Ching Y. Loh

Near Field Screech Noise Computation for an Underexpanded Supersonic Jet by the CE/SE Method

The space-time conservation element and solution element (CE/SE) method is employed to numerically study the near-field axisymmetric screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. For the computed cases, corresponding to fully expanded Mach numbers of 1.10, 1.15 and 1.19, the self-sustained feedback loop is automatically established. The computed shock-cell structure, acoustic wave length, screech tone frequencies, and sound pressure levels are in good agreement with experimental results.

Computing Axisymmetric Jet Screech Tones using Unstructured Grids

The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

Jet Screech Noise Computation

The near-field screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle is simulated numerically. The self-sustained feedback loop is automatically established in the simulation. The computed shockcell structure, acoustic wave length, screech-tone frequencies, and sound pressure levels in the near field are in good agreement with existing experimental results. I. Introduction J ET noise is an important and still challenging topic in aeroacoustics. Many of its aspects are of primary practical importance, and the associated complicated physical phenomena are the topic of many experimental and theoretical investigations. In Refs. 1‐4, a comprehensive discussion and further references are provided. Under/overexpanded supersonic jets emit mixing noise, broadband shock-associated noise, as well as screech tones under certain conditions. The mixing noise is directly associated with large-scale structures, or instability waves, in the jet shear layer, and the broadband shock-associated noise is caused by the interaction of these waves with the shock-cell structure in the jet core. The screech tones arise due to a feedback loop involving the large-scale structures developing in the jet shear layer, their interaction with the jetcore shock-cell structure producing upstream propagating acoustic waves, and regeneration of the large-scale structures at, or in the vicinity of, the nozzle lip. This feedback loop leading to screech tones is sensitive to small changes in the system conditions, and the understanding of the phenomena to date is based mostly on experimental observations. 5−9 Screech is of particular interest not only because of general noise-reduction concerns, but also because of po

Noise Computation of a Shock-Containing Supersonic Axisymmetric Jet by the CE/SE Method

The space-time conservation element solu- tion element (CE/SE) method (l) is em- ployed to numerically study the near-field of a typical under-expanded jet. For the computed case-a circular jet with Mach number Mj = 1.19-the shock-cell struc- ture is in good agreement with experimen- tal results (2, 31. The computed noise field is in general agreement with the experi- ment, although further work is needed to properly close the screech feedback loop.

Computation of Feedback Aeroacoustic System by the CE/SE Method

It is well known that due to vortex shedding in high speed flow over cutouts, cavities, and gaps, intense noise may be generated. Strong tonal oscillations occur in a feedback cycle in which the vortices shed from the upstream edge of the cavity convect downstream and impinge on the cavity lip, generating acoustic waves that propagate upstream to excite new vortices. Numerical simulation of such a complicated process requires a scheme that can : (a) resolve acoustic waves with low dispersion and numerical dissipation, (b) handle nonlinear and discontinuous waves (e.g. shocks), and (c) have an effective (near field) non-reflecting boundary condition (NRBC). The new space time conservation element and solution element method, or CE/SE for short, is a numerical method that meets the above requirements [1–4]. A detailed description of the 2-D CE/SE Euler scheme can be found in [1, 2], only a brief sketch is given here.

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However, even with these up-to-date improvements, the basic upwind scheme is still plagued by the socalled “pathological behaviors,” e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the method.

Computation of an Underexpanded 3-D Rectangular Jet by the CE/SE Method

Recently, an unstructured three-dimensional space-time conservation element and solution element (CE/SE) Euler solver was developed. Now it is also developed for parallel computation using METIS for domain decomposition and MPI (message passing interface). The method is employed here to numerically study the near-field of a typical 3-D rectangular under-expanded jet. For the computed case-a jet with Mach number Mj = 1.6. with a very modest grid of 1.7 million tetrahedrons, the flow features such as the shock-cell structures and the axis switching, are in good qualitative agreement with experimental results.

Aeroacoustics Computation for Nearly Fully Expanded Supersonic Jets Using the CE/SE Method

In this paper, the space-time conservation element solution element (CE/SE) method is tested in the classical axisymmetric jet instability problem, rendering good agreement with the linear theory. The CE/SE method is then applied to numerical simulations of several nearly fully expanded axisymmetric jet flows and their noise fields and qualitative agreement with available experimental and theoretical results is demonstrated.

A Robust Absorbing Boundary Condition for Compressible Flows

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper [2] by the author. The absorbing NRBC technique is based on a first principle of nonreflecting, which contains the essential physics that a plane wave solution [1] (Fourier mode) of the Euler equations remains intact across the boundary. When combined with the hyperbolic conservation laws, the NRBC is simple and robust, provided the numerical scheme maintains locally a solution of second order (or higher) accuracy near the boundary. Several numerical examples in multi-dimensional spaces are illustrated to demonstrate its robustness in practical computations.

Near-Field Noise Computation for a Supersonic Circular Jet

Abstract A fully expanded, high-Reynolds-number, su-personic circular jet of Mach number 1 . 4 issimulated, using a 3-D finite-volume Navier-Stokes solver, with emphasis on the near fieldnoise. The numerical results are generallyin good agreement with existing experimentalfindings. 1 Introduction The reductionof aircraftnoise is an importanttechno-logical challenge as a result of the environmentallimita-tions and economical consequences of airport noise pol-lution. Jet noise, a major noise component for moderncommercial aircraft engines, consists of turbulent mix-ing noise and, in the case of imperfectly expanded su-personic jets, broadbandshock-associated noise (as wellas, discrete screech tones under certain circumstances).Jet noise has been a vital part of aeroacoustics since theearly 1950s and continues to be a topic of many exper-imental and theoretical investigations; Refs. [1–3] pro-vide a comprehensive discussion and further references.Arapidadvanceinitsunderstandinghasoccurredduringthe last decade,perhapsin conjunctionwith the develop-ment of computational aeroacoustics (CAA), as well asbetter measurement techniques. The issues, challenges,and contributions of CAA are discussed in Refs. [4–6],and the Rayleigh-scattering technique [7–9] is an exam-ple of advances in experimental methods for high-speedjets.For supersonic jet mixing noise, it is generally agreedthat there are two different sources [10–12]. One is as-sociatedwith the convection/evolutionoflarge-scaletur-bulence structures in the jet and which produces intensesound propagating downstream at angles close to the jetaxis. Traditionally, this has been referred to as eddyMach wave radiation. The other noise source is asso-ciated with the fine scale turbulence in the jet shear flowandwhichproducessoundpropagatingpredominantlyinthe lateral (90