Juergen Dierke

Linear- and Non-Linear Perturbation Equations with Relaxation Source Terms for Forced Eddy Simulation of Aeroacoustic Sound Generation

Turbulence related sound is generated by the dynamics of fluctuating vorticity. For example, trailing edge noise is caused by vorticity traveling past the trailing edge. To excite fluctuating vorticity by forcing the linearized Euler equations (LEE) with right-hand side source terms, one peculiar problem is observable: while the rise of vorticity levels by external sources poses no problem, to properly lower them, the right-hand side terms must act as a sink, being exactly in anti-phase to the vorticity levels as present in the LEE solution. However, the accurate prediction of vorticity in terms of phase cannot be guaranteed, especially for approximately modeled sources e.g. using stochastic methods. Thus in general there will be a mismatch between actual induced and intended levels of vorticity. In this paper a new class of relaxation source terms is introduced that enables the proper excitation of vorticity levels in linear and non-linear perturbation equations and as such enables an accurate control over the vorticity magnitudes. The source can be formulated to act selectively in wave-number space, i.e. without directly affecting the dynamics of resolved low wave-number vorticity components whereas the resolved high wave-number part is piloted by the fluctuating vorticity imposed as a reference solution. The reformulation of the Navier-Stokes equations in primitive variables and non-linear perturbation form is presented. Direct noise computation of sound radiated from a vortex shedding cylinder in laminar cross flow verify their implementation. The relaxation source term without forcing is applied to the unstable jet problem of the 4th CAA Workshop on Benchmark Problems. The forcing of frozen and decaying stochastic turbulence in conjunction with the relaxation source term is studied. First results for high-lift noise prediction with forced eddy simulation are presented.

Application of a Discontinuous Galerkin Method to Predict Airframe Noise

Unstructured grids greatly ease the mesh generation process in the case of complex geometries. The Discontinuous Galerkin Method (DGM) provides a robust, high-order accurate discretization even on this type of grid. The goal of the work reported herein is the prediction of broadband airframe noise generated by an airfoil with a deployed slat. Focus is on the noise generated by the slat, and two spatial dimensions are considered as a first step. The particularly employed DGM employs Lagrange polynomials as shape functions. They enable a simple and cheap truncation of the flux quantities of the underlying Acoustic Perturbation Equations (APE). The method is tested by computing the sound field of a monopole placed in a laminar boundary layer. Computations are stable, and very good agreement with other computations and with theoretical results is observed. Considering the prediction of broadband slat noise, the turbulent source term of the APE is computed efficiently via the stochastic FRPM (Fast Random Particle Mesh) method. Very encouraging results are obtained, and these will be analyzed in the next step.

3D Computation of Broadband Slat Noise from Swept and Unswept High-Lift Wing Sections

In previous work a RANS based simulation technique for the simulation of broadband slat noise was established. Good agreement was found between predicted and measured slat noise spectra. These predictions were based on 2D CAA computations and a connection to 3D measured data is only possible assuming a certain functional behavior of the spanwise coherence of the essential slat noise source. For this purpose, results from trailing edge noise measurements were used. In this work the simulation strategy is extended to 3D CAA computations, resolving the spanwise slat noise coherence as part of the CAA computations. The considered wing span is one main-chord, which is large enough to establish a realistic 3D problem for the turbulence as well as for the sound radiation. The Fast Random Particle Mesh (FRPM) method is applied for this study to generate fluctuating sound sources from steady RANS turbulence statistics. The study is conducted for the 30P30N airfoil with 0.457m main chord. The Mach number is 0.17 and the angle of attack is 4∘. Good agreement is found between the previous 2D and the 3D results as well as with unsteady simulations published in the literature. The influence of sweep on slat noise generation is studied.

The Fast Random Particle Method for Combustion Noise Prediction

A new, highly efficient approach for combustion noise prediction is introduced. The model is based on a mechanism for stochastic sound source reconstruction that reshapes turbulent dynamics via statistical input from steady CFD-RANS calculations. The utilized source term formulation is based on turbulent temperature fluctuations. The methodology includes the computation of sound propagation with linearized Euler equations in the time-domain, where the stochastic method delivers the temperature variance based unsteady sources as right hand side pressure equation terms. The source reconstruction and sound pressure level prediction capability of the hybrid method including the FRPM (Fast Random Particle Method) in conjunction with combustion noise monopole sources (FRPM-CN) is verified with a semi-analytical approach. The application cases DLR-A, -B and H3 flame are employed for validation purposes with experimental sound pressure spectra and to prove the method’s ability to account for Reynolds scalability. In the same context, a semi-analytical approach based on CFD-RANS statistics is introduced to predict the shape of jet flame noise spectra. A second order Langevin decorrelation model for evolving turbulence is incorporated.

Jet Noise Prediction with Eddy Relaxation Source Model

Previously, a hybrid CFD/CAA approach has been applied for jet noise prediction utilizing a stochastic realization of the Tam & Auriault (T&A) and the Tam, Pastouchenko and Viswanathan (TPV) source models. These models describe two-point cross-correlation functions of a mixing noise source in the jet shear-layer. All input data needed for the modeling can be derived from RANS. The uctuating acoustic sources are generated stochastically by the Fast Random Particle-Mesh (FRPM) method. For sound propagation a CAA code PIANO is applied with linearized or non-linearized Euler equations in perturbed form. In comparison to measurements, CAA results with the T&A and TPV source models have proven a relatively high accuracy for jet mixing noise prediction of dierent isolated nozzle congurations (single/dual stream jets, static and forward-ight conguration, hot/cold).

A generic computational study of broadband high-liftnoise generation for simplified slat and flap problems

In previous work a RANS based simulation technique for the simulation of broadband slat noise was established. The computational approach is based on acoustic perturbation equations forced by stochastic sound sources to simulate sound generation and radiation in space and time. Good agreement was found between predicted and measured slat noise spectra and for trailing edge noise generated at a NACA 0012 airfoil. In this work the simulation approach is applied to generic high-lift noise problems defined in the framework of the European project VALIANT. The problems considered are sound generation at the slat and the flap of simplified high-lift geometries. Results of the time-averaged mean flow and turbulence statistics from RANS are evaluated and compared to measurements. A comparison of the statistics of the stochastic fluctuations computed with the stochastic turbulence model FRPM with flow data is provided. Sound generated by the stochastic source model is evaluated and compared to measurements. As a general outcome of the study, the agreement between the RANS flow fields to measurements is quite good. The reconstruction of the turbulence statistics by FRPM is in general accurate, but in some reagions it differes from the target statistic. The agreement of the acoustic far field predictions to the measured data is satisfyings. The overall procedure is with a computational effort of around two days quite short.

The influence of realistic 3D viscous mean flow on shielding of engine-fan noise by a 3-element high-lift wing

The prediction of aeroacoustic shielding often rests on tools using constant mean flow thus neglecting mean flow inhomogeneities such as shear layers. This study analyses the influence of this simplification on shielding. As an example we considered engine-fan noise shielding at a 3-element high-lift wing. A Computational Aeroacoustic (CAA) approach was chosen. The simulations were carried out with the DLR CAA code PIANO. PIANO solves the Linearized Euler Equations (LEE) over steady viscous mean flow. To determine the mean flow influence three sets were computed. One rests on a realistic viscous Reynolds Averaged Navier-Stokes (RANS) solution, the second makes use of a simple constant mean flow and the third uses constant mean flow in conjunction with a flat plate with the same chord length to replace the wing. An axisymmetric solution of the finite element simulation code ACTRAN predicted the fan sound propagation from the engine intake through the non-uniform flow to a cylindrical interface. Subsequently, the data was coupled to the CAA computational domain via a Thompson boundary condition. It is shown that this condition meets the coupling requirements well. This study shows that the viscous mean flow has a significant influence on the predicted shielding potential of a high-lift wing. That is, the shielding benefit of a simplified prediction based on uniform flow propagation and a simplified geometrical significantly overestimate the potential shielding benefits considerably.

Efficient Full 3D Turbulent Combustion Noise Simulation Based on Stochastic Sound Sources

A combustion noise simulation approach with full dimensional treatment of time-domain sound source modeling and sound propagation is introduced. The hybrid, highly efficient method FRPM-CN (Fast Random Particle Method for Combustion Noise prediction) contains a stochastic sound source reconstruction algorithm. Sources are built according to turbulence statistics which can be derived from reacting CFD-RANS simulations. Sound propagation is modeled via Linearized Euler Equations with accountance for the local CFD mean flow field and combustion induced sources as right hand side forcing of the pressure equation in the acoustic near field. Verification of the approach is carried out on a generic testcase for local oneand two-point source field statistics reproduction ability as well as for analytically derived far-field spectra. The approach is validated for the nonpremixed DLR-A and DLR-B jet flames: The results of CFD-RANS simulations are compared to experimental data, giving a sufficiently accurate representation. Subsequently, numerical results with FRPM-CN for full 3D source modeling and sound propagation are presented. It is shown that the temperature-variance based ansatz pursued in this work delivers accurate absolute sound pressure levels without significant artificial correction. Furthermore, Reynolds-scalability of FRPM-CN for low Mach number jet flames is analyzed by incorporating a Mach number scaling law.

On the performance of airframe noise prediction on unstructured grids

Airframe noise of complex geometries may conveniently be computed on unstructured grids, which can be generated automatically and quickly. The particular goal of this work is to predict broadband airframe noise of a specific three-element high-lift airfoil configuration on such a grid. Therefore, a discontinuous Galerkin (DG) method provides the spatial discretization of the acoustic perturbation equations, whose turbulent source term is modelled efficiently via the fast random particle-mesh method based on RA NS data. Time integration is carried out by means of the standard, explicit Runge-Kutta scheme of order four (RK4). In two space dimensions, the DG computation on an unstructured triangular grid turned out to be as efficient as a finite difference-based simulationon a sophisticated block-structured grid. Local time stepping significantly increases the performance of the RK4-DG simulation even further. Nevertheless, acoustic results agree well with elaborate scale-resolving approaches.