A kinematic subgrid scale model for large-eddy simulation of turbulence generated sound

In the hybrid approach of large-eddy simulation (LES) and Lighthill’s acoustic analogy for turbulence-generated sound, the turbulence source fields are obtained using an LES and the turbulence-generated sound at far fields is calculated from Lighthill’s acoustic analogy. As only the velocity fields at resolved scales are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill’s acoustic equation, has to be evaluated from the resolved velocity fields. As a result, the contribution from the unresolved velocity fields is missing in the conventional LES. The sound of missing scales is shown to be important and hence needs to be modeled. The present study proposes a kinematic subgrid-scale (SGS) model which recasts the unresolved velocity fields into Lighthill’s stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with the imposed temporal statistics, which is consistent with the random sweeping hypothesis. The kinematic SGS model is used to calculate sound power spectra from isotropic turbulence and yields an improved result: the missing portion of the sound power spectra is approximately recovered in the LES.

Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Numerical simulation of a single fluid particle rising in non-Newtonian fluids

In this work, a level set method is developed for simulating the motion of a fluid particle rising in non-Newtonian fluids described by generalized Newtonian as well as viscoelastic model fluids. As the shear-thinning model we use a Carreau-Yasuda model, and the viscoelastic effect can be modeled with Oldroyd-B constitutive equations. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The level set method is implemented to compute the motion of a bubble in a Newtonian fluid as one of typical examples for validation, and the computational results are in good agreement with the reported experimental data．The level set method is also applied for simulating a Newtonian drop rising in Carreau-Yasuda and Oldroyd-B fluids．Numerical results including noticeably negative wake behind the drop and viscosity field are obtained, and compare satisfactorily with the known literature data.

Monte Carlo Simulation Of Thermal Fluctuations Below The Onset Of Rayleigh-Benard Convection

The density fluctuations below the onset of convection in the Rayleigh-Benard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Benard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.

Improved sampling techniques for the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a widely used approach for flow simulations having rarefied or nonequilibrium effects. It involves heavily to sample instantaneous values from prescribed distributions using random numbers. In this note, we briefly review the sampling techniques typically employed in the DSMC method and present two techniques to speedup related sampling processes. One technique is very efficient for sampling geometric locations of new particles and the other is useful for the Larsen-Borgnakke energy distribution.

Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899(2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 0° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves VLFWs� are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [ Li et al., AIAA J. 46, 2899 (2008) ], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

An Improved CE/SE Scheme for Numerical Simulation of Gaseous and Two-Phase Detonations

A new structure of solution elements and conservation elements based on rectangular mesh was pro- posed and an improved space-time conservation element and solution element (CE/SE) scheme with sec- ond-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simu- lated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular pat- terns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.

Numerical Simulation of Liquefaction Deformation of Sand Layer around Bucket Foundations under Dynamic Loadings

Bucket Foundations under Dynamic Loadings The liquefaction deformation of sand layer around a bucket foundation is simulated under equivalent dynamic ice-induced loadings. A simplified numerical model is presented by taking the bucket-soil interaction into consideration. The development of vertical and horizontal liquefaction deformations are computed under equivalent dynamic ice-induced loadings. Firstly, the numerical model and results are proved to be reliable by comparing them with the centrifuge testing results. Secondly, the factors and the development characteristics of liquefaction deformation are analyzed. Finally, the following numerical simulation results are obtained: the liquefaction deformation of sand layer increases with the increase of loading amplitude and with the decrease of loading frequency and sand skeleton’s strength. The maximum vertical deformation is located on the sand layer surface and 1/4 times of the bucket’s height apart from the bucket’s side wall (loading boundary). The maximum horizontal deformation occurs at the loading boundary. When the dynamic loadings is applied for more than 5 hours, the vertical deformation on the sand layer surface reaches 3 times that at the bottom, and the horizontal deformation at 2.0 times of the bucket height apart from the loading boundary is 3.3% of which on the loading boundary.

Dimensionless Analysis of the Simulation of Bucket Foundations under Dynamic Load

Firstly, the main factors are obtained by use of dimensionless analysis. Secondly, the time scaling factors in centrifuge modeling of bucket foundations under dynamic load are analyzed based on dimensionless analysis and control- ling equation. A simplified method for dealing with the conflict of scaling factors of the inertial and the percolation in sand foundation is presented. The presented method is that the material for experiments is not changed while the effects are modified by perturbation method. Thirdly, the characteristic time of liquefaction state and the characteristic scale of affected zone are analyzed.