Turbulent Energy Model Research Articles

Large eddy simulation of particle hydrodynamic characteristics in a dense gas-particle bubbling fluidized bed

A subgrid scale particle kinetic turbulent energy model coupled with a second order moment model is developed to describe the particle hydrodynamic characteristics in dense gas-particle fluidized bed. Anisotropic behaviors of particle dispersions and interactions between gas and particle are fully revealed by means of two-phase Reynolds stresses transport eqs. A four-way coupling strategy for the consideration of particle-particle collisions is modeled by frictional granular temperature transport equation. Simulation results by large eddy simulation are validated by experimental measurement with acceptable agreement. Heterogenous flow structures, anisotropic characteristics of particle dispersions and wider-size distribution behaviors of bubbles are indicated. At the height of 0.2 m, the largest dominant frequency of porosity is 25.0 Hz at lateral 0.375 cm away from center, it is approximately 5.0 times larger than that of lateral 9.375 cm. Compared to 0.45 m, the standard deviations of 82.5 cm/s at lateral region is approximately 1.5 times larger than that of center region.

IMPLEMENTATION OF THE K-EPSILON (K–Ε) MODEL FOR THE SIMULATION OF COAL GASIFIER /REACTOR

The objective of the present research is to use the standard turbulent kinetic energy and turbulent dissipation (k-e) model to do a numerical modelling and simulation of the gasification chamber or reactor which was used to gasifier Lafia-Obi bituminous coal. The numerical modelling and simulation were implemented with the aid of AutoCAD and Ansys softwares. The gasifier/reactor geometry was modelled using AutoCAD and then imported to Ansys workbench for simulation. Results show the modelled reactor geometry comprising a height of 0.9m, diameter of 0.5m and volume of 0.177m 3. Simulation results show mass fraction of producer gas components comprising of 16% carbon monoxide, 14% hydrogen, 2.7% methane and 18% carbon dioxide. The producer gas yield is in conformity with standard producer gas yield. Temperature profile around the modelled gasifier/reactor was displayed with a maximum of 960K.

Optical and thermal analysis of solar parabolic dish cavity receiver system for hydrogen production using deep learning

The solar thermochemical cycle, responsible for converting solar energy to chemical fuel, is an emerging clean hydrogen production technique. The distribution of the concentrated heat flux and temperature on the receiver is crucial in deciding solar-to-fuel conversion efficiency. Thus, the optimum configuration of a solar parabolic dish collector (PDC) is necessary for providing efficient thermal energy. The dish diameter, rim angle, and distance of the receiver aperture from the focal point of the dish characterize the optimization of the PDC. The non-uniform heat flux captured is coupled with a heat transfer model of a solar thermochemical reactor for a thermal dissociation of ZnO involved in a ZnO/Zn thermochemical cycle for hydrogen production. The directly irradiated rotating reactor comprises a cylindrical cavity packed with insulation layers and a quartz glass window. The rotating cavity is loaded with ZnO granular particles held by a centrifugal force. A 3D CFD numerical model is analyzed by coupling the Eulerian multiphase model for ZnO particle dynamics, fluid flow of gaseous mixture, RNG k-ԑ turbulence model, Energy and Discrete Ordinates (DO) radiation model, and Arrhenius reaction rate chemical reaction of ZnO dissociation. A numerical model with non-uniform heat flux input is validated for a cavity temperature, mass fraction of zinc and oxygen, and oxygen molar flow rate at the reactor outlet. An artificial neural network model is adopted to predict the heat flux and uniformity factor values of PDC. Correlation Coefficient (R2), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) error metrices were used to evaluate the model's performance having the receiver diameter (d), the dish diameter (D), the rim angle (φ), and the distance between the focus and receiver (h) as input variables.

Hydrodynamics affected by submerged vegetation with different flexibility under unidirectional flow

Submerged vegetation changes the hydrodynamic characteristics of rivers, lakes, wetlands, and coastal zones. However, only a few studies have focused on the effect of flexible submerged vegetation on hydrodynamic characteristics under unidirectional flow. Therefore, laboratory experiments were conducted to study the effects of submerged vegetation with different flexibility on the flow structure and turbulence characteristics under unidirectional flow. The results showed that the reconfiguration and coordination of wave motion of flexible submerged vegetation redistribute flow velocity, Reynolds stress, and turbulent kinetic energy inside and outside of the vegetation canopy. With a gradual decrease in the deflection height of vegetation, the differences in dimensionless velocity, dimensionless mixed layer thickness, bulk drag coefficient, averaged turbulent kinetic energy, and the averaged contribution rate of its shear production term for the vegetation canopy also decrease; the trend of the penetration depth of Reynolds stress is opposite. Based on the turbulent kinetic energy budget equation, a turbulent kinetic energy model (TKE model) was established, which can be used to predict the turbulent kinetic energy and its shear production term within the vegetation canopy. Here, the scaling factor was determined by the vegetation canopy Cauchy number. The TKE model can be applied under unidirectional flow conditions for submerged vegetation with different flexibilities with high accuracy. It is a simple method to predict vegetation-induced turbulence and the characteristics of sediment and material transport under the influence of submerged vegetation with different flexibility.

Flow and turbulence in unevenly obstructed channels with rigid and flexible vegetation

The pattern of vegetation along the cross-section of macrophyte-dominated shallow waters is generally uneven, which affects water velocity and turbulence. This study examined the velocity and turbulence in the open channel with an uneven transverse distribution of vegetation in laboratory flume experiments. Two vegetation patterns were tested: emergent vegetation which covered part of the channel, and a symmetrical combination of submerged and emergent vegetation canopies along the lateral direction of the flume. The flow was measured using a three-dimensional Acoustic Doppler Velocimeter. The velocity and turbulence characteristics were analyzed under three vegetation densities and five discharge scenarios. Results showed that the longitudinal mean velocity changed with vegetation density and flow discharge when vegetation was unevenly distributed in a lateral direction. The strong variation in shear stress at the emergent vegetation–open water intersections and submerged–emergent vegetation intersections resulted in large-scale vortices at the interfaces. The formation processes of stem-scale turbulence and shear-scale turbulence under different vegetation scenarios were discussed. A turbulent kinetic energy model within partly obstructed vegetation canopies was established, which helped to identify the development of horizontal and vertical coherent vertices.

Parameter Sensitivity for Wave-Breaking Closures in Boussinesq-Type Models

We consider the issue of wave-breaking closure for the well-known Green–Naghdi model and attempt at providing some more understanding of the sensitivity of some closure approaches to the numerical set-up. More precisely and based on Kazolea and Ricchiuto (Ocean Model 123:16–39, 2018), we used two closure strategies for modeling wave-breaking of a solitary wave over a slope. The first one is the hybrid method consisting of suppressing the dispersive terms in a breaking region and the second one is an eddy viscosity approach based on the solution of a turbulent kinetic energy model. The two closures use the same conditions for the triggering of the breaking mechanisms. Both the triggering conditions and the breaking models themselves use case depended/ad/hoc parameters which are affecting the numerical solution while changing. The scope of this work is to make use of sensitivity indices computed by means of analysis of variance to provide the sensitivity of wave-breaking simulation to the variation of parameters such as the mesh size and the breaking parameters specific to each breaking model. The sensitivity analysis is performed using the UQlab framework for uncertainty quantification (Marelli et al., UQLab user manual—sensitivity analysis, Technical report, Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Switzerland, 2019).

Wind–Wave Misalignment Effects on Langmuir Turbulence in Tropical Cyclone Conditions

AbstractThis study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.

A consistent multi-level subgrid scale closure for large eddy simulation of compressible flow using adaptive mesh refinement

A novel subgrid closure model is proposed for performing Large Eddy Simulation (LES) of turbulent compressible flows with block structured Adaptive Mesh Refinement (AMR) strategy. The new approach, henceforth called as AMRLES, is an improvement over the well-established one-equation based subgrid turbulent kinetic energy model with corrections proposed to consistently handle the total resolved turbulent kinetic energy across a multi-level AMR grid hierarchy. The proposed correction for the subgrid kinetic energy is based on an explicit on-the-fly filtering operation from finer grids to underlying coarser grids. The effect of the inter-grid correction is demonstrated by investigating advection of decaying isotropic turbulence across a coarse/fine and fine/coarse AMR grid interface. In the case of fine-to-coarse transition, the multi-level model is shown to correctly recover the subgrid turbulent kinetic energy. AMRLES is then applied to study the canonical problem of shock turbulent interaction. Two different Reynolds numbers are considered and the behavior of the inter-grid corrections on the subgrid turbulent kinetic energy and the subgrid turbulent stresses are analyzed for both the cases. Comparison with filtered DNS results indicates that AMRLES is able to predict the behavior of turbulent statistics across the shock in a satisfactory manner.

Weakly sheared turbulent flows generated by multiscale inhomogeneous grids

A group of three multiscale inhomogeneous grids have been tested to generate different types of turbulent shear flows with different mean shear rate and turbulence intensity profiles. Cross hot-wire measurements were taken in a wind tunnel with Reynolds number$Re_{D}$of 6000–20 000, based on the width of the vertical bars of the grid and the incoming flow velocity. The effect of local drag coefficient$C_{D}$on the mean velocity profile is discussed first, and then by modifying the vertical bars to obtain a uniform aspect ratio the mean velocity profile is shown to be predictable using the local blockage ratio profile. It is also shown that, at a streamwise location$x=x_{m}$, the turbulence intensity profile along the vertical direction$u^{\prime }(y)$scales with the wake interaction length$x_{\ast ,n}^{peak}=0.21g_{n}^{2}/(\unicode[STIX]{x1D6FC}C_{D}w_{n})$($\unicode[STIX]{x1D6FC}$is a constant characterizing the incoming flow condition, and$g_{n}$,$w_{n}$are the gap and width of the vertical bars, respectively, at layer$n$) such that$(u^{\prime }/U_{n})^{2}\unicode[STIX]{x1D6FD}^{2}(C_{D}w_{n}/x_{\ast ,n}^{peak})^{-1}\sim (x_{m}/x_{\ast ,n}^{peak})^{b}$, where$\unicode[STIX]{x1D6FD}$is a constant determined by the free-stream turbulence level,$U_{n}$is the local mean velocity and$b$is a dimensionless power law constant. A general framework of grid design method based on these scalings is proposed and discussed. From the evolution of the shear stress coefficient$\unicode[STIX]{x1D70C}(x)$, integral length scale$L(x)$and the dissipation coefficient$C_{\unicode[STIX]{x1D716}}(x)$, a simple turbulent kinetic energy model is proposed that describes the evolution of our grid generated turbulence field using one centreline measurement and one vertical profile of$u^{\prime }(y)$at the beginning of the evolution. The results calculated from our model agree well with our measurements in the streamwise extent up to$x/H\approx 2.5$, where$H$is the height of the grid, suggesting that it might be possible to design some shear flows with desired mean velocity and turbulence intensity profiles by designing the geometry of a passive grid.

Relationship between turbulence energy and density variance in the solar neighbourhood molecular clouds

[abridged] We determine the relationship between turbulence energy and gas density variance for 15 molecular clouds in the Solar neighbourhood. We use the linewidths of the CO molecule as the probe of the turbulence energy (sonic Mach number, $\cal{M}_\mathrm{s}$) and three-dimensional models to reconstruct the density probability distribution function ($\rho$-PDF) of the clouds, derived using near-infrared extinction and Herschel dust emission data, as the probe of the density variance ($\sigma_\mathrm{s}$). We find no significant correlation between $\cal{M}_\mathrm{s}$ and $\sigma_\mathrm{s}$ among the studied clouds, however, we also cannot rule out a weak correlation. In the context of turbulence-dominated gas, the range of the $\cal{M}_\mathrm{s}$ and $\sigma_\mathrm{s}$ values corresponds with the model predictions. The data cannot constrain whether or not the turbulence driving parameter, $b$, and/or thermal-to-magnetic pressure ratio, $\beta$, vary among the sample clouds. Most clouds are not in agreement with field strengths stronger than given by $\beta \lesssim 0.05$. A model with $b^2 \beta / (\beta+1) = 0.30 \pm 0.06$ provides an adequate fit to the cloud sample as a whole. When considering the average behaviour of the sample, we can rule out three regimes: (i) strong compression combined with a weak magnetic field ($b \gtrsim 0.7$ and $\beta \gtrsim 3$), (ii) weak compression ($b \lesssim 0.35$), and (iii) strong magnetic field ($\beta \lesssim 0.1$). Including independent magnetic field strength estimates to the analysis, the data rule out solenoidal driving ($b < 0.4$) for the majority of the Solar neighbourhood clouds. However, most clouds have $b$ parameters larger than unity, which indicates a discrepancy with the turbulence-dominated picture; we discuss the possible reasons for this.

A Diagnosis of Excessive Mixing in Smagorinsky Subfilter-Scale Turbulent Kinetic Energy Models

Abstract Large-eddy simulation (LES) models are widely used to study atmospheric turbulence. The effects of small-scale motions that cannot be resolved need to be modeled by a subfilter-scale (SFS) model. The SFS contribution to the turbulent fluxes is typically significant in the surface layer. This study presents analytical solutions of the classical Smagorinsky SFS turbulent kinetic energy (TKE) model including a buoyancy flux contribution. Both a constant length scale and a stability-dependent one as proposed by Deardorff are considered. Analytical expressions for the mixing functions are derived and Monin–Obukhov similarity relations that are implicitly imposed by the SFS TKE model are diagnosed. For neutral and weakly stable conditions, observations indicate that the turbulent Prandtl number (PrT) is close to unity. However, based on observations in the convective boundary layer, a lower value for PrT is often applied in LES models. As a lower Prandtl number promotes a stronger mixing of heat, this may cause excessive mixing, which is quantified from a direct comparison of the mixing function as imposed by the SFS TKE model with empirical fits from field observations. For a strong stability, the diagnosed mixing functions for both momentum and heat are larger than observed. The problem of excessive mixing will be enhanced for anisotropic grids. The findings are also relevant for high-resolution numerical weather prediction models that use a Smagorinsky-type TKE closure.

Effect of solid mass flux on anisotropic gas–solid flow in risers determined with an LES-SOM model

Within the framework of the two-fluid approach, gas was treated with a large-eddy simulation and a sub-grid-scale (SGS) turbulent kinetic energy model while particles were treated with a second-order-moment method to describe the anisotropy of the fluctuating velocity. A modified Simonin model was derived for the gas–solid interphase fluctuating energy transfer. The anisotropic gas–solid flow in a circulating fluidized bed was investigated. Predictions were in good agreement with experimental data. The distributions of the second-order moment of particles and SGS-turbulent kinetic energy of gas were simulated at different solid mass fluxes. The effects of the solid mass flux on the particle second-order moment, particle anisotropic behavior, gas SGS-turbulent kinetic energy and gas SGS energy dissipation were analyzed for the circulating fluidized bed.

The onset of sediment transport in vegetated channels predicted by turbulent kinetic energy

AbstractThis laboratory study advances our understanding of sediment transport in vegetated regions, by describing the impact of stem density on the critical velocity, Ucrit, at which sediment motion is initiated. Sparse emergent vegetation was modeled with rigid cylinders arranged in staggered arrays of different stem densities. The sediment transport rate, Qs, was measured over a range of current speeds using digital imaging, and the critical velocity was selected as the condition at which the magnitude of Qs crossed the noise threshold. For both grain sizes considered here (0.6–0.85 mm and 1.7–2 mm), Ucrit decreased with increasing stem density. This dependence can be explained by a threshold condition based on turbulent kinetic energy, kt, suggesting that near‐bed turbulence intensity may be a more important control than bed shear stress on the initiation of sediment motion. The turbulent kinetic energy model unified the bare bed and vegetated channel measurements.

Assessment of LES Subgrid-scale Models and Investigation of Hydrodynamic Behaviour for an Axisymmetrical Bluff Body Flow

This work is concerned with the investigation of fluid-mechanical behaviour and the performance of different subgrid-scale models for LES in the numerical prediction of a confined axisymmetrical bluff-body flow. Four subgrid-scale turbulence models comprising the Smagorinsky model, Dynamic Smagorinsky model, WALE model and subgrid turbulent kinetic energy model, are validated and compared directly against the experimental data. Two different mesh counts are used for the LES studies, one with a higher mesh resolution in the shear layer than the other. It is found that increasing the mesh resolution improves the time-averaged fluctuating velocity profiles, but has less effect on the time-averaged filtered velocity profiles. A comparison against experiment shows that the recirculation zone length is well predicted using LES. The accuracy of the four different subgrid scale models is then assessed by comparing the LES results using the dense mesh with the experiment. Comparisons with the time-averaged axial and radial velocity profiles demonstrate that LES displays good agreement with the experimental data, with the essential flow features captured both qualitative and quantitatively. The subgrid velocity also matches well with the experimental results, but a slight underprediction of the inner shear layer is observed for all subgrid models. In general, it is found that the Smagorinsky and WALE models are more dissipative than the Dynamic Smagorinsky model and subgrid TKE model. Comparison of the spectra against the experiment shows that LES can capture dominant features of the turbulent flow with reasonable accuracy, and weak spectral peaks related to the Kevin-Helmholtz instability and helical vortex shedding are present.

Large Eddy Simulations in Astrophysics

In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid-scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid-scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamic procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid-scale turbulence energy model allows for a particularly elegant and physically well-motivated way of preserving momentum and energy conservation in adaptive mesh refinement (AMR) simulations. Moreover, the notion of shear-improved models for in-homogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.

E–ε Model of Spray-Laden Near-Sea Atmospheric Layer in High Wind Conditions

Abstract In-depth understanding and accurate modeling of the interaction between ocean spray and a turbulent flow under high wind conditions is essential for improving the intensity forecasts of hurricanes and severe storms. Here, the authors consider the E–ε closure for a turbulent flow model that accounts for the effects of the variation of turbulent energy and turbulent mixing length caused by spray stratification. The obtained analytical and numerical solutions show significant differences between the current E–ε model and the lower-order turbulent kinetic energy (TKE) model considered previously. It is shown that the reduction of turbulent energy and mixing length above the wave crest level, where the spray droplets are generated, that is not accounted for by the TKE model results in a significant suppression of turbulent mixing in this near-wave layer. In turn, suppression of turbulence causes an acceleration of flow and a reduction of the drag coefficient that is qualitatively consistent with field observations if spray is fine (even if its concentration is low) or if droplets are large but their concentration is sufficiently high. In the latter case, spray inertia may become important. This effect is subsequently examined. It is shown that spray inertia leads to the reduction of wind velocity in the close proximity of the wave surface relative to the reference logarithmic profile. However, at higher altitudes the suppression of flow turbulence by the spray still results in the wind acceleration and the reduction of the local drag coefficient.

Three-Dimensional Modeling of Storm Surge and Inundation Including the Effects of Coastal Vegetation

Two-dimensional (2D) and three-dimensional (3D) hydrodynamic models are used to simulate the hurricane-induced storm surge and coastal inundation in regions with vegetation. Typically, 2D storm surge models use an enhanced Manning coefficient while 3D storm surge models use a roughness height to represent the effects of coastal vegetation on flow. This paper presents a 3D storm surge model which accurately resolves the effects of vegetation on the flow and turbulence. First, a vegetation-resolving 1DV Turbulent Kinetic Energy model (TKEM) is introduced and validated with laboratory data. This model is both robust enough to accurately model flows in complex canopies, while compact and efficient enough for incorporation into a 3D storm surge-wave modeling system: Curvilinear Hydrodynamics in 3D-Surface WAves Nearshore (CH3D-SWAN). Using the 3D vegetation-resolving model, three numerical experiments are conducted. In the first experiment, comparisons are made between the 2D Manning coefficient approach and the 3D vegetation-resolving approach for simple wind-driven flow. In a second experiment, 2D and 3D representations of vegetation produce similar inundations from the same hurricane forcing, but differences in momentum are found. In a final experiment, varying inundation between seemingly analogous 2D and 3D representations of vegetation are demonstrated, pointing to a significant scientific need for data within wetlands during storm surge events. This study shows that the complex flow structures within vegetation canopies can be accurately simulated using a vegetation-resolving 3D storm surge model, which can be used to assess the feasibility for future wetland restoration projects.

A robust k − ε − [formula omitted]/k elliptic blending turbulence model applied to near-wall, separated and buoyant flows

This paper first reconsiders evolution over 20years of the k−ε−v2¯−f strand of eddy-viscosity models, developed since Durbin’s (1991)original proposal for a near-wall eddy viscosity model based on the physics of the full Reynolds stress transport models, but retaining only the wall-normal fluctuating velocity variance, v2¯, and its source, f, the redistribution by pressure fluctuations. Added to the classical k−ε (turbulent kinetic energy and dissipation) model, this resulted in three transport equations f or k, epsilon and v2¯, and one elliptic equation for f, which accurately reproduced the parabolic decay of v2¯/k down to the solid wall without introducing wall-distance or low-Reynolds number related damping functions in the eddy viscosity and k−ε equations. However, most v2¯−f variants have suffered from numerical stiffness making them unpractical for industrial or unsteady RANS applications, while the one version available in major commercial codes tends to lead to degraded and sometimes unrealistic solutions. After considering the rationale behind a dozen variants and asymptotic behaviour of the variables in a number of zones (balance of terms in the channel flow viscous sublayer, logarithmic layer, and wake region, homogenous flows and high Reynolds number limits), a new robust version is proposed, which is applied to a number of cases involving flow separation and heat transfer. This k−ε type of model with v2¯/k anisotropy blends high Reynolds number and near-wall forms using two dimensionless parameters: the wall-normal anisotropy v2¯/k and a dimensionless parameter alpha resulting from an elliptic equation to blend the homogeneous and near-wall limiting expressions of f. The review of variants and asymptotic cases has also led to modifications of the epsilon equation: the second derivative of mean velocity is reintroduced as an extra sink term to retard turbulence growth in the transition layer (i.e. embracing the E term of the Jones and Launder (1972)k−ε model), the homogeneous part of epsilon is now adopted as main transported variable (as it is less sensitive to the Reynolds number effects), and the excessive growth of the turbulent length-scale in the absence of production is corrected (leading to a better distinction between log layer and wake region of a channel flow). For each modification numerical stability implications are carefully considered and, after implementation in an industrial finite-volume code, the final model proved to be significantly more robust than any of the previous variants.

Application of the Algebraic Subgrid Turbulent Kinetic Energy Model in LES Model

In this study the dynamic Smagorinsky model (DSM model) and an algebraic model for the subgrid turbulent kinetic energy have been implemented into KIVA3VLES code to investigate the atomization and evaporation processes of diesel spray in a constant volume vessel. Based on the experimental results of the liquid and vapor phase distributions as well as the results obtained by the differential subgrid scale kinetic energy (K-equation) model, the paper reveals the influence of the turbulent kinetic energy model on the fuel spray prediction. Computational results show that by combining the DSM model and the algebraic subgrid turbulent energy model, the turbulent diffusion of droplets can be reasonably simulated, the liquid penetration and the predicted liquid and fuel vapor mass fraction contours are close to the experiment results. At the same time, the turbulent kinetic energy given by the DSM model is in agreement with the results by the K-equation model, but with less computational cost..

Large eddy simulation of fuel injection and mixing process in a diesel engine

The large eddy simulation (LES) approach implemented in the KIVA-3V code and based on one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine. Computational results are compared with those obtained by an RANS (RNG k-ɛ) model as well as with experimental data. The sensitivity of the LES results to mesh resolution is also discussed. The results show that LES generally provides flow and spray characteristics in better agreement with experimental data than RANS; and that small-scale random vortical structures of the in-cylinder turbulent spray field can be captured by LES. Furthermore, the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result, and the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model. Finally, it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber.