The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

Evaluation of Subgrid-scale Models in Large-eddy Simulations of Turbulent Flow in a Centrifugal Pump Impeller

The current research of large eddy simulation （LES） of turbulent flow in pumps mainly concentrates in applying conventional subgrid-scale （SGS） model to simulate turbulent flow, which aims at obtaining the flow field in pump. The selection of SGS model is usually not considered seriously, so the accuracy and efficiency of the simulation cannot be ensured. Three SGS models including Smagorinsky-Lilly model, dynamic Smagorinsky model and dynamic mixed model are comparably studied by using the commercial CFD code Fluent combined with its user define function. The simulations are performed for the turbulent flow in a centrifugal pump impeller. The simulation results indicate that the mean flows predicted by the three SGS models agree well with the experimental data obtained from the test that detailed measurements of the flow inside the rotating passages of a six-bladed shrouded centrifugal pump impeller performed using particle image velocimetry （PIV） and laser Doppler velocimetry （LDV）. The comparable results show that dynamic mixed model gives the most accurate results for mean flow in the centrifugal pump impeller. The SGS stress of dynamic mixed model is decompose into the scale similar part and the eddy viscous part. The scale similar part of SGS stress plays a significant role in high curvature regions, such as the leading edge and training edge of pump blade. It is also found that the dynamic mixed model is more adaptive to compute turbulence in the pump impeller. The research results presented is useful to improve the computational accuracy and efficiency of LES for centrifugal pumps, and provide important reference for carrying out simulation in similar fluid machineries.

Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method

A novel method is proposed to combine the wall-modeled large-eddy simulation(LES) with the diffuse-interface direct-forcing immersed boundary(IB) method.The new developments in this method include:(i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model;(ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.

Parameterization of Sheared Entrainment in a Well-Developed CBL.Part I:Evaluation of the Scheme through Large-Eddy Simulations

The entrainment flux ratio Ae and the inversion layer （IL） thickness are two key parameters in a mixed layer model. Ae is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of Ae is derived from the TKE budget in the first- order model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness, The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized Ae and IL thickness agree well with the LES outputs.

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number:Turbulent wake and sound radiation

The flows past a number 3900 are simulated circular cylinder at Reynolds using large-eddy simulation （LES） and the far-field sound is calculated from the LES results. A low dissipation energy-conserving finite volume scheme is used to discretize the incompressible Navier- Stokes equations. The dynamic global coefficient version of the Vreman＇s subgrid scale （SGS） model is used to com- pute the sub-grid stresses. Curie＇s integral of Lighthill＇s acoustic analogy is used to extract the sound radiated from the cylinder. The profiles of mean velocity and turbulent fluctua- tions obtained are consistent with the previous experimental and computational results. The sound radiation at far field exhibits the characteristic of a dipole and directivity. The sound spectra display the -5/3 power law. It is shown that Vreman＇s SGS model in company with dynamic procedure is suitable for LES of turbulence generated noise.

Recent improvements of actuator line-large-eddy simulation method for wind turbine wakes

In a large wind farm,the wakes of upstream and downstream wind turbines can interfere with each other,affecting the overall power output of the wind farm.To further improve the numerical accuracy of the turbine wake dynamics under atmosphere turbulence,this work proposes some improvements to the actuator line-large-eddy simulation(AL-LES)method.Based on the dynamic k-equation large-eddy simulation(LES),this method uses a precursor method to generate atmospheric inflow turbulence,models the tower and nacelle wakes,and improves the body force projection method based on an anisotropic Gaussian distribution function.For these three improvements,three wind tunnel experiments are used to validate the numerical accuracy of this method.The results show that the numerical results calculated in the far-wake region can reflect the characteristics of typical onshore and offshore wind conditions compared with the experimental results.After modeling the tower and nacelle wakes,the wake velocity distribution is consistent with the experimental result.The radial migration velocity of the tip vortex calculated by the improved blade body force distribution model is 0.32 m/s,which is about 6%different from the experimental value and improves the prediction accuracy of the tip vortex radial movement.The method proposed in this paper is very helpful for wind turbine wake dynamic analysis and wind farm power prediction.

Large-eddy Simulation of Fluid Flow and Heat Transfer in a Mixing Tee Junction

The temperature fluctuation caused by thermal striping phenomena of hot and cold fluids mixing results in cyclical thermal stress fatigue failure of the pipe wall. Mean temperature difference between hot and cold fluids was often used as thermal load in previous analysis of thermal fatigue failure, thereby the influences of the amplitude and frequency of temperature fluctuation on thermal fatigue failure were neglected. Based on the mechanism of flow and heat transfer which induces thermal fatigue, the turbulent mixing of hot and cold water in a tee junction is simulated with FLUENT platform by using the Large-eddy simulation（LES） turbulent flow model with the sub-grid scale（SGS） model of Smagorinsky-Lilly（SL） to capture the amplitude and frequency of temperature fluctuation. In a simulation case, hot water with temperature of 343.48 K and velocity of 0.15 m/s enters the horizontal main duct with the side length of 100 mm, while cold water with temperature of 296.78 K and velocity of 0.3 m/s enters the vertical branch duct with the side length of 50 mm. The numerical results show that the mean and fluctuating temperatures are in good agreement with the previous experimental data, which describes numerical simulation with high reliability and accuracy; the power spectrum density（PSD） on top wall is higher than that on bottom wall（as the frequency less than 1 Hz）, while the PSD on bottom wall is relatively higher than that on top wall （as the frequency of 1-10Hz）. The temperature fluctuations in full mixing region of the tee junction can be accurately captured by LES and can provide the theoretical basis for the thermal stress and thermal fatigue analyses.

Large-eddy simulation of fluid mixing in tee with sintered porous medium

Mixing processes of hot and cold fluids in a tee with and without sin- tered copper spheres are simulated by FLUENT using the large-eddy simulation （LES） turbulent flow model and the sub-grid scale （SGS） Smagorinsky-Lilly （SL） model with buoyancy. Comparisons of numerical results of the two cases with and without sintered copper spheres show that the porous medium significantly reduces velocity and temper- ature fluctuations because the porous medium can effectively restrict the fluid flow and enhance heat transfer. The porous medium obviously increases the pressure drop in the main duct. The porous medium reduces the power spectrum density （PSD） of tempera- ture fluctuations in the frequency range from 1 Hz to 10 Hz.

Large-Eddy Simulation of Wind Turbine Wake and Aerodynamic Performance with Actuator Line Method

A hybrid method is presented to numerically investigate the wind turbine aerodynamic characteristics.The wind turbine blade is replaced by an actuator line model.Turbulence is treated using a dynamic one-equation subgrid-scale model in large eddy simulation.Detailed information on the basic characteristics of the wind turbine wake is obtained and discussed.The rotor aerodynamic performance agrees well with the measurements.The actuator line method large-eddy simulation(ALM-LES)technique demonstrates its high potential in providing accurate load prediction and high resolution of turbulent fluctuations in the wind turbine wakes and the interactions within a feasible cost.

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation （LES） using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment （SOM） SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM＋wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures.

A study of a supersonic capsule/rigid disk-gap-band parachute system using large-eddy simulation

The aerodynamic performances and flow features of the capsule/rigid disk-gap-band(DGB)parachute system from the Mach number 1.8 to 2.2 are studied.We use the adaptive mesh refinement(AMR),the hybrid tuned center-difference and weighted essentially non-oscillatory(TCD-WENO)scheme,and the large-eddy simulation(LES)with the stretched-vortex subgrid model.The simulations reproduce complex interaction of the flow structures,including turbulent wakes and bow shocks,as well as bow shocks and expansion waves.The results show that the calculated aerodynamic drag coefficient agrees well with the previou simulation.Both the aerodynamic drag coefficient and the aerodynamic drag oscillation of the parachute system decrease with the increase of the initial Mach number of the fluid.It is found that the position and angle of the bow shock ahead of the canopy change as the Mach number increases,which makes the flow inside the canopy and the turbulent wake behind the canopy more complex and unstable.

Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow

We analyze the error of large-eddy simulation(LES)in wall pressure fluctuation of a turbulent channel flow.To separate different sources of the error,we conduct both direct numerical simulations(DNS)and LES,and apply an explicit filter on DNS data to obtain filtered DNS(FDNS)data.The error of LES is consequently decomposed into two parts:The first part is the error of FDNS with respect to DNS,which quantifies the influence of the filter operation.The second part is the difference between LES and FDNS induced by the error of LES in velocity field.By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation,it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation.The present study provides a basis on future LES studies of the wall pressure fluctuation.

Turbulent Inlet Conditions Modeling using Large-eddy Simulations

Turbulence is a phenomenon which presents peculiarities when it is experimented or simulated.This occurs due to its complexity and high sensibility to the inlet conditions of the turbulent flow fields,as well as the presence of a large range of time and length scales.A simplification for this situation is obtained with the use of approximations and turbulence models.In the present work,the Largeeddy Simulations methodology was applied,aiming the modeling of the previously mentioned complexity,which consists in using a filter to resolve the large scales while the remaining scales were determined by classical and dynamic Smagorinsky models.Three different approximations for the inlet conditions were applied:white noise,Random Flow Generation(RFG)and Synthetic Eddy Method(SEM).It was possible to realize that the use of the dynamic Smagorinky model and the RFG or SEM methodologies resulted in a better characterization of the studied flow.

A new numerical framework for large-eddy simulation of waves generated by objects piercing water surface

A novel numerical framework is developed for large-eddy simulation(LES) of interactions among air, water, and solid bodies. The motions of air and water are solved on a fixed block-structured mesh, with the air–water interface captured using the volume-of-fluid method. A new sub-grid scale stress model based on the vortex identifier is used to improve the robustness and efficiency of the simulation flows with air–water interface. The new framework is tested in the context of bow waves and Kelvin waves generated by a water-surface vehicle. Wave breaking at the bow of the vehicle is captured in LES. The LES results of wave geometry approaches the measurements progressively as the grid resolution is refined. The simulation results indicate that LES is a useful tool for studying wave dynamics of water-surface vehicles.

Large-eddy simulations of a forced homogeneous isotropic turbulence with polymer additives

Large-eddy simulations （LES） based on the temporal approximate deconvolution model were performed for a forced homogeneous isotropic turbulence （FHIT） with polymer additives at moderate Taylor Reynolds number. Finitely extensible nonlinear elastic in the Peterlin approximation model was adopted as the constitutive equation for the filtered conformation tensor of the polymer molecules. The LES results were verified through comparisons with the direct numerical simulation results. Using the LES database of the FHIT in the Newtonian fluid and the polymer solution flows, the polymer effects on some important parameters such as strain, vorticity, drag reduction, and so forth were studied. By extracting the vortex structures and exploring the flatness factor through a high-order correlation function of velocity derivative and wavelet analysis, it can be found that the small-scale vortex structures and small-scale intermittency in the FHIT are all inhibited due to the existence of the polymers. The extended self-similarity scaling law in the polymer solution flow shows no apparent difference from that in the Newtonian fluid flow at the currently simulated ranges of Reynolds and Weissenberg numbers.

Temporal Large-Eddy Simulations of the Near-Field of an Aircraft Wake

The near-field dynamics of an aircraft wake is studied by means of temporal large-eddy simulations, with and without considering the effect of engine jets. In the absence of jets, the simulations showed the roll-up of the initial vorticity sheet shed by the wing and the occurrence of short-wavelength instability in a pair of primary co-rotating vortices. The main consequence of the instability is the modification of the internal structure of the vortex, compared to the two-dimensional stable behavior. The presence of engine jets affects the roll-up of the vorticity sheet and causes an enlargement of the final merged vortex core compared to the case without jets.

Assessment of subgrid-scale models in wall-modeled large-eddy simulations of turbulent channel flows

Considering the demanding of grid requirements for high-Reynolds-number wall-bounded flow,the wall-modeled large-eddy simulation(WMLES)is an attractive method to deal with near wall turbulence.However,the effect of subgrid-scale(SGS)models for wall-bounded turbulent flow in combination with wall stress models is still unclear.In this paper,turbulent channel flow at Reτ=1000 are numerically simulated by WMLES in conjunction with four different SGS models,i.e.,the wall-adapting local eddy-viscosity model,the dynamic Smagorinsky model,the dynamic SGS kinetic energy model and the dynamic Lagrangian model.The mean velocity profiles are compared with the law of the wall,and the velocity fluctuations are compared with direct numerical simulation data.The energy spectrum of velocity and wall pressure fluctuations are presented and the role of SGS models on predicting turbulent channel flow with WMLES is discussed.

Numerical modeling of current-induced scour around multi-wall foundation using large-eddy simulation

Scouring is one of the primary triggers of failure for bridges across rivers or seas.However,research concerning the scour mechanism of multi-wall foundations(MWFs)remains scarce,hindering the further application of MWFs.In this study,for the first time,the scouring effect caused by unidirectional flow around MWFs was examined numerically using FLOW-3D involving a large-eddy simulation.Initially,the applicability of the scouring model and input parameters was validated using a case study based on published measured data.Subsequently,the scouring effects of four MWFs with different wall arrangements and inflow angles,including the flow field analysis and scour pit and depth,were investigated thoroughly.It was found that the maximum scour depth of MWFs with an inflow angle of 0°was smaller than that of those with an inflow angle of 45°,regardless of the wall arrangement.Meanwhile,changing the inflow angle significantly affects the scour characteristics of MWFs arranged in parallel.In practical engineering,MWFs arranged in parallel are preferred considering the need for scouring resistance.However,a comparative analysis should be performed to consider comprehensively whether to adopt the form of a round wall arrangement when the inflow angle is not 0°or the inflow direction is changeable.

Investigation of flow characteristics in a rotor-stator cavity under crossflow using wall-modelled large-eddy simulation

Rotor-stator cavities are frequently encountered in engineering applications such as gas turbine engines.They are usually subject to an external hot mainstream crossflow which in general is highly swirled under the effect of the nozzle guide vanes.To avoid hot mainstream gas ingress,the cavity is usually purged by a stream of sealing flow.The interactions between the external crossflow,cavity flow,and sealing flow are complicated and involve all scales of turbulent unsteadiness and flow instability which are beyond the resolution of the Reynolds-average approach.To cope with such a complex issue,a wall-modeled large-eddy simulation(WMLES)approach is adopted in this study.In the simulation,a 20°sector model is used and subjected to a uniform pre-swirled external crossflow and a stream of radial sealing flow.It is triggered by a convergent Reynoldsaveraged Navier-Stokes(RANS)result in which the shear stress transport(SST)turbulent model is used.In the WMLES simulation,the Smagoringsky sub-grid scale(SGS)model is applied.A scalar transportation equation is solved to simulate the blending and transportation process in the cavity.The overall flow field characteristics and deviation between RANS and WMLES results are discussed first.Both RANS and WMLES results show a Batchelor flow mode,while distinct deviation is also observed.Deviations in the small-radius region are caused by the insufficiency of the RANS approach in capturing the small-scale vortex structures in the boundary layer while deviations in the large-radius region are caused by the insufficiency of the RANS approach in predicting the external crossflow ingestion.The boundary layer vortex and external ingestion are then discussed in detail,highlighting the related flow instabilities.Finally,the large-flow structures induced by external flow ingress are analyzed using unsteady pressure oscillation signals.