Direct Numerical Simulation Calculations Research Articles

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.

Swept wing boundary-layer receptivity to localized surface roughness

AbstractThe receptivity to localized surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolized stability equations (PSEs). The DNS is laid out to reproduce wind tunnel experiments performed by Saric and coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSEs is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE methods are 40 % of those measured in the experiments. Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.

High-order methods for decaying two-dimensional homogeneous isotropic turbulence

Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is investigated for direct numerical simulations (DNS) of homogeneous isotropic two-dimensional decaying turbulent flows. The numerical accuracy of compact difference, explicit central difference, Arakawa, and dispersion-relation-preserving schemes are analyzed and compared with the Fourier–Galerkin pseudospectral scheme. In addition, several explicit Runge–Kutta schemes for time integration are investigated. We demonstrate that the centered schemes suffer from spurious Nyquist signals that are generated almost instantaneously and propagate into much of the field when the numerical resolution is insufficient. We further show that the order of the scheme becomes increasingly important for increasing cell Reynolds number. Surprisingly, the sixth-order schemes are found to be in perfect agreement with the pseudospectral method. Considerable reduction in computational time compared to the pseudospectral method is also reported in favor of the finite difference schemes. Among the fourth-order schemes, the compact scheme provides better accuracy than the others for fully resolved computations. The fourth-order Arakawa scheme provides more accurate results for under-resolved computations, however, due to its conservation properties. Our results show that, contrary to conventional wisdom, difference methods demonstrate superior performance in terms of accuracy and efficiency for fully resolved DNS computations of the complex flows considered here. For under-resolved simulations, however, the choice of difference method should be made with care.

Experimental and numerical investigation of isothermal flow in an idealized swirl combustor

PurposeThe main purpose of the paper is the validation of different modelling strategies for turbulent swirling flow of an incompressible fluid in an idealized swirl combustor.Design/methodology/approachExperiments have been performed and computations carried out for a water test rig, for a Reynolds number of 4,600 based on combustor inlet mean axial velocity and diameter. Two cases have been investigated, one low swirl and the other high swirl intensity. Measurements of time‐averaged velocity components and corresponding rms turbulence intensities were measured using laser Doppler anemometer, along radial traverses at different axial locations. In the three‐dimensional, unsteady computations, large eddy simulation (LES) and URANS (Unsteady Reynolds Averaged Navier‐Stokes Equations or Reynolds Averaged Numerical Simulations) RSMs (Reynolds‐stress models) are basically employed as modelling strategies for turbulence. To model subgrid‐scale turbulence for LES, the models due to Smagorinsky and Voke are used. No‐model LES and coarse‐grid direct numerical simulation computations are also performed for one of the cases.FindingsThe predictions are compared with the measurements and reveal that LES provided the best overall accuracy for all of the cases, whereas no significant difference between the Smagorinsky and Voke models are observed for the time‐averaged velocity components.Originality/valueThis paper provides additional valuable information on the performance of various modelling strategies for turbulent swirling flows.

Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion

Direct numerical simulations (DNS) of the wake of a circular disk placed normal to a uniform flow show that, as the Reynolds number is increased, the flow undergoes a sequence of successive bifurcations, each state being characterized by specific time and space symmetry breaking or recovering (Fabre, Auguste & Magnaudet, Phys. Fluids, vol. 20 (5), 2008, p. 1). To explain this bifurcation scenario, we investigate the stability of the axisymmetric steady wake in the framework of the global stability theory. Both the direct and adjoint eigenvalue problems are solved. The threshold Reynolds numbers Re and characteristics of the destabilizing modes agree with the study of Natarajan & Acrivos (J. Fluid Mech., vol. 254, 1993, p. 323): the first destabilization occurs for a stationary mode of azimuthal wavenumber m = 1 at RecA = 116.9, and the second destabilization of the axisymmetric flow occurs for two oscillating modes of azimuthal wavenumbers m ± 1 at RecB = 125.3. Since these critical Reynolds numbers are close to one another, we use a multiple time scale expansion to compute analytically the leading-order equations that describe the nonlinear interaction of these three leading eigenmodes. This set of equations is given by imposing, at third order in the expansion, a Fredholm alternative to avoid any secular term. It turns out to be identical to the normal form predicted by symmetry arguments. Though, all coefficients of the normal form are here analytically computed as the scalar product of an adjoint global mode with a resonant third-order forcing term, arising from the second-order base flow modification and harmonics generation. We show that all nonlinear interactions between modes take place in the recirculation bubble, as the contribution to the scalar product of regions located outside the recirculation bubble is zero. The normal form accurately predicts the sequence of bifurcations, the associated thresholds and symmetry properties observed in the DNS calculations.

Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions

An experimental and numerical systematic study of the growth of the Richtmyer–Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ = ( r 2 - r 1 ) / 2 , and the laminar maximum velocity is Re δ = 3500 . A Prandtl number Pr = 0.71 and a radius ratio r ∗ = 0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q ∗ = q 1 / q 2 , on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q ∗ = 1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q ∗ on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q ∗ varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q ∗ from 1 to 100, lead to opposite trends.

Using Graphics Processors for High-Performance Computation and Visualization of Plasma Turbulence

Direct numerical simulation (DNS) of turbulence is computationally intensive and typically relies on some form of parallel processing. The authors present techniques to map DNS computations to modern graphics processing units (GPUs), which are characterized by very high memory bandwidth and hundreds of SPMD (single-program-multiple-data) processors.

Direct numerical simulation of a realistic acoustic wave interacting with a premixed flame

The interaction of an acoustic wave with a turbulent flame and its consequences are still not well understood at present time. In the present paper the interaction of a syngas turbulent premixed flame with an acoustic wave is considered. At the difference of previous publications, a realistic, sinusoidal acoustic wave is considered for several periods. The interaction process is investigated by Direct Numerical Simulations (DNS) involving detailed physical models, so that an excellent accuracy is obtained. The DNS computations are systematically carried out twice, once with and once without adding an acoustic wave at the inlet, all other conditions being fixed. By a difference between both results, it is possible to quantify the interaction process. Local amplification, damping and structural modifications of the initially planar acoustic wave can be identified and analyzed. Moreover, a possible influence of the direction of propagation (acoustic wave reaching the flame from the fresh or from the burnt gas) has been investigated. Since a detailed reaction scheme is employed, the effect of each individual species on the wave amplification or damping can be quantified through the local Rayleigh’s criterion. It can be proved that the direction of propagation has no influence, confirming that amplification or damping is in the mean mainly controlled by the coupling process between pressure and heat release fluctuations through the chemical reactions. For the present case, species CO2, H and H2O mostly control wave amplification, while species O, OH and CO dominate damping. Two different reaction mechanisms have been employed and deliver almost identical results. The local version of the classical Rayleigh’s criterion presented in previous works is extended to take into account flame movement, which is now noticeable. Nevertheless, the results prove that the variation of flame position with time has a negligible influence on the coupling mechanism.

Direct Numerical Simulation Modeling of Bilayer Cathode Catalyst Layers in Polymer Electrolyte Fuel Cells

A pore-scale description of species and charge transport through a bilayer cathode catalyst layer (CL) of a polymer electrolyte fuel cell using a direct numerical simulation (DNS) model is presented. Two realizations of the bilayer catalyst layer structure are generated using a stochastic reconstruction technique with varied electrolyte and void phase volume fractions. The DNS calculations predict that a higher electrolyte phase volume fraction near the membrane–CL interface provides an extended active reaction zone and exhibits enhanced performance. A higher void phase fraction near the gas diffusion layer aids in better oxygen transport. The effects of cell operating conditions in terms of low inlet relative humidity and elevated cell operating temperature on the bilayer CL performance are also investigated. Low humidity and elevated temperature operations exhibit overall poorer performance compared to the high humidity and the low-temperature operations, respectively.

Lattice Boltzman Method Simulation of Aeroacoustics and Nonreflecting Boundary Conditions

A lattice Boltzmann method that can recover the first coefficient of viscosity and the specific heat ratio correctly has been adopted for one-step aeroacoustic simulations because it can recover the speed of sound correctly. Instead of solving the Navier-Stokes equations as in the case of direct numerical simulation, the lattice Boltzmann method only needs to solve one transport equation for the collision function. Other flow properties are obtained by integrating this collision function over the particle velocity space. The lattice Boltzmann method is effective only if appropriate nonreflecting boundary conditions for open computational boundaries are available, just like the direct numerical simulation. Four different nonreflecting boundary conditions are commonly used with direct numerical simulation for one-step aeroacoustic simulations. Among these are the characteristics-based method, the perfectly matched layer method, the C 1 continuous method, and the absorbing layer method. Not all nonreflecting boundary conditions are applicable when used with the lattice Boltzmann method; some might not be appropriate, whereas others could be rather effective. This paper examines some existing nonreflecting boundary conditions plus other new proposals, their appropriateness, and their suitability for the lattice Boltzmann method. The assessment is made against two classic aeroacoustic problems: propagation of a plane pressure pulse and propagation of acoustic, entropy, and vortex pulses in a uniform stream. A reference solution is obtained using direct numerical simulation assuming a relatively large computational domain without any specified nonreflecting boundary conditions. The results, obtained with a computational domain half the size of that used for the direct numerical simulation calculations, show that the absorbing layer method and the extrapolation method with assumed filter perform the best.

An intrinsic stabilization scheme for proper orthogonal decomposition based low-dimensional models

Despite the temporal and spatial complexity of common fluid flows, model dimensionality can often be greatly reduced while both capturing and illuminating the nonlinear dynamics of the flow. This work follows the methodology of direct numerical simulation (DNS) followed by proper orthogonal decomposition (POD) of temporally sampled DNS data to derive temporal and spatial eigenfunctions. The DNS calculations use Chorin’s projection scheme; two-dimensional validation and results are presented for driven cavity and square cylinder wake flows. The flow velocity is expressed as a linear combination of the spatial eigenfunctions with time-dependent coefficients. Galerkin projection of these modes onto the Navier-Stokes equations obtains a dynamical system with quadratic nonlinearity and explicit Reynolds number (Re) dependence. Truncation to retain only the most energetic modes produces a low-dimensional model for the flow at the decomposition Re. We demonstrate that although these low-dimensional models reproduce the flow dynamics, they do so with small errors in amplitude and phase, particularly in their long term dynamics. This is a generic problem with the POD dynamical system procedure and we discuss the schemes that have so far been proposed to alleviate it. We present a new stabilization algorithm, which we term intrinsic stabilization, that projects the error onto the POD temporal eigenfunctions, then modifies the dynamical system coefficients to significantly reduce these errors. It requires no additional information other than the POD. The premise that this method can correct the amplitude and phase errors by fine-tuning the dynamical system coefficients is verified. Its effectiveness is demonstrated with low-dimensional dynamical systems for driven cavity flow in the periodic regime, quasiperiodic flow at Re=10000, and the wake flow. While derived in a POD context, the algorithm has broader applicability, as demonstrated with the Lorenz system.

A quadrature closure for the reaction-source term in conditional-moment closure

A Gaussian-quadrature closure is introduced for the conditional reaction-source term in conditional-moment closure, motivated by the desire to accurately model the dynamics of homogeneous extinction and re-ignition in turbulent non-premixed flames. A priori analysis of the quadrature model was performed using results of direct numerical simulations (DNS) of isotropic turbulence which included a mixture fraction and reaction-progress variable with a reversible chemical-source term. The DNS calculations for three Damköhler numbers, each exhibiting a different degree of extinction and all exhibiting re-ignition, were used to demonstrate the shortcomings of the Taylor-series closure. A quantitative validation was completed, and the quadrature closure showed significantly less error than the Taylor-series closures for all of the conditions considered.

CFD and DNS methodologies development for fuel bundle simulations

Development and application of computational fluid dynamics (CFD) and direct numerical simulation (DNS) approaches to the reproduction of coolant flow inside nuclear fuel bundles are discussed, focusing on the advantages and limitations of the different methodologies and on their synergetic potential. High Reynolds number flow cases are analyzed with the adoption of an improved anisotropic turbulence model, which includes a non-linear stress strain correlation and an enhanced near wall treatment. The capability of the model to predict the coolant flow distribution inside rod bundles is shown and discussed on the base of comparison with experimental data for a variety of geometrical and Reynolds number conditions. In particular predictions for wall shear stresses, velocity, and secondary flow distributions are shown. Moreover, DNS computations are performed adopting an algorithm based on the finite difference method, extended to boundary fitted coordinate systems in order to efficiently concentrate grids near the distorted wall boundaries. The validity and significance of the results is discussed underlying the importance of the insights into the turbulence structure. The calculations are further extended to higher Reynolds numbers, which cannot in general be treated with DNS approach, renouncing to the estimation of the higher-order moments, but limited to the evaluation of the averaged velocity profiles, turbulence intensities and Reynolds stresses.

Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow

Over the last decade, lattice Boltzmann methods have proven to be reliable and efficient tools for the numerical simulation of complex flows. The specifics of such methods as turbulence solvers, however, are not yet completely documented. This paper provides results of direct numerical simulations (DNS), by a lattice Boltzmann scheme, of fully developed, incompressible, pressure-driven turbulence between two parallel plates. These are validated against results from simulations using a standard Chebyshev pseudo-spectral method. Detailed comparisons, in terms of classical one-point turbulence statistics at moderate Reynolds number, with both numerical and experimental data show remarkable agreement. Consequently, the choice of numerical method has, in sufficiently resolved DNS computations, no dominant effect at least on simple statistical quantities such as mean flow and Reynolds stresses. Since only the method-independent statistics can be credible, the choice of numerical method for DNS should be determined mainly through considerations of computational efficiency. The expected practical advantages of the lattice Boltzmann method, for instance against pseudo-spectral methods, are found to be significant even for the simple geometry and the moderate Reynolds number considered here. This permits the conclusion that the lattice Boltzmann approach is a promising DNS tool for incompressible turbulence.

Effect of particle inertia and gravity on the turbulence in a suspension

A theoretical model is presented for the effect of particle inertia and gravity on the turbulence in a homogeneous suspension. It is an extension of the one-fluid model developed by L’vov, Ooms, and Pomyalov [Phys. Rev. E 67, 046314 (2003)], in which the effect of gravity was not considered. In the extended model the particles are assumed to settle in the fluid under the influence of gravity due to the fact that their density is larger than the fluid density. The generation of turbulence by the settling particles is described, with special attention being paid to the turbulence intensity and spectra. A comparison is made with direct numerical simulation calculations and experimental data. Also a sensitivity study is carried out to investigate at which conditions the gravity effect becomes important.

Influence of curvature on the onset of autoignition in a corrugated counterflow mixing field

This study investigates experimentally and theoretically the preignition state of a nonpremixed corrugated counterflow of nitrogen-diluted n-heptane versus heated air under atmospheric pressure. Instantaneous images of Rayleigh scattering and laser-induced fluorescence (LIF) of formaldehyde were collected simultaneously. Mixture fraction and temperature images were calculated from the Rayleigh images using flamelet profiles. From the resulting instantaneous mixture fraction fields, the local curvature of the isomixture fraction contours was determined. Elevated relative concentrations of formaldehyde are observed mainly in the mixing zone of the two flows at locations that are concave toward the air side. As formaldehyde is a typical intermediate species that is formed in cool flames and under low-temperature oxidation conditions, these results indicate that preignition chemistry depends significantly on the curvature of the mixture fraction field. Based on the experimental findings, a flamelet formulation was derived that explicitly accounts for curvature effects. Numerical calculations using a detailed mechanism with 72 elementary reactions among 37 species were performed to predict the influence of curvature. The results confirm the experimentally observed influence of this parameter. They also are consistent with previous direct numerical simulation calculations for H 2/O 2 ignition that predict development of ignition kernels at such distinct locations.

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-e and the two-phase k-l model is evaluated.

Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence

Capabilities for turbulence calculations of the Lagrangian averaged Navier–Stokes (LANS-α) equations are investigated in decaying and statistically stationary three-dimensional homogeneous and isotropic turbulence. Results of the LANS-α computations are analyzed by comparison with direct numerical simulation (DNS) data and large eddy simulations. Two different decaying turbulence cases at moderate and high Reynolds numbers are studied. In statistically stationary turbulence two different forcing techniques are implemented to model the energetics of the energy-containing scales. The resolved flows are examined by comparison of the energy spectra of the LANS-α with the DNS computations. The energy transfer and the capability of the LANS-α equations in representing the backscatter of energy is analyzed by comparison with the DNS data. Furthermore, the correlation between the vorticity and the eigenvectors of the rate of the resolved strain tensor is studied. We find that the LANS-α equations capture the gross features of the flow, while the wave activity below the scale α is filtered by a nonlinear redistribution of energy.