Direct Numerical Simulation Calculations Research Articles

About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

Scallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. Anad hoccorrection applied to the turbulent closure and due to Hanrattyet al.(Thorsnesset al.,Chem. Engng Sci., vol. 33, issue 5, 1978, pp. 579–592; Abrams & Hanratty,J. Fluid Mech., vol. 151, issue 1, 1985, p. 443; Frederick & Hanratty,Exp. Fluids, vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.

Direct numerical simulation of an unsteady wall-bounded turbulent flow configuration for the assessment of large-eddy simulation models

A new benchmark case for the evaluation of direct numerical simulation (DNS) and large-eddy simulation (LES) models and methods is presented in this study. The known Taylor–Green vortex is modified by replacing the periodic boundary conditions in one direction with a no-slip boundary. A passive scalar is added and transported from the wall into the fluid. The addition of walls allows for the study of transient-instationary flows in a simple geometry with clean boundary and initial conditions, which is a key requirement for the assessment of LES modeling strategies. The added scalar mimics heat transfer through the wall. The case features reasonable computational cost for highly-resolved LES and DNS calculations. Simulations of the wall-bounded Taylor–Green vortex are easy to setup and do not require additional modeling. The proposed modification of the case is compared to the default Taylor–Green vortex and the difference in flow-physics is discussed. A detailed convergence study with four meshes, each of them refined by a factor of 2, has been conducted. The results reveal that converged second-order statistics can be obtained up to a dimensionless time of t/t_0 = 20. Beyond that, due to the unsteady chaotic nature of the flow, some uncertainties remain. The results show that the case features challenging (near-wall) flow dynamics, which cannot be covered using the default Taylor–Green vortex and hence, justify the proposed case as a useful benchmark.

Damping of three-dimensional waves on coating films dragged by moving substrates

Paints and coatings often feature interfacial defects due to disturbances during the deposition process, which, if they persist until solidification, worsens the product quality. In this article, we investigate the stability of a thin liquid film dragged by a vertical substrate moving against gravity, a fundamental flow configuration in various coating processes. The receptivity of the liquid film to three-dimensional disturbances is analyzed with Direct Numerical Simulations (DNS) and an in-house Integral Boundary Layer (IBL) film model. The latter was used for linear stability analysis and nonlinear wave propagation analysis. The numerical implementation of the IBL film model combines a finite volume formulation with a pseudo-spectral approach for the capillary terms that allows one to investigate non-periodic surface tension-dominated flows. The numerical model was successfully validated with DNS computations. The combination of these numerical tools allows one to describe the mechanisms of capillary and nonlinear damping and identify the instability threshold of the coating processes. The results show that transverse modulations can be beneficial for damping two-dimensional waves within the range of operational conditions considered in this study, which are relevant to air-knife and slot-die coating.

Numerical prediction of turbulent flow and heat transfer in buoyancy-affected liquid metal flows

The present paper investigates the capabilities of some selected Reynolds-Averaged Navier Stokes (RANS) based turbulence models in reproducing liquid metals thermal hydraulics Direct Numerical Simulation (DNS) data. For this purpose, forced and mixed convection conditions, both addressing buoyancy-aided and buoyancy-opposed flow, are considered. The paper mainly focuses on velocity and temperature fields estimation, providing a comparison between the RANS and DNS computations. The capabilities of the turbulence models are discussed with the aim to highlight which ones provide the best predictions.In particular, attention is paid to the approach adopted for the calculation of the turbulent heat flux contributions. Together with models assuming the commonly adopted Simple Gradient Diffusion Hypothesis (SGDH) approach and the Reynolds analogy, a model including the Algebraic Heat Flux Model (AHFM) approach is considered. While being a practical and robust approach to deal with turbulent heat fluxes, the SGDH approach shows intrinsic limitation in dealing with liquid metal thermal hydraulics, mainly because of their low-Prandtl number. The adoption of a more advanced AHFM method may instead relevantly improve the quality of the obtained predictions.The obtained results show that the selected model adopting the AHFM method provides definitively better predictions of the addressed phenomena with respect to the ones considering the SGDH approach. While some discrepancies are still observed for the velocity fields, the temperature fields are captured very well, suggesting a clear superiority of the AHFM model. The present paper thus provides further validation and supports the use of AHFM as a valuable tool to predict turbulent heat fluxes.

Computation of Intrinsic Instability and Sound Generation From Auto-Ignition Fronts

Abstract Burning carbon-free fuels such as hydrogen in gas turbines promise power generation with minimal emissions of greenhouse gases. A two-stage sequential combustor architecture with a propagation-stabilized flame in the first stage and an auto-ignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the auto-ignition-stabilized flame and the acoustic modes of the combustor may result in self-sustained thermoacoustic oscillations, which severely affect the stable operation of the combustor. In this paper, we study an “intrinsic” thermoacoustic feedback mechanism in which acoustic waves generated by unsteady heat release rate oscillations of the auto-ignition front propagate upstream and induce flow perturbations in the incoming reactant mixture, which, in turn, act as a disturbance source for the ignition front. We first perform detailed reactive Navier–Stokes (direct numerical simulation (DNS)) and Euler computations of an auto-ignition front in a one-dimensional setting to demonstrate the occurrence of intrinsic instability. Self-excited ignition front oscillations are observed at a characteristic frequency and tend to become more unstable as the acoustic reflection from the boundaries is increased. The Euler computations yield identical unsteady ignition front behavior as the DNS computations, suggesting that diffusive mechanisms have a minor effect on the instability. In the second part of this work, we present a simplified framework based on the linearized Euler equations (LEE) to compute the sound field generated by an unsteady auto-ignition front. Unsteady auto-ignition fronts create sources of sound due to local fluctuations in gas properties, in addition to heat release oscillations, which must be accounted for. The LEE predictions of the fluctuating pressure field in the combustor agree well with the DNS data. The findings of this work are essential for understanding and modeling thermoacoustic instabilities in reheat combustors with auto-ignition-stabilized flames.

Single-Mode Solutions for Convection and Double-Diffusive Convection in Porous Media

This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal.

Numerical modelling of steady detonations with a variational streamline approach

Previous studies (Watt et al. in J Eng Math 75(1):1, 2012; Cartwright and Falle in J Eng Math 115(1):157, 2019) have shown that a streamline based approach to modelling of steady state detonations can produce good results for rate laws which have maximal reaction at the shock. In this paper we consider a Variational Streamline Approximation (VSA) which introduces streamline curvature. Comparing results with Direct Numerical Simulations (DNS) and the existing Straight Streamline Approximation (SSA) model, we find that the VSA improves the predictive accurary of streamlines modelling compared to DNS calculations, capturing the shock front and sonic surfaces with greater accuracy than SSA.

Homogenized Modeling of Anisotropic Impact Damage in Rolled AZ31B with Aligned Second-Phase Particles

Magnesium is attractive for ballistic applications due to its high specific strength, but is not widely used due to its lower ductility as compared to other traditionally used materials (e.g. aluminum, titanium, and steel). Additionally, the behavior of magnesium is highly complex and is not well understood due to its HCP crystal structure and significant anisotropy. This work builds on direct numerical simulations (DNS) of rolled AZ31B magnesium with explicitly modeled second-phase particles subject to high strain rate uniaxial tension. The second-phase particles are preferentially aligned along the rolling direction, which induces anisotropies in void nucleation rates and void coalescence as a function of loading orientation. We propose a straightforward approach to account for these damage anisotropies in an anisotropic extension of the Gurson–Tvergaard–Needleman (GTN) homogenized damage model. The resulting anisotropic GTN model is calibrated against the uniaxial tension stress–strain responses predicted from DNS calculations for seven different loading orientations. The calibrated anisotropic GTN model is utilized to probe orientation effects in ballistic simulations. Two ballistic cases are conducted: (i) magnesium plate impacted with a steel sphere and (ii) magnesium plate impacted with a steel plate. The results quantify the degree to which preferential alignment of second-phase particles degrades the ballistic performance along the normal direction. This degradation is significant for a spherical impactor case, but fairly insensitive under plate impact. Consequently, the spall strength of rolled AZ31B is fairly insensitive to particle alignment.

Data-driven surrogate modeling of multiphase flows using machine learning techniques

This study focuses on the development of a theoretical framework and corresponding algorithms to establish spatio-temporal surrogate models for multiphase flow processes using Gaussian process (GP) based machine learning technique trained by direct numerical simulation (DNS) data. The training (and testing) datasets are obtained by solving the incompressible form of the Navier Stokes equations with surface tension in an Eulerian reference frame. The liquid-gas interfacial evolution is resolved using a volume-of-fluid (VOF) interface capturing method. The overall framework proceeds in four steps: 1) design of experiments study to identify the training and testing points and generation of corresponding datasets using DNS calculations; 2) dimensionality reduction using proper orthogonal decomposition; 3) Gaussian process regression (supervised training) over the reduced training dataset over the entire range of operating conditions under consideration; and 4) Galerkin reconstruction and error quantification by comparing the emulated flowfields (at test conditions) with the testing dataset. The machine learning framework predicts both the spatial basis-functions and the time-coefficients, thus, predicting the entire flowfield in time and space. The capabilities of the algorithm are demonstrated for two canonical flow configurations: 1) flow over a circular cylinder for a range of Reynolds numbers from 10 to 200; and 2) diesel jet injected into a quiescent nitrogen environment at chamber pressure of 30 atm and room temperature conditions, and injection velocities from 10 to 55 m/s, corresponding to a range of gas-based Weber numbers from 11.5 to 348. The emulations from the learned GP algorithm show excellent agreement with high-fidelity numerical data for test conditions; average error (in both space and time) at the testing point of Re = 185 for the flow over cylinder case is 4.4%, and for the diesel jet injection configuration at a testing point corresponding to velovity of 22.5 m/s is found to be 15.5%. The tip penetration location of the diesel jet is predicted within 2.5% of the DNS calculations. Corresponding to these two representative test points, speedup of 256 and 8000 is achieved for flow over cylinder and diesel jet atomization configurations, respectively. This paper represents the first effort of its kind on the development of a general machine learning framework to predict multiphase flows.

On the influence of two-dimensional hump roughness on laminar–turbulent transition

The presence of large surface irregularities such as humps, where the height is similar to the local boundary-layer (BL) displacement thickness, introduces regions of localized strong streamwise gradients in the base flow quantities. These large gradients can significantly modify the spatial development of incoming disturbances that lead to laminar–turbulent transition in wall-bounded flows [e.g., Tollmien–Schlichting (TS) waves]. Techniques such as Parabolized Stability Equations (PSE) are not suited for BL instability analysis in such regions: their formulation assumes that streamwise variations of base flow and disturbance quantities are small, allowing a marching procedure for their resolution. On the other hand, the Adaptive Harmonic Linearized Navier–Stokes (AHLNS) equations can handle these large streamwise gradients by using a fully elliptic system of equations, similar to Linearized Navier–Stokes (LNS), Harmonic LNS (HLNS), or Direct Numerical Simulation (DNS). Moreover, in AHLNS (as in PSE), a wave-like character of the instabilities is assumed, leading to a significant reduction in the number of streamwise grid points required compared with LNS, HLNS, or DNS computations. In the present study, an efficient combination of PSE and AHLNS is used to investigate the effect of height, length, and shape of a single hump placed on a flat plate in a two-dimensional flow field at Ma∞ = 0.5 without pressure gradient. The effect of this hump on the spatial evolution of TS waves, in terms of N-factors, is presented. An expected laminar–turbulent transition onset, via the eN methodology, is also described. It is shown that the shape of the surface irregularity, together with the height and length, plays an important role for the location of laminar–turbulent transition onset in convectively unstable flows.

Vortex pairing in jets as a global Floquet instability: modal and transient dynamics

The spontaneous pairing of rolled-up vortices in a laminar jet is investigated as a global secondary instability of a time-periodic spatially developing vortex street. The growth of subharmonic perturbations, associated with vortex pairing, is analysed both in terms of modal Floquet instability and in terms of transient growth dynamics. The article has the double objective to outline a toolset for the global analysis of time-periodic flows, and to leverage such an analysis for a fresh view on the vortex pairing phenomenon. Axisymmetric direct numerical simulations (DNS) of jets with single-frequency inflow forcing are performed, in order to identify combinations of the Reynolds and Strouhal numbers for which vortex pairing is naturally observed. The same DNS calculations are then repeated with an added time-delay control term, which artificially suppresses pairing, so as to obtain time-periodic unpaired base flows for linear stability analysis. It is demonstrated that the natural occurrence of vortex pairing in nonlinear DNS coincides with a linear subharmonic Floquet instability of the underlying unpaired vortex street. However, DNS results suggest that the onset of pairing involves much stronger temporal growth of subharmonic perturbations than that predicted by modal Floquet analysis, as well as a spatial distribution of these fast-growing perturbation structures that is inconsistent with the unstable Floquet mode. Singular value decomposition of the phase-shift operator (the operator that maps a given perturbation field to its state one flow period later) is performed for an analysis of optimal transient growth in the vortex street. Non-modal mechanisms near the jet inlet are thus found to provide a fast route towards the limit-cycle regime of established vortex pairing, in good agreement with DNS observations. It is concluded that modal Floquet analysis accurately predicts the parameter regime where sustained vortex pairing occurs, but that the bifurcation scenario under typical conditions is dominated by transient growth phenomena.

Towards a Direct Numerical Simulation of a Simplified Pressurized Thermal Shock

The aim of this research work is to perform high quality direct numerical simulations (DNS) of a simplified single phase pressurized thermal shock (PTS) scenario with and without buoyancy effects. In that context, the objectives of this paper are (i) to present the road towards the DNS of a PTS design without buoyancy effects and (ii) to demonstrate that the code NEK5000 is adequate for true DNS analyses. This DNS of the PTS design will serve as a reference to validate low order CFD approaches. The higher order spectral element code NEK5000 is selected to perform the high quality DNS computations. The capabilities of this code, in order to perform the DNS for PTS like geometries, have been extensively assessed for a well-known turbulent channel flow configuration with Reτ = 180 (turbulent Reynolds number based on the wall friction velocity). Different numerical parameters of NEK5000 have been thoroughly tested and their influence has been studied to obtain high quality turbulence statistics. This assessment of NEK5000 is further extended for the application of highly skewed hexahedral (non-orthogonal) meshes in a turbulent channel flow. The obtained results have shown that NEK5000 is capable of producing high quality DNS solution for a PTS like complex flow configuration for skewed elements (meshes) up to 60 degrees. Finally, this tested numerical framework is adopted to perform the targeted DNS computations of the simplified PTS design.

Correlation of pressure fluctuations in turbulent wall layers

Profiles of $\ensuremath{\langle}p\phantom{\rule{0}{0ex}}p{\ensuremath{\rangle}}^{+}$ from direct numerical simulation calculations are correlated for various Reynolds numbers. The correlating functions are unusual; a single function in the outer region and a defect function in the inner region. This is exactly opposite of the correlating functions for the mean velocity.

Explicit and implicit LES closures for Burgers turbulence

In this work, we perform an aposteriori error analysis on implicit and explicit large eddy simulation closure models for solving the Burgers turbulence problem. Our closure modeling efforts include both functional and structural models equipped with various low-pass filters. We introduce discrete binomial smoothing filters and an enhanced version of the Van Cittert algorithm to accelerate the convergence of approximate deconvolution processes including regularization and relaxation filtering approaches. Our implicit modeling efforts consist of various high-order schemes including compact and non-compact fifth-order upwind schemes as well as weighted essential non-oscillatory (WENO) and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are shown to effectively converge to the direct numerical simulation (DNS) for increasing resolutions. Comparing with DNS and underresolved DNS computations, our numerical assessments illustrate the ability of these methods to capture the energy content near grid cut-off scale.

Assessment of dynamic closure for premixed combustion large eddy simulation

Turbulent piloted Bunsen flames of stoichiometric methane–air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

AbstractWhen a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

Numerical investigations of shock wave interactions with a supersonic turbulent boundary layer

Direct numerical simulations (DNS) are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. The accuracies of DNS calculations are established by checking the convergence of flow statistics for various grids, by comparing the generated results with those in the literature and also by the balance of contributing terms in the turbulent kinetic energy equation. Instantaneous flow visualizations show the significant effect of shock on turbulence structure in the shock-boundary layer interaction zone and also in the flow downstream of the interaction region. The separation bubbles exhibit highly unsteady and three-dimensional behavior and are larger for stronger shocks but the maximum probability of flow separation is found to be independent of the shock strength. The differences between Reynolds- and Favre-averaged quantities are also observed to be small and largely independent of the shock intensity. The turbulent kinetic energy is amplified across the shock, mainly by the production term in the turbulent kinetic energy equation. The amplification of enstrophy across the shock zone is found to be due to the vortex stretching term in the enstrophy transport equation. A detailed examination of the terms in the turbulent kinetic equation shows a strong coupling between the mean and turbulent fields in the interaction region with energy being continuously exchanged from one field to another. However, the compressibility-related terms in the transport equations for turbulent kinetic energy and enstrophy are found to be small for the simulated flows.

Competition of rotation and stratification in flux concentrations

In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable to spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, called the negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios where most of the magnetic field resides in the bulk of the convection zone, and not at the bottom. Recent work using the mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1.}{Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity from direct numerical simulations (DNS) and compare with earlier work.}{To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the $\tau$ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the 3D hydromagnetic equations in a Cartesian domain.}{We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below about 0.06. In that case, kinetic and magnetic helicities are found to be weak. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated.}{Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the upper-most layers of the Sun, where the convective turnover time is less than 2 hours.}

Direct numerical simulation of flow and surface reaction in de-NOx catalyst

Selective catalytic reaction is a very efficient method to reduce NOx emissions from thermal power plants and is widely used in Japan. To develop a higher performance de-NOx system and optimize its maintenance schedule, it is important to understand the NOx reduction mechanism in the honeycomb channel which supports the de-NOx catalysts. In this study, the effects of duct channel flow behavior on the de-NOx reaction at the catalyst surface were investigated using a direct numerical simulation (DNS). The DNS computations were performed for three inflow conditions, one laminar and two turbulent. The results show that although the flow transitions from turbulent to laminar flow as the flow moves downstream for the turbulent inflow conditions, de-NOx reaction rates for the turbulent inflow conditions are higher than that for the laminar inflow condition even in the downstream region. This is because of the remaining cross-sectional fluid motions caused by the inflow turbulence. As a result, de-NOx efficiencies for the turbulent conditions are higher than that for the laminar case. For both laminar and turbulent inflow conditions, de-NOx reaction is suppressed in the corner regions due to the flow stagnation.

Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.