Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem

Jet Aeroacoustics: Noise Generation Mechanism and Prediction

Progress associated with research in (1) physics and prediction of turbulent mixing noise from supersonic jets, and (2) numerical simulation of supersonic jet noise is reported

Jet Aeroacoustics: Noise Generation Mechanism and Prediction

This report covers the third year research effort of the project. The research work focussed on the fine scale mixing noise of both subsonic and supersonic jets and the effects of nozzle geometry and tabs on subsonic jet noise. In publication 1, a new semi-empirical theory of jet mixing noise from fine scale turbulence is developed. By an analogy to gas kinetic theory, it is shown that the source of noise is related to the time fluctuations of the turbulence kinetic theory. On starting with the Reynolds Averaged Navier-Stokes equations, a formula for the radiated noise is derived. An empirical model of the space-time correlation function of the turbulence kinetic energy is adopted. The form of the model is in good agreement with the space-time two-point velocity correlation function measured by Davies and coworkers. The parameters of the correlation are related to the parameters of the k-epsilon turbulence model. Thus the theory is self-contained. Extensive comparisons between the computed noise spectrum of the theory and experimental measured have been carried out. The parameters include jet Mach number from 0.3 to 2.0 and temperature ratio from 1.0 to 4.8. Excellent agreements are found in the spectrum shape, noise intensity and directivity. It is envisaged that the theory would supercede all semi-empirical and totally empirical jet noise prediction methods in current use

Computation of Large Turbulence Structures and Noise of Supersonic Jets

Our research effort concentrated on obtaining an understanding of the generation mechanisms and the prediction of the three components of supersonic jet noise. In addition, we also developed a computational method for calculating the mean flow of turbulent high-speed jets. Below is a short description of the highlights of our contributions in each of these areas: (a) Broadband shock associated noise, (b) Turbulent mixing noise, (c) Screech tones and impingement tones, (d) Computation of the mean flow of turbulent jets

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA

Numerical and Physical Modeling of the Response of Resonator Liners to Intense Sound and Grazing Flow

Two significant advances have been made in the application of computational aeroacoustics methodology to acoustic liner technology. The first is that temperature effects for discrete sound are not the same as for broadband noise. For discrete sound, the normalized resistance appears to be insensitive to temperature except at high SPL. However, reactance is lower, significantly lower in absolute value, at high temperature. The second is the numerical investigation the acoustic performance of a liner by direct numerical simulation. Liner impedance is affected by the non-uniformity of the incident sound waves. This identifies the importance of pressure gradient. Preliminary design one and two-dimensional impedance models were developed to design sound absorbing liners in the presence of intense sound and grazing flow. The two-dimensional model offers the potential to empirically determine incident sound pressure face-plate distance from resonator orifices. This represents an important initial step in improving our understanding of how to effectively use the Dean Two-Microphone impedance measurement method

Investigating Continual Learning Strategies in Neural Networks

This paper explores the role of continual learning strategies when neural networks are confronted with learning tasks sequentially. We analyze the stability-plasticity dilemma with three factors in mind: the type of network architecture used, the continual learning scenario defined and the continual learning strategy implemented. Our results show that complementary learning systems and neural volume significantly contribute towards memory retrieval and consolidation in neural networks. Finally, we demonstrate how regularization strategies such as elastic weight consolidation are more well-suited for larger neural networks whereas rehearsal strategies such as gradient episodic memory are better suited for smaller neural networks

Benchmark problems and solutions

The scientific committee, after careful consideration, adopted six categories of benchmark problems for the workshop. These problems do not cover all the important computational issues relevant to Computational Aeroacoustics (CAA). The deciding factor to limit the number of categories to six was the amount of effort needed to solve these problems. For reference purpose, the benchmark problems are provided here. They are followed by the exact or approximate analytical solutions. At present, an exact solution for the Category 6 problem is not available