Large-eddy simulations (LES) of a compressible mixing layer at high Reynolds number (R-e Theta= 220, 000) were carried out to study the effect of various sub-grid modeling approaches. All terms of the Reynolds stress transport equation (RSTE) were computed and used to estimate the amount numerical dissipation present in the solution. It was demonstrated that the numerical dissipation replaces any unresolved turbulent dissipation, acting as a sub-grid model and validating the implicit LES approach. Explicit sub-grid models, Smagorinsky and dynamic Smagorinsky, are compared to the implicit approach. Results show that the amount of numerical dissipation varied inversely with the dissipation from the sub-grid models and the total dissipation from both sources remained the same. A study varying the coefficient in the Smagorinsky model was undertaken to find an optimal value where all the turbulent dissipation is produced by the sub-grid model and the effect of the numerical dissipation on the RSTE is minimized. This optimal value was much higher than those normally used. The dynamic Smagorinsky model, where the coefficient is computed within the model, yielded results similar to the standard Smagorinsky model with a coefficient 4 times smaller than the optimal value. Using an explicit sub-grid model reduces the number and increases the size of the turbulent eddies present in the solution as compared to implicit LES. A grid resolution study showed that explicit sub-grid modeling yielded better grid convergence than the implicit simulations. Grids containing at least 41 points across the mixing layer thickness were required to reduce the errors in the peak Reynolds stresses to below 10 percent. Spectra of turbulent kinetic energy indicate that the sub-grid modeled cases show the turbulent dissipation beginning at lower-frequencies, reducing the extent of the inertial subrange. Simulations were also performed at lower Reynolds numbers (R-e Theta= 22, 000, 2, 200 and 220). The flow was found to be largely Reynolds number independent until the simulation Reynolds number fell below the mixing transition Reynolds number at R-e Theta= 220. At this point the flow characteristics changed dramatically.

Large-eddy simulation (LES) was used to study the turbulent flow over a backward facing step. The simulations examine the details of the turbulent flow's separated and reattaching regions created by the step geometry. An explicit high-order of accuracy/high resolution finite-difference computational fluid dynamics solver was used for both LES and Reynolds-averaged Navier-Stokes (RANS) simulations. The experimental data from the backward facing step experiment of Driver and Seegmiller was used for comparison. Data presented are derived from a RANS simulation using the Spalart-Allmaras turbulence model and LES simulations using the implict LES assumption on three different grids of varying resolution. The RANS solution agrees with past work. It does an adequate job of predicting the flowfield and reattachment point, but misses details such as the strength of the recirculating region and magnitudes of the Reynolds stresses. The synthetic eddy method was used to provide a turbulent inflow to the quasi-2D LES domains. For the LES, the coarse grid was of insufficient resolution and under-predicted the skin friction coefficient and over-predicted the normal stresses. The finer grid LES results accurately predict the skin friction coefficient and provide more accurate Reynolds stresses. Triple product velocity correlations are also computed from the LES and the finer grid results did a good job predicting the magnitudes of the curves and the shapes were reasonably represented. It is recommended that future work include investigating the turbulent inflow domain length, width of the quasi-2D domain, and additional grid refinement.

In the context of Large- Eddy Simulations (LES), Boundary-layer inflow turbulence is simulated using both the Synthetic Eddy Model (SEM) and Digital Filtering (DF). The effects of the projection error are investigated. The effect of the prescribed length scales on the adjustment region was found to be negligible for length scales less than one-tenth of the boundary-layer thickness. While it was conjectured that one method of the two might be more robust than the other, our results show that both the Digital Filtering Method and the Synthetic Eddy Method accurately replicate the boundary layer while successfully accounting for inflow turbulence.

Large-eddy simulations were used to investigate turbulent temperature fluctuations and turbulent heat flux in hot jets. A high-resolution finite difference Navier-Stokes solver was used to compute the flow from a 2in. round nozzle. Three different flow conditions of varying jet Mach numbers and temperature ratios were examined. The large-eddy simulation results showed that the temperature field behaved similarly to the velocity field but with a more rapidly spreading mixing layer. Predictions of the mean u>i and fluctuating velocities were compared to particle image velocimetry data. Predictions of the mean T and fluctuating T temperatures were compared to data obtained using Rayleigh scattering and Raman spectroscopy. Very good agreement with experimental data was demonstrated for the mean and fluctuating velocities. The large-eddy simulation correctly predicted the behavior of the turbulent temperature field but overpredicted the levels of the fluctuations. The turbulent heat flux was examined and compared to the Reynolds-averaged Navier-Stokes results. The large-eddy simulation and Reynolds-averaged Navier-Stokes simulations produced very similar results for the radial heat flux. However, the axial heat flux obtained from the large-eddy simulation differed significantly from the Reynolds-averaged Navier-Stokes result in both structure and magnitude, indicating that the Reynolds-averaged Navier-Stokes model was inadequate. Finally, the large-eddy simulation data were used to compute the turbulent Prandtl number and verify that a constant value of 0.7, which is typically used in the Reynolds-averaged Navier-Stokes models, was a reasonable assumption.

In the context of Large Eddy Simulations (LES), the effects of inflow turbulence are investigated through the Synthetic Eddy Method (SEM). The growth rate of a turbulent compressible mixing layer corresponding to operating conditions of GeobelDutton Case 2 is investigated herein. The effects of spanwise width on the growth rate of the mixing layer is investigated such that spanwise width independence is reached. The error in neglecting inflow turbulence effects is quantified by comparing two methodologies: (1) Hybrid-RANS-LES methodology and (2) SEM-LES methodology. Best practices learned from Case 2 are developed herein and then applied to a higher convective mach number corresponding to Case 4 experiments of GeobelDutton.

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

Reynolds-averaged Navier-Stokes computations of a shock-wave/boundary-layer interaction (SWBLI) created by a Mach 2.85 flow over an axisymmetric 30-degree compression corner were carried out. The objectives were to evaluate four turbulence models commonly used in industry, for SWBLIs, and to evaluate the suitability of this test case for use in further turbulence model benchmarking. The Spalart-Allmaras model, Menter's Baseline and Shear Stress Transport models, and a low-Reynolds number k- model were evaluated. Results indicate that the models do not accurately predict the separation location; with the SST model predicting the separation onset too early and the other models predicting the onset too late. Overall the Spalart-Allmaras model did the best job in matching the experimental data. However there is significant room for improvement, most notably in the prediction of the turbulent shear stress. Density data showed that the simulations did not accurately predict the thermal boundary layer upstream of the SWBLI. The effect of turbulent Prandtl number and wall temperature were studied in an attempt to improve this prediction and understand their effects on the interaction. The data showed that both parameters can significantly affect the separation size and location, but did not improve the agreement with the experiment. This case proved challenging to compute and should provide a good test for future turbulence modeling work.

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

The objective of this work is to compare a high-order solver with a low-order solver for performing large-eddy simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the high-order method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.

High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

The modeling of turbulent free shear flows is crucial to the simulation of many aerospace applications, yet often receives less attention than the modeling of wall boundary layers. Thus, while turbulence model development in general has proceeded very slowly in the past twenty years, progress for free shear flows has been even more so. This paper highlights some of the fundamental issues in modeling free shear flows for propulsion applications, presents a review of past modeling efforts, and identifies areas where further research is needed. Among the topics discussed are differences between planar and axisymmetric flows, development versus self-similar regions, the effect of compressibility and the evolution of compressibility corrections, the effect of temperature on jets, and the significance of turbulent Prandtl and Schmidt numbers for reacting shear flows. Large-eddy simulation greatly reduces the amount of empiricism in the physical modeling, but is sensitive to a number of numerical issues. This paper includes an overview of the importance of numerical scheme, mesh resolution, boundary treatment, sub-grid modeling, and filtering in conducting a successful simulation.

You have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Tucker P. G. and DeBonis J. R. 2014Aerodynamics, computers and the environmentPhil. Trans. R. Soc. A.3722013033120130331http://doi.org/10.1098/rsta.2013.0331SectionYou have accessIntroductionAerodynamics, computers and the environment P. G. Tucker P. G. Tucker Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK [email protected] Google Scholar Find this author on PubMed Search for more papers by this author and J. R. DeBonis J. R. DeBonis NASA Glenn Research Center, Cleveland, OH 44135, USA Google Scholar Find this author on PubMed Search for more papers by this author P. G. Tucker P. G. Tucker Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK [email protected] Google Scholar Find this author on PubMed and J. R. DeBonis J. R. DeBonis NASA Glenn Research Center, Cleveland, OH 44135, USA Google Scholar Find this author on PubMed Published:13 August 2014https://doi.org/10.1098/rsta.2013.03311. IntroductionWe are faced with global warming and dramatic increases in the world aircraft fleet. Computing power continues to inexorably rise, and machines are now powerful enough to make new technological break-throughs in the aerospace industry. This Theme Issue seeks to explore how computers should be used in future and how they may impact critical problems in aviation and its impact on the environment. However, the work also has wider relevance to the general fields of transport and energy.The environmental impact of aircraft with respect to emissions, including noise, is an area of critical importance. In many instances, aerodynamic performance and noise are intrinsically linked through turbulence. Go to any major international conference on turbulence, and one would be hard pressed to find many delegates who could agree on a definition of what turbulence actually is. As the Nobel prize winner Richard Feynman said 'Turbulence is the last great unsolved problem in classical physics'. This makes the mathematical modelling of turbulence challenging. Equations complete enough to virtually exactly describe turbulent flow—the Navier–Stokes equations—have been available for over a century. Until recently, the standard practice in computational fluid dynamics (CFD) is to solve a time-averaged version of the Navier–Stokes equations, using a simplified model to represent the turbulence—the Reynolds-averaged Navier–Stokes (RANS) approach. However, computing powers have increased to the point where one can seriously consider the near-direct solution1 (NDS) of these equations for practically relevant flows. Thus, armed with high-performance computing (HPC), modern computer graphics and analysis tools we can now, for practically relevant systems, unlock turbulence's secrets and thus intelligently manipulate the turbulent flow field, to improve performance and so address global environmental challenges.This situation was not unforeseen. Chapman (see [1]), director of aeronautics at NASA, proposed, using generally well-founded scientific arguments, that when computers reached 1014 FLOPS (floating point operations per second) we could perform NDS that would begin to rival aerodynamic tests. Modern HPC provision now exceeds Chapman's expectations reaching petascale with exascale computing due around 2018. Hence, now the ability to directly predict turbulence, for complex engineering systems, without recourse to accuracy reducing assumptions is close at hand. Computer-processing speeds have increased by a factor of around one million in the past 25 years (see Jameson [2]), and continued improvements are expected.Currently, flow physics insights from NDS are allowing the improvement of reduced-order mathematical models for design. In addition, simulations that potentially offer greater accuracy than tremendously expensive rig tests are now emerging. A notable shoot from the emerging era is work of Morton et al. [3] (US Air force Laboratory), who performed an NDS variant for an F/A-18 fighter configuration. Tail buffet was explored, and successful comparison made with real flight data. There are many other examples.Thus, after waiting with eager expectation, for several decades, Chapman's prophecy is coming closer to fulfilment. This Theme Issue explores what is needed to complete the fulfilment, how will things gradually change as the fulfilment is approached, what might the new era look like and when it will arrive. Obviously, what is meant by fulfilment is a complex thing, because aerospace systems involve a wide range of components with very different flows and degrees of coupling/dependence with other components. Hence, different flows will come to fruition at vastly different times.The Theme Issue comprises 12 papers exploring the abovementioned theme. The papers typically look at the status of computational modelling around 2030–2035.2. AeroenginesMenzies [4] at Rolls-Royce plc focuses on aeroengines. The emissions targets in terms of CO2, NOx and noise are defined. The paper has a positive message on the future role of CFD and its particular importance for simulating coupled airframe and engine interactions where rig tests will be especially expensive.In relation to aeroengines, Bistetti et al.'s [5] paper shows how direct numerical simulation can enhance our understanding of the science of pollution generation. The focus is very much on soot, which is of critical environmental importance but not what one immediately expects when considering environmental issues. The use of direct numerical simulation to refine NDS approaches such as large eddy simulation is discussed.Designing stable compressors is a critical issue for axial gas turbines, and so is the focus of the strongly prophetic paper by Gourdain et al. [6]. Currently, studying compressor stability is a great challenge for CFD. Interestingly, it is pointed out that the problem sizes being tackled substantially lag the growth in the power of computers. The potential for the gas lattice Boltzmann method for NDS is identified. There is discussion on how research in relation to Google and Facebook may offer assistance with the issue of dealing with the massive datasets from NDS. This is also discussed in the paper by Lele & Nichols [7]. Specific numerical challenges relating to turbomachinery—such as phase lagged boundary conditions—are discussed and potential algorithms to overcome them are given.It is well known that to improve the performance of gas turbine aeroengines it is necessary to increase the temperature of the combustion gases entering the turbine. However, these, even now, are well above the melting temperatures of ordinary metals. Hence, turbine blade cooling is a critical area. Tafti et al. [8] discuss turbine blade cooling. The strong benefits of improved numerical predictions on reducing environmental impact are clearly made. The paper offers a balanced, positive, perspective on the future outlook for NDS for internal blade cooling modelling. Notably, cooling flows typically seek to produce large-scale turbulent structures that enhance mixing. Hence, as noted in that paper, such flows are well suited to NDS. Notably, such flows are Reynolds number independent and so do not suffer from the extreme growth in computational cost with Reynolds number found in zones with attached boundary layers. Fortunately for NDS, the low-pressure turbine, which provides around 80% of the thrust of aeroengines, involves modest Reynolds number (Re∼5×105 for a medium-sized gas turbine engine). Hence, as acknowledged by Medic & Sharma [9] (United Technologies Research Centre), this is an area where NDS could also already be used in design in some sense. However, for the flows found in airframes, the Reynolds numbers are substantially higher, creating a challenge of a massively different scale. This aspect is outlined by Slotnick et al. [10].3. AirframesSlotnick, at Boeing, and a range of co-workers again outline the serious environmental challenges posed by the increasing use of air transport. For example, the forecast of 1.5 billion tonnes of annual CO2 emissions by 2025 is given. The paper has a strong focus on airframes, but there is some discussion on propulsion modelling with Pratt and Whitney input. The need for validation data is discussed and this is an important point. The authors also point out that in order to bring the transformative change in CFD for industry to fruition, there is a need to link education in computer science to sustainable aviation for future graduates and postgraduates. In addition, the need for more investment in applied mathematics and computer science in general is noted. This all seems critical to realize the bold vision identified by Slotnick et al. The need for international collaboration is also stressed. A wealth of new computer science and algorithms are identified in the paper. The recent stagnation of CFD methods is noted. Capabilities for the management of large databases are discussed, and the need for methods to merge data from various sources such as measurements, high fidelity CFD and low-order simulation results. In accord with Giles & Reguly [11], it is also stressed that it is necessary to keep an eye on novel computational technologies such as quantum and molecular computing. It is further pointed out that sustained exaFLOPS (1018 operations a second) for an actual CFD calculation will probably not be achieved until at least 2020. Evidently, current predictions suggest 30 exaFLOPS should be possible in 2030. Like Gourdain et al. and also Lele & Nichols [7], a future role for lattice Boltzmann methods is noted. A greater understanding of these methods' numerical traits might well be helpful.Deck et al. [12] present a range of exciting cutting-edge examples showing the application of hybrid RANS–NDS to various airframe-related flows. The zones where RANS and NDS are used, and the local modelling methodologies are solidly rationally based. This paper very much shows how NDS approaches are being actively used now for real aerospace systems and hence makes the future prospects even more exciting.NDS approaches open up the possibility of reliably exploring flow control and deeply understanding how the flow control strategy interacts with the flow field. Fujii [13], at the Japanese Aerospace Exploration Agency, gives a positive aerospace perspective for the use of NDS to explore flow control. The paper focuses on plasma actuators and their use on high lift-configured aerofoils. Simulations use the Japanese petaFLOPS supercomputer 'K'. This facility allows a volume of large (reaching one billion cells) high-order simulations to be made. Strong potential for the use of NDS to reduce the environmental impact of aircraft at low Reynolds numbers is identified in this paper. Fujii sees that the time to move from what he describes as 'geometry design' to 'device design' is close. The latter term reflects that a flat plate with control devices can replicate the role of an aerofoil and that with modem supercomputers this radical step can be realized.4. Computers and algorithmsThe paper by Larsson & Wang [14] gives some interesting insights into pressing technological needs to allow the use of design optimization with NDS. There is discussion on space–time parallelization, the performance of temporal schemes and the potential for hybrid implicit–explicit temporal schemes and the zonalization of such methods. The discussion on the use of design optimization with NDS and the problems faced when using adjoint design optimization for NDS-based design make a very interesting contribution to the issue.A substantial number of papers identify that high-order methods have potential benefits, such as, for example, reducing the amount of data that needs to be transferred in massively parallel simulations. In addition, for certain methods, there is the potential for less grid sensitivity. Hence, the paper by Wang [15], considering high-order methods, seems especially important. Wang identifies grid generation for high order as a critical component. As noted in the paper, the current scarcity of high-order solvers, particularly commercial, stunts the development of high-order grid generation. Numerical stiffness and storage, scaling with scheme order to the power six are identified as potential research challenges. Perhaps another area where work is required is exploring the properties of high-order schemes at high wave numbers and hence how they will interact with subgrid-scale parametrizations. Certain high-order schemes appear dissipative at high wave numbers. However, this trait could advantageously be turned to being used as the dissipative component of subgrid-scale models. Hence, there seems a need for modified equation analysis for more exotic high-order schemes.Giles & Reguly [11] look at trends in HPC. As well as looking at hardware, the paper explores software forms necessary to be compatible with future hardware and offers advice for code developers. It is noted that the life of a piece of CFD software is massive relative to the short time scales over which hardware is currently evolving. Advice on dealing with this is given. Interesting potential algorithms for reducing data transfer are discussed, this being seen as the critical issue.Clearly, computer power will always be limited and hence some form of turbulence modelling needed. Piomelli [16] gives a nice survey of subgrid modelling with NDS, hybrid RANS–NDS approaches and related methods. Algorithmic needs are also explored. The critical issue of the way the numerical scheme, grid and the subgrid-scale model work together, and that it is vital to get this aspect right is discussed. Use of integral scale estimates to design grids, so that the resolution is effectively uniform, is proposed.5. AeroacousticsThe paper by Lele & Nichols [7]—a second golden age of aeroacoustics—has a wide-looking perspective that encompasses some practical engineering needs to deep issues associated with modelling and performing large-scale acoustic simulations. Computational algorithms for aeroacoustics are discussed. Examples of cutting-edge simulations are given. Most areas of aerospace noise are considered, such as turbomachinery, including jet, fan and turbine noise. For airframes: slat, trailing edge and landing gear noise are addressed. In addition, propulsion–airframe interactions are considered. Hence, the need for large-scale coupled simulations and how these will enforce the need to retain low-order models are addressed. In addition, the paper has a section dedicated to data-driven modelling and uncertainty quantification. Lele and Nichols explore algorithms. They classify simulation algorithms that are likely to remain important and how these need to be considered in the future design of hardware. In addition, new algorithms emerging that could help with massively parallel simulations are covered. Lele and Nichols are prophetic, indicating that eddy resolving simulations could be used in aerospace for non-wall bounded flows in design in the next 5–10 years. The paper wisely seeks problems that are readily amenable to NDS, for example high-speed jets, where the noise from the large scales, which dominate the noise generation process, is relatively easy to deal with. As would be expected the severe demands for wall bounded flows are noted.6. The futureClearly, with the closer integration of engines and airframes, to meet the pressing environmental challenges arising from the growth of air transport, the need for coupled simulations grows. This and the high Reynolds numbers found in many areas of aerospace applications will impose substantial modelling content on simulations. However, it is clear from the contributions to this Theme Issue that the simulation environment around 2030 and beyond will be very different to what it is now. This will mean that revised best practices will required, because there will be a considerable migration to NDS and hybridizations of it (with current modelling methods) and this will need revised CFD best practices. Although such aspects seem dull, they are of critical importance. Currently, where NDS is attempted, for more industrial applications, frequently the grid resolutions used are inappropriate. Clearly, as also pointed out by Slotnick et al., there is a pressing need to reignite research into algorithms, computer science and applied mathematical methods, related to CFD. This area has tended to stagnate and has not matched the expected pace of developments in the Chapman era. It is clear from this issue that CFD has an increasing and pivotal role in the design of clean, silent and thus environmentally friendly aircraft.Footnotes1 This term is intended to encompass large eddy simulation and quasi-direct numerical simulation.One contribution of 13 to a Theme Issue 'Aerodynamics, computers and the environment'.© 2014 The Author(s) Published by the Royal Society. All rights reserved.References1Chapman DR, Mark H& Pirtle MW. 1975Computers vs. wind tunnels for aerodynamic flow simulations. Astronaut. Aeronaut. 13, 12–35. Google Scholar2Jameson A. 2008Formulation of kinetic energy preserving conservative schemes for gas dynamics and direct numerical simulation of one-dimensional viscous compressible flow in a shock tube using entropy and kinetic energy preserving schemes. J. Sci. Comput. 34, 188–208. (doi:10.1007/s10915-007-9172-6). Crossref, ISI, Google Scholar3Morton SA, Cummings RM& Kholodar DB. 2007High resolution turbulence treatment of F/A-18 tail buffet. 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Citations and impact Keywordsaerodynamicslarge eddy simulationturbulence Subjectsmechanical engineering

Research into large-eddy simulation (LES) for application to jet noise is described. The LES efforts include in-house code development and application at NASA Glenn along with NASA Research Announcement sponsored work at Stanford University and Florida State University. Details of the computational methods used and sample results for jet flows are provided.

A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.

A workshop on the computational fluid dynamics (CFD) prediction of shock boundary-layer interactions (SBLIs) was held at the 48th AIAA Aerospace Sciences Meeting. As part oldie workshop, numerous CFD analysts submitted solutions to four experimentally measured SBLIs. This paper describes the assessment of the CID predictions. The assessment includes an uncertainty analysis of the experimental data, the definition of an error metric, and the application of that metric to the CFD solutions. The CFD solutions provided very similar levels of error and, in general, it was difficult to discern clear trends in the data. For the Reynolds-averaged Navier-Stokes (RANS) methods, the choice of turbulence model appeared to be the largest factor in solution accuracy. Scale-resolving methods, such as large-eddy simulation (LES), hybrid RANS/LES, and direct numerical simulation, produced error levels similar to RANS methods but provided superior predictions of normal stresses.

This work examines the grid requirements necessary for a properly resolved large-eddy simulation (LES) of a compressible jet. The numerical scheme used for the analysis and its corresponding computational grid are used to estimate, a priori, the resolution of the simulation. This estimated resolution, expressed in terms of wave number, is compared to the resolution in the turbulent spectra obtained from the simulation. Two levels of grid resolution are examined. The solution yields good agreement with experimental data for mean flow and first-order turbulent statistics. The estimated resolution of the analysis properly predicts the trends with respect to the computed turbulent spectra.