Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.     

Numerical study on supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder

Characteristics of supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder are investigated numerically using hybrid RANS/LES (Reynolds-Averaged Navier–Stokes/Large-Eddy Simulation) method. Two types of inflow boundary layer are considered. One is a laminar-like boundary layer with inflow thickness of $\delta_{\inf } = 0.0$ and the other is a turbulent boundary layer with inflow thickness of $\delta_{\inf } = 2.5\,{\text{mm}}$ . The hybrid RANS/LES method acts as a DES (Detached Eddy Simulation) model for the laminar-like inflow condition and a wall-modeled LES for the turbulent inflow condition where the recycling/rescaling method is adopted. Although the turbulent inflow seems to have just minor influences on the supersonic cavity flow without fuel injection, its effects on the mixing and combustion processes are great. It is found that the unsteady turbulent structures in upstream incoming boundary layer interact with the injection jet, resulting in fluctuations of the upstream recirculation region and bow shock, and induce quick dispersion of the hydrogen fuel jet, which enhances the mixing as well as subsequent combustion.     

A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers

A synthetic turbulence generation (STG) method for subsonic and supersonic flows at low and moderate Reynolds numbers to provide inflow distributions of zonal Reynolds-averaged Navier–Stokes (RANS) – large-eddy simulation (LES) methods is presented. The STG method splits the LES inflow region into three planes where a local velocity signal is decomposed from the turbulent flow properties of the upstream RANS solution. Based on the wall-normal position and the local flow Reynolds number, specific length and velocity scales with different vorticity content are imposed at the inlet plane of the boundary layer. The quality of the STG method for incompressible and compressible zero-pressure gradient boundary layers is shown by comparing the zonal RANS–LES data with pure LES, pure RANS, and direct numerical simulation (DNS) solutions. The distributions of the time and spanwise wall-shear stress, Reynolds stress distributions, and two point correlations of the zonal RANS–LES simulations are smooth in the transition region and in good agreement with the pure LES and reference DNS findings. The STG approach reduces the RANS-to-LES transition length to less than four boundary-layer thicknesses.     

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.     

The structure of a three-dimensional boundary layer subjected to streamwise-varying spanwise-homogeneous pressure gradient

A spatially-evolving three-dimensional boundary layer, subjected to a streamwise-varying spanwise-homogeneous pressure gradient, equivalent to a body force, is investigated by way of direct numerical simulation. The pressure gradient, prescribed to change its sign half-way along the boundary layer, provokes strong skewing of the velocity vector, with a layer of nearly collateral flow forming close to the wall up to the position of maximum spanwise velocity. A wide range of flow-physical properties have been studied, with particular emphasis on the near-wall layer, including second-moments, major budget contributions and wall-normal two-point correlations of velocity fluctuations and their angles, relative to wall-shear fluctuations. The results illustrate the complexity caused by skewing, including a damping in turbulent mixing and a significant lag between strains and stresses. The study has been undertaken in the context of efforts to develop and test novel hybrid LES–RANS schemes for non-equilibrium near-wall flows, with an emphasis on three-dimensional near-wall straining. Fundamental flow-physical issues aside, the data derived should be of particular relevance to a priori studies of second-moment RANS closure and the development and validation of RANS-type near-wall approximations implemented in LES schemes for high-Reynolds-number complex flows.     

The Numerical Decomposition of Turbulent Fluctuations in a Compressible Boundary Layer

In many flows the turbulence is weakly compressible even at large Mach number. For example, in a compressible boundary layer Ma<5, the differences relative to an incompressible boundary layer understood as being caused by density variations that accompany variations temperature across the layer. Turbulent fluctuations in a boundary layer are therefore expected to be dominated by the effects nonconstant temperature, and low Mach number theories in which fluctuations are not dominant should be applicable to the fluctuating field. However, the analysis of compressible boundary layer DNS data reveals presence of significant acoustic fluctuations. To distinguish acoustic and thermal effects, a numerical decomposition procedure compressible boundary layer fluctuations is applied to determine the and nonacoustic fluctuations. Except for very near the wall, where decomposition procedure is not valid, it is found that the fluctuations are only weakly coupled to the acoustic fluctuations at numbers as high as 6. Received 13 March 2000 and accepted 21 May 2001     

The effect of inflow conditions on the transition to turbulence in large eddy simulations of spatially developing mixing layers

Large Eddy Simulations (LES) of spatially developing turbulent mixing layers have been performed for flows of uniform density and Reynolds numbers of up to 50,000 based on the visual thickness of the layer and the velocity difference across it. On a fine LES grid, a validation simulation performed with a hyperbolic tangent inflow profile produces flow statistics that compare extremely well with reference Direct Numerical Simulation (DNS) data. An inflow profile derived from laminar Blasius profiles produces a flow that is significantly different to the reference DNS, particularly with respect to the initial development of the flow. When compared with experimental data, however, it is the boundary layer-type inflow simulation produces the better prediction of the flow statistics, including the mean transition location. It is found that the boundary layer inflow condition is more unstable than the hyperbolic tangent inlet profile. A suitably designed coarse LES grid produces good predictions of the mean transition location with boundary layer inflow conditions at a low computational cost. The results suggest that hyperbolic tangent functions may produce unreliable DNS data when used as the initial condition for studies of the transition in the mixing layer flow.     

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.     

Implicit large eddy simulation of a supersonic flat-plate boundary layer flow by weighted compact nonlinear scheme

The performance of implicit large eddy simulation (ILES) of a supersonic flat-plate turbulent boundary layer flow by weighted compact nonlinear scheme (WCNS) has been investigated. In view of features of WCNS and ILES, it was expected that ILES by WCNS could be an efficient approach to perform LES of supersonic turbulent flows. The flowfield calculated by WCNS was of lower turbulent intensity compared with an explicit LES data obtained by a numerical scheme of the same order of accuracy on a computational grid of similar resolution. It was concluded that the numerical dissipation inherent in WCNS is so large that applying WCNS to ILES of this flowfield is inefficient compared with explicit LES.     

LES/RANS方法混合函数特性研究

将两方程k-ω SST湍流模型和Sagaut的混合尺度亚格子模型通过一个混合函数相结合, 构造出一种混合大涡/雷诺平均N-S方程模拟方法(hybird large eddy simulation/reynolds-averaged navier-stokes, Hybrid LES/RANS), 采用这种混合模拟方法结合5阶WENO格式对Ma=2.8平板湍流边界层进行了数值模拟, 并在计算区域上游入口处采用“回收/调节”方法生成湍流脉动边界条件, 通过考查RANS区域向LES区域的过渡参数及网格分辨率对这种混合模拟方法进行了评价. 计算结果表明: 该文采用的混合模拟方法可以捕捉到湍流边界层中的大尺度结构且入口边界层平均参数不会发生漂移, 混合函数应当将RANS区域和LES区域的过渡点设置在对数律层和尾迹律层的交界处, 而过渡应当迅速以获得正确的雷诺剪切应力分布, 在该文采用的模型及数值方法的条件下, 流向及展向的网格小至与Escudier混合长相当时, 能够获得可以接受的脉动速度的单点-二阶统计值.     

A Band-Width Filtered Forcing Based Generation of Turbulent Inflow Data for Direct Numerical or Large Eddy Simulations and its Application to Primary Breakup of Liquid Jets

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of spatially inhomogeneous flows strongly depend on turbulent inflow boundary conditions. Realistic coherent structures need to be prescribed to avoid the immediate damping of random velocity fluctuations. A new turbulent inflow data generation method based on an auxiliary simulation of forced turbulence in a box is presented. The new methodology combines the flexibility of the synthetic turbulence generation with the accuracy of precursor simulation methods. In contrast to most auxiliary simulations, the new approach provides full control over the turbulence properties and computational costs remain reasonable. The lack of physical information and artificiality attested with pseudo-turbulence methods is overcome since the inflow data stems from a solution of the Navier-Stokes equations. The generated velocity fluctuations are by construction divergence-free and exhibit the non-Gaussian characteristics of turbulence. The generated inflow data is applied to the simulation of multiphase primary breakup.     

LES of spatially developing 3D compressible mixing layer

The spatial development of a turbulent compressible mixing layer is investigated by means of large eddy simulation (LES). The subgrid viscosity is represented by the so-called mixed-scale model, adapted to compressible flows. Two different shock capturing schemes and three sets of inlet white-noise perturbations are investigated. The comparison between numerical and experimental results gives an overall good agreement.     

Reconstruction of turbulent fluctuations for hybrid RANS/LES simulations using a Synthetic-Eddy Method

A coupling methodology between an upstream Reynolds Averaged Navier–Stokes (RANS) simulation and a Large Eddy Simulation (LES) further downstream is presented. The focus of this work is on the RANS-to-LES interface inside an attached turbulent boundary layer, where an unsteady LES content has to be explicitly generated from a steady RANS solution. The performance of the Synthetic-Eddy Method (SEM), which generates realistic synthetic eddies at the inflow of the LES, is investigated on a wide variety of turbulent flows, from simple channel and square duct flows to the flow over an airfoil trailing edge. The SEM is compared to other existing methods of generation of synthetic turbulence for LES, and is shown to reduce substantially the distance required to develop realistic turbulence downstream of the inlet.     

An LES Turbulent Inflow Generator using A Recycling and Rescaling Method

The present paper describes a recycling and rescaling method for generating turbulent inflow conditions for Large Eddy Simulation. The method is first validated by simulating a turbulent boundary layer and a turbulent mixing layer. It is demonstrated that, with input specification of mean velocities and turbulence rms levels (normal stresses) only, it can produce realistic and self-consistent turbulence structures. Comparison of shear stress and integral length scale indicates the success of the method in generating turbulent 1-point and 2-point correlations not specified in the input data. With the turbulent inlet conditions generated by this method, the growth rate of the turbulent boundary/mixing layer is properly predicted. Furthermore, the method can be used for the more complex inlet boundary flow types commonly found in industrial applications, which is demonstrated by generating non-equilibrium turbulent inflow and spanwise inhomogeneous inflow. As a final illustration of the benefits brought by this approach, a droplet-laden mixing layer is simulated. The dispersion of droplets in the near-field immediately downstream of the splitter plate trailing edge where the turbulent mixing layer begins is accurately reproduced due to the realistic turbulent structures captured by the recycling/rescaling method.     

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flow-modeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the time-averaged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology.Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.     

Investigation of a compressible turbulent boundary layer in the presence of tangential blowing and a positive pressure gradient

The present study is devoted to the computational investigation of the compressible turbulent boundary layer and flow that are formed during tangential blowing of various gases in a thick boundary layer for large positive pressure gradients. Such flows occur in elements of the gas-dynamic channel of turbojet engines and liquid-fuel rocket engines, ejector pumps, and other technical devices. Using a numerical method we investigate the effect of various factors (the Mach number of blowing, the type of blown gas, and the intensity of variation of the pressure gradient) on the stability of the boundary layer up to its separation.     

The effect of boundary layer fluctuations on the streamwise vortex structure in simulated plane turbulent mixing layers

This paper details the influence of the magnitude of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. The fluctuations are physically-correlated, and produced by an inflow generation technique. The imposed high-speed side boundary layer fluctuation magnitude is varied from a low-level, up to a magnitude sufficiently high that the boundary layer can be considered, in a mean sense, as nominally laminar. Cross-plane flow visualisation shows that each simulation contains streamwise vortices in the laminar and turbulent regions of the mixing layer. Statistical analysis of the secondary shear stress reveals that mixing layers originating from boundary layers with low-level fluctuations contain a spatially stationary streamwise structure. Increasing the high-speed side boundary layer fluctuation magnitude leads to a weakening of this stationary streamwise structure, or its removal from the flow entirely. The mixing layer growth rate reduces with increasing initial fluctuation level. These findings are discussed in terms of the available experimental data on mixing layers, and recommendations for both future experimental and numerical research into the mixing layer are made.     

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 temporally developing juncture flows

Large eddy simulation (LES) results are reported for temporally developing solid–solid and solid–rigid-lid juncture flows. A MacCormack-type scheme that is second-order in time, and fourth-order in space for the convective terms and second-order in space for the viscous terms, is used. The simulations are obtained for a low subsonic Mach number. The subgrid-scale stresses (SGS) are modeled using the dynamic modeling procedure. The turbulent flow field generated on a flat-plate boundary layer is used to initialize the juncture flow simulations. The results of the flat-plate boundary layer simulations are validated with experimental and direct numerical simulations (DNS) data. In juncture flow simulations, the presence of an adjacent solid-wall/rigid-lid boundary altered the mean and the turbulent field, setting up gradients in the anisotropy of normal Reynolds stresses resulting in the formation of turbulence-induced secondary vortices. The relative size of these secondary vortices and the distribution of mean and turbulent quantities are in qualitative agreement with the experimental observations for the solid–solid juncture. The overall distribution of the mean and turbulence quantities showed close resemblance between the solid–solid and the solid–rigid-lid junctures; except for the absence of a second vortical region near the rigid-lid boundary. In agreement with the experimental observations, it was found that the normalized anisotropy term exhibited similarity when plotted against the distance from the boundary, regardless of the type of boundary, i.e. solid-wall or rigid-lid. The turbulent kinetic energy increased near the rigid-lid boundary. While the surface normal velocity fluctuations decreased to zero at the rigid-lid boundary, the other two velocity components showed an increase in their energy, which is also consistent with the experimental observations. © 1998 John Wiley & Sons, Ltd.     

Large-eddy simulation of a turbulent forced plume

This paper reports on an application of large-eddy simulation (LES) to a spatially-developing round turbulent buoyant jet. The numerical method used is based on a low-Mach-number version of the governing equations for compressible flow which can account for density variations. The second-order centre-difference scheme is used for spatial discretization and an Adams–Bashforth scheme for temporal discretization. Comparisons are made between LES results, experimental measurements and plume theory for the forced plume under moderate Reynolds number and good agreement has been achieved. It is found that the plume spreading and the centerline maximum mean velocity strongly depend on the forcing conditions imposed on the inflow plane. The helical mode of instability leads to a larger spreading rate as compared to an axisymmetric mode. The enhanced entrainment is directly related to the strong turbulent momentum and energy transports between the plume and surrounding fluid induced by vortex dynamics. The entrainment ratio is about 0.09 and falls into the range of experimentally determined values. Budgets of the mean momentum and energy equations are analyzed. It is found that the radial turbulent transport nearly balances the streamwise convection and the buoyancy force in the axial momentum equation. Also, the radial turbulent stress is balanced by the streamwise convection in the energy equation. The energy-spectrum for the axial velocity fluctuations shows a −5/3 power law of the Kolmogorov decay, while the power spectrum for the temperature fluctuations shows both −5/3 and −3 power laws in the inertial-convective and inertial-diffusive ranges, respectively.