Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Large eddy simulation of aircraft wake vortex with self-adaptive grid method

A self-adaptive-grid method is applied to numerical simulation of the evolu- tion of aircraft wake vortex with the large eddy simulation （LES）. The Idaho Falls （IDF） measurement of run 9 case is simulated numerically and compared with that of the field experimental data. The comparison shows that the method is reliable in the complex atmospheric environment with crosswind and ground effect. In addition, six cases with different ambient atmospheric turbulences and Brunt V^iis/il^i （BV） frequencies are com- puted with the LES. The main characteristics of vortex are appropriately simulated by the current method. The onset time of rapid decay and the descending of vortices are in agreement with the previous measurements and the numerical prediction. Also, sec-ondary structures such as baroclinic vorticity and helical structures are also simulated. Only approximately 6 million grid points are needed in computation with the present method, while the number can be as large as 34 million when using a uniform mesh with the same core resolution. The self-adaptive-grid method is proved to be practical in the numerical research of aircraft wake vortex.

Wave-current interaction with a vertical square cylinder at different Reynolds numbers

Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a constant of 0.6 for all cases. The Strouhal number, the mean and the RMS values of the effective drag coefficient in the streamwise and transverse directions are computed for various Reynolds numbers, and the velocity of a rep- resentative point in the turbulent zone is simulated to find the turbulent feature. It is found that the wave-current interaction should be considered as three-dimensional flow when the Reynolds number is high; under wave-current effect, there exists a critical Reynolds number, and when the Reynolds number is smaller than the critical one, current effect on wave can be nearly neglected; conversely, with the Reynolds number increasing, wave-currentstructure interaction is sensitive to the Reynolds number.

Footprint Characteristics of Scalar Concentration in the Convective Boundary Layer

Footprint characteristics for passive scalar concentration in the convective boundary layer （CBL） are investigated. A backward Lagrangian stochastic （LS） dispersion model and a large eddy simulation （LES） model are used in the investigation. Typical characteristics of the CBL and their responses to the surface heterogeneity are resolved from the LES. Then the turbulence fields are used to drive the backward LS dispersion. To remedy the spoiled description of the turbulence near the surface, MoninObukhov similarity is applied to the lowest LES level and the surface for the modeling of the backward LS dispersion. Simulation results show that the footprint within approximately 1 km upwind predominates in the total contribution. But influence from farther distances also exists and is even slightly greater than that from closer locations. Surface heterogeneity may change the footprint pattern to a certain degree. A comparison to three analytical models provides a validation of the footprint simulations, which shows the possible influence of along-wind turbulence and the large eddies in the CBL, as well as the surface heterogeneity.

Experimental and numerical investigation of inclined air/SF_6 interface instability under shock wave

The shock tube experiments of inclined air/SF6 interface instability under the shock wave with the Mach numbers 1.23 and 1.41 are conducted. The numerical simulation is done with the parallel algorithm and the multi-viscous-fluid and turbulence （MVFT） code of the large-eddy simulation （LES）. The developing process of the interface accelerated by the shock wave is reproduced by the simulations. The complex wave structures, e.g., the propagation, refraction, and reflection of the shock wave, are clearly revealed in the flows. The simulated evolving images of the interface are consistent with the experimental ones. The simulated width of the turbulent mixing zone （TMZ） and the displacements of the bubble and the spike also agree well with the experimental data. Also, the reliability and effectiveness of the MVFT in simulating the problem of interface instability are validated. The more energies are injected into the TMZ when the shock wave has a larger Mach number. Therefore, the perturbed interface develops faster.

Large eddy simulations of a circular orifice jet with and without a cross-sectional exit plate

The effect of a cross-sectional exit plane on the downstream mixing characteristics of a circular turbulent jet is in- vestigated using large eddy simulation （LES）. The turbulent jet is issued from an orifice-type nozzle at an exit Reynolds number of 5 ×104. Both instantaneous and statistical velocity fields of the jet are provided. Results show that the rates of the mean velocity decay and jet spread are both higher in the case with the exit plate than without it. The existence of the plate is found to increase the downstream entrainment rate by about 10% on average over the axial range of 8-30de （exit diameter）. Also, the presence of the plate enables the formation of vortex rings to occur further downstream by 0.5-1 .Ode. A physical insight into the near-field jet is provided to explain the importance of the boundary conditions in the evolution of a turbulent jet. In addition, a method of using the decay of the centreline velocity and the half-width of the jet to calculate the entrainment rate is proposed.

Simulation of Terrestrial Dust Devil Patterns

Introducing the surface properties [initial vortex, ground temperature and surface momentum impact height （SMIH）] for the boundary conditions, dust-devil-scale large eddy simulations （LES） were carried out. Given three parameters of initial vortex, ground temperature and the SMIH based on Sinclair＇s observation, the dust devil physical characteristics, such as maximum tangential velocity, updraft velocity, pressure drop in the inner core region, and even reverse flow at the top of the core region, are predicted, and are found to be close to the observations, thus demonstrating the ability of the simulation. The physical characteristics of different modeled dust devils are reproduced and compared to the values predicted by Renno et al.＇ theory. Even for smaller temperature differences or weaker buoyancy, severe dust devils may be formed by strong incipient vortices. It is also indicated that SMIH substantially affects the near-surface shape of terrestrial dust devils.

Study of numerical errors in direct numerical simulation and large eddy simulation

By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numerical simulation （DNS） and large eddy simulation （LES） are investigated, The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Pade compact difference schemes are studied. The truncated Navier-Stokes （TNS） equation model with Pade discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

Multi-relaxation-time lattice Boltzmann simulations of lid driven flows using graphics processing unit

Large eddy simulation （LES） using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components （D2Q9） lattice Boltzmann equation （LBE） with multi-relaxation-time （MRT） to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 10^7. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit （GPU） with a computing unified device architecture （CUDA） is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large.

Large eddy simulation of water flow over series of dunes

Large eddy simulation was used to investigate the spatial development of open channel flow over a series of dunes. The three-dimensional filtered Navier-Stokes （N-S） equations were numerically solved with the fractional-step method in sigma coordinates. The subgrid-scale turbulent stress was modeled with a dynamic coherent eddy viscosity model proposed by the authors The computed velocity profiles are in good agreement with the available experimental results. The mean velocity and the turbulent Reynolds stress affected by a series of dune-shaped structures were compared and analyzed. The variation of turbulence statistics along the flow direction affected by the wavy bottom roughness has been studied. The turbulent boundary layer in a complex geographic environment can be simulated well with the proposed large eddy simulation （LES） model.

Simple lattice Boltzmann approach for turbulent buoyant flow simulation

In the present work, a simple large eddy simulation （LES）-based lattice Boltz- mann model （LBM） is developed for thermal turbulence research. This model is validated by some benchmark tests. The numerical results demonstrate the good performance of the present model for turbulent buoyant flow simulation.

LES NUMERICAL SIMULATION OF CAVITATION BUBBLE SHEDDING ON ALE 25 AND ALE 15 HYDROFOILS

A cavitation calculation scheme is developed and applied to ALE 15 and ALE 25 hydrofoils, based on the Bubble Two-phase Flow （BTF） cavity model with a Large Eddy Simulation （LES） methodology. The Navier-Stokes equations including cavitation bubble clusters are solved through the finite-volume approach with a time-marching scheme. Simulations are carried out in a 3-D field with a hydrofoil ALE 15 or ALE 25 at an angle of attack of 8^0 and cavitation number σ = 2.3 with α 2× 10^6, meshing system. With the time-marching, the cavitation bubble gradually grows to a steady lump shape and then produces an irregular small bubble behind the main cavitation bubble, finally shedding from the leading edge of the cloud cavitation structure. The calculated results including velocity field and pressure field are consistent with experiment data at the same Reynolds number and cavitation number. The vortex and reverse flow are observed on the hydrofoil surface.

THE CALCULATION OF THE PROFILE-LINEAR AVERAGE VELOCITY IN THE TRANSITION REGION FOR ULTRASONIC HEAT METER BASED ON THE METHOD OF LES

The measurement accuracy of an ultrasonic heat meter depends on the relationship of the profile-linear average velocity.There are various methods for the calculation of the laminar and turbulence flow regions,but few methods for the transition region.At present,the traditional method to deal with the transition region is to adopt the relationship for the turbulent flow region.In this article,a simplified model of the pipe is used to study the characteristics of the transition flow with specific Reynolds number.The k-εmodel and the Large Eddy Simulation（LES）model are,respectively,used to calculate the flow field of the transition region,and a comparison with the experiment results shows that the LES model is more effective than the k-εmodel,it is also shown that there will be a large error if the relationship based on the turbulence flow is used to calculate the profile-linear average velocity relationship of the transition flow.The profile-linear average velocity for the Reynolds number ranging from 5 300 to 10 000 are calculated,and the relationship curve is obtained.The results of this article can be used to improve the measurement accuracy of ultrasonic heat meter and provide a theoretical basis for the research of the whole transition flow.

Some notes on numerical simulation and error analyses of the attached turbulent cavitating flow by LES

In this letter, the attached turbulent cavitating flow around the Clark-Y hydrofoil is investigated by the numerical simulation with special emphasis on error analysis of large eddy simulation（LES） for the unsteady cavitation simulation. The numerical results indicate that the present simulation can capture the periodic cavity shedding behavior and show a fairly good agreement with the available experimental data. Further analysis demonstrates that the cavitation has a great influence on LES numerical error and modeling error. The modeling error and numerical error are almost on the same order of magnitude, while the modeling error often shows a little bit larger magnitude than numerical error. The numerical error and modeling error sometimes can partially offset each other if they have the opposite sign. Besides, our results show that cavitation can extend the magnitudes and oscillation levels of numerical error and modeling error.

A high-fidelity design methodology using LES-based simulation and POD-based emulation:A case study of swirl injectors

Engineering design is undergoing a paradigm shift from design for performance to design for affordability, operability, and durability, seeking multi-objective optimization. To facilitate this transformation, significantly extended design freedom and knowledge must be available in the early design stages. This paper presents a high-fidelity framework for design and optimization of the liquid swirl injectors that are widely used in aerospace propulsion and power-generation systems. The framework assembles a set of techniques, including Design Of Experiment(DOE), high-fidelity Large Eddy Simulations(LES), machine learning, Proper Orthogonal Decomposition(POD)-based Kriging surrogate modeling(emulation), inverse problem optimization, and uncertainty quantification. LES-based simulations can reveal detailed spatiotemporal evolution of flow structures and flame dynamics in a high-fidelity manner, and identify important injector design parameters according to their effects on propellant mixing, flame stabilization, and thermal protection.For a given a space of design parameters, DOE determines the number of design points to perform LES-based simulations. POD-based emulations, trained by the LES database, can effectively explore the design space and deduce an optimal group of design parameters in a turn-around time that is reduced by three orders of magnitude. The accuracy of the emulated results is validated, and the uncertainty of prediction is quantified. The proposed design methodology is expected to profoundly extend the knowledge base and reduce the cost for initial design stages.

Large eddy simulation of turbulent attached cavitating flow with special emphasis on large scale structures of the hydrofoil wake and turbulence-cavita-tion interactions

In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simula- tion （LES） method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the Q- criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.

Three-dimensional large eddy simulation and vorticity analysis of unsteady cavitating flow around a twisted hydrofoil

Large Eddy Simulation （LES） was coupled with a mass transfer cavitation model to predict unsteady 3-D turbulent cavita- ting flows around a twisted hydrofoil. The wall-adapting local eddy-viscosity （WALE） model was used to give the Sub-Grid Scale （SGS） stress term. The predicted 3-D cavitation evolutions, including the cavity growth, break-off and collapse downstream, and the shedding cycle as well as its frequency agree fairly well with experimental results. The mechanism for the interactions between the cavitation and the vortices was discussed based on the analysis of the vorticity transport equation related to the vortex stretching, volumetric expansion/contraction and baroclinic torque terms along the hydrofoil mid-plane. The vortical flow analysis demonstrates that cavitation promotes the vortex production and the flow unsteadiness. In non-cavitation conditions, the streamline smoothly passes along the upper wall of the hydrofoil with no boundary layer separation and the boundary layer is thin and attached to the foil except at the trailing edge. With decreasing cavitation number, the present case has O＂ = 1.07, and the attached sheet cavitation beco- mes highly unsteady, with periodic growth and break-off to form the cavitation cloud. The expansion due to cavitation induces boun- dary layer separation and significantly increases the vorticity magnitude at the cavity interface. A detailed analysis using the vorticity transport equation shows that the cavitation accelerates the vortex stretching and dilatation and increases the baroclinic torque as the major source of vorticity generation. Examination of the flow field shows that the vortex dilatation and baroclinic torque terms in- crease in the cavitating case to the same magnitude as the vortex stretching term, while for the non-cavitating case these two terms are zero.

LARGE-EDDY SIMULATION OF FLOW AROUND CYLINDER ARRAYS AT A SUBCRITICAL REYNOLDS NUMBER

The complex three-dimensional turbulent flows around a cylinder array with four cylinders in an in-line square configuration at a subcritical Reynolds number of 1.5 × 10^4 with the spacing ratio at L/D = 1.5 and 3.5 were investigated using the Large Eddy Simulation （LES）. The full field vorticity and velocity distributions as well as turbulent quantities were calculated in detail and the near wake structures were presented. The results show that the bi-stable flow nature was observed at L/D = 1.5 and distinct vortex shedding of the upstream cylinders occurred at L/D = 3.5 at Re = 1.5 × 10^4. The techniques of Laser Doppler Anemometry （LDA） and Digital Particle Image Velocimetry （DPIV） are also employed to validate the present LES method. The results show that the numerical predictions are in excellent agreement with the experimental measurements. Therefore, the full field instantaneous and mean quantities of the flow field, velocity field and vorticity field can be extracted from the LES results for further study of the complex flow characteristics.

LARGE EDDY SIMULATION OF OPEN CHANNEL FLOWS WITH NONSUBMERGED VEGETATION

Results of several Large Eddy Simulations （LES） this article. It is shown that the vegetation can make the flow of open channel flows with non-submerged vegetation are presented in structure in the mainstream direction uniform for both supercritical and subcritical flows. For subcritical flows, the LES results of the ensemble-average of time-averaged velocity distributions at four vertical sections around a single plant are in good agreement with measurements. The velocity sees double peaks at the upper and lower positions of flows. For supercritical flows, the ensemble-average velocities see some discrepancy between LES and measurement results. Some secondary flow eddies appear near the single plant, and they just locate in the positions of the double peaks in stream-wise velocity profiles. It is also found that the vegetation drag coefficient deceases as the Froude number increases.

APPLICATION OF LBM-SGS MODEL TO FLOWS IN A PUMPING-STATION FOREBAY

A 2-D Lattice Boltzmann Method（LBM） coupled with a Sub-Grid Stress（SGS） model is proposed and validated by flows around a non-submerged spur dike in a channel.And then the LBM-SGS model is further applied to flows in a pumping-station forebay.Shallow water equations are numerically solved by the LBM and the turbulence can be taken into account and modeled efficiently by the Large Eddy Simulation（LES） model.The bounce-back scheme of the non-equilibrium part of the distribution function is used at the inlet boundary,the normal gradient of the distribution function is set as zero at the outlet boundary and the bounce-back scheme is applied to the solid wall to ensure non-slip boundary conditions.Firstly,the model successfully predicts the flow characteristics around a spur dike,such as circulating flow,velocity and water depth distributions.The results are verified by the experimental data and compared to the results obtained by conventional Smagoringsky Model（SM） of LES.Finally,the LBM-SGS model is used to further predict the flow characteristics in a forebay,such as secondary flow and water level.The comparisons show that the model scheme has the capacity to simulate complex flows in shallow water with reasonable accuracy and reliability.