Noise prediction for a turbulent jet using different hybrid methods

The acoustic field of a cold single stream jet at Mach number 0.9 and Reynolds number 3600 is determined via computational aeroacoustics (CAA) methods. The jet computation of the acoustical field is performed by two hybrid approaches using a large-eddy simulation (LES) for the flow field and various systems of equations for the acoustical field to construct a robust, efficient, and reliable LES/CAA solver. The acoustic equations are the Ffowcs Williams-Hawkings equation (FWH) in the frequency domain and the acoustic perturbation equations (APE). The pronounced impact of the data windowing and the radial and streamwise extension of the integration surface on the directivity of the FWH solution is discussed at length. The comparison with available experimental and numerical results at similar flow conditions based on the noise characteristics in the near field shows the solution of the APE system to match the results of the direct LES more accurately than the FWH approach. The APE solution is less susceptible to the size of the source term region than the FWH approach to the location of the source surface. In conjunction with the APE formulation the LES domain can be chosen smaller than for the FWH ansatz resulting in less computational cost for the jet flow. The dominant source term in the APE system for cold jet noise is shown to be the Lamb vector.     

Aerodynamic noise simulation of the flow past an airfoil trailing-edge using a hybrid zonal RANS-LES

This paper document the evaluation of a zonal RANS-LES approach for the prediction of broadband and tonal noise generated by the flow past an airfoil trailing edge at a high Reynolds number. A multi-domain decomposition is considered, where the acoustic sources are resolved with a LES sub-domain embedded in the RANS domain. At the RANS-LES interface, a stochastic vortex method is used to generate synthetic turbulent perturbations. The simulations are performed with the general-purpose unstructured control-volume code FLUENT. The far-field noise is calculated using the aeroacoustic analogy of Ffowcs-Williams and Hawkings. The results of the simulation are compared with available acoustic and mean velocity measurements. The investigation demonstrates the ability of this approach to predict the aerodynamic and aeroacoustic properties of the flow. Two simulations are performed in order to address the sensitivity of the results to the perturbation model. The comparison clearly indicates the critical influence of the model.     

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.     

The simulation of binaural hearing caused by a moving sound source

Auditory perception of the sound with respect to a moving sound source passing by the observer was investigated in this work. The sound pressure at the entrance of the external ear canal was calculated by the solution of the Ffowcs Williams–Hawkings equation. Furthermore, the Hilbert Huang transformation is used to find the instantaneous frequencies of acoustic signal. Results show that the Interaural Level Difference and the frequencies shifting are eventful cues to perceive the direction and the speed of the moving sound source. In addition, the perceived loudness level will be larger in the motional case than that found in the stationary cases.     

Prediction of sound generated by a rod-airfoil configuration using EASM DES and the generalised Lighthill/FW-H analogy

Sound generated by an airfoil in the wake of a rod is predicted numerically by using a Detached-Eddy Simulation (DES) unsteady flow field and a Ffowcs Williams and Hawkings acoustic analogy formulation for the far field computation. Volume sources from the rod wake are found to play a non-negligible role at high frequencies and surface contributions might be flawed if the surfaces cross highly turbulent flow regions even if surrounding volume terms are accounted for. The DES approach is based on a novel cubic explicit algebraic stress turbulence model which is built on a two-equation k-ε model from Lien and Lechziner. This DES has been recently implemented at the Berlin University of Technology in the compressible Navier-Stokes flow solver ELAN. The aerodynamic results are compared to experimental data obtained at the ECL by Jacob et al., as well as to previous Large Eddy Simulations results from the Proust/Turbflow code by Boudet et al. and DES simulations from Greschner et al. based on standard turbulence models. The acoustic analogy is applied both with and without volume terms to rigid and permeable control surfaces surrounding the rod-airfoil system. Aeroacoustic results are compared to experimental data from the literature, showing that the inclusion of volume terms improves the aeroacoustic prediction in the broadband high frequency range.     

Large-eddy simulation in the near-field of a transient multi-component gas jet with density gradients

Large-eddy simulation (LES) is a research tool that is increasingly being used to study practical engineering flows because of continuous improvements in computational power. This paper outlines an LES model developed for the study of multi-component transient gas jets with density gradients. The compressible LES formulation together with the numerical model, boundary conditions, perturbation, and parallelization are discussed. A non-dissipative sixth-order finite difference scheme is used to discretize the governing equations, and a low-pass sixth-order spatial filtering scheme is employed to avoid the growth of high-frequency modes. The conditions at the boundaries are implemented using Navier–Stokes characteristic boundary conditions. In addition to code performance, results are presented from a study of an impulsively started jet at high pressure and temperature with an injected to ambient gas density ratio of approximately 3.5.     

Broadband slat noise prediction based on CAA and stochastic sound sources from a fast random particle-mesh (RPM) method

The application of a low-cost computational aeroacoustics (CAA) approach to a slat noise problem is studied. A fast and efficient stochastic method is introduced to model the unsteady turbulent sound sources in the slat-cove of a high-lift airfoil. It is based on the spatial convolution of spatiotemporal white-noise and can reproduce target distributions of turbulence kinetic energy and length scales, such as that provided by a RANS computation of the time-averaged turbulent flow problem. The computational method yields a perfectly solenoidal velocity field. For homogeneous isotropic turbulence, the complete second-order two-point velocity correlation tensor is realized exactly. Two RANS turbulence models are applied to the slat noise problem to study how sensitive the aeroacoustics predictions depend on turbulence kinetic energy predictions. Results for the sound generation at the slat are given for a Menter SST turbulence model with and without Kato-Launder modification. The aeroacoustic simulations yield a characteristic narrow band spectrum that compares very well with the experimental data. The directivities found point toward an edge noise mechanism at the slat as the main cause for slat noise sound generation.     

A hybrid algorithm for far-field noise minimization

A general unsteady adjoint formulation is applied to a hybrid acoustic prediction algorithm to provide an efficient far-field noise minimization algorithm. Two-dimensional unsteady Navier-Stokes (NS) computations for calculating the properties of acoustic sources are combined with the Ffowcs Williams and Hawkings (FW-H) wave propagation formulation to calculate the resulting far-field noise. Two different time-marching methods, namely an implicit multi-stage and an implicit multi-step method, are used for time discretization. The hybrid NS/FW-H solver is verified by comparison to an analytical solution and a Navier-Stokes solution. A discrete-adjoint Newton-Krylov algorithm is used to enable gradient-based shape optimization to minimize far-field noise computed using the hybrid solver. Objective functions considered include remote inverse shape designs for verification as well as the far-field pressure fluctuations for a blunt trailing edge airfoil in an unsteady turbulent flow environment. The examples presented demonstrate that the combination of a discrete-adjoint Newton-Krylov algorithm with a hybrid NS/FW-H far-field noise prediction method can be an efficient design tool for reducing aerodynamically generated noise.     

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.     

Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering

An isothermal circular jet with a Mach number of M = 0.9 and a Reynolds number of Re_D = 4 × 10⁵ is computed by compressible large eddy simulation (LES). The LES is carried out using an explicit filtering to damp the scales discretized by less than four grid points without affecting the resolved large scales. The jet features are thus found not to appreciably depend on the filtering procedure. The flow development is also shown from simulations on different grids to be independent of the location of the grid boundaries. The flow and the sound field obtained directly by LES are compared to measurements of the literature. The acoustic radiation especially displays spectra and azimuthal correlation functions which behave according to the observation angle as expected for a high Reynolds number. Furthermore the two components of jet noise usually associated to large structures and to fine-scale turbulence, respectively, are apparently found.     

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 variational multiscale method for laminar and turbulent flow

Summary  The present article reviews the variational multiscale method as a framework for the development of computational methods for the simulation of laminar and turbulent flows, with the emphasis placed on incompressible flows. Starting with a variational formulation of the Navier-Stokes equations, a separation of the scales of the flow problem into two and three different scale groups, respectively, is shown. The approaches resulting from these two different separations are interpreted against the background of two traditional concepts for the numerical simulation of turbulent flows, namely direct numerical simulation (DNS) and large eddy simulation (LES). It is then focused on a three-scale separation, which explicitly distinguishes large resolved scales, small resolved scales, and unresolved scales. In view of turbulent flow simulations as a LES, the variational multiscale method with three separated scale groups is refered to as a “variational multiscale LES”. The two distinguishing features of the variational multiscale LES in comparison to the traditional LES are the replacement of the traditional filter by a variational projection and the restriction of the effect of the unresolved scales to the smaller of the resolved scales. Existing solution strategies for the variational multiscale LES are presented and categorized for various numerical methods. The main focus is on the finite element method (FEM) and the finite volume method (FVM). The inclusion of the effect of the unresolved scales within the multiscale environment via constant-coefficient and dynamic subgrid-scale modeling based on the subgrid viscosity concept is also addressed. Selected numerical examples, a laminar and two turbulent flow situations, illustrate the suitability of the variational multiscale method for the numerical simulation of both states of flow. This article concludes with a view on potential future research directions for the variational multiscale method with respect to problems of fluid mechanics.     

High-Resolution Finite Volume Methods on Unstructured Grids for Turbulence and Aeroacoustics

In this paper we focus on the application of a higher-order finite volume method for the resolution of Computational Aeroacoustics problems. In particular, we present the application of a finite volume method based in Moving Least Squares approximations in the context of a hybrid approach for low Mach number flows. In this case, the acoustic and aerodynamic fields can be computed separately. We focus on two kinds of computations: turbulent flow and aeroacoustics in complex geometries. Both fields require very accurate methods to capture the fine features of the flow, small scales in the case of turbulent flows and very low-amplitude acoustic waves in the case of aeroacoustics. On the other hand, the use of unstructured grids is interesting for real engineering applications, but unfortunately, the accuracy and efficiency of the numerical methods developed for unstructured grids is far to reach the performance of those methods developed for structured grids. In this context, we propose the FV-MLS method as a tool for accurate CAA computations on unstructured grids.     

Large-eddy simulation of vortex breakdown in compressible swirling jet flow

Vortex breakdown in a compressible swirling jet flow is investigated by large-eddy simulation (LES) using the approximate deconvolution model. Conditions are chosen similar to recent experimental investigations by Liang and Maxworthy [Liang H, Maxworthy T. An experimental investigation of swirling jets. J Fluid Mech 2005;525:115] for incompressible flow. LES results are presented for two simulations of a swirling jet at Mach number Ma = 0.6 with and without inflow forcing by imposed linear instability disturbances. Both the forced and the self-excited jet show three-dimensional helical waves developing in the jet breakdown zone. The features observed in the two simulations are compared to each other as well as to the experiments with respect to flow statistics and instability behaviour. Both simulations show favourable qualitative agreement with the experiment.     

Large Eddy Simulation of a turbulent non-premixed propane-air reacting flame in a cylindrical combustor

Large Eddy Simulation (LES) is applied to investigate the turbulent non-premixed combustion flow, including species concentrations and temperature, in a cylindrical combustor. Gaseous propane (C₃H₈) is injected through a circular nozzle which is attached at the centre of the combustor inlet. Preheated air with a temperature of 773 K is supplied through the annulus surrounding of this fuel nozzle. In LES a spatial filtering is applied to the governing equations to separate the flow field into large-scale and small-scale eddies. The large-scale eddies which carry most of the turbulent energy are resolved explicitly, while the unresolved small-scale eddies are modelled using the Smagorinsky model with C_s = 0.1 as well as dynamically calibrated C_s. The filtered values of the species mass fraction, temperature and density, which are the functions of the mixture fraction (conserved scalar), are determined by integration over a beta probability density function (β-PDF). The computational results are compared with those of the experimental investigation conducted by Nishida and Mukohara [1]. According to this experiment, the overall equivalence ratio of 0.6, which is calculated from the ratio of the air flow rate supplied to the combustion chamber to that of the stoichiometric reaction, is kept constant so that the turbulent combustion at the fuel nozzle exit starts under the fuel-rich conditions.     

Large-eddy simulation of hypersonic flows. Selective procedure to activate the sub-grid model wherever small scale turbulence is present

A new method for the localization of the regions where small scale turbulent fluctuations are present in hypersonic flows is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function f$f$ which represents the magnitude of the stretching–tilting term of the vorticity equation normalized with the enstrophy (Tordella et al., 2007) [3]. For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that f$f$ is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field of f$f$ in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching–tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain, and with those of a standard Euler simulation with the same resolution. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy, mean velocity and density distributions and of the energy and density spectra are substantially improved.     

A zonal RANS-LES method to determine the flow over a high-lift configuration

High Reynolds number flows are particularly challenging problems for large-eddy simulations (LES) since small-scale structures in thin and often transitional boundary layers are to be resolved. The range of the turbulent scales is enormous, especially when high-lift configuration flows are considered. For this reason, the prediction of high Reynolds number flow over the entire airfoil using LES requires huge computer resources. To remedy this problem a zonal RANS-LES method for the flow over an airfoil in high-lift configuration at Re_c=1.0×10⁶ is presented. In a first step, a 2D RANS solution is sought, from which boundary conditions are formulated for an embedded LES domain, which comprises the flap and a sub-part of the main airfoil. The turbulent fluctuations in the boundary layers at the inflow region of the LES domain are generated by controlled forcing terms, which use the turbulent shear stress profiles obtained from the RANS solution. The comparison with an LES solution for the full domain and with experimental data shows likewise results for the velocity profiles and wall pressure distributions. The zonal RANS-LES method reduces the computational effort of a full domain LES by approx. 50%.     

Large-eddy simulation in a complex hill terrain enabled by a compact fractional step OpenFOAM® solver

We report computational fluid dynamics (CFD) code developments using the high-level programming syntax of the open source C++ library OpenFOAM®. CFD simulations utilizing the large-eddy simulation (LES) approach are carried out using the developed code in a real-world application. We investigate wind flowing over the Bolund hill, Denmark. In the present configuration a west–east wind meets the steep west side of the hill. Such conditions lead to flow separation at the location of a sharp cliff. A full scale simulation, with a simulation duration of over one month, is carried out on a supercomputer. Physically, about 45 min of real time is simulated in the LES enabling the statistical averaging of the results. The novelty of the paper consists of the following features: (1) we report validation results of the newly developed LES code for the Bolund hill case, (2) we show the high-level LES solver code in its entirety in a few tens of code lines which promotes transparency in CFD-code development in the OpenFOAM® environment, (3) the study is the first study to use LES in pointing out the complex 3d characteristics of the Bolund hill case with the computationally challenging west–east (270°) wind direction, and (4) based on the comparison with previous experimental data, and Reynolds averaged Navier–Stokes (RANS) simulations, the present LES gives so far the best match for the turbulent kinetic energy increase at the considered measurement positions.     

Large eddy simulations of round jet with spectral element method

This paper studies round jet with large eddy simulation (LES) method, in which spectral element technique is used as spacial discritization for the large eddy simulation Navier-Stokes equations. A local spectral discretization associated with Legendre polynomials is employed on each element of the structured mesh, which allows for high accurate simulations of turbulent flows. Discontinuities across the interfaces of the elements are resolved using a Riemann solver. An isoparametric representation of the geometry is implemented, with boundaries of the domain discretized to the same order of accuracy as the solution, and explicit low-storage Runge-Kutta methods are used for time integration. LES results of round jet are presented, in which the instantaneous and statistical turbulence structures of the round jet have been captured. The probability density function, and the spectral density function of the round jet that can reflect properties of turbulence have also been estimated. The work serves the purpose of allowing fast, convenient computations and comparisons with theoretical results and the ultimate goal is to develop it into an LES code featuring spectral accuracy with minimum dissipation and dispersion, a valuable tool for round jet computations.     

A computer simulation of turbulent jet flow

The evolution of a round turbulent jet is simulated numerically under the constraint of axial symmetry. The vortex sheet shed from the orifice is represented by vortex ring elements, with a velocity field cut-off to control close encounters. Large-scale vortex clusters form in the model jet, similar to those inferred from laboratory flow visualization experiments. However, comparisons of statistical properties reveal significant differences between the axisymmetric model flow and real turbulent jets.