Noise radiated by a non-isothermal, temporal mixing layer

The ability of Lighthill's analogy to predict the sound radiated by a transitional mixing layer is evaluated by means of direct numerical simulation (DNS). The specific case of low Mach number flows with density variations is investigated. In order to limit the global computational cost, the acoustic source information is based on numerical results where the sound waves have been removed. It is shown that the low Mach number approximation coupled with the acoustic analogy can lead to very accurate predictions for the radiated sound if the acoustic sources in Lighthill's equation are taken into account carefully. Results for the acoustic intensity deduced from a repeated use of the Lighthill's analogy over a wide range of Mach numbers allow us to discuss the adequacy of scaling laws proposed by previous authors (J. Sound Vib. 28(3), 563–585, 1973; 31(4), 391–397, 1973; 48(1), 95–111, 1976) for the prediction of noise from hot jets.     

An aeroacoustic hybrid approach for non‐isothermal flows at low Mach number

This paper presents an aeroacoustic hybrid technique for the study of non‐isothermal flows at low Mach number. The flow dynamics and the acoustic production and propagation are computed separately. The fully compressible Navier–Stokes equations are modified through an expansion of the physical quantities using a low Mach number approximation. Compressibility effects are thus removed in the CFD while inhomogeneities of the flow related to heat transfer are preserved. One advantage is a reduction of the time step constraint. Another advantage is that the Mach number does not appear explicitly and a simple rescaling allows a study over a relatively wide band of subsonic Mach number flows with a single dynamic simulation. Compatible acoustic source terms for LEE based propagation have been defined and the procedure is implemented in the case of a temporal mixing layer. Compressible simulations for Mach numbers of 0.2, 0.3 and 0.4 are compared with the numerical results obtained using the proposed method. Very good agreement is obtained even at relatively high subsonic Mach number demonstrating the efficiency of the proposed technique. Copyright © 2004 John Wiley & Sons, Ltd.     

Mach Wave Radiation by Mixing Layers. Part II: Analysis of the Source Field

In Part II a large-scale sound source in a time-developing planar free mixing layer is studied using an acoustic analogy approach. It is shown that only the non-compact character of the source resembles well the character of the corresponding source in a spatially developing flow. A model based on a continuous assembly of wave packets is derived and applied to direct numerical simulation results of two supersonic time-developing mixing layers undergoing transition to turbulence. The analysis predicts two distinctive dominant Mach wave sources in agreement with the direct analysis of Part~I. The first dominates during the stage of the Λ-vortex structure and the second just prior to the final breakdown to a fine-scale structure. The convective velocity of the second Mach wave source is higher than the first and thus its Mach angle of radiation is higher. The second source has a reduced strength at the higher free-stream Mach number. Directivity and frequency spectra compare well with the results of Part I, demonstrating that the assumptions inherent in the analogy are quite reasonable. Received 5 August 1997 and accepted 6 April 1998     

可压缩自由剪切流混合转捩大涡模拟

针对湍流气动光学效应与冲压发动机气体混合机理问题,开展了可压缩混合层流动空间模式大涡模拟和时间模式直接数值模拟研究.通过对流场(包含亚/亚混合、超/亚混合两种情况)失稳、转捩直至完全湍流的空间发展过程的研究表明,对流Mach数0.4状态下流场失稳以二维最不稳定扰动为主;非线性发展中,基频涡对并及展向涡撕裂主控流动转捩,流场发生混合转捩;转捩后脉动流场基本达到局部各向同性,此时,湍流Mach数低于0.3,流动压缩性可近似忽略.     

Mach Wave Radiation by Mixing Layers. Part I: Analysis of the Sound Field

In Part I a wave packet model is used to show that a time-developing mixing layer produces a Mach wave pattern similar to the one produced by a spatial-developing mixing layer. However, this kind of similarity does not exist for the sound emitted by subsonic sound sources. A method to analyse temporal direct numerical simulation (DNS) results for the Mach wave pattern is then developed and demonstrated using numerical results of the wave-packet model. The method is applied to the temporal DNS results of a supersonic mixing layer undergoing transition to turbulence. Two dominant Mach waves are revealed. The first wave originates from about the time of the Λ-vortex structure dominance in the layer. The second wave appears just prior to the final breakdown of the layer to a fine-scale turbulence structure. The second wave shows a higher level of a finite-amplitude wave behaviour and a smaller-scale source structure than the first wave. Directivity plots and frequency spectra are provided and discussed. Received 5 August 1997 and accepted 6 April 1998     

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e ^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D-LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.     

External Intermittency Simulation in Turbulent Round Jets

Direct numerical and large eddy simulation (DNS and LES) are applied to study passive scalar mixing and intermittency in turbulent round jets. Both simulation techniques are applied to the case of a low Reynolds number jet with Re = 2,400, whilst LES is also used to predict a high Re = 68,000 flow. Comparison between time-averaged results for the scalar field of the low Re case demonstrate reasonable agreement between the DNS and LES, and with experimental data and the predictions of other authors. Scalar probability density functions (pdfs) for this jet derived from the simulations are also in reasonable accord, although the DNS results demonstrate the more rapid influence of scalar intermittency with radial distance in the jet. This is reflected in derived intermittency profiles, with LES generally giving profiles that are too broad compared to equivalent DNS results, with too low a rate of decay with radial distance. In contrast, good agreement is in general found between LES predictions and experimental data for the mixing field, scalar pdfs and external intermittency in the high Reynolds number jet. Overall, the work described indicates that improved sub-grid scale modelling for use with LES may be beneficial in improving the accuracy of external intermittency predictions by this technique over the wide range of Reynolds numbers of practical interest.     

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     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling of thermal wall boundary conditions with temperature-dependent material properties for use in RANS

The present work extends a recently proposed P-function based model for describing the near-wall variation of temperature in forced convective turbulent flow to the case with temperature-dependent material properties. The extension essentially modifies the model formulations for describing the local variation of the turbulent mixing length and the turbulent Prandtl number. Direct Numerical Simulations (DNS) and experimental measurements are carried to provide comprehensive validation data for a wide range of Reynolds numbers, considering molecular Prandtl numbers well beyond unity. The observed good agreement of the predictions with the DNS data and experiments proves the present extended model as a well-suited approach for prescribing reliable thermal boundary conditions in Reynolds Averaged Navier-Stokes (RANS) simulations, assuming temperature-dependent material properties.     

Comparison of magnetic resonance concentration measurements in water to temperature measurements in compressible air flows

Magnetic resonance imaging (MRI) measurements in liquid flows provide highly detailed 3D mean velocity and concentration data in complex turbulent mixing flow applications. The scalar transport analogy is applied to infer the mean temperature distribution in high speed gas flows directly from the MRI concentration measurements in liquid. Compressibility effects on turbulent mixing are known to be weak for simple flows at high subsonic Mach number, and it was not known if this would hold in more complex flows characteristic of practical applications. Furthermore, the MRI measurements are often done at lower Reynolds number than the compressible application, although both are generally done in fully turbulent flows. The hypothesis is that the conclusions from MRI measurements performed in water are transferable to high subsonic Mach number applications. The present experiment is designed to compare stagnation temperature measurements in high speed airflow (M = 0.7) to concentration measurements in an identical water flow apparatus. The flow configuration was a low aspect ratio wall jet with a thick splitter plate producing a 3D complex downstream flow mixing the wall-jet fluid with the mainstream flow. The three-dimensional velocity field is documented using magnetic resonance velocimetry in the water experiment, and the mixing is quantified by measuring the mean concentration distribution of wall-jet fluid marked with dissolved copper sulfate. The airflow experiments are operated with a temperature difference between the main stream and the wall jet. Profiles of the stagnation temperature are measured with a shielded thermocouple probe. The results show excellent agreement between normalized temperature and concentration profiles after correction of the temperature measurements for the effects of energy separation. The agreement is within 1 % near the edges of the mixing layer, which suggests that the mixing characteristics of the large scale turbulence structures are the same in the two flows.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.     

Optimized group velocity control scheme and DNS of decaying compressible turbulence of relative high turbulent Mach number

To overcome the difficulty in the DNS of compressible turbulence at high turbulent Mach number, a new difference scheme called GVC8 is developed. We have succeeded in the direct numerical simulation of decaying compressible turbulence up to turbulent Mach number 0.95. The statistical quantities thus obtained at lower turbulent Mach number agree well with those from previous authors with the same initial conditions, but they are limited to simulate at lower turbulent Mach numbers due to the so‐called start‐up problem. The energy spectrum and coherent structure of compressible turbulent flow are analysed. The scaling law of compressible turbulence is studied. The computed results indicate that the extended self‐similarity holds in decaying compressible turbulence despite the occurrence of shocklets, and compressibility has little effects on relative scaling exponents when turbulent Mach number is not very high. Copyright © 2005 John Wiley & Sons, Ltd.     

PSE as applied to problems of transition in compressible boundary layers

A new idea of using the parabolized stability equation (PSE) method to predict laminar-turbulent transition is proposed. It is tested in the prediction of the location of transition for compressible boundary layers on flat plates, and the results are compared with those obtained by direct numerical simulations (DNS). The agreement is satisfactory, and the reason for this is that the PSE method faithfully reproduces the mechanism leading to the breakdown process in laminar-turbulent transition, i. e., the modification of mean flow profile leads to a remarkable change in its stability characteristics.     

Explicit algebraic Reynolds stress model (EARSM) for compressible shear flows

We develop an explicit algebraic Reynolds stress model (EARSM) for high-speed compressible shear flows and validate the model with direct numerical simulation (DNS) data of homogeneous shear flow and experimental data of high-speed mixing-layers. Starting from a pressure–strain correlation model that incorporates compressibility effects, the weak-equilibrium assumption is invoked to derive the EARSM closure expression. The resulting closure is fully explicit and physically realizable and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of DNS quite well. Linear EARSM calculations of a plane supersonic mixing-layer are performed, and comparison with experimental data shows good agreement. Salient results are agreement of streamwise velocity similarity profiles, mixing-layer spreading rates, and capturing the Langley curve trend.     

Noise Investigation of a High Subsonic, Moderate Reynolds Number Jet Using a Compressible Large Eddy Simulation

This study investigates the noise radiated by a subsonic circular jet with a Mach number of 0.9 and a Reynolds number of 65000 computed by a compressible Large Eddy Simulation (LES). First, it demonstrates the feasibility of using LES to predict accurately both the flow field and the sound radiation on a domain including the acoustic field. Mean flow parameters, turbulence intensities, velocity spectra and integral length scales are in very good agreement with experimental data. The noise generated by the jet, provided directly by the simulation, is also consistent with measurements in terms of sound pressure spectra, levels and directivity. The apparent location of the sound sources is at the end of the potential core in accordance with some experimental observations at similar Reynolds numbers and Mach numbers. Second, the noise generation mechanisms are discussed in an attempt to connect the flow field with the acoustic field. This study shows that for the simulated moderate Reynolds number jet, the predominant sound radiation in the downstream direction is associated with the breakdown of the shear layers in the central jet zone. Received 24 January 2002 and accepted 16 July 2002 Published online 3 December 2002 RID="*" ID="*" A preliminary version of some of the results presented here was reported in AIAA Paper 2000–2009 presented at the 6th AIAA/CEAS Aeroacoustics Conference in Lahaina, Hawaii, June 2000. Computing time was supplied by the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS – CNRS). Communicated by T.B. Gatski     

基于直接数值模拟的可压缩湍流模型评估和改进

对来流Mach数2.25和6的平板边界层湍流进行了直接数值模拟, 并通过与理论、实验及他人计算结果的对比对数值结果进行了验证. 基于直接数值模拟得到的湍流数据库, 对常用的湍流模型进行了先验评估. 评估的湍流模型有k-εvarepsilon模型(包括标准k-εvarepsilon 模型、可实现的k-εvarepsilon模型及低Reynolds数k-εvarepsilon模型)、SA模型及BL模型. 结果显示, 对于Mach2.25的平板边界层, 可实现的k-εvarepsilon 模型及低Reynolds 数k-εvarepsilon模型具有较好的预测能力, 而标准k-εvarepsilon模型预测的湍流黏性系数偏高; SA模型在边界层内层预测准确度较高, 而在外层预测值偏高. 而对于Mach6的平板边界层, k-εvarepsilon模型及SA模型预测的湍流黏性系数均偏高, 尤其是标准k-εvarepsilon模型. 对于Mach6的平板边界层, BL模型低估了内-外层交界位置, 造成湍流黏性系数预测值严重偏低. 作者通过修改模型系数及内-外层交界位置对BL模型进行了修改, 修改后模型预测的湍流黏性系数与DNS给出的值吻合较好.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

利用高阶分区并行算法实现直接数值模拟

在基于MPI环境的分布式内存机群上,结合高阶WENO-RF格式的特点,实现了5阶WENO-RF格式的分区并行计算方法,计算精度不受分区和节点数量影响。使用该分区并行算法以三维可压缩时间发展混合层为例进行了直接数值模拟,验证了并行算法的准确性,表明机群并行运算可以显著扩展微机的计算能力,并行效率高,减少了计算的墙上时间,适合在小型高速局域网内进行大规模数值模拟计算。