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NASA NTRS1991

Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗

NASA NTRS1992

Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992

The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Liou, William W.↗

NASA NTRS1995

Conservative properties of finite difference schemes for incompressible flow

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Morinishi, Youhei↗

NASA NTRS2001

Large Eddy Simulation of Gravitational Effects on Transitional and Turbulent Gas-Jet Diffusion Flames

The basic objective of this work is to assess the influence of gravity on "the compositional and the spatial structures" of transitional and turbulent diffusion flames via large eddy simulation (LES), and direct numerical simulation (DNS). The DNS is conducted for appraisal of the various closures employed in LES, and to study the effect of buoyancy on the small scale flow features. The LES is based on our "filtered mass density function"' (FMDF) model. The novelty of the methodology is that it allows for reliable simulations with inclusion of "realistic physics." It also allows for detailed analysis of the unsteady large scale flow evolution and compositional flame structure which is not usually possible via Reynolds averaged simulations.

Givi, Peyman↗

NASA NTRS2003

Large Eddy Simulation Of Gravitational Effects In Transitional And Turbulent Gas-Jet Diffusion Flames

The influence of gravity on the spatial and the compositional structures of transitional and turbulent hydrocarbon diffusion flames are studies via large eddy simulation (LES) and direct numerical simulation (DNS) of round and planar jets. The subgrid-scale (SGS) closures in LES are based on the filtered mass density function (FMDF) methodology. The FMDF represents the joint probability density function (PDF) of the SGS scalars, and is obtained by solving its transport equation. The fundamental advantage of LES/FMDF is that it accounts for the effects of chemical reaction and buoyancy exactly. The methodology is employed for capturing some of the fundamental influences of gravity in equilibrium flames via realistic chemical kinetic schemes. Some preliminary investigation of the gravity effects in non-equilibrium flames is also conducted, but with idealized chemical kinetics models.

Jaberi, Farhad A.↗

NASA NTRS2013

Influence of Computational Drop Representation in LES of a Droplet-Laden Mixing Layer

Multiphase turbulent flows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent flows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of pollutant dispersion, etc. Two-phase flows contain millions and sometimes billions of particles. For flows with volumetrically dilute particle loading, the most accurate method of numerically simulating the flow is based on direct numerical simulation (DNS) of the governing equations in which all scales of the flow including the small scales that are responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary. Because of high computational cost, numerical simulations of such flows cannot track all these drops. The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics, and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provide minimal error in flow prediction. For this purpose, several Large Eddy Simulation (LES) of a mixing layer with evaporating drops have been performed by using coarse, medium, and fine grid spacings and computational drops, rather than physical drops. To define computational drops, an integer NR is introduced that represents the ratio of the number of existing physical drops to the desired number of computational drops; for example, if NR=8, this means that a computational drop represents 8 physical drops in the flow field. The desired number of computational drops is determined by the available computational resources; the larger NR is, the less computationally intensive is the simulation. A set of first order and second order flow statistics, and of drop statistics are extracted from LES predictions and are compared to results obtained by filtering a DNS database. First order statistics such as Favre averaged stream-wise velocity, Favre averaged vapor mass fraction, and the drop stream-wise velocity, are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when NR is less than 32, and by the coarse mesh LES reasonably accurately for all NR values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.

Bellan, Josette↗

NASA NTRS2018

Görtler Instability and Its Control via Surface Suction over an Axisymmetric Cone at Mach 6

The characteristics of Görtler instability over an axisymmetric cone with an aft concave section are studied via linear and nonlinear instability analysis and direct numerical simulations. Several options for the cone geometry have been investigated numerically, subject to a fixed forecone section and constraints on the maximum cone diameter, overall cone length, and minimum N-factor for the most amplified Görtler modes. Computations show that it is possible to design a cone with a peak N-factor of Nmax > 8 at the target Reynolds number of 12.1×10(exp 6) per meter, corresponding to the maximum quiet Reynolds number in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. Direct numerical simulations show that an array of roughness elements corresponding to a peak roughness height of 0.1006 mm at the center can excite Görtler vortices that evolve into sufficiently strong streamwise streaks that may break down via high-frequency secondary instability. Thus, the selected axisymmetric configuration of interest should provide an acceptable baseline to investigate the feasibility of several aspects of laminar-flow control via boundary-layer suction. The apparatus that is being used for measurements in the Boeing/AFOSR Quiet Tunnel is described, along with some preliminary experimental results.

Gortler vortices↗

NASA NTRSDate not supplied

Simulations of a Turbulent Flow Subjected to Favorable and Adverse Pressure Gradients

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted “speed bump” geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proven to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest-fidelity simulation techniques. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation, and development of internal layers where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units, which is found to provide a significant speedup compared to an earlier solver optimized for central processing unit architectures.

Ali Uzun↗

NASA NTRS1994

Studying Turbulence Using Numerical Simulation Databases. 5: Proceedings of the 1994 Summer Program

Direct numerical simulation databases were used to study turbulence physics and modeling issues at the fifth Summer Program of the Center for Turbulence Research. The largest group, comprising more than half of the participants, was the Turbulent Reacting Flows and Combustion group. The remaining participants were in three groups: Fundamentals, Modeling & LES, and Rotating Turbulence. For the first time in the CTR Summer Programs, participants included engineers from the U.S. aerospace industry. They were exposed to a variety of problems involving turbulence, and were able to incorporate the models developed at CTR in their company codes. They were exposed to new ideas on turbulence prediction, methods which already appear to have had an impact on their capabilities at their laboratories. Such interactions among the practitioners in the government, academia, and industry are the most meaningful way of transferring technology.

Source record↗

NASA NTRS2000

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharamonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. D.↗

NASA NTRS2003

Consistent large eddy simulation of a temporal mixing layer laden with evaporating drops; part 2: a priori modeling

Large eddy simulation models are presented and evaluated on a database obtained from direct numerical simulation of a three-dimensional temporal mixing layer with evaporating drops.

Large Eddy Simulation LES Direct Numerical Simulat↗

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 ill 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 application 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 Direct Numerical Simulation (DNS) of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS2004

Model of Mixing Layer With Multicomponent Evaporating Drops

A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The study is motivated by the fact that typical real petroleum fuels contain hundreds of chemical species. Previously, for the sake of computational efficiency, spray studies were performed using either models based on a single representative species or models based on surrogate fuels of at most 15 species. The present multicomponent model makes it possible to perform more realistic simulations by accounting for hundreds of chemical species in a computationally efficient manner. The model is used to perform Direct Numerical Simulations in continuing studies directed toward understanding the behavior of liquid petroleum fuel sprays. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and the drops, respectively. This representation is consistent with the expected volumetrically small loading of the drops in gas (of the order of 10 3), although the mass loading can be substantial because of the high ratio (of the order of 103) between the densities of liquid and gas. The drops are treated as point sources of mass, momentum, and energy; this representation is consistent with the drop size being smaller than the Kolmogorov scale. Unsteady drag, added-mass effects, Basset history forces, and collisions between the drops are neglected, and the gas is assumed calorically perfect. The model incorporates the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a distribution function. Distribution functions generally depend on many parameters. However, for mixtures of homologous species, the distribution can be approximated with acceptable accuracy as a sole function of the molecular weight. The mixing layer is initially laden with drops in its lower stream, and the drops are colder than the gas. Drop evaporation leads to a change in the gas-phase composition, which, like the composition of the drops, is described in a probabilistic manner

Bellan, Josette↗

NASA NTRS1989

The analysis and modeling of dilatational terms in compressible turbulence

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Sarkar, S.↗

NASA NTRS1991

The analysis and modelling of dilatational terms in compressible turbulence

Sarkar, S.↗

NASA NTRS1992

The influence of bulges on boundary-layer instability

Local disturbances caused by a spanwise surface corrugation affect the position of the boundary-layer transition, and so the drag, of an object. This premature transition from laminar to turbulent flow is often associated with a separation of the laminar boundary-layer from its surface. Also the roughness-induced separation bubble provides an important link between the pressure and velocity fluctuations in the environment and the development of the disturbance in the laminar boundary-layer, i.e., the receptivity problem. To investigate the influence of a laminar separation bubble on boundary-layer instability, a separated flow generated by a velocity gradient over a flat plate was analyzed by direct numerical simulation using finite-difference solutions of the Navier-Stokes equations. The bubble acts as a strong amplifier of the instability waves and a highly nonlinear flow field is shown to develop downstream of the bubble. Consequently, the results of the direct numerical simulation differ noticeably from those of the classical linear stability theory proving the fact that the nonparallel effects together with the nonlinear interactions are crucial to this flow development. In the present paper, the effect of physical perturbations such as humps and hollows on boundary-layer instability is analyzed. This problem has been considered theoretically by several researchers (e.g., Nayfeh et al., 1987 and 1990; Cebeci et al., 1988). They used linear stability theory in their approach which does not include the nonparallel nor the nonlinear effects. Therefore, to account for these important effects in studying flow over humps and hollows the direct simulation technique is being implemented in generalized coordinates.

Elli, S.↗