# Direct Numerical Simulation of Turbulent Flow Past an Acoustic Cavity Resonator

**Principal Investigator:** Lewin Stein, Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin (Germany)

**HPC Platform:** Hazel Hen of HLRS

**Date published: **November 2018

**HLRS Project ID:** AcouTurb

*A cavity (a hollow in an object) in a turbulent gas flow often leads to an interaction of vortex structures and acoustics. By exploiting this interaction, in some applications sound can be suppressed: silencers for jet engines (so-called Liner) or exhausts. In other cases, sound can be equally produced: squealing of open wheel-bays (i.e. aircraft during take-off and landing), sunroof and window buffeting (any vehicle), noise of pipeline intersection and tones of wind instruments (i.e. transverse flute, pipe organ). Typically, in expansive experimental runs, various configurations are tested in order to fulfill the design objectives of the respective application. Based on a `Direct Numerical Simulation’, the aim is to improve the understanding of the interactions between turbulence and acoustics of cavity resonators and to develop standalone sound prediction models, which improve and simplify the design process.*

**The challenge**

Under the projects DFG SE 824/29-1 `Acoustic Investigation of a Hollow Chamber in Turbulent Flow’ and DFG SE 824/23-1 `Shape Optimization and Sensitivity Analysis of a Liner under Grazing Flow’ of the German Research Foundation (DFG) acoustic cavity resonators driven by turbulent flow are simulated, studied and modelled.

The rise of high-performance computing allows simulating the dynamics of the turbulence-acoustic interaction by the high-quality method of a `Direct Numerical Simulation’. For the first time, the three-dimensional geometry is studied numerically in full detail without simplification. An unprecedented database is set up. So far numerical studies of cavity resonators with neck shape do not consider an inflowing turbulent boundary layer or do not resolve all system scales but assume some form of approximation.

A key challenge is either to prevent cavity noise before it arises or to reduce existing tonal noise by installing cavity absorbers. As a response to both challenges, this project develops a more realistic acoustic model. This model supports the layout of acoustically resonant cavities by predicting which sound frequencies are damped and which frequencies are excited in dependency on the geometrical dimensions and the flow properties.

**Why supercomputing power?**

A 'Direct Numerical Simulation’ of turbulent flow is computationally intensive since all system scales need to be resolved. To give an example: The smallest vortex present in the investigated case extends about a tenth of one mm. The entire simulated cavity resonator has an approximate size of one decimeter. Thus, in each dimension, three orders of magnitude need to be resolved by the computational mesh. Altogether, in three dimensions, about a billion mesh points are required. Since both turbulence and acoustics play a key role together, no simplified or approximative equations can be utilized, but the most general/complex form of single-phase gas equations needs to be solved (so-called compressible Navier-Stokes Equations). In contrast to experimental measurements all spatial and temporal information of pressure, velocity and temperature can be evaluated, without being distorted by the measurement process itself. The widest range of effects is taken into account by the `Direct Numerical Simulation’. Characteristic structures of the flow can be revealed from the database, which facilitates the understanding and modeling of physical processes.

*Figure 1: Setup of the studied cavity resonator under turbulent flow. In red and blue vortex isosurfaces are shown. The simulation domain consists of three vertically stacked blocks: A top block with turbulent inflow in the streamwise x-direction; a very flat cavity opening in the middle; and a large lower cavity. All dimensions are given in units of the 99% boundary layer thickness δ, defined at the upstream opening edge of the cavity. *© *TU Berlin*

**What are the findings/knowledge gained?**

A universal acoustic model of a cavity resonator under turbulent flow is derived, based on the new numerical database, previous theories by M. S. Howe, and experiments by J. Golliard. This acoustic model stands out by its uniquely defined and physically meaningful parameters, instead of fitted constants. The model consists of exchangeable elements which guarantee a flexible use. The model enables the user to understand and to trace back how a modification of design parameters like the spatial form or the type of incoming flow affects the sound spectrum. In doing so the theoretical model is standalone, i.e. it does not depend anymore on additional experiments or supercomputer simulations.

**Who did/will benefit from the insights gained? In what way?**

An industrial user is no longer dependent on expensive and time-consuming test series. The design process of cavity absorbers is greatly simplified: A priori, rather than by trial-and-error approach, the sound absorption spectrum can be easily tuned for certain frequencies. Furthermore, the model predicts vortex and acoustic resonance conditions and such allows the design engineer to avoid tonal cavity noise in advance. Thus, noise pollution and material wear can be circumvented, before it occurs.

*Figure 2: Two different time steps (left and right side of the figure) of the cavity simulation. Here, just a detailed section near the opening of the cavity is visible (compare with Figure 1). The top row shows an XY side view, the bottom row shows the corresponding XZ top view of the same time step. Vortex isosurfaces with a rotation frequency of 3000 Hertz are colored in red. Pressure isosurfaces with 100 010 Pascal are marked in blue. Walls are visualized in black. In the bottom row (XZ top view), the underlying opening of the cavity is highlighted by a whitish rectangle. *© *TU Berlin*

**Publications:**

Stein, L.: How to Predict the Sound Spectrum of a Helmholtz Resonator under Grazing Turbulent Flow. In: Fortschritte Der Akustik - DAGA 2018 44. Jahrestagung Für Akustik, ISBN 9783939296133, pp. 497–500. Deutsche Gesellschaft für Akustik, Munich (2018)

Stein, L., Sesterhenn, J.: Direct Numerical Simulation of Turbulent Flow Past an Acoustic Cavity Resonator. In: High Performance Computing in Science and Engineering ' 18. Springer (2019) (submitted, accepted)

Stein, L.: Simulation and Modeling of a Helmholtz Resonator under Grazing Turbulent Flow. Unpublished doctoral thesis. Technische Universität Berlin (2019)

Stein, L., Sesterhenn, J.: An Acoustic Model of a Helmholtz Resonator under a Grazing Turbulent Boundary Layer. Acta Mech. (in review process)

**Scientific Contact:**

Lewin Stein

Fachgebiet für Numerische Fluiddynamik (CFD group)

Institut für Strömungsmechanik und Technische Akustik (ISTA)

Technische Universität Berlin

Müller-Breslau-Str. 15, D-10623 Berlin (Germany)

e-mail: Lewin.Stein [at] tu-berlin.de

*HLRS Project ID: AcouTurb*

*November 2018*