Numerical Large Eddy Simulation Research Articles

Study on turbulence drag reduction of riblet plate in hypersonic turbulent flows

This paper focuses on turbulence drag reduction of riblet plate in hypersonic turbulent flows. We use direct numerical simulation (DNS) and large eddy simulation (LES) to simulate three-dimensional spatially-developing boundary layer over the flat plate and riblet plate with a free-stream Mach number [Formula: see text]. The results reveal the influence of different riblet heights [Formula: see text] and riblet distances [Formula: see text] on drag reduction effect. The drag reduction effect increases with the increase of riblet height and the decrease of riblet distance within suitable range of parameter values. Through analysis, it can be seen that the riblet plate affects the turbulent contribution of the skin friction by suppressing or destroying the large-scale vortex structure. Combined with the actual engineering design requirements, we can use the riblet plate with appropriate parameters to achieve the purpose of turbulence control.

Effects of random disturbances on the stability of a temporally evolving incompressible plane wake

Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of a three-dimensional, temporally evolving incompressible plane wake are performed, seeking to evidence differences in stability, transition and onset of both coherent and fine-scale structures arisen from random perturbations of different amplitudes. The perturbations are generated by the Random-Flow-Generator (RFG) technique, being imposed in the flow as initial conditions. The Navier-Stokes equations are solved in a prismatic domain with periodic boundary conditions in all directions, using a Fourier pseudospectral method. The invariants of the velocity gradient tensor were evaluated for cases with wakes subjected to random perturbations of amplitude 10−3,10−4 and 10−5. Moreover, maps of the second and third invariants of the rate-of-strain tensor were analyzed, seeking to evidence the differences in local flow strain and topological characteristics of the dissipation of kinetic energy. In order to assess the fine-scale structures, isosurface plots of the Q-criterion, as well as vorticity contours were used, allowing visual identification of the coherent structures and confirming patterns predicted by the invariant maps. It was found that the characteristic teardrop correlation map is well defined for higher disturbance amplitudes. Based on the analysis of the simulation results, it can be concluded that the fluid element topology allowed a comparative study of the effects of perturbation amplitude on pairing mechanisms.

Numerical simulation of double jet impinging a flat and fixed wall with WALE model

This work focuses on the study of the averaged velocity and the turbulent intensity of the double jet impingement is used to separate two adjacent cellule. Numerical LES investigations are carried out in this study. A jet impingement against a flat and smooth surface without recirculation was used for this. The WALE (Wall Adapting Local Eddy) structure models the sub grid-scale tensor. The jet opening ratio is H/e = 10 and the Reynolds Number Re= 2000. Result comparisons to available experimental measurements are performed and good agreements are noticed.

On the mesh resolution of industrial LES based on the DNS of flow over the T106C turbine

A high-order Navier-Stokes solver based on the flux reconstruction (FR) or the correction procedure via reconstruction (CPR) formulation is employed to perform a direct numerical simulation (DNS) and large eddy simulations (LES) of a well-known benchmark problem – transitional flow over the low-pressure T106C turbine cascade. Hp-refinement studies are carried out to assess the resolution requirement. A 4th order (p3) simulation on the fine mesh is performed with a DNS resolution to establish a "converged" solution, including the mean pressure and skin-friction distributions, and the power spectral density in the wake. Then LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the solution. In particular, we study the error in the transition location, the mean skin-friction distribution, and the mean lift and drag coefficients. These h- and p-refinement studies provide a much-needed guideline in h- and p- resolutions to achieve a certain level of accuracy for industrial LES applications.

Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks

A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjogreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016) is examined for long-time integrations of computational aeroacoustics (CAA) turbulence applications. This class of schemes was designed for an improved nonlinear stability and accuracy for long-time integration of compressible direct numerical simulation and large eddy simulation computations for both shock-free turbulence and turbulence with shocks. They are based on the skew-symmetric splitting version of the high-order central base scheme in conjunction with adaptive low-dissipation control via a nonlinear filter step to help with stability and accuracy capturing at shock-free regions as well as in the vicinity of discontinuities. The central dispersion-relation-preserving schemes as well as classical central schemes of arbitrary orders fit into the framework of skew-symmetric splitting of the inviscid flux derivatives. Numerical experiments on CAA turbulence test cases are validated.

The layered structure of stably stratified turbulent shear flows

The data of numerical simulation of stably stratified turbulent Couette flows are analyzed for various values of the Richardson number. Two different methods were used: Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). It is shown that the flow contains large organized structures, along with chaotic turbulence, regardless of the simulation method. These structures appear as inclined layers in the temperature field with weakly stable stratification, separated by very thin layers with large temperature gradients. The existence of such layered structures in nature is indirectly confirmed by the analysis of field measurement data on the meteorological mast, where temperature gradient distribution histograms are found to be far from the normal distribution and similar to temperature gradient probability distributions obtained by numerical models data. The simulations indicate an increase of the turbulent Prandtl number with increasing of the gradient Richardson number. It is highly likely that the identified structures serve as effective barriers for vertical turbulent heat flux, without the blocking of momentum transfer. We proposed the hypothesis, that it is precisely these structures that serve as the physical mechanism for maintaining turbulence under supercritically stable stratification.

Numerical study of unsteady cavitating flows with RANS and DES models

Unsteady cavitating flow with high Reynolds number and significant instability commonly exists in fluid machinery and engineering system. The high-resolution approaches, such as direct numerical simulation and large eddy simulation, are not practical for engineering issues due to the significant cost in the computational resource. The objective of this paper is to provide the approach with Detached-Eddy Simulation (DES) model based on the Reynolds-averaged Navier–Stokes (RANS) equations for predicting unsteady cavitating flows. The credibility of the approach is validated by a set of numerical examples of its application: the unsteady cavitating flows around the two-dimensional (2D) Clark-Y hydrofoil and the three-dimensional (3D) blunt body. It is found that the calculated cavity shapes, cavity lengths and unsteady characteristics by DES model agree well with the experimental measurements and observations. Further analysis indicates that the turbulent eddy viscosity around the cavity and wake region is well predicted by the DES model, which results in the development of large-scale vortexes, and further cavitation instability. The DES model, which exhibits a significantly unsteady 3D behavior, is a more comprehensive turbulence model for unsteady cavitating flows.

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(105)) moving bodies, utilizing many computational cores (O(105)), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

Layered Structure of Stably Stratified Turbulent Shear Flows

The data of numerical simulation of stably stratified turbulent Couette flows are analyzed for various values of the Richardson number. Two different methods were used: Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). It is shown that the flow contains large organized structures, along with chaotic turbulence, regardless of the simulation method. These structures appear as inclined layers in the temperature field with weakly stable stratification, separated by very thin layers with large temperature gradients. The existence of such layered structures in nature is indirectly confirmed by the analysis of field measurement data on the meteorological mast, where temperature gradient distribution histograms are found to be far from the normal distribution and similar to temperature gradient probability distributions obtained by numerical models data. The simulations indicate an increase of the turbulent Prandtl number with increasing of the gradient Richardson number. It is highly likely that the identified structures serve as effective barriers for vertical turbulent heat flux, without the blocking of momentum transfer. We proposed the hypothesis, that it is precisely these structures that serve as the physical mechanism for maintaining turbulence under supercritically stable stratification.

Computationally efficient prediction of cycle-to-cycle variations in spark-ignition engines

Cycle-to-cycle variations are important to consider in the development of spark-ignition engines to further increase fuel conversion efficiency. Direct numerical simulation and large eddy simulation can predict the stochastics of flows and therefore cycle-to-cycle variations. However, the computational costs are too high for engineering purposes if detailed chemistry is applied. Detailed chemistry can predict the fuels’ tendency to auto-ignite for different octane ratings as well as locally changing thermodynamic and chemical conditions which is a prerequisite for the analysis of knocking combustion. In this work, the joint use of unsteady Reynolds-averaged Navier–Stokes simulations for the analysis of the average engine cycle and the spark-ignition stochastic reactor model for the analysis of cycle-to-cycle variations is proposed. Thanks to the stochastic approach for the modeling of mixing and heat transfer, the spark-ignition stochastic reactor model can mimic the randomness of turbulent flows that is missing in the Reynolds-averaged Navier–Stokes modeling framework. The capability to predict cycle-to-cycle variations by the spark-ignition stochastic reactor model is extended by imposing two probability density functions. The probability density function for the scalar mixing time constant introduces a variation in the turbulent mixing time that is extracted from the unsteady Reynolds-averaged Navier–Stokes simulations and leads to variations in the overall mixing process. The probability density function for the inflammation time accounts for the delay or advancement of the early flame development. The combination of unsteady Reynolds-averaged Navier–Stokes and spark-ignition stochastic reactor model enables one to predict cycle-to-cycle variations using detailed chemistry in a fraction of computational time needed for a single large eddy simulation cycle.

Assessment of the validity of RANS knock prediction using the resonance theory

Following the resonance theory by Bradley and co-workers, engine knock is a consequence of an auto-ignition in the developing detonation regime. Their detonation diagram was developed using direct numerical simulations and was applied in the literature to engine knock assessment using large eddy simulations. In this work, it is analyzed if the detonation diagram can be applied for post-processing and evaluation of predicted auto-ignitions in Reynolds-averaged Navier–Stokes simulations even though the Reynolds-averaged Navier–Stokes approach cannot resolve the fine structures resolved in direct numerical simulations and large eddy simulations that lead to the prediction of a developing detonation. For this purpose, an engine operating point at the knock limit spark advance is simulated using Reynolds-averaged Navier–Stokes and large eddy simulations. The combustion is predicted using the G-equation and the well-stirred reactor model in the unburnt gases based on a detailed gasoline surrogate reaction scheme. All the predicted ignition kernels are evaluated using the resonance theory in a post-processing step. According to the different turbulence models, the predicted pressure rise rates and gradients differ. However, the predicted ignition kernel sizes and imposed gas velocities by the auto-ignition event are similar, which suggests that the auto-ignitions predicted by Reynolds-averaged Navier–Stokes simulations can be given a meaningful interpretation within the detonation diagram.

Large-scale performance of a DSL-based multi-block structured-mesh application for Direct Numerical Simulation

SBLI (Shock-wave/Boundary-layer Interaction) is a large-scale Computational Fluid Dynamics (CFD) application, developed over 20 years at the University of Southampton and extensively used within the UK Turbulence Consortium. It is capable of performing Direct Numerical Simulations (DNS) or Large Eddy Simulation (LES) of shock-wave/boundary-layer interaction problems over highly detailed multi-block structured mesh geometries. SBLI presents major challenges in data organization and movement that need to be overcome for continued high performance on emerging massively parallel hardware platforms. In this paper we present research in achieving this goal through the OPS embedded domain-specific language. OPS targets the domain of multi-block structured mesh applications. It provides an API embedded in C/C++ and Fortran and makes use of automatic code generation and compilation to produce executables capable of running on a range of parallel hardware systems. The core functionality of SBLI is captured using a new framework called OpenSBLI which enables a developer to declare the partial differential equations using Einstein notation and then automatically carryout discretization and generation of OPS (C/C++) API code. OPS is then used to automatically generate a wide range of parallel implementations. Using this multi-layered abstractions approach we demonstrate how new opportunities for further optimizations can be gained, such as fine-tuning the computation intensity and reducing data movement and apply them automatically. Performance results demonstrate there is no performance loss due to the high-level development strategy with OPS and OpenSBLI, with performance matching or exceeding the hand-tuned original code on all CPU nodes tested. The data movement optimizations provide over 3× speedups on CPU nodes, while GPUs provide 5× speedups over the best performing CPU node. The OPS generated parallel code also demonstrates excellent scalability on nearly 100K cores on a Cray XC30 (ARCHER at EPCC) and on over 4K GPUs on a CrayXK7 (Titan at ORNL).

Including analytically reduced chemistry (ARC) in CFD applications

Reacting numerical simulations today are often based on either fitted global reaction schemes, comprised of a few empirical reactions, or pre-tabulated laminar flame solutions computed with detailed chemistry. Although both methods can accurately predict global quantities such as laminar flame speed and burnt gas composition, they have significant limitations. In particular, neither are able to directly and adequately describe the complexity of pollutant chemistry. In the context of reducing harmful emissions of the next generation of aeronautical combustors, however, including these needed additional kinetic details in combustion simulations is becoming essential. Direct integration of detailed chemistry in accurate turbulent combustion models is not a viable option in the foreseeable future, because of excessive computational demands and numerical stiffness. In this context, Analytically Reduced Chemistry (ARC) represents an attractive compromise between accuracy and efficiency, and is already employed in relatively complex Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). ARCs are knowledge-based compact mechanisms retaining only the most relevant kinetic information as extracted directly, and without fitting, from detailed chemical models using specialized reduction techniques (important species identification through graph search, lumping of species with similar features, short-living species identification, etc.). In recent years, several multi-step efficient and automated reduction tools have been developed, enabling the easy generation of ARCs with minimum input and knowledge from the user. The main objective of this paper is to present a review of ARCs for fuels ranging from methane to aviation kerosene surrogates, recently derived with such a multi-step automated reduction tool: YARC. Information about the applicability and range of validity of each derived mechanism are given, along with further references. Each one was specifically derived to be convenient to use in CFD; in particular, the stiffness was regarded as a key factor and the final number of transported species never exceeds thirty. In a final section, the great potential of the methodology is illustrated in a multi-phase, reactive LES application where the fuel is a real multi-component transportation fuel. To that end, an ARC based on a Jet A described by the novel Hybrid Chemistry (HyChem) approach is coupled with the Dynamically Thickened Flame LES (DTFLES) model and directly integrated into the LES solver AVBP. A Lagrangian spray description is used. Results are compared to experimental data in terms of temperature and major species (CO2, H2O, CO, NO) mass fractions, leading to very satisfying results.

Numerical Investigations on the Effect of Isothermal Multi-Jets in Air Curtains with LES Approach

This work focuses on the analysis of the turbulent intensity of the flow field resulting from planar jets applied in air curtains systems, which are used in various industry sectors. The air curtains allow realizing cellular containment. Hence, the main objective is to improve the quality of confinement’s separation by air curtains. In order to achieve this target, the jet flow must be as laminar as possible. Numerical LES investigations are carried out in this study. A jet impingement against a flat and a smooth surface without recirculation has been used for this assessment. The WALE (Wall Adapting Local Eddy) structure models the subgrid-scale tensor. First, the configuration of air curtain with a single jet and then with a twin-jet are investigated. Result comparisons to available experimental measurements have been performed and good agreements have been noticed. The study is then extended for the first time to air curtain configurations with more than two planar jets. The configuration of the triple jet indicates a lower turbulence level than the single jet and the twin-jet ones. This improves the confinement’s separation quality. However, increasing the number of jets highlights a limit because the turbulence decrease will be not significant beyond a certain number of jets taking into account the operating conditions. In this study, an effective process shows that, the four jets configuration is considered as the better compromise under the considered operating conditions.

Air exchange in urban canyons with variable building width: a numerical LES approach.

The aim of this work is to gain further insight into the role played by the building aspect ratio (ARB, i.e., the ratio of the building width, WB, to the building height, H) and its influence on street canyon flow. We carried out a series of large eddy simulations with arrays of obstacles with different widths, ranging from 0.5 to 2.0, and two canyon aspect ratios (ARC, i.e., the ratio of the canyon width, W, to H) ARC = 0.5 and ARC = 1.0. Experimental data was obtained in a water channel for the corresponding configuration and used to validate numerical simulations. Results were found strongly dependent on the building aspect ratios, with two distinct behaviours identified with respect to the canyon aspect ratio. The residence time decreases with decreasing ARB, irrespective of the canyon aspect ratio, suggesting that ARB and ARC can be optimised to guarantee optimal street canyon ventilation in urban planning.

Air exchange in urban canyons with variable building width: a numerical LES approach

The aim of this work is to gain further insight into the role played by the building aspect ratio (ARB, i.e., the ratio of the building width, WB, to the building height, H) and its influence on street canyon flow. We carried out a series of large eddy simulations with arrays of obstacles with different widths, ranging from 0.5 to 2.0, and two canyon aspect ratios (ARC, i.e., the ratio of the canyon width, W, to H) ARC = 0.5 and ARC = 1.0. Experimental data was obtained in a water channel for the corresponding configuration and used to validate numerical simulations. Results were found strongly dependent on the building aspect ratios, with two distinct behaviours identified with respect to the canyon aspect ratio. The residence time decreases with decreasing ARB, irrespective of the canyon aspect ratio, suggesting that ARB and ARC can be optimised to guarantee optimal street canyon ventilation in urban planning.

Reduction of internal-solitary-wave-induced forces on a circular cylinder with a splitter plate

Internal solitary wave (ISW) of depression type widely exists in stratified water, with upper layer having a lower density caused by salinity or temperature. The ISW-induced force on the pile is different from that induced by pure current due to the feature of different flow directions between these two layers. The question remains whether the method commonly used for reduction of forces acting on a pile under pure current can still be applied in case of ISW propagation. In this study, a splitter plate deployed upstream of the pile with its frontal face normal to the wave propagation is used to explore the reduction of forces on an erected cylindrical pile. The ISWs-induced forces acting on a pile with different splitter plates are simulated by means of the large eddy numerical simulation. Extra laboratory experiments on the propagation of the ISWs around an erected cylindrical pile without a splitter plate are carried out for verifying the numerical models. It is found that the splitter plate has prominent influences on the force distribution of the pile in the upper layer. However, it hardly has an effect on the counterpart in the lower layer during the propagation of the ISWs of depression type. In addition, the pattern of vortex structures existing behind the splitter plate does play an important role in reducing the forces on the frontal side of the pile. Numerical results also reveal that the length of the splitter plate and the distance between the splitter plate and the frontal side of the pile characterize the feature of vortex structures around the pile. It is important to restrain the parameters of splitter plates at an appropriate level. Otherwise, over-reduction would occur and the ISWs-induced forces acting on a pile with the splitter plate would be unexpectedly larger than forces on the single pile without a splitter plate.

Definitions of vortex vector and vortex

Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

A five-equation model for the simulation of miscible and viscous compressible fluids

Typical multispecies compressible Navier–Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces between gases of differing ratio of specific heat capacities which degrade the convergence rate of the algorithm. Adding quasi-conservative equations for volume fraction can solve this error, however this approach has been derived only for immiscible fluids. Here, a five-equation quasi-conservative model is proposed that includes the effects of species diffusion, viscosity and thermal conductivity. The derivation of the model is presented, along with a numerical method to solve the governing equations at second order accuracy in space and time. Formal convergence studies demonstrate the expected order of accuracy is achieved for three benchmark problems, cross-validated against two standard mass fraction models. In these test cases, the new model has between 2 and 10 times lower error for a given grid size. Simulations of a two-dimensional air-SF6 Richtmyer–Meshkov instability demonstrate that the new model converges to the solution with four times fewer points in each direction when compared to the mass fraction model in an identical numerical framework. This represents an ≈40 times lower computational cost for an equivalent error in two-dimensional computations. The proposed model is thus very suitable for Direct Numerical Simulation and Large Eddy Simulation of compressible mixing.

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

In the present work, a highly efficient incompressible flow solver with a semi-implicit time advancement on a fully staggered grid using a high-order compact difference scheme is developed firstly in the framework of approximate factorization. The fourth-order compact difference scheme is adopted for approximations of derivatives and interpolations in the incompressible Navier–Stokes equations. The pressure Poisson equation is efficiently solved by the fast Fourier transform (FFT). The framework of approximate factorization significantly simplifies the implementation of the semi-implicit time advancing with a high-order compact scheme. Benchmark tests demonstrate the high accuracy of the proposed numerical method. Secondly, by applying the proposed numerical method, we compute turbulent channel flows at low and moderate Reynolds numbers by direct numerical simulation (DNS) and large eddy simulation (LES). It is found that the predictions of turbulence statistics and especially energy spectra can be obviously improved by adopting the high-order scheme rather than the traditional second-order central difference scheme.