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NASA NTRS2021

The Near and Intermediate Wake of a Thick Flat Plate with a Circular Trailing Edge

The near and intermediate wake regions of a thick flat plate with a circular trailing edge (TE) are investigated with a direct numerical simulation (DNS). The focus is on the region x/D < 43.0(D is the diameter of the TE). The upper and lower separating boundary layers are both turbulent and are statistically identical; the resulting wake is symmetric in the mean. The present study is a continuation of an earlier investigation (Case AX). The earlier research dealt with shed vortex structure, in particular the persistence of the coherence of these vortices with increasing streamwise distance (except for infrequent, random disruption/rupture). In addition, across-centerline movement (ACM)of shed vortices, that is prevalent past x/D = 20.0 in a cylinder case at a comparable Reynolds number, was found to be essentially absent in Case AX. In the present investigation, an underlying cause for the occasional disruption/rupture of shed vortices is explored. Strong interactions between subsequent shed vortices in the trailing edge region is found to be an important contributor to this phenomenon. The distributions of phase-averaged streamwise and cross-stream components of intensity and the corresponding budget terms in the near wake are compared with those obtained in the intermediate wake here. In addition, the main features of the distribution of the phase-averaged velocity pressure-gradient term are compared with those of the production term, for the two intensity components. Except for a change in sign, the important features in the two budget terms are qualitatively similar for both components.

Direct Numerical Simulations of Flat Plate Wake↗

NASA NTRS1991

Proper orthogonal decomposition based turbulence modeling

The proper orthogonal decomposition is utilized to provide one mode estimates of various turbulence quantities in the near-wall region of the turbulent boundary layer. The experimental data of Herzog (1986) and the direct numerical simulation (DNS) results of Zang (1991) proved the two-point correlation tensor. The correlation tensor is then used as the kernel in the integral eigenvalue problem from which the proper orthogonal modes are obtained. The one mode estimates of the turbulent kinetic energy, dissipation, and triple moments all exhibit the proper asymtotic behavior near the wall. As a validation test, a model for the triple moments is developed and its near-wall behavior is studied. This information can then be used to obtain an estimate of the damping function near the wall, which is then compared to known existing behavior. Since this is an initial investigation, the streamwise and spanwise dependence is surpressed and only the wall normal direction (y+) behavior of various turbulence statistics near the wall is studied. Before examining one mode estimates of the triple moments and the dissipation (on which the model is based), various second order moments are examined. If these do not exhibit the proper behavior near the wall (as discussed by Speziale et al 1990) it does not seem reasonable to expect the one mode estimate of the triple moment and dissipation to have the right behavior. Only the results obtained using the experimental data of Herzog are discussed since the results from the simulations of Zang exhibit similar behavior as discussed above.

Glauser, Mark N.↗

NASA NTRS2022

Interaction of a Tunnel-like Acoustic Disturbance Field with a Blunt Cone Boundary Layer at Mach 8

The existing measurements of laminar-to-turbulent transition over circular cones in conventional (i.e., “noisy”) hypersonic wind tunnels have established that the transition location moves downstream when the nose radius is increased from zero. However, this initially downstream movement slows down and ultimately reverses beyond a critical value of the nose radius, and may be related to external forcing in the form of freestream disturbances and/or surface roughness. To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, hypersonic boundary-layer receptivity to broadband freestream acoustic disturbances from the nozzle wall of a digital conventional wind tunnel is investigated by both direct numerical simulations (DNS) and modal and nonmodal stability analysis. A Mach 8 flow over a 7 deg half-angle cone with a nose radius of 𝑅 𝑛 = 5.2mm and freestream Reynolds number of 12.2 × 10 6 m -1 is considered. The results show that the broadband tunnel noise in the free stream of a convectional hypersonic wind tunnel (i.e., outside of the nozzle-wall turbulent boundary layer) can be well represented by an acoustic model with an ansatz of slow acoustic waves. With successful calibration of the model parameters against the precursor tunnel DNS, such an acoustic ansatz can successfully reproduce both the frequency-wavenumber spectra and the temporal evolution of the broadband tunnel noise radiated from the nozzle wall. Additionally, the DNS of the Mach 8 blunt cone with tunnel-like acoustic input above the bow shock showed that the spectra of wall-pressure and heat-transfer fluctuations recovers the signature of the axisymmetric waves predicted by the nonmodal analysis. Furthermore, the azimuthal wavenumber and frequency spectrum of the temperature fluctuations as a function of the wall-normal distance show higher amplitudes for three-dimensional waves above the boundary-layer edge. The numerical schlieren contours show the inclined structures commonly observed in blunt cone experiments, demonstrating that they correspond to three-dimensional structures due to freestream disturbances in the presence of an entropy layer.

Boundary-layer transition↗

NASA NTRS1987

EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it

It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.

Bertoglio, J. P.↗

NASA NTRS1993

The production of premixed flame surface area in turbulent shear flow

In the present work, we use three-dimensional Direct Numerical Simulation (DNS) of premixed flames in turbulent shear flow to characterize the effect of a mean shear motion on flame surface production. The shear is uniform in the unburnt gas, and simulations are performed for different values of the mean shear rate, S. The data base is then used to estimate and compare the different terms appearing in the Sigma-equation as a function of S. The analysis gives in particular the relative weights f the turbulent flow and mean flow components, a(sub T) and A(sub T), of the flame surface production term. This comparison indicates whether the dominant effects of a mean flow velocity gradient on flame surface area are implicit and scale with the modified turbulent flow parameters, kappa and epsilon, or explicit and scale directly with the rate of deformation.

Trouve, A.↗

NASA NTRSDate not supplied

Understanding the Role of CFD, Including RANS, DES, LES and DNS, in Hypersonic Propulsion Design and Analysis

Computational fluid dynamics (CFD) has matured to the point where it is becoming ubiquitous in the design and analysis of aerospace vehicles and their propulsion systems. The current state-of-the-art of CFD in hypersonic propulsion design and analysis as well as a historical perspective of its development over the last 50 years is presented. The current state-of-the-art for the design of finite rate chemically reacting turbulent hypersonic flow is shown to currently be Reynolds averaged simulations (RAS) where the Reynolds averaged Navier-Stokes (RAS) equations are solved to obtain steady state solutions. An overview of the physical modeling techniques employed by RAS for the simulation of hypersonic chemically reacting flow are presented. However, scale resolving simulation techniques, such as detached eddy simulation (DES), large eddy simulations (LES), hybrid RAS/LES and direct numerical simulations (DNS), are becoming becoming powerful tools for point design analysis. One example of such a scale resolving technique, hybrid RAS/LES, will be briefly described as well as how it can be used to help address model form uncertainties in RAS.

Hypersonic↗

NASA NTRS2015

DNS/LES Simulations of Separated Flows at High Reynolds Numbers

Direct numerical simulations (DNS) and large-eddy simulations (LES) simulations of flow through a periodic channel with a constriction are performed using the dynamic Smagorinsky model at two Reynolds numbers of 2800 and 10595. The LES equations are solved using higher order compact schemes. DNS are performed for the lower Reynolds number case using a fine grid and the data are used to validate the LES results obtained with a coarse and a medium size grid. LES simulations are also performed for the higher Reynolds number case using a coarse and a medium size grid. The results are compared with an existing reference data set. The DNS and LES results agreed well with the reference data. Reynolds stresses, sub-grid eddy viscosity, and the budgets for the turbulent kinetic energy are also presented. It is found that the turbulent fluctuations in the normal and spanwise directions have the same magnitude. The turbulent kinetic energy budget shows that the production peaks near the separation point region and the production to dissipation ratio is very high on the order of five in this region. It is also observed that the production is balanced by the advection, diffusion, and dissipation in the shear layer region. The dominant term is the turbulent diffusion that is about two times the molecular dissipation.

Balakumar, P.↗

NASA NTRS1996

The effects of complex chemistry on triple flames

The structure, ignition, and stabilization mechanisms for a methanol (CH3OH)-air triple flame are studied using Direct Numerical Simulations (DNS). The methanol (CH3OH)-air triple flame is found to burn with an asymmetric shape due to the different chemical and transport processes characterizing the mixture. The excess fuel, methanol (CH3OH), on the rich premixed flame branch is replaced by more stable fuels CO and H2, which burn at the diffusion flame. On the lean premixed flame side, a higher concentration of O2 leaks through to the diffusion flame. The general structure of the triple point features the contribution of both differential diffusion of radicals and heat. A mixture fraction-temperature phase plane description of the triple flame structure is proposed to highlight some interesting features in partially premixed combustion. The effects of differential diffusion at the triple point add to the contribution of hydrodynamic effects in the stabilization of the triple flame. Differential diffusion effects are measured using two methods: a direct computation using diffusion velocities and an indirect computation based on the difference between the normalized mixture fractions of C and H. The mixture fraction approach does not clearly identify the effects of differential diffusion, in particular at the curved triple point, because of ambiguities in the contribution of carbon and hydrogen atoms' carrying species.

Echekki, T.↗

NASA NTRS2000

Towards LES Models of Jets and Plumes

As pointed out by Rodi standard integral solutions for jets and plumes developed for discharge into infinite, quiescent ambient are difficult to extend to complex situations, particularly in the presence of boundaries such as the sea floor or ocean surface. In such cases the assumption of similarity breaks down and it is impossible to find a suitable entrainment coefficient. The models are also incapable of describing any but the most slowly varying unsteady motions. There is therefore a need for full time-dependent modeling of the flow field for which there are three main approaches: (1) Reynolds averaged numerical simulation (RANS), (2) large eddy simulation (LES), and (3) direct numerical simulation (DNS). Rodi applied RANS modeling to both jets and plumes with considerable success, the test being a match with experimental data for time-averaged velocity and temperature profiles as well as turbulent kinetic energy and rms axial turbulent velocity fluctuations. This model still relies on empirical constants, some eleven in the case of the buoyant jet, and so would not be applicable to a partly laminar plume, may have limited use in the presence of boundaries, and would also be unsuitable if one is after details of the unsteady component of the flow (the turbulent eddies). At the other end of the scale DNS modeling includes all motions down to the viscous scales. Boersma et al. have built such a model for the non-buoyant case which also compares well with measured data for mean and turbulent velocity components. The model demonstrates its versatility by application to a laminar flow case. As its name implies, DNS directly models the Navier-Stokes equations without recourse to subgrid modeling so for flows with a broad spectrum of motions (high Re) the cost can be prohibitive - the number of required grid points scaling with Re(exp 9/4) and the number of time steps with Re(exp 3/4). The middle road is provided by LES whereby the Navier-Stokes equations are formally filtered with the filter chosen to only exclude the smallest turbulent motions. If successful, LES should provide much of the detail available to DNS but at more bearable cost. Fatica et al. in comparing LES with DNS for a low Reynolds number jet showed that the LES could simulate the temporally evolving behavior including growth of the jet thickness. It is the intention of this report to explore the application of an LES model to jets and plumes. As always, before tackling complex situations, the model must be tested for the simplest of cases and so we address only two, a non-buoyant axisymmetric jet issuing steadily from an orifice into a semi-infinite stationary environment and a buoyant jet in the same environment. The work is a continuation of Basu and Mansour.

Webb, A. T.↗

NASA NTRS1993

Numerical simulation of shock/turbulent boundary layer interaction

Most flows of aerodynamic interest are compressible and turbulent. However, our present knowledge on the structures and mechanisms of turbulence is mostly based on incompressible flows. In the present work, compressibility effects in turbulent, high-speed, boundary layer flows are systematically investigated using the Direct Numerical Simulation (DNS) approach. Three-dimensional, time-dependent, fully nonlinear, compressible Navier-Stokes equations were numerically integrated by high-order finite-difference methods; no modeling for turbulence is used during the solution because the available resolution is sufficient to capture the relevant scales. The boundary layer problem deals with fully-turbulent compressible flows over flat geometries. Apart from its practical relevance to technological flows, turbulent compressible boundary layer flow is the simplest experimentally realizable turbulent compressible flow. Still, measuring difficulties prohibit a detailed experimental description of the flow, especially in the near-wall region. DNS studies provide a viable means to probe the physics of compressible turbulence in this region. The focus of this work is to explore the paths of energy transfer through which compressible turbulence is sustained. The structural similarities and differences between the incompressible and compressible turbulence are also investigated. The energy flow patterns or energy cascades are found to be directly related to the evolution of vortical structures which are generated in the near-wall region. Near-wall structures, and mechanisms which are not readily accessible through physical experiments are analyzed and their critical role on the evolution and the behavior of the flow is documented extensively.

Biringen, Sedat↗

NASA NTRS2020

Direct Numerical Simulations of Acoustic Disturbances in Various Rectangular Nozzle Configurations

We perform Direct Numerical Simulations (DNS) to study the acoustic freestream disturbances radiating from the turbulent boundary layers along the contoured nozzle walls of a hypersonic wind tunnel with a rectangular test section. To begin with, the effects of the spanwise end walls are suppressed by confining the spanwise computational domain to a finite segment of the overall nozzle cross section and by imposing periodic boundary conditions across that spanwise domain. Besides providing a building-block configuration to reveal par- tial effects of the enclosed acoustic environment within the wind tunnel, these computations serve as a stepping stone toward the goal of fully-3D computations including the nozzle end walls. Building upon the earlier simulations of Deegan et al. (2018), we show that the computed acoustic characteristics in the spanwise periodic simulations are insensitive to changes in the grid resolution parameters (e.g., x+ and z+). This is relative to the previous simulations that involved a coarser resolution in the streamwise and wall-normal directions, especially up- stream of the test section. Furthermore, we outline a comparison of the pressure fluctuations induced by the turbulent boundary layers over the contoured nozzle walls and several other calculations involving boundary layers over a single flat plate at nearly the same value of the edge Mach number. We also show the impact of having only one turbulent boundary layer instead of two within the computational setup. Various flow statistics, including the first and second moments of the unsteady flow field, are computed for the different flow configurations. Good comparisons of the statistics of the nozzle-wall boundary-layer turbulence and of the freestream acoustic disturbances between the simulations of coarser and finer grids confirms DNS procedure, but also the insensitivity of noise characteristics t section to the inflow turbulence generation technique.

Hildebrand, Nathaniel↗

NASA NTRS1996

A new methodology to determine kinetic parameters for one- and two-step chemical models

In this paper, a new methodology to determine kinetic parameters for simple chemical models and simple transport properties classically used in DNS of premixed combustion is presented. First, a one-dimensional code is utilized to performed steady unstrained laminar methane-air flame in order to verify intrinsic features of laminar flames such as burning velocity and temperature and concentration profiles. Second, the flame response to steady and unsteady strain in the opposed jet configuration is numerically investigated. It appears that for a well determined set of parameters, one- and two-step mechanisms reproduce the extinction limit of a laminar flame submitted to a steady strain. Computations with the GRI-mech mechanism (177 reactions, 39 species) and multicomponent transport properties are used to validate these simplified models. A sensitivity analysis of the preferential diffusion of heat and reactants when the Lewis number is close to unity indicates that the response of the flame to an oscillating strain is very sensitive to this number. As an application of this methodology, the interaction between a two-dimensional vortex pair and a premixed laminar flame is performed by Direct Numerical Simulation (DNS) using the one- and two-step mechanisms. Comparison with the experimental results of Samaniego et al. (1994) shows a significant improvement in the description of the interaction when the two-step model is used.

Mantel, T.↗

NASA NTRS2000

A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

Constantinescu, G.S.↗

NASA NTRS2017

Shed Vortex Structure and Phase-Averaged Velocity Statistics in Symmetric/Asymmetric Turbulent Flat Plate Wakes

The near wake of a flat plate is investigated via direct numerical simulations (DNS). Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large theta divided by D (sub TE) values (theta is the boundary layer momentum thickness towards the end of the plate and D (sub TE) is the trailing edge thickness). In the present study the emphasis is on relatively thick plates with circular trailing edges (CTE) resulting in theta divided by D values less than one (D is the plate thickness and the diameter of the CTE), and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 x 10 (sup 6) and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor 1.27 weaker in terms of peak phase-averaged spanwise vorticity at first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x divided by D) that occurs nears the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x divided by D. Both these effects are examined in detail and the important contributors are identified.

direct numerical simulations↗

NASA NTRS2012

A Posteriori Study of a DNS Database Describing Super critical Binary-Species Mixing

Currently, the modeling of supercritical-pressure flows through Large Eddy Simulation (LES) uses models derived for atmospheric-pressure flows. Those atmospheric-pressure flows do not exhibit the particularities of high densitygradient magnitude features observed both in experiments and simulations of supercritical-pressure flows in the case of two species mixing. To assess whether the current LES modeling is appropriate and if found not appropriate to propose higher-fidelity models, a LES a posteriori study has been conducted for a mixing layer that initially contains different species in the lower and upper streams, and where the initial pressure is larger than the critical pressure of either species. An initially-imposed vorticity perturbation promotes roll-up and a double pairing of four initial span-wise vortices into an ultimate vortex that reaches a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equation set uses transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid scale (SGS) fluxes, a new SGS term that is a pressure correction in the momentum equation. This additional term results from filtering of Direct Numerical Simulation (DNS) equations, and represents the gradient of the difference between the filtered pressure and the pressure computed from the filtered flow field. A previous a priori analysis, using a DNS database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of high-densitygradient magnitude regions that populated the entire flow; in the study, models were proposed for the SGS fluxes as well as this new term. In the present study, the previously proposed constantcoefficient SGS-flux models of the a priori investigation are tested a posteriori in LES, devoid of or including, the SGS pressure correction term. The present pressure-correction model is different from, and more accurate as well as less computationally intensive than that of the a priori study. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC), in conjunction with the Yoshizawa (YO) model for the trace, the Gradient (GRC) and the Scale Similarity (SSC) models, all exercised with the a priori study constant coefficients calibrated at the transitional state. The LES comparison is performed with the filtered- and-coarsened (FC) DNS, which represents an ideal LES solution. Expectably, an LES model devoid of SGS terms is shown to be considerably inferior to models containing SGS effects. Among models containing SGS effects, those including the pressure-correction term are substantially superior to those devoid of it. The sensitivity of the predictions to the initial conditions and grid size are also investigated. Thus, it has been discovered that, additional to the atmospheric-pressure models currently used, a new model is necessary to simulate supercritical-pressure flows. This model depends on the thermodynamic characteristics of the chemical species involved.

Bellan, Josette↗

NASA NTRS2018

Direct Numerical Simulation of Acoustic Disturbances in the Rectangular Test Section of a Hypersonic Wind Tunnel

Direct numerical simulations (DNS) of the full-scale rectangular nozzle of a hypersonic wind tunnel are conducted to study the acoustic freestream fluctuations radiating from turbulent boundary layers (TBLs) along the nozzle walls. The nozzle geometry and the flow conditions of the DNS match those of the NASA 20-Inch Mach 6 Tunnel, and the DNS has been completed for a domain without spanwise sidewall boundary conditions. The turbulent boundary layer parameters based on the DNS compare well with those derived from Reynolds Averaged Navier-Stokes (RANS) calculations as well as with the predictions based on Pate’s correlation. A similarly good comparison is observed for both the Mach number distribution and the Reynold’s stresses obtained from the DNS and RANS calculations, respectively. Various characteristics of the acoustic pressure fluctuations within the inviscid core of the nozzle flow are compared with those associated with a single flat plate at a similar freestream Mach number. The frequency spectrum and bulk propagation speeds match well between the nozzle and the flat plate, but the rms pressure fluctuation is higher for the nozzle configuration, likely due to the combined effect of acoustic radiation from the top and bottom walls. Spatial contours of the two-point correlation coefficient display elliptical tails with approximately equal but opposite angles corresponding to the preferred directionality of acoustic structures radiated from both walls. Future work will focus on DNS of the full nozzle configuration, including the effects of the nozzle side walls.

Deegan, Cole P.↗

NASA NTRS2013

Numerical Study of Pressure Fluctuations due to a Mach 6 Turbulent Boundary Layer

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a Mach 6 turbulent boundary layer with nominal freestream Mach number of 6 and Reynolds number of Re(sub t) approx. =. 464. The emphasis is on comparing the primarily vortical pressure signal at the wall with the acoustic freestream signal under higher Mach number conditions. Moreover, the Mach-number dependence of pressure signals is demonstrated by comparing the current results with those of a supersonic boundary layer at Mach 2.5 and Re(sub t) approx. = 510. It is found that the freestream pressure intensity exhibits a strong Mach number dependence, irrespective of whether it is normalized by the mean wall shear stress or by the mean pressure, with the normalized fluctuation amplitude being significantly larger for the Mach 6 case. Spectral analysis shows that both the wall and freestream pressure fluctuations of the Mach 6 boundary layer have enhanced energy content at high frequencies, with the peak of the premultiplied frequency spectrum of freestream pressure fluctuations being at a frequency of omega(delta)/U(sub infinity) approx. = 3.1, which is more than twice the corresponding frequency in the Mach 2.5 case. The space-time correlations indicate that the pressure-carrying eddies for the higher Mach number case are of smaller size, less elongated in the spanwise direction, and convect with higher convection speeds relative to the Mach 2.5 case. The demonstrated Mach-number dependence of the pressure field, including radiation intensity, directionality, and convection speed, is consistent with the trend exhibited in experimental data and can be qualitatively explained by the notion of "eddy Mach wave" radiation.

Duan, Lian↗

NASA NTRS1993

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗