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.

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation (LES) to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale (SGS) model can correctly predict Lagrangian time correlations (LTCs). Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation (DNS) and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid-scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.

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.

Effects of Subgrid-Scale Modeling on Time Correlations in Large Eddy Simulation

The effects of the unresolved subgrid-scale (SGS) motions on the energy balance of the resolved scales in large eddy simulation (LES) have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the two-point, two-time Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation (DNS) with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the two-point correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES

Effects Of Subgrid-Scale Modeling On Lagrangian Statistics In Large-Eddy Simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

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.

Small scale turbulence in high Karlovitz number premixed flames

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω² = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_η, just as in homogeneous isotropic turbulence. As τ_η is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO₂ and soot production to increasing engine efficiency.

The analysis of large-scale turbulence characteristics in the Indonesian seas derived from a regional model based on the Princeton Ocean Model

Turbulence characteristics in the Indonesian seas on the horizontal scale of order of 100 km were calculated with a regional model of the Indonesian seas circulation in the area based on the Princeton Ocean Model (POM). As is well known, the POM incorporates the Mellor–Yamada turbulence closure scheme. The calculated characteristics are: twice the turbulence kinetic energy per unit mass, <i>q</i>²; the turbulence master scale, &ell;; mixing coefficients of momentum, <i>K</i>_M; and temperature and salinity, <i>K</i>_H; etc. The analyzed turbulence has been generated essentially by the shear of large-scale ocean currents and by the large-scale wind turbulence. We focused on the analysis of turbulence around important topographic features, such as the Lifamatola Sill, the North Sangihe Ridge, the Dewakang Sill, and the North and South Halmahera Sea Sills. In general, the structure of turbulence characteristics in these regions turned out to be similar. For this reason, we have carried out a detailed analysis of the Lifamatola Sill region because dynamically this region is very important and some estimates of mixing coefficients in this area are available. <br><br> Briefly, the main results are as follows. The distribution of <i>q</i>² is quite adequately reproduced by the model. To the north of the Lifamatola Sill (in the Maluku Sea) and to the south of the Sill (in the Seram Sea), large values of <i>q</i>² occur in the deep layer extending several hundred meters above the bottom. The observed increase of <i>q</i>² near the very bottom is probably due to the increase of velocity shear and the corresponding shear production of <i>q</i>² very close to the bottom. The turbulence master scale, &ell;, was found to be constant in the main depth of the ocean, while &ell; rapidly decreases close to the bottom, as one would expect. However, in deep profiles away from the sill, the effect of topography results in the &ell; structure being unreasonably complicated as one moves towards the bottom. Values of 15 to 20 × 10^&minus;4 m² s^-1 were obtained for <i>K</i>_M and <i>K</i>_H in deep water in the vicinity of the Lifamatola Sill. These estimates agree well with basin-scale averaged values of 13.3 × 10^&minus;4 m² s^-1 found diagnostically for <i>K</i>_H in the deep Banda and Seram Seas (Gordon et al., 2003) and a value of 9.0 × 10^&minus;4 m² s^-1 found diagnostically for <i>K</i>_H for the deep Banda Sea system (van Aken et al., 1988). The somewhat higher simulated values can be explained by the presence of steep topography around the sill.

A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models

A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

A regime-dependent parametrization of subgrid-scale cloud water content variability

The subgrid-scale spatial variability in cloud water content can be described by a parameter f called the fractional standard deviation. This is equal to the standard deviation of the cloud water content divided by the mean. This parameter is an input to schemes that calculate the impact of subgrid-scale cloud inhomogeneity on gridbox-mean radiative fluxes and microphysical process rates. A new regime-dependent parametrization of the spatial variability of cloud water content is derived from CloudSat observations of ice clouds. In addition to the dependencies on horizontal and vertical resolution and cloud fraction included in previous parametrizations, the new parametrization includes an explicit dependence on cloud type. The new parametrization is then implemented in the Global Atmosphere 6 (GA6) configuration of the Met Office Unified Model and used to model the effects of subgrid variability of both ice and liquid water content on radiative fluxes and autoconversion and accretion rates in three 20-year atmosphere-only climate simulations. These simulations show the impact of the new regime-dependent parametrization on diagnostic radiation calculations, interactive radiation calculations and both interactive radiation calculations and in a new warm microphysics scheme. The control simulation uses a globally constant f value of 0.75 to model the effect of cloud water content variability on radiative fluxes. The use of the new regime-dependent parametrization in the model results in a global mean which is higher than the control's fixed value and a global distribution of f which is closer to CloudSat observations. When the new regime-dependent parametrization is used in radiative transfer calculations only, the magnitudes of short-wave and long-wave top of atmosphere cloud radiative forcing are reduced, increasing the existing global mean biases in the control. When also applied in a new warm microphysics scheme, the short-wave global mean bias is reduced.

Small scale turbulence and mixing in semi-enclosed seas (Persian Gulf)

Turbulence and internal waves are probably important in generating layered structures in frontal region of marine environments (e.g. near river plumes outflow into the sea). Here we investigate the role of normal modes of internal waves in generation of layered structure in a part of Persian Gulf where river plume inters and in some laboratory experiments. The model prediction and observations show that layers so formed have a thickness of about 2m based on salinity variations with depth, but layers (about 5m) based on horizontal velocity profiles. Laboratory experiments with a plume outflow in a Filling Box profile also generate normal mode layered structure with 21H=0.5 (where A is layer thickness and H is the plume depth). In these experiments as Re of the flow is smaller than the Re of field flow. The normal modes are substantially dissipated with depth. Typical values of dissipation factor is about 0(100). This factor for field observation is 0(10) which is still substantial. Qualitative comparison between layered structure in field and laboratory is good. It should be emphasized that field observation is for semi-enclosed seas but the laboratory experiments are for enclosed region. Hence some of the discrepancies in the results of two cases are inevitable. Layered structures in marine environments are also produced by double diffusive convection. In this region this should be studied separately.

Prediction of particle distribution in isotropic turbulence by large-eddy simulation

The recent application of large-eddy simulation (LES) to particle-laden turbulence requires that the LES with a subgrid scale (SGS) model could accurately predict particle distributions. Usually, a SGS particle model is used to recover the small-scale structures of velocity fields. In this study, we propose a rescaling technique to recover the effects of small-scale motions on the preferential concentration of inertial particles. The technique is used to simulate particle distribution in isotropic turbulence by LES and produce consistent results with direct numerical simulation (DNS). Key words: particle distribution, particle-laden turbulence, large-eddy simulation, subgrid scale model.

Large-scale two-dimensional turbulence in the atmosphere

Global FGGE data are used to investigate several aspects of large-scale turbulence in the atmosphere. The approach follows that for two-dimensional, nondivergent turbulent flows which are homogeneous and isotropic on the sphere. Spectra of kinetic energy, enstrophy and available potential energy are obtained for both the stationary and transient parts of the flow. Nonlinear interaction terms and fluxes of energy and enstrophy through wavenumber space are calculated and compared with the theory. A possible method of parameterizing the interactions with unresolved scales is considered. Two rather different flow regimes are found in wavenumber space. The high-wavenumber regime is dominated by the transient components of the flow and exhibits, at least approximately, several of the conditions characterizing homogeneous and isotropic turbulence. This region of wavenumber space also displays some of the features of an enstrophy-cascading inertial subrange. The low-wavenumber region, on the other hand, is dominated by the stationary component of the flow, exhibits marked anisotropy and, in contrast to the high-wavenumber regime, displays a marked change between January and July.