火箭发动机喷流噪声数值模拟及声振分析

为给火箭系统结构振动响应分析提供有效载荷,采用雷诺平均N S（Reynolds averaged N S,RANS）方程求解喷流流场与用非线性声学求解器（Non linear Acoustics Solver,NLAS）求解喷流声场相结合的方法,对某高超声速火箭液体发动机喷流噪声进行数值模拟.用有限元法和统计能量分析相结合的方法,求解发动机模型在噪声作用下的全频段振动响应.计算结果表明：发动机喷流噪声声压级大小与喷流流场的湍流动能密切相关,湍流强度大的位置喷流噪声声压大;喷流流场初始段混合层内产生的噪声在高频段大于过渡区内产生的噪声,但中低频段却相反.     

The numerical computation of turbulent flows

The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy $\text{k}$ and its dissipation rate ?, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.     

A comparative study of turbulence models performance for separating flow in a planar asymmetric diffuser

This paper presents a computational study of the separated flow in a planar asymmetric diffuser. The steady RANS equations for turbulent incompressible fluid flow and six turbulence closures are used in the present study. The commercial software code, FLUENT 6.3.26, was used for solving the set of governing equations using various turbulence models. Five of the used turbulence models are available directly in the code while the v²–f turbulence model was implemented via user defined scalars (UDS) and user defined functions (UDF). A series of computational analysis is performed to assess the performance of turbulence models at different grid density. The results show that the standard k–ω, SST k–ω and v²–f models clearly performed better than other models when an adverse pressure gradient was present. The RSM model shows an acceptable agreement with the velocity and turbulent kinetic energy profiles but it failed to predict the location of separation and attachment points. The standard k–ε and the low-Re k–ε delivered very poor results.     

Assessment of multiscale resolution for hybrid turbulence model in unsteady separated transonic flows

This paper presents results of a computational study conducted to assess the multi-scale resolution capabilities of a hybrid two-equation turbulence model in predicting unsteady separated high speed flows. Numerical solutions are obtained using a third order Roe scheme and the SST (shear-stress-transport) two-equation-based hybrid turbulence model for three-dimensional transonic flow over an open cavity. A detailed assessment of the effects of the computational grid and the hybrid turbulence model coefficient is presented for the unsteady flow field. Computed results are presented for both the resolved and the modeled turbulent kinetic energy (TKE) and for the predicted sound pressure level (SPL) spectra, which are compared to available experimental data and large Eddy simulation (LES) results. The comparison shows that the predicted SPL spectra agree well with the experimental results over a frequency range up to 2500 Hz, and that hybrid turbulence effectively models the shorter wavelengths. The results demonstrate improved agreement with experimental SPL spectra with increased grid resolution and a reduced hybrid turbulence model coefficient. In addition, they show that energy dissipation of the unresolved scales is over-predicted at low resolutions and that the hybrid coefficient influences the grid resolution requirements.     

Large and Small Eddies Matter: Animating Trees in Wind Using Coarse Fluid Simulation and Synthetic Turbulence

Animating trees in wind has long been a problem in computer graphics. Progress on this problem is important for both visual effects in films and forestry biomechanics. More generally, progress on tree motion in wind may inform future work on two‐way coupling between turbulent flows and deformable objects. Synthetic turbulence added to a coarse fluid simulation produces convincing animations of turbulent flows but two‐way coupling between the enriched flow and objects embedded in the flow has not been investigated. Prior work on two‐way coupling between fluid and deformable models lacks a subgrid resolution turbulence model. We produce realistic animations of tree motion by including motion due to both large and small eddies using synthetic subgrid turbulence and porous proxy geometry. Synthetic turbulence at the subgrid scale is modulated using turbulent kinetic energy (TKE). Adding noise after sampling the mean flow and TKE transfers energy from small eddies directly to the tree geometry. The resulting animations include both global sheltering effects and small scale leaf and branch motion. Viewers, on average, found animations, which included both coarse fluid simulation and TKE‐modulated noise to be more accurate than animations generated using coarse fluid simulation or noise alone.     

Improved parameterisation for the numerical modelling of air pollution within an urban street canyon

Numerical modelling for application to wind flow and dispersion in urban environments has noticeably progressed in recent years, to currently represent a widely used tool for simulating mechanical processes governing air pollution in complex geometries. In particular, Computational Fluid Dynamic (CFD) techniques based on RANS (Reynolds-Averaged Navier–Stokes equations) models, are extensively used to produce detailed simulations of the wind flow and turbulence in the urban canopy. However, several studies have indicated that RANS models, and in particular the widely used standard k–? turbulence model, are sensitive to the particular form of inlet profiles for turbulence and velocity. In the present study, simulations of the wind flow and dispersion within an idealised street canyon were carried out using the standard k–? turbulence model provided by the commercial software FLUENT. The aim of this study was to improve the standard k–? model performance by modifying the model parameters according to the chosen form of inlet profiles for velocity and turbulence. Capability of the model to reproduce real wind flow fields, turbulence and concentration patterns was evaluated by comparing the model results against recently published wind tunnel data. Results for turbulent kinetic energy and concentration showed that the redefinition of the default dispersive parameters can significantly enhance the model performance. The newly proposed parameterisations of the standard k–? turbulence model can be readily implemented within commercial CFD software packages, offering a reliable modelling tool for application to urban air pollution and other environmental studies.     

Verification of RANS solvers with manufactured solutions

This paper discusses code verification of Reynolds-Averaged Navier Stokes (RANS) solvers with the method of manufactured solutions (MMS). Examples of manufactured solutions (MSs) for a two-dimensional, steady, wall-bounded, incompressible, turbulent flow are presented including the specification of the turbulence quantities incorporated in several popular eddy-viscosity turbulence models. A wall-function approach for the MMS is also described. The flexiblity and usefulness of the MS is illustrated with calculations performed in three different exercises: the calculation of the flow field using the manufactured eddy-viscosity; the calculation of the eddy-viscosity using the manufactured velocity field; the calculation of the complete flow field coupling flow and turbulence variables. The results show that the numerical performance of the flow solvers is model dependent and that the solution of the complete problem may exhibit different orders of accuracy than in the exercises with no coupling between the flow and turbulence variables.     

A new second-order closure model for rough-wall turbulent flows using the Brinkman equation

A second-order turbulence closure is developed for the new rough-wall layer modeling approach using the Brinkman equation for turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. Interface stress jump conditions including the Reynolds stress components are also considered. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The rough-wall second-order closure is developed by adopting an existing smooth-wall model. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented and compared with those obtained by using a previously developed two-equation turbulence closure. The results show that the new rough-wall layer modeling approach with the second-order turbulence closure model satisfactorily predicted the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress. However, the results for the Reynolds normal stresses are different from the measured data in the inner 20-60% of the boundary layer due to the interface stress jump conditions employed in the present rough-wall layer modeling approach.     

Explicit algebraic Reynolds stress model of incompressible turbulent flow in rotating square duct

An explicit algebraic Reynolds stress model (EARSM) is proposed for the simulation of the incompressible three-dimensional Reynolds averaged Navier-Stokes (RANS) equations. The spatial discretization of the RANS equations is performed by a finite volume method with nonstaggered variable arrangement.The EARSM model which accounts for rotational effects is used to compute the turbulent flows in rotating straight square duct. The Reynolds number of 48,000 is based on the bulk velocity and the hydraulic diameter of the duct and is kept constant in the range of the rotational numbers. The second order closure (EARSM) yields an asymmetric mean velocity profile as well as turbulence properties. Effects of rotation near the cyclonic (suction side) and anticyclonic (pressure side) walls are well observed. Direct numerical simulation and large eddy simulation data are available for this case. The comparison of EARSM results with these accurate simulations shows a very good agreement.     

Application of the Boltzmann kinetic equation to the eddy problems

The main purpose of this work is to investigate the feasibility of applying a kinetic approach to the problem of modeling turbulent and unstable flows. First, initial value problems with the Taylor–Green (TG) type and isotropic velocity conditions for compressible flow in two-dimensional (2D) and three-dimensional (3D) periodic domains are considered. Further, 3D direct numerical simulation of decaying isotropic turbulence is performed. Macroscopic flow quantities of interest are examined. The simulation is based on the direct numerical solution of the Boltzmann kinetic equation using an explicit–implicit scheme for the relaxation stage. Comparison with the solution of the Bhatnagar–Gross–Krook (BGK) model equation obtained by using an implicit scheme is carried out for the decaying isotropic turbulence problem and demonstrates a small difference. For the TG initial condition results show a fragmentation of the large initial eddies and subsequently the full damping of the system. Numerical data are close to the analytic solution of TG problem. A dependence of the kinetic energy on the wave number is obtained by means of the Fourier expansion of velocity components. A power-law exponent for the kinetic energy spectrum tends to the theoretical value “−3” for 2D turbulence in 2D case and to the famous Kolmogorov value “−5/3” in 3D case.     

Application of Compact Schemes to Large Eddy Simulation of Turbulent Jets

We present 3-D large eddy simulation (LES) results for a turbulent Mach 0.9 isothermal round jet at a Reynolds number of 100,000 (based on jet nozzle exit conditions and nozzle diameter). Our LES code is part of a Computational Aeroacoustics (CAA) methodology that couples surface integral acoustics techniques such as Kirchhoff's method and the Ffowcs Williams– Hawkings method with LES for the far field noise estimation of turbulent jets. The LES code employs high-order accurate compact differencing together with implicit spatial filtering and state-of-the-art non-reflecting boundary conditions. A localized dynamic Smagorinsky subgrid-scale (SGS) model is used for representing the effects of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in very good agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by the LES is coupled with the Ffowcs Williams–Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with experimental measurements of jets at similar flow conditions. The aeroacoustics results are encouraging and suggest further investigation of the effects of inflow conditions on the jet acoustic field.     

Simulation of isotropic turbulence degeneration based on the large-eddy method

In this paper, the simulation of isotropic turbulence degeneration is studied. The turbulent process is modeled based on filtered three-dimensional unsteady Navier-Stokes equations. For the closure of the main equations, a viscous model of turbulence is used. The problem is solved numerically, i.e., in solving the equation of motion the modified method of fractional steps using compact schemes is employed and the equation for pressure is solved by the Fourier method in combination with matrix factorization. Temporal variations in the kinetic energy of turbulence and changes in the micro scale of turbulence and longitudinal-transverse correlation functions have been obtained. Longitudinal and transverse one-dimensional spectra have been found.     

Pseudo-spectral numerical simulation of miscible fluids with a high density ratio

A computational algorithm is described for direct numerical simulation (DNS) of turbulent mixing of two incompressible miscible fluids having greatly differing densities. The algorithm uses Fourier pseudo-spectral methods to compute spatial derivatives and a fractional step method involving the third-order Adams-Bashforth-Moulton predictor-corrector scheme to advance the solution in time. The pressure projection technique is shown to eliminate stability problems, previously observed, when the ratio of the densities in the two streams is as high as 35. The algorithm is investigated in detail for mixing in isotropic homogeneous turbulence of two fluids with a density ratio of 10. The limit on the density ratio is imposed so that the flow is both everywhere turbulent and spatially resolved. Both fluids have the same molecular viscosities, the nominal Schmidt number is 0.7, and the initial nominal Reynolds number based on the integral length scale and the rms velocity is 158. No body force is considered. It is shown that the pressure projection scheme does not limit the temporal accuracy of the solution when periodic boundary conditions are used, but that it significantly affects the stability of the simulations. It is also shown that the rate at which turbulence kinetic energy dissipates averaged for the whole computational domain is almost unaffected by density ratio.     

Study on the rapid pressure-strain rate in the second-moment closure for turbulent flows undergoing strong compression and large distortion

To clarify applicability of the existing models for the rapid pressure-strain correlation in the Reynolds-stress closures, modifications accounting for the nonzero divergence of the mean velocity have been set into five turbulence models. These are two models of Launder et al. (LRR1 and LRR2), model of Speziale et al. (SSG), model of Johansson et al. and model of Lee. Computations have been carried out with these models for compression process in the cylinder of an internal combustion engine. The calculation results of the mean turbulent kinetic energy, the anisotropic tensor of Reynolds stress and rapid pressure-strain have been compared with the analytical solutions of rapid distortion theory in order to identify a suitable model for turbulent flows undergoing strong compressions as in the engines. The results demonstrate that the linear model of Lee which includes the history effect of the total strain can even give the same accurate predictions as those of the Johansson's nonlinear models up to fourth order in the Reynolds-stress-anisotropic tensor.     

Effects of Chemical Reaction on Two-Dimensional Turbulence

Direct numerical simulations of compressible two-dimensional homogeneous turbulent reacting flows are conducted to investigate the interactions between turbulence and chemical reaction. Both isothermal and exothermic nonpremixed reactions are considered. In isothermal reacting simulations, the turbulence is not affected by the reaction and is characterized by the large scale coherent vortices and vorticity-gradient sheet structures. The spatial structures of the density and temperature fields are similar to that of vorticity. However, mixing and reaction occur in the layer like (lamellar) structures which are mainly formed in the hyperbolic flow regions, where the vorticily-gradient sheets are present and the turbulent stretching dominates the circulation. Analysis of the simulations with exothermic reactions indicates that the heat of reaction has significant influence on thc spatial and the compositional structure of velocity, scalar and thermodynamic variables. The fluctuations of the density, the temperature, the pressure and the dilatation are substantially increased due to nonuniform heat release. The heat of reaction also modifies the small scale solenoidal velocity field. At early times, when the reaction is significant, the magnitude of the vorticity (enstrophy) is enhanced by the baroclinic vorticity generation. At late times, when the reaction is almost completed, the molecular dissipation is dominant and the magnitude of vorticity decays continuously. Examination of the energy transfer among the rotational and the compressive components of the kinetic energy and the internal energy indicates that the energy of reaction is transfered to the compressive component of the kinetic energy by the pressure-dilatation correlations. The turbulent advection then transfer the energy from the compressive component of the kinetic energy to its rotational component.     

CFD modeling of scale effects on turbulence flow and scour around bridge piers

Sediment scour near bridge piers is a problem of nationwide concern because it has resulted in more bridge failures than all other causes in recent years. The existing bridge scour equation from HEC-18 was developed from laboratory experiments in relatively small scale. Field studies by Mueller [Mueller D, Wagner Chad R. Analysis of pier scour predictions and real-time field measurements. In: Proceedings of ICSF-1 first international conference on scour of foundations, Texas A&M University, College Station, Texas, USA; 2002] indicate that it is difficult to verify the scour equation with field data obtained from large bridge piers. In this study, computational model simulations using a 3D CFD model were conducted to examine scale effects on turbulent flow and sediment scour. For the large-scale model, the physical scale and boundary velocity were set up from the small scale model based on the Froude similarity law. Results of flow and sediment scour were obtained from two different approaches: (a) Froude similarity which is commonly used in physical modeling and (b) full scale 3D CFD modeling. Unlike physical modeling in which the effect of turbulent Reynolds number is ignored, the CFD model employs a 2nd order turbulent model to calculate turbulent velocity and sediment scour. Effects of scale on turbulence flow and sediment scour were investigated by comparing different results obtained from a full scale numerical model to those derived from the Froude similarity method.     

Studies of shock/turbulent shear layer interaction using Large-Eddy Simulation

Shock/shear/turbulence interactions are simulated using Large-Eddy Simulation (LES) with a new localized subgrid closure approach. Both normal and oblique shocks interactions with turbulence are considered. The LES methodology adopted here combines a hybrid numerical scheme that switches automatically and locally between a shock-capturing scheme and a low-dissipation high-order central scheme.The fundamental role of the diffusion of turbulent kinetic energy by pressure fluctuations in the problem of normal shock/isotropic turbulence interaction is stressed in the DNS study, and accounted for in the closure model. The study of the interaction between two oblique shocks and a turbulent shear layer shows that the turbulence evolution is mostly affected by two competing phenomena. An amplification of the turbulent levels occurs downstream of the interaction, and the mixing layer growth rate is significantly increased. However, the integrated production of turbulent energy across the mixing layer is reduced, and the increase in mixing is found to be localized in space, the turbulent statistics quickly relaxing to their undisturbed levels. Furthermore, the increase in vorticity from the compression of the mixing layer remains small, unaffected by the presence of turbulent and coherent structures.     

Implementation of synthetic turbulence inlet for turbomachinery LES

Large eddy simulation (LES) has the potential to model complex separated flows, where Reynolds Averaged Navier–Stokes (RANS) based methods often fail. An important aspect of LES is specifying correlated turbulent fluctuations at the inlet boundary. This is particularly important in turbomachines, where turbulence length scale and intensity play a key role in the correct prediction of component performance.In this work, a method is implemented into an unstructured Computational Fluid Dynamics (CFD) solver to impose correlated turbulent fluctuations in a compressible form. It is shown that compressibility effects are particularly important in turbomachinery and must be taken into account. The method uses a pre-processing method to generate a cube of isotropic, homogeneous turbulence. The velocity fluctuations so obtained are used to determine a fluctuating Mach number in order to evaluate the instantaneous total pressure and temperature fluctuations at domain inlet. In the authors knowledge this is one of the first attempts to define correlated fluctuations in a compressible form.The method is successfully applied to two turbomachinery related flows. Firstly, the jet flow from a propelling nozzle is investigated. Following this, the flow over a low pressure (LP) turbine blade is predicted. Results from the LES simulations show that modifications to the inlet conditions can significantly affect flow development. For the jet, changes in the shear layer and peak shear stress are shown, important in the context of high frequency sideline noise generated by the jet. Despite what is suggested in the literature the differences in shear stresses are important also in a non-swirling jet.For the LP turbine, incoming turbulent fluctuations modify the onset of transition and the extent of separation bubble. Without imposed turbulence fluctuations, loss is overpredicted by up to 50%. Moreover it is important to use a compressible solver. Despite the fact that the majority of the results proposed in literature on LP turbine is using incompressible solvers, the difference in terms of pressure coefficient, Cp, is comparable to turbulence contribution.     

Time domain computation of flow induced sound

We present a recently developed numerical scheme for computational aeroacoustics (CAA). Therewith, we solve the flow field by a large eddy simulation (LES) and the generation as well as propagation of acoustic noise by Lighthill’s analogy applying the finite element method. The developed scheme allows a direct coupling in time domain as well as a sequential coupling in frequency domain and provides the acoustic sound field not only in the far field but also in the region of the flow. Furthermore, we can directly investigate the acoustic source terms in the flow region. The scheme is well suited for interior aeroacoustic problems with complex geometries as well as for fluid-structure interaction problems. Implementation is validated and a two-dimensional simple application example is used to investigate the acoustic sources and to evaluate the acoustic pressure field from both transient and harmonic analyses.