Direct numerical simulation of a supersonic jet and its acoustic field

Project Acronym	SJN (Supersonic Jet Noise)
Scientific Discipline	Fluid Dynamics
Principal Investigator(s)	Dr. J. Sesterhenn
Leading Institution	Fachgebiet, Stroemungsmechanik, Technische Universitaet Muenchen, Germany
Partner Institution(s)	Ecole Centrale de Lyon, France (D. Juve, C. Bailly) Ecole Polytechnique, France (P. Schmid
DEISA Home Site	LRZ

Project summary and results

Shock-induced noise is generated by supersonic jets which are not perfectly expanded. This means that their nozzle exit pressure is above or below the ambient pressure. The flow adapts to the ambient pressure by a series of oblique shocks, compression and expansion waves. These interact with the shear layers, producing shock-induced or shock-associated noise. To this end direct numerical simulation was performed to study the physical processes responsible, many of which have not yet been clearly identified. The main challenge was to simultaneously resolve the small-scale nonlinear turbulent structures and at the same time the large-scale, small amplitude acoustic waves they produce.

In this project, the method of direct numerical simulation was used to compute a three-dimensional supersonic rectangular jet that is not perfectly expanded, as it is found at the nozzle exit of jet engines for aircraft. Numerical methods of high order of accuracy were chosen for the direct solution of the compressible Navier-Stokes equations. This gave us the possibility to compute the sound field that was generated by the supersonic jets, directly.

Consider a supersonic jet, e.g. at the exit of a jet engine, in the over- or under-expanded case. A regular pattern of compression and expansion waves will be found within the supersonic part of the jet flow. A compression wave incident on the sonic line will be reflected as an expansion wave, and vice versa. At the location of interaction between the compression wave and the turbulent mixing layer, acoustic waves are generated. This shock-induced noise also plays an important role in what is called jet screech. This phenomenon manifests itself by a strong and sharp peak in the sound pressure level spectrum, corresponding to a tonal noise at high amplitude (up to 160 dB), which may cause damage to parts that are near the nozzle due to the high dynamic loads. Screech is induced by shock-induced acoustic waves traveling upstream and forcing the "young" shear-layer at the nozzle exit. At this point Kelvin-Helmholtz instabilities are growing to vortices, transported downstream and interacting with the shock tips which are emanating noise again and closing a feedback loop.

The compressible Navier-Stokes equations were solved, based on a characteristic-type formulation on an orthogonal grid (approx. 300 million grid points) stretched in both the stream-wise and the transverse directions. Along the span-wise direction, periodicity and statistical homogeneity were assumed. To capture the sound generation and propagation processes, spatial discretization was done using a finite difference compact scheme of sixth order and a spectral like method in the periodic direction.The code is parallelized using the Massage Passing Interface (MPI). For the current setup 1020 CPU's were used on a SGI-Altix 4700 with Itanium2 Madison 9M processors. Approx. 12 TB of data were written to disk and 0.5 TB of main memory were used.

In fig. 1 an iso-surface of the vorticity (|rot(u)|) is shown in a three-dimensional sketch with a plane of the dilertation field (div(u)). A dominant noise source seems to be close to the nozzle exit (between the first and second shock-cell). The absolute velocity is presented in fig. 2 which visualizes the persisting shock-cell structure in the jet core.