Victoria Suponitsky

Linear and nonlinear mechanisms of sound radiation by instability waves in subsonic jets

Linear and nonlinear mechanisms of sound generation in subsonic jets are investigated by numerical simulations of the compressible Navier–Stokes equations. The main goal is to demonstrate that low-frequency waves resulting from nonlinear interaction between primary, highly amplified, instability waves can be efficient sound radiators in subsonic jets. The current approach allows linear, weakly nonlinear and highly nonlinear mechanisms to be distinguished. It is demonstrated that low-frequency waves resulting from nonlinear interaction are more efficient in radiating sound when compared to linear instability waves radiating directly at the same frequencies. The results show that low-frequency sound radiated predominantly in the downstream direction and characterized by a broadband spectral peak near St = 0.2 can be observed in the simulations and described in terms of the nonlinear interaction model. It is also shown that coherent low-frequency sound radiated at higher angles to the jet axis (? = 60°–707°) is likely to come from the interaction between two helical modes with azimuthal wavenumbers n = ±1. High-frequency noise in both downstream and side-line directions seems to originate from the breakdown of the jet into smaller structures

The generation of streaks and hairpin vortices from a localized vortex disturbance embedded in unbounded uniform shear flow

The similarity of the coherent structures (streaks and hairpin vortices) naturally occurring in different fully developed bounded turbulent shear flows as well as in transitional flows suggests the existence of a basic mechanism responsible for the formation of these structures, under various base flow conditions. The common elements for all such flows are the shear of the base flow and the presence of a localized vortical disturbance. The objective of the present numerical study is to examine the capability of a simple model of interaction, between a localized vortical disturbance and laminar uniform unbounded shear flow, to reproduce the generation mechanism and characteristics of the coherent structures that naturally occur in turbulent bounded shear flows. The effects of the disturbance ‘localized character’ in the stream-wise and spanwise directions as well as its initial orientation relative to the base flow are investigated by using several geometries of the initial disturbance. The results demonstrate that a small-amplitude initial disturbance (linear case) eventually evolves into a streaky structure independent of its initial geometry and orientation, whereas, a large-amplitude disturbance (strongly nonlinear case) evolves into a hairpin vortex (or a packet of hairpin vortices) independent of its geometry over a wide range of the initial disturbance orientations. The main nonlinear effects are: (i) self-induced motion, which results in the movement of the vortical structure relative to the base flow and the destruction of its streamwise symmetry, and (ii) the alignment of the vortical structure with the vorticity lines. This is unlike the linear case, where there is a strong deviation of the vorticity vector from the direction of the vortical structure. Qualitatively, the disturbance evolution is sufficiently independent of its initial geometry, whereas the associated quantitative characteristics, i.e. inclination angle, centre and strength (which is governed by the transient growth mechanism), strongly depend on the disturbance geometry. The Reynolds number is found to have a negligible effect on the kinematics of the vortical structure, but does have a significant effect on its transient growth. Finally, the formation of the asymmetric hairpin vortex, due to minor spanwise asymmetries of the initial disturbance, is demonstrated.

DNS of fully turbulent jet flows in flight conditions including a canonical nozzle

Direct numerical simulations are conducted of a canonical nozzle/jet conflguration. The ∞ow exiting the nozzle into a laminar co-∞ow is fully turbulent and serves as a well deflned turbulent inlet condition for the study of sound radiation from fully turbulent jets. The sound radiation from this conflguration is studied for three subsonic jet Mach numbers and varying co-∞ows. The target Reynolds number, based on jet exit centreline velocity and nozzle diameter is Rej = 7; 500 for all cases. Pressure power spectral densities (PSD) obtained from within the hydrodynamic fleld show that most of the energy is contained in the axisymmetric mode, although the PSD amplitudes of azimuthal modes with m > 0 exhibit very similar energy levels over the entire spectrum when considering locations within the jet shear layer. In the acoustic fleld, the amplitudes of the spectra at small angles with respect to the streamwise axis are considerably higher than at large angles, in particular for low frequencies. In contrast to the PSDs from the hydrodynamic fleld, the energy content in the acoustic fleld decreases rapidly for higher mode numbers. Contours of pressure in the frequency domain suggest the presence of trailing-edge noise for selected azimuthal modes and frequencies. The directivity of the overall sound pressure level flts the expected directivity behaviour of subsonic jets. An unexpected result is that the velocity scaling of mean square far-fleld pressure is found to be close to u 4 over the range of Mach numbers considered here.

Re-engineering a DNS code for high-performance computation of turbulent flows

Software re-engineering of a direct numerical simul ation (DNS) code for highperformance computation of turbulent flows has been carried out. The SBLI parallel highorder finite-difference code was primarily develope d for simulation of a shock wave interacting with a turbulent boundary layer developing over a bump geometry. The code has proved to be very adaptable with its variants being used for a wide range of turbulent flows, including transonic cavity flows, turbulent spot in teractions and separation bubbles on an airfoil at incidence. To bring these recent develop ments back to a unique version, the code has been re-engineered, applying modern software engineering concepts and techniques, including modular design and concurrent version control, as well as a comprehensive approach to verification and validation for both fu nctional tests and benchmark cases that were designed to exercise key elements of the code. Furthermore, the code has been upgraded from a quasi-3D curvilinear to a fully-3D curvilinear grid treatment. A new version has shown good agreements with theoretical and experimental data, and other published results. To improve the efficiency when t he code is applied to simpler geometries, a pre-compiler is developed and used. Finally, this re-engineered SBLI code has demonstrated very good parallel scalability.

Nonlinear mechanisms of sound radiation in a subsonic jet

Nonlinear mechanisms of sound generation from subsonic jets are investigated by direct numerical simulations. The main goal is to obtain further physical insight into a recently proposed nonlinear mechanism, based on the idea that nonlinear interaction between two primary instability waves results in a difierence frequency mode that can be an e‐cient sound radiator in subsonic jets. The current approach allows linear, weakly nonlinear and highly nonlinear (turbulent) mechanisms to be isolated. The results show that broadband low-frequency sound radiated predominantly in the downstream direction can be attributed to the large-scale structures and described in terms of the nonlinear interaction model. Additionally, a signiflcant part of the low-frequency sound radiated in the side-line direction is likely to come from the interaction between two helical modes with azimuthal numbers n = §1. High-frequency noise in both downstream and side-line directions seems to originate from the breakdown of the jet into smaller structures with ultimate transition into turbulence after the end of the potential core.

DNS of a canonical compressible nozzle flow

Simulations of subsonic free jets can only compute noise contributions from sources connected with the large-scale structures occurring close to the potential core region and their breakdown to fine-scale turbulence (Freund, 2001). To account for additional noise sources associated with fine-scale turbulence in the initial shear layers and the interaction of flow with the nozzle lip, the nozzle must be included in the simulation and, moreover, the flow inside the nozzle must be fully turbulent. Previous work including realistic nozzle geometries in the simulation failed to achieve fully turbulent flow at the nozzle exit (e.g. (Uzun and Hussaini, 2009)). To overcome the difficulties encountered when using realistic geometries, the problem can be simplified by using a canonical nozzle with well defined turbulent exit conditions. The ultimate goal of this ongoing study is to use a round pipe with sufficient length as a canonical nozzle for direct noise computations of jets. This paper focuses on whether the flow conditions at the pipe exit can be used as well defined turbulent upstream conditions for such calculations. From this perspective the following issues are of interest: (i) the effect of the inflow boundary conditions on the length of the pipe required to obtain fully developed turbulent pipe flow (development length); and (ii) the effect of compressibility on the temperature field. The former is needed to specify the length of the nozzle for full jet calculations, while the latter is related to the correct prescription of the ambient temperature. The spatially developing pipe flow using a turbulent inflow generation was chosen for this study instead of the alternative recycling or precursor simulation techniques because it avoids introducing an undesired artificial recycling frequency, the need to impose a pressure gradient, and minimizes the computational cost and memory requirements.

Localized Disturbances and Their Relation to Turbulent Shear Flows

The resemblance among coherent structures naturally occurring in fully developed bounded turbulent shear flows, transitional flows and free shear layers suggests the existence of a basic single mechanism responsible for the formation of the structures under various base flow conditions. The common elements in all such flows are the shear of the base flow and the presence of a localized vortical disturbance within this shear. The objective of the present study is to examine the capability of a simple model of interaction between a localized vortical disturbance and the surrounding ‘simple’ laminar shear flow where the velocity vector is (at most) a linear function of the coordinates, to reproduce the generation mechanism and characteristics of the coherent structures that naturally occur in turbulent bounded shear flows (counter-rotating vortex pairs and hairpin vortices) and free shear layers (‘rib vortices’). The research combines numerical, experimental and theoretical approaches. Numerically, we follow the evolution of a localized vortical disturbance in an unbounded pure shear flow. The results demonstrate that a small amplitude initial disturbance eventually evolves into a streaky structure independent of its initial geometry and orientation, whereas, a large amplitude disturbance evolves into a hairpin vortex. The main nonlinear eect is the self-induced motion, which results in the movement of the vortical structure relative to the base flow. Experimentally, 2D flow visualization and a Holographic Particle Image Velocimetry (HPIV) system are employed to study the evolution of coherent structures artificially generated in a plane Poiseuille air flow. The 2D visualization demonstrates (in accordance with the CFD results) that a small amplitude disturbance evolves into a counter-rotating vortex pair, and if the amplitude is suciently large a train of hairpin vortices is formed. The HPIV method is utilized to obtain the instantaneous topology of the hairpin vortex and its associated 3D distributions of the two (streamwise and spanwise) velocity components as well as the corresponding wall-normal vorticity. The quantitative distribution of the latter (when properly scaled) agrees well with the CFD results, further supporting our above mentioned view of a basic universal mechanism. Finally, the generation of an intensified counter-rotating vortex pair from a localized vortex disturbance in plane stagnation flow is studied theoretically, following the temporal evolution of its fluid impulse. Good agreement with complementary CFD results is obtained.

Evolution of Localized Vortex Disturbance in Uniform Shear Flow: Numerical Investigation

The possibility that a simple model of interaction between a localized vortical disturbance and laminar uniform unbounded shear flow is capable of reproducing the generation mechanism and characteristics of coherent structures naturally occurring in wall bounded turbulent flows is examined numerically. Gaussian and toroidal vortices are used as the initial disturbances. The concentrated vorticity field of the Gaussian vortex is defined by a single length scale 6, which is assumed to be much smaller than the characteristic scale of the base flow. The toroidal disturbance is defined by two length scales r 0 and δ, corresponding to the radius and thickness of the torus, respectively

Application of a truncated Navier-Stokes approach to study sound radiation from subsonic jets

Nonlinear and linear mechanisms of sound radiation by instability waves in subsonic jets are studied by a truncated Navier-Stokes equations approach. Particular attention is given to the model problems of a single-frequency in∞ow forcing (linear mechanism) and flnite amplitude two-frequency in∞ow forcing (nonlinear mechanism) at difierent subsonic Mach numbers. The results showed that while at high subsonic Mach numbers (M = 0:9) both mechanisms play a vital role in the downstream sound generation, the contribution from the linear mechanism to the overall sound decreases signiflcantly with the reduction of the jet Mach number. For sound radiation at shallow angles to the downstream jet axis, a higher e‐ciency of the nonlinear mechanism can be explained by an analysis of the pressure spectra with a focus on the part with a supersonic phase velocity. Such an analysis on its own, however, fails to explain sound radiation observed also at higher angles to the jet axis in the case of two-frequency forcing (i.e. the nonlinear mechanism). The ability of the current approach to reproduce key features of subsonic jets acoustic spectra (a broadband low-frequency peak at St … 0:2 in particular) is demonstrated by subjecting isothermal and hot jets to flnite amplitude broadband forcing at difierent Mach numbers. The cold jet was found to be signiflcantly noisier compared with the isothermal and hot jets at the same acoustic Mach number.