Based on the fifth-order scheme in our previous work (Deng et. al (2019) [28]), a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called PnTm−BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm), are designed by employing high-order upwind-biased interpolations and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. We devise the new schemes up to eleventh order in an efficient way by directly increasing the order of the underlying upwind scheme using high order polynomials. The analysis of the spectral property and accuracy tests show that the new reconstruction strategy well preserves the low-dissipation property of the underlying upwind schemes with high-order polynomials for smooth solution over all wave numbers and realizes n+1 order convergence rate. The performance of new schemes is examined through widely used benchmark tests, which demonstrate that the proposed schemes are capable of simultaneously resolving small-scale flow features with high resolution and capturing discontinuities with low dissipation. With outperforming results and simplicity in algorithm, the new reconstruction strategy shows great potential as an alternative numerical framework for computing nonlinear hyperbolic conservation laws that have discontinuous and smooth solutions of different scales.

In this paper, we investigate designing a new type of high-order finite difference multi-resolution trigonometric weighted essentially non-oscillatory (TWENO) schemes for solving hyperbolic conservation laws and some benchmark highly oscillatory problems. We only use the information defined on a hierarchy of nested central spatial stencils in a trigonometric polynomial reconstruction framework without introducing any equivalent multi-resolution representations. These new finite difference trigonometric WENO schemes use the same large stencils as the classical WENO schemes [26, 41], could obtain the optimal order of accuracy in smooth regions, and simultaneously suppress spurious oscillations near strong discontinuities. The linear weights of such multi-resolution trigonometric WENO schemes can be any positive numbers on condition that their summation is one. This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finite difference trigonometric WENO schemes. These new trigonometric WENO schemes are simple to construct and can be easily implemented to arbitrary high-order accuracy in multi-dimensions. Some benchmark examples including some highly oscillatory problems are given to demonstrate the robustness and good performance of these new trigonometric WENO schemes.

Anisotropic prismatic/strand meshes are often used to capture viscous boundary layer effects in Reynolds Averaged Navier Stokes (RANS) simulations of high Reynolds number flows. This paper describes a new algorithm for generation of prismatic meshes using the minimum distance field of the surface tessellation. The algorithm starts with initial point placement using both the direction of best visibility and the direction to the closest point on the minimum distance iso-surface. Initial point placement is followed by a constrained smoothing operation based on an elastic spring analogy. The constraints ensure movement of nodes is restricted to the iso-surface of the distance field and within the region of visibility. Simulations are performed using a dual-mesh infrastructure, where the prismatic meshes transition to a Cartesian background mesh a short distance from the wall. This overset mesh system is processed by a domain connectivity method to establish connections between self-intersecting strand meshes and strand/Cartesian mesh systems. Mesh and flow simulation results are presented for test cases of varying complexity.

We present a new closure model for Large Eddy Simulation to introduce dissipation in under–resolved turbulent simulation using discontinuous Galerkin (DG) schemes applied to the compressible Navier–Stokes equations. The development of the method is based on a thorough analysis of the numerical dissipation mechanisms in DG schemes. In particular, we use upwind Riemann solvers for inter–element dissipation, and a Spectral Vanishing Viscosity (SVV) method for interior dissipation. First, these mechanisms are analysed using a linear von Neumann analysis (for a linear advection–diffusion equation) to characterise their properties in wave–number space. Second, their behaviour is tested using the three–dimensional Taylor–Green Vortex Navier–Stokes problem to assess transitional/turbulent flows. The results of the study are subsequently used to propose a DG–SVV approach that uses a mode-selection Smagorinsky LES model to compute the turbulent viscosity. When the SVV technique is combined with a low dissipation Riemann solver, the scheme is capable of maintaining low dissipation levels for laminar flows, while providing the correct dissipation for all wave–number ranges in turbulent regimes. The developed approach is designed for polynomial orders N ≥ 2 and is specially well suited for high order schemes. This new DG–SVV approach is calibrated with the Taylor–Green test case; to then show its accuracy in an under–resolved (y+>8) channel flow at Reynolds number Reτ=183.

We present a systematic framework for the evaluation of shock sensors in high-resolution hybrid compact/WENO algorithms, with the goals of testing robustness and establishing accuracy in wavenumber space, with the intent to go beyond mere case-by-case comparison of solvers/sensors. Several sensors are considered, including classical ones, sensors based on multi-resolution wavelet analysis, and WENO-based shock sensors. The crucial issue of identification of suitable thresholds for the various shock sensors is tackled through a series of static tests and numerical simulations. Whereas any shock sensor with suitably low threshold is found to be effective in capturing shocks, not all of them perform equally well for waves. Performance degradation in numerical simulation of wave-like phenomena is here characterized by introducing an effective band-width for each sensor, which is found to be quite narrow for classical sensors, and much wider for WENO-based shock sensors. Based on this analysis, we also identify a new shock sensor which can be easily implemented in existing WENO-based codes. The new sensor doesn’t suffer from contamination from the WENO numerical error even for waves resolved with as few as three points-per-wavelength. This property translates into improved performance in wavenumber space, and greater resolving power in flow cases involving shocks and compressible turbulence, as demonstrated through a series of numerical tests. We emphasize that this sensor can be applied more broadly to any algorithm which contains similar smoothness indicators as classical WENO.

Particle migration in laminar boundary layers is extensively studied, but in the near-leading-edge region, this process is not fully understood, yet. In this paper, the lateral migration of heavy particles entering the laminar boundary layer near the leading edge of a flat plate is investigated. First, numerical and analytical studies show that the high-vertical-velocity zone outside the laminar boundary layer near the leading edge plays a key role in the particle's lateral migration. Then, based on the analytical result, a transverse Stokes number which accounts for the effect of the high-vertical-velocity zone and the particle's lateral inertia is proposed. Finally, results of twenty-seven simulation cases are collected and analyzed, and this number is proved to be a more suitable criterion than the Stokes number in predicting the particle's lateral migration regime near the leading edge of a flat plate.

A hyperbolic method for incompressible Navier-Stokes equations is presented in a cell-centered finite volume framework on unstructured meshes. Solution algorithms were introduced on triangular meshes in 2D and on tetrahedral meshes in 3D. Justification of the absolute Jacobian approximation is discussed, and a solution reconstruction algorithm utilizing the robust and effective wrapping stencil is illustrated. The effectiveness of the unconditionally stable implicit solution strategy was demonstrated by comparison to an explicit scheme. A series of test cases are presented in order of study accuracy and as a comparison with other reference computational and experimental results, namely Kovasznay flow, driven cavity flow, and flow past a circular cylinder in 2D and a sphere in 3D. The equal order of accuracy feature of the hyperbolic method, namely the second order accuracy in solution and the gradient variables, was verified. The superior accuracy of the current hyperbolic scheme in terms of predicting the velocity gradient on a solid surface was emphasized by comparison with standard second order finite volume results.

The normal shock wave–boundary layer interaction (SBLI) phenomenon is known to constitute a main factor limiting the aerodynamic performance in many aeronautical applications (transonic wings, helicopter rotor blades, compressor and turbine cascades). The interaction process highly disturbs the boundary layer, often causing flow separation and onset of large scale unsteadiness (e.g. airfoil buffet or supersonic inlet buzz). In certain conditions it may also initiate a dramatic increase of acoustic emission levels (e.g. high-speed impulsive noise). To limit the negative impact of the phenomenon various flow control strategies are implemented, here in a form of a passive control system realised by placing a shallow cavity covered by a perforated plate just beneath the shock. Details of the flow structure obtained by this method are studied numerically. Three distinctive experimental set-ups are considered with the interaction taking place: on a flat wall (transonic nozzle, ONERA), on a convex wall (curved duct, University of Karlsruhe), and on an airfoil (NACA 0012, NASA Langley). Depending on the relative cavity length the ventilation process leads to a transformation of the normal shock topology into: a large λ-foot structure (classical, short cavity), a system of oblique waves (extended cavity), or a gradual compression (full-chord perforation). The reference and flow control cases are simulated with the SPARC code (RANS) with Spalart–Allmaras turbulence and Bohning–Doerffer transpiration models. The results are compared with the measurements, emphasizing the streamwise evolution of the boundary layer profiles and integral parameters during the interaction. The prediction capabilities of the solver in terms of the shock wave–boundary layer interaction control by wall ventilation are assessed and presented in details for the investigated range of flow configurations and conditions.

High parallel efficiency for large-scale coupled multiphysics simulations requires the computational load to be evenly distributed among all compute cores. For complex applications and massively parallel computations, even minor load imbalances can have a severe impact on the overall performance and resource usage. Exemplarily for a volume-coupled multiphysics simulation, a direct-hybrid method is considered, in which a CFD and a CAA simulation are performed concurrently on the same parallel subdomains. For differing load compositions on each subdomain, accurate computational weights for CFD and CAA cells must be known to determine an efficient domain decomposition. Therefore, a dynamic load balancing scheme is presented, which allows to increase the efficiency of complex coupled simulations with non-trivial domain decompositions. A fully-coupled three-dimensional jet simulation with approximately 300 million degrees of freedom demonstrates the effectiveness of the approach to reduce load imbalances. A detailed performance analysis substantiates the necessity of dynamic load balancing. Furthermore, the results of a strong scaling experiment show the benefit of load balancing to be proportional to the degree of parallelism. In addition, it is shown that the approach allows to attenuate imbalances also for parallel computations on heterogeneous computing hardware. The acoustic field of a chevron nozzle will also be discussed.

The present paper extends the conservative finite element convective scheme proposed by Charnyi et al.(Journal of Computational Physics 337, 2017, 289 - 308) originally formulated for incompressible flows to the low Mach regime. Similar to Lehmkuhl et al.(Journal of Computational Physics 390, 2019, 51 - 65) stabilisation is only introduced for the continuity equation by means of a non-incremental fractional-step method, modified in order to account for variable density flows. The final scheme preserves momentum and angular momentum for variable density flows. The error of kinetic energy conservation is of order O(δthk+1), thus dissipation is limited. Standard stabilised finite elements are used for the scalars. Time integration is carried out by means of an explicit third order Runge-Kutta scheme for all equations. The proposed strategy is tested on a set of relevant cases with available reference data using large-eddy simulations. First, an anisothermal turbulent channel flow is assessed. Later, a technically premixed turbulent flame in a swirl-stabilized configuration is considered. And finally, a turbulent jet diffusion flame in a low-velocity co-flow has been studied. In all cases the performance of the presented low Mach formulation is fairly good, showing better accuracy than skew-symmetric like strategies.

The use of a CFD/CAA method, where fluctuations are extracted on a surface and propagated analytically to the far-field, is becoming a practical approach for industrial jet noise prediction. However, the placement of the surface can be problematic and a source of error, so here an efficient LES/APE coupling method that relies on volumetric sources is utilised. This allows the use of an existing, well validated and robust finite volume LES code to compute the unsteady flow, from which the volumetric sources are extracted, to then compute the propagation of the acoustic waves to the far-field using a high-order finite element APE code with a grid more appropriate for this task. Furthermore, this coupled methodology allows the studying of noise propagation in complex configurations in which the use of surface integral methods could be challenging. In this work, a coupling strategy is used in which all the necessary data is exchanged directly via the high-speed communication network using an open-source library. The efficiency of the parallel-coupling strategy is demonstrated by applying it to a 2D canonical case and comparing it with an existing file-based approach. For the acoustic propagation, the APE solver used is called AcousticSolver, part of the high-order spectral/hp finite element open-source code Nektar++. The present LES/APE framework is fist validated for 3D jet applications by studying the noise propagation of a low-Reynolds number case. Then the method is applied to a more realistic high Reynolds number jet obtaining encouraging results in terms of flow and acoustic predictions.

Spray A from ECN, representative of diesel-like sprays, is modelled in the frame of Large-Eddy Simulations (LES) with a Dynamic Structure (DS) turbulence model in conjunction with an Unsteady Flamelet Progress Variable (UFPV) combustion model. In this work, the spray flow field is first calibrated under inert conditions against experimental data. In a second step, the reactive spray is simulated in order to describe the flame internal structure when varying ambient temperature. The model shows a good agreement with experimental results and describes the trends observed in flame global parameters, such as ignition delay (ID) and lift-off length (LOL). Low fluctuations are observed in LOL positioning revealing an intense chemical activity at the height of the base of the flame, which stabilizes the reaction in spite of the turbulent fluctuations. The analysis of the LES instantaneous fields shows how ignition kernels appear upstream of the base of the flame, clearly detached from the reaction zone, and grow and merge with the main flame in agreement with previous reported experimental and modelling results. The ambient temperature has a clear impact on the flame structure described by the model and the whole set of results reveal that in the frame of LES simulations the UFPV model is suitable for the calculation of diesel flames.

We focus on simulating the consequences of material interpenetration and mixing arising from perturbations at shocked material interfaces, as vorticity is introduced by the impulsive loading of shock waves, e.g., as in Inertial Confinement Fusion (ICF) capsule implosions. The flow physics is driven by flow instabilities such as Richtmyer-Meshkov, Kelvin-Helmholtz, Rayleigh-Taylor, and vortex stretching; it is capturable with both, classical large-eddy simulation (LES) and implicit LES (ILES) – where small-scale flow dynamics is presumed enslaved to the dynamics of the largest scales. Beyond the complex multiscale resolution issues of shocks and variable density turbulence, we must address the difficult problem of predicting flow transitions promoted by energy deposited at the material interfacial layers during the shock interface interactions. Transition involves unsteady large-scale coherent-structure dynamics resolvable by the coarse grained simulation but not by Reynolds-Averaged Navier-Stokes (RANS) modeling based on equilibrium turbulence assumptions and single-point-closures. We describe a dynamic blended hybrid RANS/LES bridging strategy for applications involving variable-density turbulent mixing applications. We report progress testing implementation of our proposed computational paradigm for relevant canonical problems, in the context of LANL’s xRAGE Eulerian hydrodynamics and BHR unsteady RANS code. Proof-of-concept cases include the Taylor-Green vortex – prototyping transition to turbulence, and a shock tube experiment – prototyping shock-driven turbulent mixing.

Computational fluid dynamics models based on Reynolds-averaged Navier–Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.

The performance prediction of two counter-rotating vertical axis hydrokinetic turbines is presented in this paper. The flow field is governed by the 3D time-dependent incompressible Navier–Stokes equations. The system of equations is discretized using the Arbitrary Lagrangian-Eulerian Variational Multi-scale formulation for turbulence modeling on moving domains. Sliding interfaces are used to handle the rotor-stator interactions. Weak enforcement of essential boundary conditions is used to relax the requirement of boundary layers resolution. A grid convergence study based on the evaluation of the grid convergence index for the computed torque and the time-averaged axial wake velocity is performed. The grid convergence study shows good convergence with grid refinement in our formulation. Experimental validation of the averaged torque is performed for two different flow conditions and different turbine rotational velocities with good agreement. The finest mesh resolution from the grid convergence study is used for the multiple turbines simulation. The simulation shows almost 25% deficiency in the averaged torque of the downstream turbine. A multi-domain method is introduced to predict the performance of the turbine array at a lower computational cost than the full array simulation. The results from the multi-domain method show good matching on the averaged torque with the full array simulation. The initial study on the effect of struts on the torque generation is presented. The results assure the robustness of the ALE-VMS formulation and how it can be used to simulate multiple turbines at full-scale and full geometric complexity.

A stable and non-dissipative numerical scheme for Cartesian methods is proposed. The proposed scheme is based on the second-order kinetic energy and entropy preserving scheme, which the authors proposed recently, and conservation is satisfied at non-conforming boundaries where the grid refinement level is different across the computational block boundaries. In the proposed scheme, ghost cells are used at computational block boundaries for efficient parallel computation, and conservation is satisfied by assigning appropriate values to the ghost cells. Also, although the five conservative variables (i.e., mass, momentum, and total energy) are typically transferred from computational cells to corresponding ghost cells at computational block boundaries, the proposed scheme transfers two more conservative variables to satisfy conservation at non-conforming block boundaries. In a vortex convection test, the convergence rates of the L2- and L∞-error norms are examined, and the proposed scheme preserves the second-order of accuracy without inducing destructive errors at non-conforming boundaries. In an inviscid Taylor-Green vortex simulation, the proposed scheme demonstrates superior numerical stability by preserving kinetic energy and entropy. Also, the proposed scheme performs more stable computations on a non-conforming computational grid than a typical kinetic energy preserving scheme calculated on a uniform computational grid.

The simulation of accidental transient sequences in the nuclear industry requires, even at a global scale, for local geometric details to be taken into account. Multi-model approaches allow the integration of such details without modifying the global scale modelling (techniques also known as numerical zooms). In the current paper, we propose two new multi-model approaches for transient fluid dynamics described by the Euler equations. This is done with the additional purpose of developing multi-model approaches for Fluid Structure Interaction (FSI) phenomenons so that a hybrid Finite Element/Finite volume discretization is used for the fluid. Both proposed multi-model approaches use the Arlequin framework for the treatment of the momentum equation while the other two equations are treated by either the Chimera method or the Arlequin method. As explicit time integrators are used, a stability study is completed and guidelines are given in order to guarantee a feasible time step. In particular, the choice of the Arlequin weight functions should be defined carefully. Spurious effects are observed and their origin explained. An approach to efficiently handle them is proposed. Two convergence studies validate the proposed approaches and present similar, if not better, convergence properties than for the Chimera method, currently the reference in the literature. Thus, these two approaches should be considered for transient fluid dynamics applications.

Hardware trends over the last decade show increasing complexity and heterogeneity in high performance computing architectures, which presents developers of CFD applications with three key challenges; the need for achieving good performance, being able to utilise current and future hardware by being portable, and doing so in a productive manner. These three appear to contradict each other when using traditional programming approaches, but in recent years, several strategies such as template libraries and Domain Specific Languages have emerged as a potential solution; by giving up generality and focusing on a narrower domain of problems, all three can be achieved. This paper gives an overview of the state-of-the-art for delivering performance, portability, and productivity to CFD applications, ranging from high-level libraries that allow the symbolic description of PDEs to low-level techniques that target individual algorithmic patterns. We discuss advantages and challenges in using each approach, and review the performance benchmarking literature that compares implementations for hardware architectures and their programming methods, giving an overview of key applications and their comparative performance.

The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo significant deformation. In the present work, we present detailed numerical simulations of such deformable wings. Our results are obtained with a fluid–structure interaction solver, coupling a mass–spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier–Stokes equations. We impose the no-slip boundary condition through the volume penalization method; the time-dependent complex geometry is then completely described by a mask function. This allows solving the governing equations of the fluid on a regular Cartesian grid. Our implementation for massively parallel computers allows us to perform high resolution computations with up to 500 million grid points. The mass–spring model uses a functional approach, thus modeling the different mechanical behaviors of the veins and the membranes of the wing. We perform a series of numerical simulations of a flexible revolving bumblebee wing at a Reynolds number Re=1800. In order to assess the influence of wing flexibility on the aerodynamics, we vary the elasticity parameters and study rigid, flexible and highly flexible wing models. Code validation is carried out by computing classical benchmarks.

The present paper describes the application of local perturbations in Large Eddy Simulation to enhance transition to turbulence applied on the heated wall of a natural convection boundary layer. Simulations are carried out with a Prandtl number Pr=0.71 and a maximum Grashof number of Gr=4.1·1011. The purpose of this work is to accelerate the transition process in the numerical domain, reducing the needed simulation effort to reach the turbulent regime in a natural convection boundary layer flow. A parametric study has been performed to identify the fastest transition to turbulence in the proposed technique. The obtained results are compared with experimental, empirical and other numerical reference data to assess the method’s performance. The analysis of the transition method contemplates its effect in the mean flow field, as well as in the resolved Reynolds stresses and turbulent heat fluxes.

In this paper, a dual splitter plate flow separation control device is introduced for a low Reynolds number flow (Re=100) around the square cylinder of length L to achieve higher drag reduction and improved wake regime control compared to the conventional single splitter plate control devices. Here, two splitter plates of the same length W (ranging from 0.25L to 2.50L) are symmetrically attached on the rear surface along the horizontal centerline of the square cylinder with a spacing H (ranging from 0.0L to 1.0L) between them. The numerical study is performed using the in-house developed flexible forcing immersed boundary-lattice Boltzmann solver [1] to investigate the effects of dual splitter plate on the flow regime and flow-induced forces. The shear layer interaction with the splitter plates, as well as the vorticity and pressure distribution in the near wake region, are significantly modified by varying W and H, and four different flow regimes (Type I to Type IV) are identified from the observations. Among these flow types, the Type III flow pattern displays an accelerating flow in the wake region that is found to be most beneficial for higher base pressure recovery and drag reduction. Furthermore, dual splitter plates suppress von-Karman vortex shedding and lift force fluctuation, and produce higher drag reduction ( ≈ 21%) at less than half of the plate length of a single splitter plate. It is also noticed that a dual splitter plate configuration seems to be an optimum arrangement, since adding more splitter plates (up to 5 numbers were tested) on the rear surface of the square cylinder does not change the wake characteristics nor shows any improvements in the drag reduction.

The pathology of aortic diseases is related to wall shear stress, which in the lattice Boltzmann method can be easily calculated using information for the unit normal vector of computational geometry. This paper proposes a method to calculate the unit normal vector. In comparison with the existing method, this approach requires a smaller number of input parameters and significantly reduces the computational cost. Tests on several geometries indicate that this method is a better choice from the viewpoint of accuracy and operability. Finally, the distribution of wall shear stress in a realistic aortic arch is obtained and found to agree with the conclusions of a previous study.

The purpose of this paper is two-fold; first, a systematic approach is developed to improve the steady state stability of cell-centered finite volume methods on unstructured meshes by optimizing boundary conditions. This approach uses the rightmost eigenpairs of the spatially discretized system of equations to determine the existence or the path to stability. This will ensure the energy stability of the system, consequently resulting in convergence to a steady state solution. To this end, it exploits first order gradients of eigenvalues with respect to the types of boundary conditions. This in turn helps in finding an optimized boundary condition type which stabilizes the steady state stability as well as expediting the convergence to the steady state for already stable problems. Secondly, the sensitivity of the rightmost eigenvalues to the solution is measured to investigate the effect of using surrogate or half-converged solutions for the purpose of linearizing the semi-discretized Jacobian.

The performance of three large-eddy simulation (LES) models in predicting the evolution of a shear layer at moderate Reynolds number in a linearly stratified background is investigated. Results of the Dynamic Smagorinsky, Ducros, and Wall-Adapting Local Eddy Viscosity (WALE) models are compared against those of direct numerical simulation (DNS). Two levels of grid refinement are employed to assess the change in the models’ capabilities with varying resolution. Of particular interest is the ability of the models to capture the evolution of instabilities as well as accurately quantify turbulence statistics. Evolution of momentum thickness, local buoyancy flux, shear, and gradient Richardson number show good agreement of the LES models with the DNS. A comparison of the turbulent kinetic energy (TKE) and its budget indicates good capture of turbulence evolution in the LES models. There is a moderate over prediction of spatially integrated TKE during a short period when the integrated TKE is at its maximum. This feature is traced to the underestimate of turbulent dissipation rate in the LES. Coarsening grid resolution significantly increases the discrepancy in dissipation between the WALE model and the DNS while defects due to the coarser grid resolution are mild in the case of the Ducros model. All of the LES models overestimate the peak values of eddy viscosity and eddy diffusivity although the Ducros model produces the closest agreement with the DNS. Furthermore, the Ducros model is found to require fewer CPU hours than the DNS or other LES models.

In this article, two schemes have been presented for applying Neumann boundary condition in thermal lattice Boltzmann method. in Scheme 1, the heat flux is directly applied to the gradients of unknown distribution functions. In the following, using the results of this scheme, Scheme 2 is introduced having simpler structure than Scheme 1. Both schemes are independent of lattice arrangement. However, D2Q9 lattice arrangement is employed in this article. These two schemes are analyzed in several examples at different relaxation times, and second-order convergence accuracy is achieved for both schemes at the relaxation times. In contrast, other conventional methods, especially the ones which are based on passive scalar approach, give second-order convergence accuracy only at particular relaxation times. Moreover, it is shown that the two proposed schemes in this paper have better accuracy than the conventional method used for simulating adiabatic boundary condition, whereas they do not impose additional computational cost. In addition, the two schemes have also been applied on curved boundaries, and good agreement has been observed with exact solution.

In this paper, co-flowing immiscible elliptic jet flow system is investigated numerically in dripping and jetting regimes using front tracking method. In these regimes, the elliptic jet is more unstable than the circular jet. In the jetting regime, the axis-switching of an elliptic liquid jet is studied numerically using front tracking method. The effect of dimensionless parameters like viscosity ratio, density ratio, Weber number, the inner Reynolds number on axis-switching parameters such as maximum jet diameter, mean jet diameter and initial wavelength is considered. The results show that the density ratio affects the initial wavelength more compared to maximum jet diameter. Increasing the viscosity ratio leads to a rise in the maximum jet diameter and a reduction in the initial wavelength. In the dripping regime, the drop formation for elliptic jets is studied, and the results are compared with experiments for elliptic jets. The effect of Weber number of the inner flow, capillary number of the outer flow, viscosity ratio and density ratio on the size of drops formed are studied. It is observed that the microdroplets formed in an elliptic jet are smaller in size compared to a circular jet.

Previous lattice Boltzmann model (LBM) studies on solid entry/exit problems are limited to the free-surface LB model in which effects of the surface tension and gas phase are neglected, the surface wettability cannot be adjusted, boundary conditions need to be applied on the interface, and the interface has to be tracked during time. In addition, conventional macroscopic models for simulating the phenomenon such as Volume Of Fluid (VOF) and Constrained Interpolation Profile (CIP) have the same difficulties with the interface, besides the higher computational cost and time. Therefore, for the first time in this paper, a robust pseudo-potential based multi-phase LB model is coupled with moving boundary LB schemes for simulating liquid entry/exit of solids with the circular cylinder as a selected case study without losing generality. The current model has none of the free-surface LBM limitations and is also superior over the conventional models by automatic interface capturing and lower computational cost and time. Furthermore, the integrated model is capable of simulating the phenomenon at relatively high We and Re numbers and density ratios as high as the water/air one. Formation and propagation of the pressure wave in the case of liquid entry are shown and discussed. Cavity and subsequent pinch-off and jets formations for a hydrophobic surface are also captured and quantified. Effects of the We, Re, Fr, and impact velocity on the pinch-off time and depth, and velocity of subsequent jets are investigated, plotted, and discussed in details. Results show that the pinch-off time and depth are independent of the surface tension and liquid viscosity, but are increased linearly with the impact velocity. Furthermore, the velocity magnitude of both downward and upward jets after the pinch-off is increased with Re and We numbers and is decreased with Fr number.

As an efficient simulation method for complex configurations and moving boundary problems in computational fluid dynamics, Chimera or overset grid techniques have been widely used in many aspects of aeronautics and astronautics. However, there are still some bottlenecks for the current hole-cutting method to handle large scale mesh, such as memory storage limitation and parallel efficiency. In this paper, a parallel implicit hole-cutting method based on unstructured background mesh is presented. The method is based on the parallel searching of donor cells for all grid nodes. In order to reduce the memory consumption of the searching procedure for the large-scale grids, a global-to-local (GTL) searching strategy as well as the background grid approach is developed. To improve the connectivity of overset domains, a parallel front advancing method is adopted to automatically distinguish the active regions. Finally, the efficiency and effectiveness of the present Chimera grid method are validated by some test cases and applications, including multi-store separation from a fighter and a missile pitching-up maneuvering with rudder deflection under a control command. The numerical results demonstrate the potential for steady and unsteady CFD simulations for complex geometries.

Despite having been thoroughly described in various simple configurations, the study of gas-fluidized systems in a CFD/DEM (Discrete Element Method) formalism becomes challenging as the computational domain size and complexity rise. For a while, attention has been drawn to the design of physical models for fluid-particles interactions, but a recent challenge for numerical tools has been to take advantage from the increasing power of distributed memory machines, in order to simulate realistic industrial systems. Furthermore, unstructured meshes are appealing for their ability to describe complex geometries and to perform local refinements, but lead to significant coding effort involving sophisticated algorithm. In a attempt to design a numerical tool able to cope with these limitations, the methodology presented here proposes an efficient non-blocking algorithm for massive parallelism management, as well as an exhaustive contact scheme to deal with arbitrarily complex geometries, all to be operated on unstructured meshes. The aim is two-fold: (i) to assist larger scale codes in their endeavor to close the solid stress tensor for example, (ii) to pave the way for complex industrial-scale systems modeling using DEM. The methodology is successfully applied to a pilot-scale fluidized bed gathering 9.6M spherical particles and enables to reach interesting physical times using reasonable computational resources.

In this article we propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and in this case the flow can simply be modeled by the incompressible Navier-Stokes equations coupled with a transport equation for the temperature and a buoyancy source term in the momentum equation. Our numerical scheme is developed starting from the work presented in [1, 2, 3], in which the spatial domain is discretized using a face-based staggered unstructured mesh. The pressure and temperature variables are defined on the primal simplex elements, while the velocity is assigned to the dual grid. For the computation of the advection and diffusion terms, two different algorithms are presented: i) a purely Eulerian upwind-type scheme and ii) an Eulerian-Lagrangian approach. The first methodology leads to a conservative scheme whose major drawback is the time step restriction imposed by the CFL stability condition due to the explicit discretization of the convective terms. On the contrary, computational efficiency can be notably improved relying on an Eulerian-Lagrangian approach in which the Lagrangian trajectories of the flow are tracked back. This method leads to an unconditionally stable scheme if the diffusive terms are discretized implicitly. Once the advection and diffusion contributions have been computed, the pressure Poisson equation is solved and the velocity is updated. As a second model for the computation of buoyancy-driven flows, in this paper we also consider the full compressible Navier-Stokes equations. The staggered semi-implicit DG method first proposed in [4] for all Mach number flows is properly extended to account for the gravity source terms arising in the momentum and energy conservation laws. In order to assess the validity and the robustness of our novel class of staggered semi-implicit DG schemes, several classical benchmark problems are considered, showing in all cases a good agreement with available numerical reference data. Furthermore, a detailed comparison between the incompressible and the compressible solver is presented. Finally, advantages and disadvantages of the Eulerian and the Eulerian-Lagrangian methods for the discretization of the nonlinear convective terms are carefully studied.

A shape optimization for tonal noise generated aerodynamically at low Mach number is performed for a cylinder with polygonal cross-section. Acoustic quantities are derived from a hybrid analytical formula, with aeroacoustic sources obtained from the incompressible solution of the direct Navier-Stokes equations in 2D at Re = 150; the solid domain is modelled by an Immersed Boundary Method. The optimization is done with the Particle Swarm Optimization (PSO) technique and performed in a cluster where each cost function evaluation is an independent flow simulation. The precision on the 4 main shape parameters is set to 0.001, consistently with the convergence criteria in time, grid and swarm. Optimal shapes for minimum drag and minimum acoustic power are relatively similar. A large range between the optimal shapes is obtained: factor 1.8 for drag and 20 dB for the acoustic power. The reduction of noise is associated with long and bluffer geometries, while the louder flows are associated with highly interacting shear layers obtained with back pointing triangles. The fluctuating lift is the major quantity to control noise at fixed length, while increasing the aspect ratio tends to reduce the noise for globally all geometries. An overall correlation between mean drag and fluctuating suction is also noticed.

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes [42] is adopted. In the classical finite volume type WENO schemes, the linear weights for candidate stencils are obtained by solving linear systems at Gaussian quadrature points of cell interface. For the three-dimensional scheme, such operations at twenty-four Gaussian quadrature points of a hexahedron would reduce the efficiency greatly, especially for the moving-mesh computation. Another drawback of the classical WENO schemes is the appearance of negative weights with irregular local topology, which affect the robustness of spatial reconstruction. For the three-dimensional WENO-AO scheme, a simple strategy of selecting big stencil and sub-stencils for reconstruction is proposed. With the reconstructed quadratic polynomial from big stencil and linear polynomials from sub-stencils, the linear weights are chosen as positive numbers with the requirement that their summation equals to one and be independent of local mesh topology. With such WENO reconstruction, a high-order gas-kinetic scheme (HGKS) is developed for both three-dimensional inviscid and viscous flows. Taken the grid velocity into account, the scheme is extended into the moving-mesh computation as well. Numerical results are provided to illustrate the good performance of such new finite volume WENO scheme. In the future, such WENO reconstruction will be extended to the unstructured meshes.

This study conducts an implicit large eddy simulation (ILES) of jet boat tail (JBT) flows to investigate its drag reduction mechanism. The concept of JBT passive flow control is to create a circumferential jet around a bluff body toward the center of the base area. It forms a jet cone to have the similar effect of a solid boat tail. The LES is performed for a baseline bluff body and a JBT model modified from the baseline. The LES predicts that the JBT reduces the averaged drag coefficient by 19.3%, a reasonable agreement with the experimental drag reduction of 22.5%. The reduced averaged wake area is also observed for the JBT model, resulting in a decreased drag. In addition, the unsteady flow structures of the baseline and JBT flow are analyzed to study the flow mixing and entrainment mechanism. For the baseline configuration, the coherent vortex structures occur far downstream of the base surface. It hence does not have strong entrainment and energy transfer from freestream to the base area. For the JBT flow, a pulsative jet is induced by the vortex shedding of the shear layer and interacts immediately with the shear layer near the base surface. It generates the small structures that are substantially larger than those of the baseline configuration. The larger vortex structures of JBT enhance the flow entrainment and transfer more energy from the freestream to the base area. It results in higher static pressure in the base area that substantially reduces the pressure drag. Proper orthogonal decomposition of flow field reveals the periodic jet pulsation pattern in the azimuthal direction.

A recently developed fourth-order accurate implicit residual smoothing scheme (IRS4) is investigated for the large eddy simulation of turbomachinery flows, characterized by moderate to high Reynolds numbers and subject to severe constraints on the maximum allowable time step if an explicit scheme is used. For structured multi-block meshes, the proposed approach leads to the inversion of a scalar pentadiagonal system by mesh direction, which can be done very efficiently. On the other hand, applying IRS4 at each stage of an explicit Runge–Kutta time scheme allows to increase the time step by a factor 5 to 10, leading to substantial savings in terms of overall computational time. With respect to standard second-order fully implicit approaches, the IRS4 does not require approximate linearization and factorization procedures nor inner Newton-Raphson subiterations. As a consequence, it represents a better cost-accuracy compromise for the numerical simulations of turbulent flows where the maximum time step is controlled by the lifetime of the smallest resolved turbulent structures. Numerical results for the well-documented high-pressure VKI LS-89 planar turbine cascade illustrate the potential of IRS4 for significantly reducing the overall cost of turbomachinery large eddy simulations, while preserving an accuracy similar to the explicit solver even for sensitive quantities like the heat transfer coefficient and the turbulent kinetic energy field.

This paper introduces a new pressure-velocity coupling algorithm based on the SIMPLEC method. The new approach considers the neighbour velocity corrections of SIMPLEC as a Taylor series expansion, introducing a first-order term to increase the accuracy of the approximation. The new term includes a velocity correction gradient which is assumed to be a scalar matrix constrained by means of a mass conservation equation. The stability of the method is analyzed via a Fourier decomposition of the error showing a better convergence rate than SIMPLE and SIMPLEC for high relaxation factors. The new method is tested in two incompressible laminar flow problems. Then, the analysis is extended to a turbulent flow case. In all cases, the conclusions of the stability analysis are verified. The current proposal sets a theoretical baseline for further improvements of SIMPLE-based algorithms.

The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor ∇u is decomposed into three components representing an irrotational straining motion (∇u)EL, a rigid-body rotation (∇u)RR, and a shearing motion (∇u)SH. Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately strong shearing motions in the absence of straining motions and rigid-body rotations. In the classical double decomposition, the velocity gradient tensor is decomposed into a rate-of-rotation tensor Ωij and a rate-of-strain tensor Sij. Regions with large ω2=2ΩijΩij can be associated with rigid-body rotations and shearing motions while those with large s2=2SijSij can be associated with irrotational straining motions and shearing motions. Therefore, vortices with rigid-body rotations and shear layers in turbulence cannot be detected solely by thresholding ω or s while they can be identified simply with (∇u)RR and (∇u)SH in the triple decomposition, respectively. The thickness of the shear layer detected in the triple decomposition is about 10 times of Kolmogorov scale, while the velocity parallel to the layer changes rapidly across the layer, in which the velocity difference across the shear layer is of the order of the root-mean-squared velocity fluctuation.

A new method is proposed for numerically solving the Poisson equation for non-continuous scalar fields on a uniform Cartesian grid. The sharp discontinuity in both the magnitude and the gradient of the scalar field normal to the interface is represented by the numerical solution with second order accuracy at the interface. This is achieved by setting up a composite solution, which is a weighted average of two fictitious scalar fields that together produce the required discontinuity within each interfacial grid cell. A smooth treatment of the Poisson coefficient in a narrow band around the interface allows sharp interfacial jumps to be expressed with second order accuracy on regular grid points around the interface using a standard signed distance function. Moreover, the jump in the gradient tangent to the interface is not needed to enforce the jump in the gradient normal to the interface. The resulting linear system is symmetric and leads to second order accurate solutions on grid points adjacent to the interface. The accuracy of the new framework is compared with other methods.

This contribution is concerned with a novel, purely methodological strategy enabling to automatically adjust the local spatial resolution in Smoothed Particle Hydrodynamics (SPH). It is built upon the fact that the accuracy of the SPH interpolation is related to zeroth- and first-order moments. Ensuing from this knowledge, a suitable measure of the SPH spatial discretization error has been derived. Using this measure as an adaptivity criterion allows to dynamically adjust the local resolution in such a way that a uniform distribution of the spatial discretization error over the model domain is achieved. This is demonstrated in the present paper. To that end, the theoretical foundation of the proposed adaptivity criterion is discussed first. After that, its applicability to both SPH fluid and solid simulations is thoroughly examined.

The non-conforming meshes are widely used in numerical simulations to solve complex flow problems and the key is to perform accurate and efficient interpolation between subdomains. This paper presents a generalized and simple implicit interpolation scheme at algebraic level for the coupling of non-conforming meshes in computational fluid dynamics (CFD). The final equations for most of numerical methods are always of an algebraic form and that is where the interpolation process is conducted. The substitution of dependent nodes with a linear combination of those in neighboring subdomains is imposed in algebraic equations to ensure continuity of variables. A simple reconstruction of the system matrix and right hand side is then executed which implements the reaction of the variable constraint of dependent nodes on replacing ones and maintains the properties of algebraic system. In other words, the proposed interpolation scheme can be regarded as a Dirichlet/Neumann condition performed on algebraic system implicitly. Compared with existing interpolation methods for non-conforming meshes, the new method escapes from the restraints of the type of problem, the form of grids, the discretization scheme and the solver. It also has advantages in simplicity and efficiency. Several benchmark problems were carried out to illustrate the accuracy of the proposed method.

In current supersonic transition models, the timescale models of the first and second modes are required to reflect the contribution to the transition onset by the development of the unstable modes. However, the existing correlations of the timescales have problems in showing the Mach number effect and temperature effect correctly. In this paper, linear stability analyses are conducted to study the existing correlations of the timescales for the first and second modes, and the Mach number effect and the temperature effect are explicitly involved and discussed in the modeling of the characteristic timescales. It is found that the existing correlation between the timescale of the first mode and the Reynolds number based on the displacement thickness is not suitable for the supersonic situation. The frequency of the most unstable first mode in supersonic cases rises rapidly with the increasing Mach number while the current timescale model fails to predict this tendency, and the step phenomenon appears in the frequency-Reynolds-number curves when the Mach number is high. For the second mode, the Mach number effect on the timescale cannot be reflected entirely in the original correlation. Additionally, the temperature effect is proved to affect the timescales of unstable modes, which is left out by the current model. Considering the Mach number, the wall temperature and the total temperature effects, new correlation models for the characteristic frequency of the first and second mode with the Reynolds number are established, in order to provide guidelines for supersonic transition modeling. Some inconsistencies between the timescale-based transition models and the linear stability theory are also commented in this paper.

The efficient and accurate access to the aerodynamic performance is important for the design and optimization of supercritical airfoils. The aerodynamic performance is usually obtained by using computational fluid dynamics (CFD) methods or wind-tunnel experiments. But the computations of CFD are very time intensive and expensive, and the prior knowledge in wind-tunnel experiments plays a decisive role in engineering. Though many surrogate methods were proposed to alleviate the costs of these traditional approaches, most of them can only calculate the low-dimensional aerodynamic performance, and is not able to provide the accurate prediction of transonic flow fields for supercritical airfoils. Since the flow fields are equipped with its own discipline as a physical system in fluid dynamics, it is therefore possible to learn this discipline via data-driven machine learning approaches. Deep learning is witness to expansive growth into diverse applications due to its immense ability to extract essential features from complicated physical systems. Generative adversarial networks (GANs) as a recent popular method in deep leaning are capable of efficiently capturing the distribution of training data. In this work, we proposed a surrogate model, ffsGAN, which leverage the property of GANs combined with convolution neural networks (CNNs) to directly establish a one-to-one mapping from a parameterized supercritical airfoil to its corresponding transonic flow field profile over the parametric space. Compared with the most existing surrogate models, the ffsGAN is superior in efficiently and accurately predicting the high-dimensional flow field rather than the low-dimensional aerodynamic characteristics. The ffsGAN method is first trained using 500 airfoils that sampled based on RAE2822. The flow fields are then predicted for unseen airfoils to evaluate the generalization of the model in terms of prediction accuracy. An investigation of the effects of various hyper-parameters in the network architectures and loss functions is performed. The experimental results show that ffsGAN is a promising tool for rapid evaluation of detailed aerodynamic performance. The elaborate flow field predicted by ffsGAN is possible to be considered in airfoil design to further improve the design and optimization quality in the future.

Directional migration of single microdroplet on a microstructured surface with multi wetting gradients plays a significant role in many industrial applications. To understand the mechanism of spontaneous movement of microdroplet on wetting gradient surfaces under different gravities, the model of microdroplet dynamics is built by 3D lattice Boltzmann method. Effects of wetting gradient, surface morphology, surface orientation and gravitational force on spontaneous movement are investigated. The results demonstrate that static contact angles are greatly affected by micropillars. Both hydrophilicity and hydrophobicity can be strengthened by micropillar arrays. As a droplet moves from hydrophobic to hydrophilic driven by net capillary force, a transition from partial Cassie state to Wenzel state can be found. A larger wetting gradient and larger solid fraction promote the spontaneous movement of microdroplet. In the process of movement, surface free energy shows an increasing tendency due to part of kinetic energy converted to surface free energy. In spite of two-layer surface capable of maintaining a droplet in partial Cassie state, it will decrease the movement velocity. For Bo≤0.0126, surface orientation has little effect on climbing-upward movement. When the Bo number ranges from 0.0126 to 0.063, gravitational coefficient should be considered in the process of microdroplet (2μm) climbing- upward movement. The surface with multi wetting gradients can be applied to remove droplets during condensation to enhance heat transfer.

In a previous work, the feasibility of coupling magnetic resonance imaging (MRI) measurements and computational fluid dynamics (CFD) was presented, called CFD-MRI. Using a lattice Boltzmann based topology optimisation approach, the method can be described as a Navier–Stokes filter for flow MRI measurements. The main objective of this article is the analysis and quantification of CFD-MRI for its ability to reduce statistical measurement noise. For this, MRI data was analysed and used as basis for synthetic data, where noise was added to a simulation result. Thus, the noise-free data is known and a thorough analysis can be performed. The results show a very high agreement with the original data, even with high statistical noise in the input data and limited information available.

In this paper, adaptive mesh refinement (AMR) is performed to simulate flows around both stationary and moving boundaries. The finite-difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from fine to coarse grid levels, while a weighted-average formula is used to transfer variables inversely to keep the law of conservation. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier-Stokes equations are numerically solved through the second-order central difference scheme in space and the third-order Runge-Kutta time integration. Three cases are investigated to check the validity of the present method: flows past a stationary circular cylinder at low Reynolds number, a forced oscillating circular cylinder in the transverse direction and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with literature and the flow fields are smooth around interfaces of different levels of refinement. Study for computational efficiency shows that the AMR approach is helpful to reduce the total grid number and speed up the time integration.

Heatlines visualization of natural convection heat transfer in trapezoidal-shape cavity filled with nanofluid (TiO2-water) and divided by horizontal porous media partition has been studied numerically using finite element method. Non-uniform temperature is applied at the bottom wall and cold temperature applied to the top wall while two inclined vertical walls were insulated. In this work the influence of many parameters such as, Rayleigh number (103≤Ra≤105), partition porous thickness (0.05≤TH≤0.6), partition porous position (0.15≤HD≤0.75), Darcy number (10−5≤Da≤10−1) and volume of fraction (0≤φ≤0.1). Results are exhibited by means heatlines, isotherms, streamlines rather than local and average Nusselt number. The results show that at a constant Rayleigh number equal to (105) and thickness of porous partition (0.1), the percentage enhancement of heat transfer along the bottom wall with the addition of nanoparticles (ϕ=0.1) is greater than enhancement with the base fluid. While, the maximum value of the percentage enhancement of heat transfer is (4.22%) occurred at porous position equal to 0.5. Also, for a constant position of porous partition (HD=0.5) the percentage enhancement of heat transfer with volume fraction of nanoparticles (0.1) along the bottom wall decreases as the thickness of porous partition and Rayleigh number increased. It can be noticed that there is a good agreement between the current study and those of Chamka and Ismeal, with an approximated absolute error 1.829%.

A modified weakly compressible lattice Boltzmann model is developed for simulating low Mach number thermal compressible flows. Using the low Mach number approximation (LMNA) and splitting the pressure into two parts, namely thermodynamic and hydrodynamic pressure, the Navier-Stokes equations at low Mach number limits with variable density are recovered from the kinetic model. The fluid density is governed by the chosen equation of state. In order to satisfy the continuity equation at large temperature variations, which leads to large density differences, a suitable compensation for the finite divergence of the velocity field is introduced via a forcing term. This relationship correlates the total derivatives of the temperature and thermodynamic pressure to the velocity field divergence. The present model is successfully validated against well-known benchmarks. Numerical experiments are conducted to predict the critical Rayleigh number in a compressible Rayleigh-Benard convection test case, where the Boussinesq approximation is no longer valid due to the large temperature differences across the domain. The results are in good agreement with theory and previously published works. Moreover, two-dimensional natural convection heat transfer in a square cavity with large temperature differences is simulated and the results agree with available literature data. One interesting aspect of the presented algorithm is its capability to be extended to two-phase liquid-gas flows to model the gas phase as thermally compressible for low Mach numbers flows.

In gas turbines, transitional flows are likely to occur over many components depending on the geometrical arrangement, inlet turbulence and Reynolds number. In the case of a low-pressure turbine, the transition from a laminar to a turbulent boundary layer is generally either a bypass process due to free stream turbulence or a separation-induced transition due to the adverse pressure gradient on the blade. The overall blade losses and the operating point are strongly dependent on the ability to predict this boundary layer state, the size and length of the separation bubble. Therefore, turbomachinery designers require tools which accurately predict the laminar-turbulent transition. The Reynolds Averaged Navier-Stokes (RANS) formalism is currently commonly used due a to relatively low computational cost. Except particular developments, this approach is not suited to predict transition processes. The Large Eddy-Simulation (LES) approach is able to predict transition processes at a higher computational cost making it suitable for low-pressure turbine applications in conjunction with inlet turbulence injection since the free-stream turbulence is generally non-negligible and affect near-wall flow behavior. The present study introduces a description of the flow in a linear cascade with an upstream hub cavity at a Reynolds number representative of low-pressure turbines by three different approaches (RANS, LES and LES with inlet turbulence injection). This study shows the influence of turbulence modelling and turbulence injection at the inlet of the domain on the boundary layer state at hub and shroud modifying the secondary vortices radial migration in the blade passage and the cancelling of suction side separation bubble at high free-stream turbulence. The Kevin-Helmholtz instability at the rim seal interface is also cancelled at high free-stream turbulence.

This paper presents the moment of fluid method as a liquid/gas interface reconstruction method coupled with a mass momentum conservative approach within the context of numerical simulations of incompressible two-phase flows. This method tracks both liquid volume fraction and phase centroid for reconstructing the interface. The interface reconstruction is performed in a volume (and mass) conservative manner and accuracy of orientation of interface is ensured by minimizing the centroid distance between original and reconstructed interface. With two-phase flows, moment of fluid method is able to reconstruct interface without needing phase volume data from neighboring cells. The performance of this method is analyzed through various transport and deformation tests, and through simple two-phase flows tests that encounter changes in the interface topologies. Exhaustive mesh convergence study for the reconstruction error has been performed through various transport and deformation tests involving simple two-phase flows. It is then applied to simulate atomization of turbulent liquid diesel jet injected into a quiescent environment. The volume conservation error for the moment of fluid method remains small for this complex turbulent case.

The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.

High-order methods gain more and more attention in computational fluid dynamics. Among these, spectral element methods and discontinuous Galerkin methods introduce element-wise approximations by means of a polynomial basis. This leads to a small number of operators consuming a large portion of the runtime of CFD applications. The present paper addresses tensor-product bases which are among the most frequent in these applications. Various implementations are developed and performance tests conducted for the interpolation operator, the Helmholtz operator, and the fast diagonalization operator. For each, up to 50 % of the peak performance is attained, beating matrix-matrix multiplication for every polynomial degree relevant for simulations. This extremely high efficiency of the method developed is then demonstrated on a combustion problem with 1.72 · 109 mesh points.

Purge air is injected in cavities at hub of axial turbines to prevent hot mainstream gas ingestion into interstage gaps. This process induces additional losses for the turbine due to an interaction between purge and mainstream flow. To deal with this issue, this paper is devoted to the study of a low speed linear cascade with an upstream cavity at a Reynolds number representative of a low-pressure turbine using RANS and LES with inlet turbulence injection. Different rim seal geometries and purge flow rates are studied. Details about numerical methods and comparison with experiments can be found in a companion paper. The analysis here focuses on the loss generation based on the description of the flow and influence of the turbulence introduced in the companion paper. The measure of loss is based on an exergy analysis (i.e. energy in the purpose to generate work) that extends a more common measure of loss in gas turbines, entropy. The loss analysis is led for a baseline case by splitting the simulation domain in the contributions related to the boundary layers over the wetted surfaces and the remaining domain (i.e. the complementary of boundary layers domains) where secondary flows and related loss are likely to occur. The analysis shows the strong contribution of the blade suction side boundary layer, secondary vortices in the passage and wake at the trailing edge on the loss generation. The study of different purge flow rates shows increased secondary vortices energy and subsequent loss for higher purge flow rates. The rim seal geometry with axial overlapping promotes a delayed development of secondary vortices in the passage compared to simple axial gap promoting lower levels of loss.

Direct numerical simulations of incident shock wave and supersonic turbulent boundary layer interactions near an expansion corner are performed at Mach number M∞=2.9 and Reynolds number Re∞=5581 to investigate the expansion effect on the characteristic features of this phenomenon. Four expansion angles, i.e. α= 00 (flat-plate), 20, 50 and 100 are considered. The nominal impingement point of the oblique shock wave with a flow deflection angle of 120 is fixed at the onset of the expansion corner, and flow conditions are kept the same for all cases. The numerical results are in good agreement with previous experimental and numerical data. Various flow phenomena, including the flow separation, the post-shock turbulent boundary layer and the flow unsteadiness in the interaction region, have been systematically studied. Analysis of the instantaneous and mean flow fields indicates that the main effect of the expansion corner is to significantly decrease the size and three-dimensionality of the separation bubble. A modified scaling analysis is proposed for the expansion effect on the interaction length scale, and a satisfactory result is obtained. Distributions of the mean velocity, the Reynolds shear stress and the turbulent kinetic energy show that the post-shock turbulent boundary layer in the downstream region experiences a faster recovery to the equilibrium state as the expansion angle is increased. The flow unsteadiness is studied using spectral analysis and dynamic mode decomposition, and dynamically relevant modes associated with flow structures originated from the incoming turbulent boundary layer are clearly identified. At large expansion angle (α=100), the unsteadiness of the separated shock is dominated by medium frequencies motions, and no low frequency unsteadiness is observed. The present study confirms that the driving mechanism of the low frequency unsteadiness is strongly related to the separated shock and the detached shear layer.

In this paper, the performance of the optimized symmetric fourth-order weighted essentially non-oscillatory scheme (WENO-OS4) in direct numerical simulation of compressible turbulence is demonstrated and compared with other three optimized WENO schemes. The compressible homogenous turbulence and channel flow with different Mach numbers and Reynolds numbers are employed to assess the dispersion and dissipation relation of WENO-OS4 scheme. And the shock wave/turbulent boundary layer interaction is directly simulated to access the ability of WENO-OS4 of simulating complex compressible turbulence with large-scale separation. The detailed turbulent structures and the shock waves are obtained. The mean profiles and other statistical data are precisely computed. This study demonstrates the capability of the WENO-OS4 and other optimized WENO scheme for DNS of compressible turbulence.

Two algorithms for a fast Cartesian mesh-based flow simulation over complex geometries are presented. As a first category, a geometric multigrid (MG) method using direct restriction of the Heaviside function, which is 0 in the body and 1 in the fluid, is presented. This method is easy to implement, readily parallelizable, and can be applied to any irregular domain. The validity and optimal performance of the current MG method are demonstrated by solving an analytically defined Poisson problem on an irregular domain. Another part of this paper is to introduce a novel efficient method for computing the signed distance function (SDF), which is a typical level-set value to represent bodies on Cartesian meshes. In the Cartesian mesh-based simulation, only the SDF near the body interface is accurately required. Based on this fact, the number of operations for computing the SDF can be significantly reduced by focusing on interface cells. In this study, the adaptive mesh refinement (AMR) strategy is employed to effectively trace the interface cells. By using these two algorithms, an in-house Cartesian mesh-based incompressible flow solver is developed. To demonstrate the applicability of the current approaches, well-known benchmark problems in 2D and 3D are simulated. Finally, as the most challenging case, simulations for flow over an underwater robot, namely Crabster, are presented.

In this paper, a multi-component generalized sphere function based gas-kinetic flux solver is developed for simulation of compressible viscous reacting flows. This work is inspired by the existing simplified gas-kinetic schemes, which use the circular or sphere function to develop single-component gas-kinetic flux solvers. The present solver applies the finite volume method to discretize the multi-component Navier-Stokes equations and evaluate the numerical flux at the cell interface by using the local solution of Boltzmann equation. In order to unify the existing circular and sphere functions, a generalized sphere function is derived from a reduced Maxwellian distribution function by assuming that all the particles are concentrated on an N-dimensional sphere. The present solver is then developed by integrating the generalized sphere function on the sphere surface. To obtain a multi-component solver, the mass fraction from both sides of the cell interface is used to compute the densities of different species. Considering the different physical properties of the species, the internal energy is computed by enthalpy, and the temperature at the cell interface is obtained by Newton iteration. In addition, to control the numerical dissipation, which is relevant to the grid aspect ratio and the chemical reaction, an improved switch function is introduced. Several benchmark problems are simulated to validate the present solver. It is shown that the developed flux solver has a satisfied performance for simulation of multi-component compressible viscous reacting flows.

In this work we consider the approximation of the isentropic Navier-Stokes equations. The model we present is capable of taking into account acoustics and flow scales at once. Once space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to impose Dirichlet boundary conditions weakly via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.

The oscillation of a levitated drop is a widely used technique for the measurement of the surface tension and viscosity of liquids. Analyses are mainly based on theories developed in the nineteenth century for surface tension driven oscillations of a spherical, force-free, liquid drop. However, a complete analysis with both analytical and numerical approaches to study the damped oscillations of a viscous liquid drop remains challenging. We first propose in this work an extension of the theory that includes the coupled effects of surface tension and viscosity. The analytical solution permits derivation of both properties simultaneously, which is of interest for fluid with unknown viscosity. Then, the robustness of an Eulerian framework to simulate the fluid flow is discussed. Simulations of different oscillations modes for a liquid iron droplet immersed in a low-density gas and comparisons with the derived theory are detailed and presented.

In this article, multi-fidelity surrogate (MFS) models of critical flutter dynamic pressures as a function of Mach number, angle of attack and thickness to chord ratio are constructed in lieu of solely using computationally expensive high-fidelity engineering analyses. Once an accurate MFS is constructed, it can be used for evaluating a large number of designs for design space exploration as well as of Monte-Carlo samples for uncertainty quantification. To demonstrate that accurate MFS models can be obtained at lower computational cost than high-fidelity ones the well known AGARD 445.6 dynamic aeroelastic test case model is employed. The highest and lowest fidelity levels considered are Euler and panel solutions, respectively, all combined with a modal structural solver.

The present work introduces a simple, yet effective particle coalescing procedure for two-dimensional SPH simulations with spatially varying resolution. In addition to the regular conservation properties of former algorithms concerning the mass and linear momentum, the current model provides the exact conservation of the angular momentum as well. The detailed discussion of the coalescing method is followed by its verification through a frozen Taylor-Green vortex example with gradually derefined particle configuration. As a demonstration of the applicability of the proposed technique, a typical weakly compressible dam break simulation and an evolution of a two-dimensional Taylor-Green vortex pattern with local refinement are presented and comparisons are made with analytical and experimental data.

The connected component labeling technique (CCL), which labels regions of connected Eulerian field data, will inaccurately identify closely spaced components when applied to the volume-of-fluid function. We present two modifications to the CCL that improve its robustness and accuracy. This Informed Component Labeling algorithm (ICL) incorporates the normal and uses multilevel thresholding to improve and refine connectivity decisions for components with spacing just larger than the grid size. Through detailed verification and validation using synthetic volume fraction data, we show that the ICL algorithm removes the bias to larger components, provide guidelines for its use, and estimate its error bounds for the smallest components. The ICL produces zero standard deviation in the number of components identified for those with radius larger than twice the grid size and can reduce it by ∼ 38% for smaller components. The modifications that comprise the ICL can be applied to any existing CCL algorithm with a known increase in computational cost. It enables robust identification of connected components for accurate transfer of information in mixed Eulerian-Lagrangian methods and statistical analysis that use the volume-of-fluid function.