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The principal objective is to extend the boundaries within which large eddy simulations (LES) and direct numerical simulations (DNS) can be applied in computational analyses of high speed reacting flows. A summary of work accomplished during the last six months is presented.
A detailed study of the dynamics of sub-Kolmogorov-size aerosol particles in stationary isotropic turbulence has been performed. The study combined direct numerical simulations (DNS; directed by Prof. Collins) and high-resolution experimental measurements (directed by Prof. Meng) under conditions of nearly perfect geometric and parametric overlap. The goal was to measure the accumulation of particles in low-vorticity regions of the flow that arises from the effect commonly referred to as preferential concentration. The grant technically was initiated on June 13, 2000; however, funding was not available until July 11, 2000. The grant was originally awarded to Penn State University (numerical simulations) and SUNY-Buffalo (experiments); however, Prof. Collins effort was moved to Cornell University on January 2002 when he joined that university. He completed the study there. A list of the specific tasks that were completed under this study is presented.
Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) have been conducted of a temporal mixing layer laden with evaporating drops, in order to assess the ability of LES to reproduce dynamic and mixing aspects of the DNS which affect combustion, independently of combustion models.
Direct Numerical Simulations (DNS) are performed using the FUN3D code ( https://fun3d.larc.nasa.gov) for three validation cases: (1) flow through a plane channel, (2) flow through a channel with a constriction, and (3) flow over a flat plate. FUN3D is a node-centered finite-volume code developed at the NASA Langley Research Center that solves the three-dimensional compressible Navier-Stokes equations on unstructured computational grids. The simulations are performed employing the 2nd-order unstructured monotonic upstream scheme for conservation laws (UMUSCL). The results are compared with available experimental and numerical data. The effect of the UMUSCL reconstruction parameter (κ) is assessed, and the results indicate that κ = 0.9 yields satisfactory results in terms of accuracy and robustness compared to available data. Further analyses of the results, along with additional test cases and grids will be presented in the final manuscript.
Direct numerical simulation (DNS) is performed using an unstructured node-based finite-volume methodology for canonical turbulent flow configurations to assess the effect of the upwinding parameter (κ) in the unstructured monotonic upstream scheme for conservation laws (UMUSCL) reconstruction scheme. The NASA FUN3D solver is used, and four turbulent validation cases are considered: periodic Taylor-Green vortex, (2) flow through a plane channel, (3) flow through a channel with a constriction, and (4) flow over a flat plate. The results are presented for κ = 0.5, 0.9 and 1 on hexahedral grids, with the last value corresponding to a zero-numerical dissipation scheme. Detailed comparisons with available reference data indicate that for the smallest length-scales simulated, κ = 0.5 is too dissipative while κ = 1 could lead to an energy build-up. Overall, κ =0.9 yields satisfactory results in terms of accuracy and robustness for all the cases considered in this study.
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.
Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
Results have been compared from Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of a temporal mixing layer laden with evaporating drops, to assess the ability of LES to reproduce detailed characteristics of DNS.
We have performed Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of forced isotropic turbulence at moderate Reynolds numbers. The subgrid scale model used in the LES is based on an eddy viscosity which adjusts instantaneously the energy spectrum of the LES to that of the DNS. The statistics of the large scales of the DNS (filtered DNS field or fDNS) are compared to that of the LES. We present results for the transfer spectra, the skewness and flatness factors of the velocity components, the PDF's of the angle between the vorticity and the eigenvectors of the rate of strain, and that between the vorticity and the vorticity stretching tensor. The above LES statistics are found to be in good agreement with those measured in the fDNS field. We further observe that in all the numerical measurements, the trend was for the LES field to be more gaussian than the fDNS field. Future research on this point is planned.
The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.
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.
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.
A wall pressure frequency spectrum model (Blake 1971 ) has been evaluated using databases from Direct Numerical Simulations (DNS) of a turbulent boundary layer (Na & Moin 1996). Good agreement is found for moderate to strong adverse pressure gradient flows in the absence of separation. In the separated flow region, the model underpredicts the directly calculated spectra by an order of magnitude. The discrepancy is attributed to the violation of the model assumptions in that part of the flow domain. DNS computed coherence length scales and the normalized wall pressure cross-spectra are compared with experimental data. The DNS results are consistent with experimental observations.
Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing and the mode selected for forcing corresponds to the most amplified secondary instability mode that, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. An inlet boundary condition is carefully designed to allow for accurate injection of instability wave modes and minimize acoustic reflections at numerical boundaries. Nonlinear parabolized stability equation (PSE) predictions compare well with the DNS in terms of modal amplitudes and modal shape during the strongly nonlinear phase of the secondary instability mode. During the transition process, the skin friction coefficient rises rather rapidly and the wall-shear distribution shows a sawtooth pattern that is analogous to the previously documented surface flow visualizations of transition due to stationary crossflow instability. Fully turbulent features are observed in the downstream region of the flow.
This paper covers the review, status, and projected future of direct numerical simulation (DNS) methodology relative to the state-of-the-art in computer technology, numerical methods, and the trends in fundamental research programs.
Direct numerical simulation (DNS) of turbulent compressible flows is performed using a higher-order space-time discontinuous-Galerkin finite-element method. The numerical scheme is validated by performing DNS of the evolution of the Taylor-Green vortex and turbulent flow in a channel. The higher-order method is shown to provide increased accuracy relative to low-order methods at a given number of degrees of freedom. The turbulent flow over a periodic array of hills in a channel is simulated at Reynolds number 10,595 using an 8th-order scheme in space and a 4th-order scheme in time. These results are validated against previous large eddy simulation (LES) results. A preliminary analysis provides insight into how these detailed simulations can be used to improve Reynoldsaveraged Navier-Stokes (RANS) modeling
The objective 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 analysis of high-speed reacting turbulent flows. In the first phase of this research, conducted within the past six months, focus was in three directions: RANS of turbulent reacting flows by Probability Density Function (PDF) methods, RANS of non-reacting turbulent flows by advanced turbulence closures, and LES of mixing dominated reacting flows by a dynamics subgrid closure. A summary of our efforts within the past six months of this research is provided in this semi-annual progress report.