation point and separation location depending upon the sphere's surface temperature. Closer to the threshold, the volume of gas adjacent to the separation region ignites homogeneously after a longer time. These results demonstrate the importance of boundary layer development and flow separation in the ignition process.     

Numerical Study on the Suppression of Shock Induced Separation on the Non-Adiabatic Wall

IntroductionThe supersonic flow inevitably encounters the shockwaves that are in contact with the solid walls on which theturbulent boundary layer is developed. This sitUationproduces locally a complex phenomenon known as shockwave/turbulent boundary layer interaction. Basic stlldiesof the complex combinations of heat transfer andcompressibility are required to understand their effects onthe turbulent boundary layer characteristics. If the shockwave is strong enough, then the boundary layer c…     

A numerical study of thermal and chemical effects in interactions of n-heptane flames with a single surface

The thermal and chemical effects of a one-dimensional, premixed flame quenching against a single surface are studied numerically. Fuels considered include n-heptane and molar-based mixtures of 95/5 and 70/30 percent n-heptane and hydrogen, respectively. A reduced gas-phase kinetic mechanism for n-heptane is employed. Wall boundary conditions investigated include both an adiabatic and an isothermal wall with temperatures ranging from 298 to 1200 K. The effects of equivalence ratio variations between 0.7 and 3 are investigated. The computations with n-heptane and n-heptane/hydrogen mixtures show that for wall temperatures greater than 400 K heat release rates have a higher value for the wall-interacting flame than for the freely propagating flame. It is also seen that the peak wall heat flux increases with increasing wall temperatures up to 1000 K. Chemical pathway analysis reveals the importance of radical recombination reactions at the surface to the heat release profiles of this study. The effect of H, O, and OH radical recombination near the inert wall is observed to lower the heat release spike on a 750 K isothermal boundary. The concentrations of intermediate hydrocarbons in the near-wall region are studied and related to unburned hydrocarbon formation in an engine cylinder. It is shown that a simple one-step global reaction rate expression for n-heptane fuel conversion cannot reproduce the flame-wall trends observed with the reduced n-heptane mechanism.     

Heat and mass transfer in a separated flow region for high Prandtl and Schmidt numbers under pulsatile conditions

Heat and mass transfer phenomena were studied in the sudden expansion region of a pipe under steady and pulsatile conditions. The Prandtl number was varied from 100 to 12 000 and the flow was characterized for both uniform and parabolic entrance velocity profiles. A uniform velocity profile was used for pulsatile flow. It was found that heat transfer in the recirculation region was maximal near the area where wall shear was minimal. Blunting of the inlet profile caused the point of maximum heat transfer to move upstream. There was a nonlinear effect of Prandtl number on heat transfer which plateaued for Pr > 10³. The wall shear rate in the separation zone varied markedly with pulsatile flows, but the wall heat transfer remained relatively constant. The time-averaged pulsatile heat transfer at the wall was approximately the same as with steady flow with the mean Reynolds number. However, the isotherms within the pulsatile flow were markedly different from steady flow. The results demonstrate the complexity of separation flows and identify characteristic regions of high and low heat/mass transfer for high Prandtl/Schmidt pulsatile flow.     

Study on Shock Wave and Turbulent Boundary Layer Interactions in a Square Duct at Mach 2 and 4

In this paper, the outline of the Mach 4 supersonic wind tunnel for the investigation of the supersonic internal flows in ducts was firstly described. Secondly, the location, structure and characteristics of the Mach 2 and Mach 4 pseudo-shock waves in a square duct were investigated by color schlieren photographs and duct wall pressure fluctuation measurements. Finally, the wall shear stress distributions on the side, top and bottom walls of the square duct with the Mach 4 pseudo-shock wave were investigated qualitatively by the shear stress-sensitive liquid crystal visualization method. The side wall boundary layer separation region under the first shock is narrow near the top wall, while the side wall boundary layer separation region under the first shock is very wide near the bottom wall.     

Direct numerical simulation of convective heat transfer in a zero-pressure- gradient boundary layer with supercritical water

Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been developed for single-phase fluids in the subcritical thermodynamic state. In the present computational study, the statistical properties of turbulent flow as well as the development of coherent flow structures in a zero-pressuregradient flat-plate boundary layer are investigated in the absence of body forces, where the working fluid is in the supercritical thermodynamic state. The simulated boundary layers are developed to a friction Reynolds number of 250 for two heat-flux to mass-flux ratios corresponding to cases where normal heat transfer and improved heat transfer are observed. In the case where improved heat transfer is observed, spanwise spacing of the near-wall coherent flow structures is reduced due to a relatively less stable flow environment resulting from the lower magnitudes of the wall-normal viscosity-gradient profile.     

On the buoyancy-induced flow arising from a heated hemisphere

An experimental study of the natural convection flow over heated hemispheres has been carried out. The boundary-layer flow adjacent to the heated surface and the buoyant flow shed above it were studied in detail. Both the upright and inverted hemisphere configurations were considered to determine the effect on the resulting flow for the two characteristic orientations. Of major interest was the way in which the heated fluid adjacent to the surface rises from it and develops into a buoyant plume above the body. Detailed measurements of the velocity and temperature fields in regions close to the top of the hemisphere were made. The measured plume flow is compared with the axisymmetric plume which would rise above a point heat source. Local and average heat-transfer rates were determined. Our measurements in the boundary region upstream of the trailing end of the hemisphere also enable us to consider further the concept of “separation” in natural convection in greater detail than heretofore. It is found that the upright hemisphere generates higher velocities and a thicker boundary region than does the inverted orientation. The average heat-transfer rate is also greater. Plume flow was also measured above an inclined hemisphere. The effect of an extended insulator base under the upright hemisphere was determined Two surface boundary conditions, uniform temperature and uniform heat flux, were studied and hemispheres of two sizes were used. Our measurements are found to be in reasonable general agreement with existing theoretical and experimental results for spheres. These results clarify many fundamental questions concerning the nature of separation in natural convection and the effect of buoyancy force orientation and of surface geometry on flow over curved surfaces. The collection of the shed boundary region fluid into a buoyant plume is an interesting and varied process.     

AXISYMMETRIC TEMPERATURE DISTRIBUTIONS ON A TRANSVERSELY ISOTROPIC SEMI-INFINITE SOLID

An exact static solution for the axisymmetric boundary value problem of a transversely isotropic semispace subjected to a point heat source is constructed by similarity transformations. The closed-form expressions for the temperature and components of displacements and stresses are derived. In the particular cases of uniform and parabolic-type temperature distributions on a circular area of the surface, the expressions for the displacements and stresses at a distance z beneath the surface are determined. The Mathematica software is used, and the numerical results are presented on graphs depicting the spatial variation of the displacements and stresses in a semispace of cobalt material.