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NASA NTRS1998

Effect of Swirl on Turbulent Structures in Supersonic Jets

Direct Numerical Simulation (DNS) is used to study the mechanism of generation and evolution of turbulence structures in a temporally evolving supersonic swirling round jet and also to examine the resulting acoustic radiations. Fourier spectral expansions are used in the streamwise and azimuthal directions and a 1-D b-spline Galerkin representation is used in the radial direction. Spectral-like accuracy is achieved using this numerical scheme. Direct numerical simulations, using the b-spline spectral method, are carried out starting from mean flow initial conditions which are perturbed by the most unstable linear stability eigenfunctions. It is observed that the initial helical instability waves evolve into helical vortices which eventually breakdown into smaller scales of turbulence. 'Rib' structures similar to those seen in incompressible mixing layer flow of Rogers and Moserl are observed. The jet core breakdown stage exhibits increased acoustic radiations.

Rao, Ram Mohan↗

NASA NTRS1998

Effect of Swirl on Turbulent Structures in Supersonic Jets

Rao, Ram Mohan↗

NASA NTRS1998

Effect of Swirl on Turbulent Structures in Supersonic Jets

Direct numerical simulation (DNS) is used to study the mechanism of generation and evolution of turbulence structures in a temporally evolving supersonic swirling round jet and also to examine the resulting acoustic radiations. Fourier spectral expansions are used in the streamwise and azimuthal directions and a 1-D b-spline Galerkin representation is used in the radial direction. Spectral-like accuracy is achieved using this numerical scheme. Direct numerical simulations, using the b-spline spectral method, are carried out starting from mean flow initial conditions which are perturbed by the most unstable linear stability eigenfunctions. It is observed that the initial.helical instability waves evolve into helical vortices which eventually breakdown into smaller scales of turbulence. 'Rib' structures similar to those seen in incompressible mixing layer flow of Rogers and Moser are observed. The jet core breakdown stage exhibits increased acoustic radiations.

Rao, Ram Mohan↗

NASA NTRS2010

Detailed Comparison of DNS to PSE for Oblique Breakdown at Mach 3

A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer. Their downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using Direct Numerical Simulations (DNS) and Parabolized Stability Equations (PSE). This abstract is the last part of an extensive study of the complete transition process initiated by oblique breakdown at Mach 3. In contrast to the previous simulations, the symmetry condition in the spanwise direction is removed for the simulation presented in this abstract. By removing the symmetry condition, we are able to confirm that the flow is indeed symmetric over the entire computational domain. Asymmetric modes grow in the streamwise direction but reach only small amplitude values at the outflow. Furthermore, this abstract discusses new time-averaged data from our previous simulation CASE 3 and compares PSE data obtained from NASA's LASTRAC code to DNS results.

Mayer, Christian S. J.↗

NASA NTRS1993

One-equation near-wall turbulence modeling with the aid of direct simulation data

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

Rodi, W.↗

NASA NTRS1996

Aeroacoustics of Turbulent High-Speed Jets

Aeroacoustic noise generation in a supersonic round jet is studied to understand in particular the effect of turbulence structure on the noise without numerically compromising the turbulence itself. This means that direct numerical simulations (DNS's) are needed. In order to use DNS at high enough Reynolds numbers to get sufficient turbulence structure we have decided to solve the temporal jet problem, using periodicity in the direction of the jet axis. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. Therefore in order to answer some questions about the turbulence we will partially compromise the overall structure of the jet. The first section of chapter 1 describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. In the second section we present preliminary work done using a TVD numerical scheme on a CM5. This work is only two-dimensional (plane) but shows very interesting results, including weak shock waves. However this is a nonviscous computation and the method resolves the shocks by adding extra numerical dissipation where the gradients are large. One wonders whether the extra dissipation would influence small turbulent structures like small intense vortices. The second chapter is an extensive discussion of preliminary numerical work using the spectral method to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which are solved in O(N) steps. A very accurate highly resolved DNS of a turbulent jet flow is expected.

Rao, Ram Mohan↗

NASA NTRS1993

Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows

The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the effects of scalar fluctuations. The implementation of the model requires the knowledge of the local values of the first two SGS moments. These are provided by additional modeled transport equations. In both a priori and a posteriori analyses, the predicted results are appraised by comparison with subgrid averaged results generated by DNS. Based on these results, the paths to be followed in future investigations are identified.

Adumitroaie, V.↗

NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗

NASA NTRS2015

DNS of Flow in a Low-Pressure Turbine Cascade Using a Discontinuous-Galerkin Spectral-Element Method

A new computational capability under development for accurate and efficient high-fidelity direct numerical simulation (DNS) and large eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy-stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy and is implemented in a computationally efficient manner on a modern high performance computer architecture. A validation study using this method to perform DNS of flow in a low-pressure turbine airfoil cascade are presented. Preliminary results indicate that the method captures the main features of the flow. Discrepancies between the predicted results and the experiments are likely due to the effects of freestream turbulence not being included in the simulation and will be addressed in the final paper.

Low-Pressure Turbine Cascade↗

NASA NTRS1994

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Givi, Peyman↗

NASA NTRS1995

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.

Adumitroaie, V.↗

NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗

NASA NTRS1991

A dynamic subgrid-scale model for compressible turbulence and scalar transport

The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

Moin, P.↗

NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations (DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those of a spatially evolving jet, a temporal jet problem was solved, using periodicity in the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible appli(,a- tion to active noise suppression. In addition, the data generated can be used to compute, various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved DNS of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS1997

Direct Numerical Simulation of Supersonic Turbulent Boundary Layers

The talk will present some initial results from the direct numerical simulation (DNS) of compressible turbulent boundary layers. We solve numerically the compressible Navier-Stokes equations using a method based on Spalart's transformation for the incompressible turbulent boundary layer. This allows the spatially developing boundary layer to be transformed to a calculation with periodic boundary conditions in the streamwise and spanwise directions. The equations are solved using Fourier expansions in the horizontal directions and B-splines in the wall-normal direction. The first simulation is at Mach 2.5 with a momentum thickness Reynolds number based on wall viscosity of R(sub theta(sup 1)) = 825. We are examining the physics of the compressible boundary layer using turbulence statistics and budget equations. The turbulence statistics include: rms (root mean square) and mean profiles, energy spectra, and two-point correlations. It is found that there are large density gradients which require significantly more resolution than the incompressible case.

Guarini, Stephen↗

NASA NTRS1995

Linear Wave Motion from Concentrated Harmonic Sources in Blasius Flow

The motion of individual linear instability waves in shear flows is well described by existing theoretical and numerical methods. However, naturally occuring sources produce coherent wave motions with broadband spanwise wavenumber and frequency spectra, and the different spectral components interact both linearly and nonlinearily. This paper describes a series of calculations for the parameters of three different experiments using locally parallel linear stability theory (LST), the Parabolized Stability Equations (PSE), and Direct Numerical Simulation (DNS). The calculations illustrate the strengths and weaknesses of the different methods, the extent to which the methods agree or disagree, and, finally the extent to which agreement with the measurements can be attained, given that the experiments also have their own difficulties.

linear↗

NASA NTRS2016

DNS of Low-Pressure Turbine Cascade Flows with Elevated Inflow Turbulence Using a Discontinuous-Galerkin Spectral-Element Method

Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.

Garai, Anirban↗

NASA NTRS1994

Navier-Stokes simulations of the effects of suction holes on a flat plate boundary layer

Direct numerical simulations (DNS) of the Navier-Stokes equations are employed to explore the effects of suction holes on transition in a laminar flat plate boundary layer. The Navier-Stokes equations are cast in vorticity-velocity form. Periodicity is imposed in spanwise direction; all other spatial derivatives are discretized with fourth order compact differences. An explicit fourth order Runge-Kutta scheme is employed for the time-integration of the vorticity transport equations. Suction is applied through a row of holes aligned in spanwise direction. For low suction strengths, each hole generates a pair of stable streamwise vortices. When the suction strength exceeds a critical value, the vortices become unstable. For high suction strengths, vortex shedding occurs right at the suction holes. Our numerical findings agree well with experimental observations.

Meitz, Hubert L.↗