Terms Of Dissipation Rate Research Articles

Temporal large eddy simulation with lattice Boltzmann methods

We provide a first investigation of using lattice Boltzmann methods (LBM) for temporal large eddy simulation (TLES). The temporal direct deconvolution model (TDDM) is injected as a closure for the filtered discrete velocity Bhatnagar–Gross–Krook (BGK) Boltzmann equation with orthogonal multiple-relaxation-time (MRT) collision. The novel combination of methods is calibrated for decaying homogeneous isotropic turbulence. The Taylor–Green vortex flow is used as a benchmark for the Reynolds numbers 800 and 3000. Various turbulence quantities are numerically evaluated. The numerical results obtained with the MRT LBM are validated against a well-established spectral element method both, with and without the proposed turbulence model. A qualitatively good agreement to reference results of direct numerical simulation is observed in terms of dissipation rate, energy spectrum and dissipation spectrum. Whereas the latter two show marginal differences compared to underresolved simulations without TLES, the dissipation rate exhibits substantial improvement through the model in capturing the peak region for low and intermediate resolutions. The consistency of the TDDM with first and second order discretization is numerically demonstrated for single-relaxation-time and MRT collision via computing the total dissipation rate error. Measuring the interaction between subgrid activity and energy spectrum error serves as a proof of concept for the proposed MRT LBM TLES. Conclusively, the model recovers and enhances the expected numerical features of LBM with respect to the target equation.

An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τ/ρ and the kinetic energy of turbulence (k=q2/2). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τ/ρ=a11−AFRiFq2/2 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov’s proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–ε model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an ε evaluated by assuming isotropic eddy viscosity behavior.

Statistical Behaviour and Modelling of Fuel Mass Fraction Dissipation Rate Transport in Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation study

Three-dimensional Direct Numerical Simulation (DNS) data of statistically planar turbulent spray flames propagating into mono-disperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd has been used to analyse the statistical behaviour of the fuel mass fraction dissipation rate overset{sim }{upvarepsilon_Y} and its transport in the context of Reynolds Averaged Navier-Stokes (RANS) simulations. Closures previously derived for high Damköhler number turbulent stratified mixture combustion have been shown not to capture the statistical behaviour of overset{sim }{upvarepsilon_Y} for turbulent spray flames, because the underlying assumptions behind the original modelling are invalid for the cases considered in this analysis. The modelling of the unclosed terms of the fuel mass fraction dissipation rate overset{sim }{upvarepsilon_Y} transport equation (i.e. the turbulent transport term T1, the density variation term T2, the scalar turbulence interaction term T3, the reaction rate term T4, the evaporation contribution terms T5 and T6, and the dissipation rate term −D2) has been analysed in the context of RANS simulations. The models previously proposed in the context of turbulent gaseous stratified flames have been considered here to assess their suitability for turbulent spray flames. Based on a-priori DNS analysis, suitable model expressions have been identified for T1, T2, T31, T32, T33, [T4 − D2 + f(D)] and [T5 + T6], which have been shown to perform generally satisfactorily for all cases considered here.

Statistical behavior of fuel mass fraction variance transport in turbulent flame–droplet interaction: A direct numerical simulation analysis

ABSTRACTThree-dimensional direct numerical simulations (DNS) data of statistically planar turbulent spray flames propagating into monodisperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd have been used to analyze the statistical behavior of the fuel mass fraction variance and its transport in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. The algebraic closure, which was previously derived for high Damköhler number turbulent stratified mixture combustion, has been shown not to capture statistical behavior of for turbulent spray flames, because the underlying assumptions behind the original modeling are invalid for the cases considered in this analysis. The modeling of the unclosed terms of the variance transport equation (i.e., the turbulent transport term T1, the reaction rate contribution T3, the evaporation contribution T4, and the dissipation rate term –D2) has been analyzed in the context of RANS simulations. The models previously proposed in the context of turbulent gaseous stratified flames have been considered here to assess their suitability for turbulent spray flames. Model expressions have been identified for and −D2 which have been shown to perform satisfactorily in all cases considered in the current study. However, the model previously proposed for T3 in the context of turbulent gaseous stratified flames has been found to be inadequate for turbulent spray flames and further consideration of the modeling of this unclosed term is therefore necessary.

The temporal scaling laws of compressible turbulence

This paper proposes temporal scaling laws of the density-weighted energy spectrum for compressible turbulence in terms of dissipation rate, frequency and the Mach number. The study adopts the incomplete similarity theory in the scaling analysis of compressible turbulence motion. The investigation shows that the temporal Eulerian and Lagrangian energy spectra approach the [Formula: see text] and [Formula: see text] power laws when the Mach number M tends to reach unity and infinity, respectively.

Exploring Stratocumulus Cloud-Top Entrainment Processes and Parameterizations by Using Doppler Cloud Radar Observations

Abstract Observations made at the Atmospheric Radiation Measurement (ARM) Program’s Southern Great Plains (SGP) site during uniform nonprecipitating stratocumulus cloud conditions for a 14-h period are used to examine cloud-top entrainment processes and parameterizations. The observations from a vertically pointing Doppler cloud radar provide estimates of vertical velocity variance and energy dissipation rate (EDR) terms in the parameterized turbulent kinetic energy (TKE) budget of the entrainment zone. Hourly averages of the vertical velocity variance term in the TKE entrainment formulation correlated strongly (r = 0.72) with the dissipation rate term in the entrainment zone, with an increased correlation (r = 0.92) when accounting for the nighttime decoupling of the boundary layer. Independent estimates of entrainment rates were obtained from an inversion-height budget using the local time derivative and horizontal advection of cloud-top height together with large-scale vertical velocity at the boundary layer inversion from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis model. The mean entrainment rate from the inversion-height budget during the 14-h period was 0.74 ± 0.15 cm s−1 and was used to calculate bulk coefficients for entrainment parameterizations based on convective velocity scale w* and TKE budgets of the entrainment zone. The hourly values of entrainment rates calculated using these coefficients exhibited good agreement with those calculated from the inversion-height budget associated with substantial changes in surface buoyancy production and cloud-top radiative cooling. The results indicate a strong potential for making entrainment rate estimates directly from radar vertical velocity variance and the EDR measurements.

Parameterization of Time-Averaged Suspended Sediment Concentration in the Nearshore

To quantify the effect of wave breaking turbulence on sediment transport in the nearshore, the vertical distribution of time-averaged suspended sediment concentration (SSC) in the surf zone was parameterized in terms of the turbulent kinetic energy (TKE) at different cross-shore locations, including the bar crest, bar trough, and inner surf zone. Using data from a large-scale laboratory experiment, a simple relationship was developed between the time-averaged SSC and the time-averaged TKE. The vertical variation of the time-averaged SSC was fitted to an equation analogous to the turbulent dissipation rate term. At the bar crest, the proposed equation was slightly modified to incorporate the effect of near-bed sediment processes and yielded reasonable agreement. This parameterization yielded the best agreement at the bar trough, with a coefficient of determination R2 ≥ 0.72 above the bottom boundary layer. The time-averaged SSC in the inner surf zone showed good agreement near the bed but poor agreement near the water surface, suggesting that there is a different sedimentation mechanism that controls the SSC in the inner surf zone.

Large eddy simulations of the Darmstadt turbulent stratified flame series

Large-eddy simulations of the Darmstadt turbulent stratified flame (TSF) burner are presented. The TSF burner is operated under a wide variety of conditions. A case without stratification or shear, and one with stratification but no shear, are considered for validation purposes. A combined mixture fraction and reaction progress variable approach is used, with the reaction rate modelled by a fractal flame wrinkling flame surface density model, where the laminar flame speed is obtained as a function of the mixture fraction. The simulation results and the suitability of the modelling approach are verified and validated through comparison of mean and variance of axial and radial velocity, temperature and mixture fraction with experimental data. The effects of stratification on the flame flow field are then studied by comparing the two reactive simulations, and studying the impact of the cross-scalar dissipation rate term. Finally, the occurrence of potential back- or front-supported stratification is examined through statistical analysis of the flame normal directions. The modelling approach employed was found to produce very good predictions of the TSF burner, with both back- and front-supported stratification modes occurring, the former being considerably more likely.

Scaling Properties of Biologically Active Scalar Concentration Fluctuations in the Atmospheric Surface Layer over a Managed Peatland

The higher-order scalar concentration fluctuation properties are examined in the context of Monin–Obukhov similarity theory for a variety of greenhouse gases that have distinct and separate source/sink locations along an otherwise ideal micrometeorological field site. Air temperature and concentrations of water vapour, carbon dioxide and methane were measured at high frequency (10 Hz) above a flat and extensive peat-land soil in the San Joaquin–Sacramento Delta (California, USA) area, subjected to year-round grazing by beef cattle. Because of the heterogeneous distribution of the sources and sinks of CO2 and especially CH4 emitted by cattle, the scaling behaviour of the higher-order statistical properties diverged from predictions based on a balance between their production and dissipation rate terms, which can obtained for temperature and H2O during stationary conditions. We identify and label these departures as ‘exogenous’ because they depend on heterogeneities and non-stationarities induced by boundary conditions on the flow. Spectral analysis revealed that the exogenous effects show their signatures in regions with frequencies lower than those associated with scalar vertical transport by turbulence, though the two regions may partially overlap in some cases. Cospectra of vertical fluxes appear less influenced by these exogenous effects because of the modulating role of the vertical velocity at low frequencies. Finally, under certain conditions, the presence of such exogenous factors in higher-order scalar fluctuation statistics may be ‘fingerprinted’ by a large storage term in the mean scalar budget.

Principal Length Scales in Second-Order Closure Models for Canopy Turbulence

Abstract Triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a pine forest were used to examine the performance of two second-order closure models put forth by Wilson and Shaw and by Wilson. Based on these measurements, it was demonstrated that Wilson’s model reproduced the longitudinal velocity standard deviation σu better than did Wilson and Shaw’s model. However, Wilson and Shaw’s model reproduced the measured mean velocity 〈u〉 near the forest–atmosphere interface better than Wilson’s model did. The primary mechanisms responsible for discrepancies between modeled and measured 〈u〉 and σu profiles were investigated. The conceptual formulations of these two closure models differ in the characteristic length scales and timescales used in the closure parameterizations of the mean turbulent kinetic energy dissipation rate term, the pressure–strain rate term, and the flux-transport term. These characteristic length scales were computed and compared with measured i...

Forming analysis of porous materials

A procedure for estimating the applied traction required for forming processes of porous material is suggested. It carries the general structure of the upper-bound approach in the sense that static equilibrium is not enforced and a detailed mechanism of pore closure is not needed. A velocity field for compressible, porosity dependent, plastic continua, is solved for plane and axisymmetric converging flow problems. By employing, in conjunction with the velocity field, Gurson's model (to characterize the effects of the mean stress and the porosity on the yielding of the material), account is taken of the work expenditure due to the dilatancy of the material, beside the other customary dissipation rate terms. The tractions are then evaluated by the limit analysis scheme, leaving the porosity at the exit as a free parameter to be fixed by minimization of the plastic dissipation. It has been found that the dissipation terms depend on the mean normal stresses and the porosity in a highly nonlinear way. In cases where the porosity and the mean stress vary moderately in the domain of the flow, closed-form expressions for the various dissipation rates are provided. They exhibit, in a systematic fashion, the exact features of the corresponding solutions of non-porous materials, but are multiplied by a set of “weight functions” which depend merely on the averaged values of the porosity and the mean normal stress. Parametric study of the presented solutions for several classical processes (wire drawing, extrusion, ironing and rolling) indicates the role of the average porosity in decreasing or increasing the loads (or moments) needed to operate the forming processes, compared to materials with zero porosity. Comparisons to various experiments, numerical solutions (FEM) and to few exact (asymptotic) solutions, validate the feasibility of the suggested scheme for extending the upper-bound analysis to metal forming of porous materials. The fact that forming loads of non-porous material are not necessarily upper bounds to forming loads of porous materials (under the same geometrical and influx speeds) may have valuable consequences.

Turbulent Kinetic Energy Budgets over Mountainous Terrain

Abstract The objective of this study is to describe the characteristics of the airflow and turbulence structure over mountainous terrain. Turbulent characteristics of the airflow were measured using well-instrumented aircraft. The shear, buoyancy, transport of energy and eddy dissipation rate terms were obtained from direct measurements. The turbulent kinetic energy budgets were determined with respect to height and horizontal distance upwind and downwind of the mountain. The change of turbulence intensity was also demonstrated by comparing power spectra as a function of height, as well as a function of distance upwind and downwind of the mountain. The results show that all measurable terms were significant. The shear production and the eddy dissipation rate were the dominant terms. The buoyancy and vertical transport terms were smaller but still important. The imbalance term was estimated to be relatively small.