DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.     

Comparative Study of DNS,LES and Hybrid LES/RANS of Turbulent Boundary Layer with Heat Transfer Over 2d Hill

This paper first presents the turbulent heat transfer phenomenon of the boundary layer over a 2-dimensional hill using the direct numerical simulation (DNS). DNS results reveal turbulent heat transfer phenomena in the boundary layer over a 2-dimensional hill affected by the flow acceleration and the concave wall at the foreface of a hill, the convex wall at the top of the hill, and the flow deceleration, separation, and reattachment and the concave wall at the back of the hill. The prediction of turbulent heat transfer, the turbulence models of LES and HLR should be assessed in such heat transfer because these models have seldom been evaluated in the complex turbulent heat transfer. Therefore, this paper also presents evaluations of predictions of LES and HLR in the complicated turbulent heat transfer which is the boundary layer with heat transfer over a 2-dimensional hill. Consequently, this paper obviously shows the detailed turbulent heat transfer phenomena of a boundary layer over a 2-dimensional hill via DNS, and the evaluation results of prediction accuracy of LES and HLR for the heat transfer. LES and HLR give good prediction in comparison with DNS results, but the predicted reattachment and separation points are slightly different from DNS.     

Investigation of the heat transfer mechanism in supersonic turbulent boundary layers

A method is described for calculating turbulent Prandtl numbers from Mach number and total temperature profiles in supersonic boundary layers. The calculations are based on boundary layer measurements in the Mach number range from 3.5 to 5. The investigations clearly indicate that in addition to accurate profile measurements reliable values of shear stress and heat flux at the wall must exist, in order to be able to calculate the turbulent Prandtl number in the viscous regime of the boundary layer. For flow conditions with and without heat transfer, the derived turbulent Prandtl numbers indicate that the turbulent transport of heat decreases much faster towards the wall than the turbulent transport of momentum. The results of the analysis show that only the unequivocal qualitative result of increasing turbulent Prandtl numbers in the viscous region of the boundary layer, can be expected. The variation of the turbulent Prandtl number can be described successfully using a simple approximation, based on the mixing length concept, and is applied to the calculation of total temperature distribution using the law of the wall for compressible flow.     

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.     

On the use of a two-layer model for large-eddy simulations of supersonic boundary layers with separation

The two-layer modeling approach has become one of the most promising and successful methodology for simulating turbulent boundary layers in the past ten years. In the present study, a mixed wall model for large-eddy simulations (LES) of high-speed flows is proposed which combine two approaches; the thin-Boundary Layer Equations (TBLE) model of Kawai and Larsson (1994) and the analytical wall-layer model of Duprat et al. (2011) for streamwise pressure gradients. The new hybrid model has been efficiently implemented into a three-dimensional compressible LES solver and validated against DNS of a spatially-evolving supersonic boundary layer (BL) under moderate and strong pressure gradients, before being employed for the prediction of nozzle flow separations at different flow conditions, ranging from weakly to highly over-expanded regimes. A good agreement is obtained in terms of mean and fluctuating quantities compared to the DNS results. Particularly, the current wall-modeled LES results are found to perfectly match the DNS data of supersonic BL with/out pressure gradient. It is also shown that the model can account for the effect of the large-scale turbulent motions of the outer layer, indicating a good interaction between the inner and the outer part of the wall layer. In terms of simulations costs and improvements of computing power, the obtained results highlight the capability of the current wall-modeling LES strategy in saving a considerable amount of computational time compared to the wall-resolved LES counterpart, allowing to push further the simulations limits. Furthermore, the application of these computationally low-costly LES simulations to nozzle flow separation allows to clearly identify the origin of the shock unsteadiness, and the existence of broadband and energetically-significant low-frequency oscillations (LFO) in the vicinity of the separation region.     

Simulation of supersonic turbulent flow in the vicinity of an inclined backward-facing step

Large eddy simulation (LES) is a viable and powerful tool to analyse unsteady three-dimensional turbulent flows. In this article, the method of LES is used to compute a plane turbulent supersonic boundary layer subjected to different pressure gradients. The pressure gradients are generated by allowing the flow to pass in the vicinity of an expansion–compression ramp (inclined backward-facing step with leeward-face angle of 25°) for an upstream Mach number of 2.9. The inflow boundary condition is the main problem for all turbulent wall-bounded flows. An approach to solve this problem is to extract instantaneous velocities, temperature and density data from an auxiliary simulation (inflow generator). To generate an appropriate realistic inflow condition to the inflow generator itself the rescaling technique for compressible flows is used. In this method, Morkovin's hypothesis, in which the total temperature fluctuations are neglected compared with the static temperature fluctuations, is applied to rescale and generate the temperature profile at inlet. This technique was successfully developed and applied by the present author for an LES of subsonic three-dimensional boundary layer of a smooth curved ramp. The present LES results are compared with the available experimental data as well as numerical data. The positive impact of the rescaling formulation of the temperature is proven by the convincing agreement of the obtained results with the experimental data compared with published numerical work and sheds light on the quality of the developed compressible inflow generator.     

Computational analysis of impinging shock-wave boundary layer interaction under conditions of incipient separation

The interaction of an oblique shock wave with a turbulent boundary layer under conditions of incipient separation is analyzed by means of large-eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) turbulence models, with the objective to explore their predictive capabilities, in particular with respect to the unsteady features of the interaction. Consistent with earlier direct numerical simulations, we have found that the flow dynamics in the interaction zone is characterized by strong intermittency associated with the formation of scattered spots of flow reversal near the nominal position of the reflected shock. Comparison with experimental results (at much larger Reynolds number) show that the qualitative features of the interaction are predicted reasonably well by both LES and RANS models. RANS models supplemented with a semi-empirical closure are also found to provide reasonable estimate of the fluctuating pressure loads at the wall.     

An investigation of thermally stratified turbulent channel flow with temperature oscillation on the bottom wall by large eddy simulation

Thermally stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel is calculated to investigate the behavior of turbulent flow and heat transfer by use of large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objective of this study is to deal with the effect of the temperature oscillation on turbulent behavior of thermally stratified turbulent channel flow and to examine the effectiveness of the LES technique for predicting statistically unsteady turbulent flow driven by time-varying buoyancy force. To validate the present calculation, thermally stratified shear turbulent channel flow is computed and compared with available data obtained by direct numerical simulation (DNS), which confirm that the present approach can be used to predict thermally stratified turbulent channel flow satisfactorily. Further, to illustrate the effect of the temperature oscillation with different Richardson numbers and periods of the oscillation on turbulence characteristics, the phase-averaged mean value and fluctuation of the resolved velocities and temperature, and instantaneous velocity fluctuation structures are analyzed.     

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.     

Near-wall scaling for turbulent boundary layers with adverse pressure gradient

A new extended inner scaling is proposed for the wall layer of wall-bounded flows under the influence of both wall shear stress and streamwise pressure gradient. This scaling avoids problems of the classical wall coordinates close to flow separation and reattachment. Based on the proposed extended velocity and length scales a universal nondimensional family of velocity profiles is derived for the viscous region in the vicinity of a wall that depend on wall distance and a parameter α quantifying the importance of the streamwise pressure gradient with respect to the wall shear stress in the momentum balance. The performance of the proposed extended scaling is investigated in two different flow fields, a separating and reattaching turbulent boundary layer and a turbulent flow over a periodic arrangement of smoothly contoured hills. Both flows are results of highly resolved direct numerical simulation (DNS). The results show that the viscous assumptions are valid up to about two extended wall units. If the profiles are scaled by the extended inner coordinates, they seem to behave in a universal way. This gives rise to the hope that a universal behavior of velocity profiles can be found in the proposed extended inner coordinates even beyond the validity of the extended viscous law of the wall.      

Statistical Characteristics of an Isothermal, Supersonic Developing Boundary Layer Flow from DNS Data

Direct numerical simulation results for a developing, supersonic boundary layer flow with either an adiabatic wall temperature condition or a cold wall (relative to adiabatic) temperature condition are evaluated to assess the comparative effect on the mean and turbulent fields. Included in the analysis are two-point turbulent spanwise spatial correlations and the corresponding one-dimensional energy spectra distributions as well as higher-order statistics including skewness and flatness factors. In addition to the mean field velocity and temperature behavior, the turbulent Reynolds stress, temperature variance, and heat and mass flux distributions are discussed. An overall focus of the analysis is to both contrast the velocity and thermal field behavior and to provide some additional insight into the dynamic balance of the various statistical correlations and their impact on model development.     

Study of the Interaction of a Streamwise-Oscillating Shock with the Boundary Layer on a Flat Plate

The distinctive features of the flow in the region of interaction between an oscillating shock and a flat-plate boundary layer are studied for the laminar, transitional, and turbulent flow regimes. The flow patterns and the pressure and heat transfer distributions in the interaction region are analyzed at different intensities, frequencies, and amplitudes of the oscillating shock. The results of the interaction of oscillating and steady shocks with the flat-plate boundary layer are compared.     

Effects of Mach number on turbulent separation behaviours induced by blunt fin

 An experimental study of the interaction between shock wave and turbulent boundary layer induced by blunt fin has been carried out at M _∞=7.8 using oil flow visualization and simultaneous measurements of fluctuating wall pressure and heat transfer. This paper presents the effects of Mach number on turbulent separation behaviours induced by blunt fin. Received: 21 July 1996/Accepted: 4 February 1998     

Numerical simulations of non‐equilibrium turbulent boundary layer flowing over a bump

Large‐eddy simulation (LES) and Reynolds‐averaged Navier–Stokes simulation (RANS) with different turbulence models (including the standard k?ε, the standard k?ω, the shear stress transport k?ω (SST k?ω), and Spalart–Allmaras (S–A) turbulence models) have been employed to compute the turbulent flow of a two‐dimensional turbulent boundary layer over an unswept bump. The predictions of the simulations were compared with available experimental measurements in the literature. The comparisons of the LES and the SST k?ω model including the mean flow and turbulence stresses are in satisfied agreements with the available measurements. Although the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall. The numerical results indicate that the boundary layer is not followed by mean‐flow separation or incipient separation as shown from the numerical results. The resolved turbulent shear stress is in a reasonable agreement with the experimental data, though the computational result of LES shows that its peak is overpredicted near the trailing edge of the bump, while the other used turbulence models, except the standard k?ε, underpredicts it. Analysis of the numerical results from LES confirms the experimental data, in which the existence of internal layers over the bump surface upstream of the summit and along the downstream flat plate. It also demonstrates that the quasi‐step increase in skin friction is due to perturbations in pressure gradient. The surface curvature enhances the near‐wall shear production of turbulent stresses, and is responsible for the formation of the internal layers. The aim of the present work is to examine the response and prediction capability of LES with the dynamic eddy viscosity model as a sub‐grid scale to the complex turbulence structure with the presence of streamline curvature generated by a bumpy surface. Aiming to reduce the computational costs with focus on the mean behavior of the non‐equilibrium turbulent boundary layer of flow over the bump surface, the present investigation also explains the best capability of one of the used RANS turbulence models to capture the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Turbulent boundary layer with positive pressure gradient on a permeable surface under nonisothermal conditions

It is known that the longitudinal pressure gradient can exert a strong influence on the friction law and the characteristics of a dynamic turbulent boundary layer. The thermal and diffusion boundary layers are more conservative to the effect of the pressure gradient, and, hence, methods of analyzing them are based, in the majority of cases, on the hypothesis of conservativity of the heat- and mass-transfer laws to the longitudinal pressure gradient [1]. This hypothesis is verified by experimental results [2, 3] on heat transfer on an impermeable surface in a turbulent stream with positive pressure gradient under almost isothermal conditions. However, such investigations under nonisothermal conditions are practically nonexistent. An approximate theoretical analysis of the heat transfer in a turbulent boundary layer of a nonisothermal stream with a positive pressure gradient is given in this paper. Experimental results are presented. The experimental investigation was conducted in a burned-out graphite diffuser both with and without injection of an inert gas through the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–49, July–August, 1976.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.     

A Rapid and Accurate Switch from RANS to LES in Boundary Layers Using an Overlap Region

An efficient recycling algorithm is developed for injecting resolved turbulent content in a boundary layer as it switches from a Reynolds Averaged Navier-Stokes (RANS) type treatment to a Large Eddy Simulation (LES) type treatment inside a generalized Detached-Eddy Simulation (DES). The motivation is to use RANS in the thinnest boundary-layer area, following the original argument in favour of DES, and LES in the thicker boundary-layer areas especially approaching separation, to improve accuracy and possibly obtain unsteady outputs. The algorithm relies on an overlap of the RANS and LES domains and, therefore, the availability of both RANS and LES solutions in the recycling region, which is about 5 boundary-layer thicknesses long. This permits a smooth transfer of the turbulent stresses from this section to the LES inflow. The continuity of the skin-friction distribution is very good, reflecting the excellent viability of the resolved turbulence. The approach is validated in a flat-plate boundary layer and an airfoil near stall, with mild pressure gradient near the interface, and then applied to the compressible flow over an idealized airliner windshield wiper. The pressure fluctuations at reattachment are 12dB more intense than under a simple boundary layer at the same speed, and the output contains all the quantities needed to calculate the transmission of sound through the glass.     

Development and Analysis of Wall Models for Internal Combustion Engine Simulations Using High-speed Micro-PIV Measurements

The performance, efficiency and emissions of internal combustion (IC) engines are affected by the thermo-viscous boundary layer region and heat transfer. Computational models for the prediction of engine performance typically rely on equilibrium wall-function models to overcome the need for resolving the viscous boundary layer structure. The wall shear stress and heat flux are obtained as boundary conditions for the outer flow calculation. However, these equilibrium wall-function models are typically derived by considering canonical flow configurations, introducing substantial modeling assumptions that are not necessarily justified for in-cylinder flows. The objective of this work is to assess the validity of several model approximations that are commonly introduced in the development of wall-function models for IC-engine applications. This examination is performed by considering crank-angle resolved high-resolution micro-particle image velocimetry (µ-PIV) measurements in a spark-ignition direct-injection single cylinder engine. Using these measurements, the performance of an algebraic equilibrium wall-function model commonly used in RANS and LES IC-engine simulations is evaluated. By identifying shortcomings of this model, a non-equilibrium differential wall model is developed and two different closures are considered for the determination of the turbulent viscosity. It is shown that both wall models provide adequate predictions if applied inside the viscous sublayer. However, the equilibrium wall-function model consistently underpredicts the shear stress if applied in the log-layer. In contrast, the non-equilibrium wall model provides improved predictions of the near-wall region and shear stress irrespective of the wall distance and the piston location. By utilizing the experimental data, significant adverse pressure gradients due to the large vortical motion inside the cylinder (induced by tumble, swirl and turbulence) are observed and included in the non-equilibrium wall model to further improve the model performance. These investigations are complemented by developing a consistent wall heat transfer model, and simulation results are compared against the equilibrium wall-function model and Woschni’s empirical correlation.     

Investigation of a hypersonic crossing shock wave/turbulent boundary layer interaction

A combined theoretical and experimental study is presented for the interaction between crossing shock waves generated by (10°, 10°) sharp fins and a flat plate turbulent boundary layer at Mach 8.3. The theoretical model is the full 3-D mean compressible Reynolds-averaged Navier-Stokes RANS) equations incorporating the algebraic turbulent eddy viscosity model of Baldwin and Lomax. A grid refinement study indicated that adequate resolution of the flowfield has been achieved. Computed results agree well with experiment for surface pressure and surface flow patterns and for pitot pressure and yaw angle profiles in the flowfield. The computations, however, significantly overpredict surface heat transfer. Analysis of the computed flowfield results indicates the formation of complex streamline and wave structures within the interaction region.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.