In the present paper, we address the important point of the proportionality between the longitudinal integral lengthscale ($L$) and the characteristic mean flow width ($δ$) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flows, irrespective of turbulence dissipation scaling. We show that $L/δ$ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension ($L_{ref}$, nozzle width or wake generator size). Furthermore, we revisit turbulence closure models such as the Prandtl mixing length \cite{prandtl1925} and the constant eddy viscosity in the light of the non-equilibrium dissipation scalings. We show that the mixing length model, with $l_m\sim δ$, does not comply with the scalings stemming from the non-equilibrium version of the theory; we instead obtain $l_m\sim δ\sqrt{Re_G/Re_{0δ}}$, where $Re_G$ and $Re_{0δ}$ are a global and local Reynolds number, respectively. Similarly, the eddy viscosity model holds in the case of the non-equilibrium version of the theory provided that the eddy viscosity is constant everywhere, not only across sections orthogonal to the streamwise direction as in the equilibrium case. We conclude comparing the results of the different models with each other and with experimental data and with an improved model (following Townsend) that accounts for the intermittency of the flow and corrects for the eddy viscosity variation across the flow boundaries.
We generate explicit height-dependent eddy viscosity coefficients in the Ekman layer from convex wind speed profiles. The solutions we obtain are parameterized in terms of the relative deflection angle between the wind directions at the top and bottom of the flow, as well as the geostrophic wind speed and a velocity scale we interpret as the transfer rate of horizontal momentum in the vertical direction. The solutions may be used to infer the thickness of the Ekman layer for a variety of deflection angles different from deflection angle of the classic Ekman spiral.
We consider the question of fundamental limitations on the performance of eddy-viscosity closure models for turbulent flows, focusing on the Leith model for 2D {Large-Eddy Simulation}. Optimal eddy viscosities depending on the magnitude of the vorticity gradient are determined subject to minimum assumptions by solving PDE-constrained optimization problems defined such that the corresponding optimal Large-Eddy Simulation best matches the filtered Direct Numerical Simulation. First, we consider pointwise match in the physical space and the main finding is that with a fixed cutoff wavenumber $k_c…
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solutio…
From the simplest models to complex deep neural networks, modeling turbulence with machine learning techniques still offers multiple challenges. In this context, the present contribution proposes a robust strategy using patch-based training to learn turbulent viscosity from flow velocities, and demonstrates its efficient use on the Spallart-Allmaras turbulence model. Training datasets are generated for flow past two-dimensional (2D) obstacles at high Reynolds numbers and used to train an auto-encoder type convolutional neural network with local patch inputs. Compared to a standard training tec…
Motivated by the concept of eddy viscosity tensor in improved Boussinesq hypothesis, a transport model of high-order eddy viscosity tensor in 2D-3C turbulence structure is derived from the second-order moment model by tensorial analysis.
The complex interactions existing between turbulence and mixing in a bluff-body stabilised flame configuration is investigated by means of a wavelet cross-correlation analysis on Large Eddy Simulations. The combined approach allows to better point out typical features of unsteady turbulent flows with mixing through the characterisation of the processes involved both in time and scales. The wavelet cross-correlation analysis of the time signals of velocity and mixture fraction fluctuations can be an an effective tool to study the processes involved in turbulent mixing flows which are of great i…
Assuming a general constitutive relation for the turbulent stresses in terms of the local large-scale velocity gradient, we constructed a class of subgrid-scale models for large-eddy simulation that are consistent with important physical and mathematical properties. In particular, they preserve symmetries of the Navier-Stokes equations and exhibit the proper near-wall scaling. They furthermore show desirable dissipation behavior and are capable of describing nondissipative effects. We provided examples of such physically-consistent models and showed that existing subgrid-scale models do not al…
In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add $ν_\mathrm{ren} \propto Π_u^{1/3} (π/Δ)^{-1/3}$ to the kinematic viscosity; here $Π_u$ is the turbulent kinetic energy flux, and $Δ$ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a $128^3$ grid and compare the results with direct numerical simulation (DNS) on a $512^3$ grid. There is a good agreement between the LES and DNS results…
Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In th…
The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortic…
The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy $k^+$ function (R. Absi, Analytical solutions for the modeled $k$-equation, ASME J. Appl. Mech. \textbf{75}, 044501, 2008) and the van Driest mixing length equation (E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. \textbf{23}, 1007, 1956) is used. The parameters …
The predictions of resolvent analysis for turbulent channel flow are evaluated for a friction Reynolds number of Retau = 550. In addition to the standard resolvent operator with kinematic viscosity, a resolvent operator augmented with the Cess eddy viscosity is considered. Adding eddy viscosity significantly alters the low-rank behavior of the resolvent. Regardless of the wave speed selected, the eddy resolvent is low-rank for spanwise wavelengths of ly+ = 80 and ly/h = 3.5 in comparison to the standard resolvent whose low-rank behavior depends on the wave speed. The leading eddy modes have hi…
Large-eddy simulations (LES) are widely-used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters, and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for modeling even in that sim…
For wall-bounded turbulent flows, Townsend's attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their distance to the wall, while their velocity scale remains constant across their size range. To investigate the existence of such structures in fully developed turbulent pipe flow, stereoscopic particle image velocimetry measurements were performed in two parallel cross-sectional planes, spaced apart by a varying distance from 0 to 9.97$R$, for $Re_τ= 1310$, 2430 and…
Turbulent mixing is a physical process of fundamental importance in high-speed premixed flames. This mixing results in enhanced transport of temperature and chemical scalars, leading to potentially large changes in flame structure and dynamics. To understand turbulent mixing in non-reacting flows, a number of classical theories have been proposed to describe the scaling and statistics of dispersing fluid particle pairs, including predictions of the effective, or turbulent, eddy diffusivity. Here we examine the validity of these classical theories through the study of fluid particle pair disper…
The inner-outer interaction model (Marusic, Mathis & Hutchins, Science, vol. 329, 2010, 193-196) and the attached-eddy model (Townsend, Cambridge University Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wall-bounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting…
Traditional large eddy simulation is based on Kolmogrov's hypothesis, and done in the inertial range. In inertial range the LES model coefficient is scale-invariant. In many cases, such as computing in the boundary layer, the filter scale is not in the inertial range, and the model coefficient changes drastically with the filter scale, thus the assumption of scale-invariance is not proper. In this paper, we propose a general principle of constraint, and then we deduce two concrete constraints based on the existing spectrum theory and priori data. The constrained dynamic Smogorinsky model can p…
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore s…
We propose a model for assessing the unresolved wrinkling factor in LES of turbulent premixed combustion. It relies essentially on a power-law dependence of the wrinkling factor to the filter size and an original expression for the active corrugating strain rate. The latter is written as a product of an efficiency function which accounts for viscous effects and the kinematic constraint of Peters, by a recent expression for the turbulent strain intensity. Yields functional expressions for the fractal dimension and the inner cut-off length scale, the latter being (i) filter-size independent and …
A previously developed modeling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical investigations of homogeneous, isotropic turbulence. A general procedure that focuses on recovering the full subgrid scale (SGS) dissipation from resolved fields is formulated, combining the advantages of both the structural and the functional strategy of modeling. The interscale energy transfer is obtained from the test-filtered velocity field, corresponding sub…
We developed a parallel Bayesian optimization algorithm for large eddy simulations. These simulations challenge optimization methods because they take hours or days to compute, and their objective function contains noise as turbulent statistics that are averaged over a finite time. Surrogate based optimization methods, including Bayesian optimization, have shown promise for noisy and expensive objective functions. Here we adapt Bayesian optimization to minimize drag in a turbulent channel flow and to design the trailing edge of a turbine blade to reduce turbulent heat transfer and pressure los…
A new computational methodology, termed "PeleLM-FDF" is developed and utilized for high fidelity large eddy simulation (LES) of complex turbulent combustion systems. This methodology is constructed via a hybrid scheme combining the Eulerian PeleLM base flow solver with the Lagrangian Monte Carlo simulator of the filtered density function (FDF) for the subgrid scale reactive scalars. The resulting methodology is capable of simulating some of the most intricate physics of complex turbulence-combustion interactions. This is demonstrated by LES of a non-premixed CO/H$_2$ temporally evolving jet fl…
We present first results of an implicit large eddy simulation of the MTU T161 low pressure turbine at a Reynolds number of 90,000 and Mach number of 0.6, both based on isentropic exit conditions, using a high order discontinuous Galerkin method. The aim is to validate the numerical setup with respect to available experimental data. We discuss the steps taken to create realistic inflow boundary conditions in terms of end wall boundary layer thickness and free stream turbulence intensity. This is achieved by tailoring the input distribution of Reynolds stresses and turbulent length scale to a Fo…
In large eddy simulations, the Reynolds averages of nonlinear terms are not directly computable in terms of the resolved variables and require a closure hypothesis or model, known as a subgrid scale term. Inspired by the renormalization group (RNG),we introduce an expansion for the unclosed terms, carried out explicitly to all orders. In leading order, this expansion defines subgrid scale unclosed terms, which we relate to the dynamic subgrid scale closure models. The expansion, which generalizes the Leonard stress for closure analysis, suggests a systematic higher order determination of the m…
This study performs a large-eddy simulation of turbulent separated and reattached flow in an enlarged annular pipe. A vortex ring is periodically shed from the sudden expansion part. A longitudinal vortex occurs around the vortex ring, making the flow three-dimensional. As a result, the vortex ring becomes unstable downstream and splits into small vortices. A tubular longitudinal vortex structure occurs downstream of the reattachment point near the wall surface on the inner pipe side. A low-frequency fluctuation occurs at each pipe diameter ratio. The smaller the pipe diameter ratio is, the mo…
By analyzing the Karman-Howarth equation for filtered velocity fields in turbulent flows, we show that the two-point correlation between filtered strain-rate and subfilter stress tensors plays a central role in the evolution of filtered-velocity correlation functions. Two-point correlations-based {\it statistical priori tests} thus enable rigorous and physically meaningful studies of turbulence models. Using data from direct numerical simulations of isotropic and channel flow turbulence we show that local eddy viscosity models fail to exhibit the long tails observed in the real subfilter stres…
A large number of models which address the dynamics of particle-laden turbulent flows have been developed based on the assumption of local isotropy and use the Kolmogorov constant that correlates the spectral distribution of turbulent kinetic energy with the turbulent dissipation rate. Many turbulence models (Stochastic and LES models) use the Kolmogorov constant in the formulation. Compilation of a large number of experimental data for different flow configurations has revealed that the Kolmogorov constant is independent of Reynolds number in the limit of high Reynolds number (Sreenivasan, 19…
Kolmogorov's (1941) theory of self-similarity implies the universality of small-scale eddies, and holds promise for a universal sub-grid scale model for large eddy simulation. The fact is the empirical coefficient of a typical sub-grid scale model varies from 0.1 to 0.2 in free turbulence and damps gradually to zero approaching the walls. This work has developed a Lattice Eddy Simulation method (LAES), in which the sole empirical coefficient is constant (Cs=0.08). LAES assumes the fluid properties are stored in the nodes of a typical CFD mesh, treats the nodes as lattices and makes analysis on…
Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two corresponding model coefficients are a function of the vortex stretching magnitude. Therefore, the model is consistent with many physical and mathematical properties of the Navier-Stokes equations and turbulent stresses, and is easy to implement. We…
A volume-filtered Euler-Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid-solid slurry flow through a horizontal pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle-particle and particle-wall collisions are modeled using a soft-sphere approach. A se…
A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear from the magnitude of the instantaneous resolved strain-rate tensor. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at two different Reynolds numbers. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are show…
Direct numerical simulation (DNS), mostly used in fundamental turbulence research, is limited to low turbulent intensities due the current and future computer resources. Standard turbulence models, like RaNS (Reynolds averaged Navier-Stokes) and LES (Large Eddy Simulation), are applied to flows in engineering, but they miss small scale effects, which are frequently of importance, see e.g. the whole area of reactive flows, flows with apparent Prandtl or Schmidt number effects, or even wall bounded flows. A recent alternative to these standard approaches is the one-dimensional turbulence (ODT) m…
We conducted WMLES to examine the performance of a simple and widely used ODE-based equilibrium wall model in a spatially-developing 3D TBL inside a bent square duct (Schwarz and Bradshaw 1994) and 3D separated flows behind a skewed bump (Ching et al. 2018a,b; Ching and Eaton 2019). From the square duct simulation, the mean velocity profiles and crossflow angles in the outer region were predicted with high accuracy for all the considered mesh resolutions. Some disagreement was observed in the crossflow angles in the bend region where the non-equilibrium effect is most significant. Also, the si…
We study the dispersion characteristics of slightly buoyant droplets in a turbulent jet using large eddy simulations (LES). The droplet number density fields are represented using an Eulerian approach with the dispersed phase modelled using the Fast-Eulerian method (Ferry & Balachandar 2001) that includes the droplet rise velocity. Radial concentration profiles and turbulent concentration fluxes for droplets of different sizes are analyzed to quantify the "trajectory crossing effect", when relative motions between particles and turbulent eddies tend to reduce turbulent diffusion. For finer LES…
A new methodology based on energy flux similarity is suggested in this paper for large eddy simulation (LES) of transitional and turbulent flows. Existing knowledge reveals that the energy cascade generally exists in transitional and turbulent flows with different distributions, and the characteristic quantity of scale interaction in energy cascade processes is energy flux. Therefore, energy flux similarity is selected as the basic criterion to secure the flow field getting from LES highly similar to the real flow field. Through a priori tests, we find that the energy flux from the tensor-diff…
Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at the bottom of rivers, where surface waters of the river permeate the deposited sediment and exchange their contents with subsurface waters. Obtaining a complete picture of this process, known as hyporheic exchange, is important for the understanding and maintenance of water quality and river ecology. Given the wide range of length scales (mm to km) and corresp…
High-fidelity large-eddy simulations of the flow around two rectangular obstacles are carried out at a Reynolds number of 10,000 based on the free-stream velocity and the obstacle height. The incoming flow is a developed turbulent boundary layer. Mean-velocity components, turbulence fluctuations, and the terms of the turbulent-kinetic-energy budget are analyzed for three flow regimes: skimming flow, wake interference, and isolated roughness. Three regions are identified where the flow undergoes the most significant changes: the first obstacle's wake, the region in front of the second obstacle,…
A simple variant of recycling and rescaling method to generate inflow turbulence using unstructured grid CFD codes is presented. The method has been validated on large eddy simulation of spatially developing flat plate turbulent boundary layer. The proposed rescaling algorithm is based on the momentum thickness which is more robust and essentially obviates the need of finding the edge of the turbulent boundary layer in unstructured grid codes. Extension of this algorithm to hybrid RANS/LES type of approaches and for wall-bounded turbomachinery flows is also discussed. Results from annular diff…
Wind-wave interaction involves wind forcing on wave surface and wave effects on the turbulent wind structures, which essentially influences the wind and wave loading on structures. Existing research on wind-wave interaction modeling ignores the inherent strong turbulences of wind. The present study aims to characterize the turbulent airflow over wave surfaces and wave dynamics under wind driving force. A high-fidelity two-phase model is developed to simulate highly turbulent wind-wave fields. Instead of using uniform wind, inherent wind turbulences are prescribed at the inlet boundary using th…
In the application of the combustion models based on low-dimensional manifolds (for instance flamelet models) to large-eddy simulation (LES) of reactive turbulent flows, the modeling simplifications of the combustion process is a critical source of uncertainty in addition to those due to the turbulent closure model and numerical discretization. The ability to quantitatively assess this uncertainty in absence of the reference result is vital to the reliable and predictive simulations of practical combustion devices.In the present study, the Pareto-efficient combustion (PEC) framework is extende…
This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analysed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh res…
We present a dynamical spectral model for Large Eddy Simulation of the incompressible magnetohydrodynamic (MHD) equations based on the Eddy Damped Quasi Normal Markovian approximation. This model extends classical spectral Large Eddy Simulations for the Navier-Stokes equations to incorporate general (non Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD and show that introducing a new eddy-damping time for the dynamics of spectral tensors in the absence of equipartition between the velocity and magnetic fields leads to better agreement with direct numerical simulations,…
The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at shear Reynolds numbers equal to 150 and 300 and corresponding a-priori and a-posteriori LES on differently coarse grids. We then tracked swarms of different inertia particles and we examined the influence of filtering and of Sub-Grid Scale (SGS) modeling for the fluid phase on particle velocity and concentration statistics. We also focused on how particle prefer…
In this work, we propose a single formula for the law of the wall, which is dubbed as the logarithmic-exponential (LOG-EXP) formula, for predicting the mean velocity profile in different regions near the wall. And then a feedforward neural network (FNN), whose inputs and training data are based on this new formula, is trained for the wall-modelled large-eddy simulation (WMLES) of turbulent channel flows. The direct numerical simulation (DNS) data of turbulent channel flows is used to evaluate the performance of both the formula and the FNN. Compared with the Werner-Wengle (WW) model for the WM…
A population balance model coupled with large eddy simulations (LES) is adapted and applied to study the evolution of oil droplets in a turbulent jet including the effects of droplet breakup. A key unknown in simulating secondary breakup in turbulent multiphase jets is the inflow size distribution generated within the primary breakup zone near the nozzle exit. A mono-disperse injection inflow condition is commonly used for simplicity, but this choice is often unrealistic. In order to provide more realistic inlet conditions for LES, we develop a one dimensional (1D) parcel model to predict the …
We present results of three-dimensional Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent gravity currents with a Discontinuous Galerkin (DG) Finite Elements method. In particular, we consider the three-dimensional lock-exchange test case as a typical benchmark for gravity currents. Since, to the best of our knowledge, non-Boussinesq three-dimensional reference DNS are not available in the literature for this test case, we first perform a DNS experiment. The three-dimensional DNS allows to correctly capture the loss of coherence of the three-dimensional turbulent…
Linear stability analysis has proven to be a useful tool in the analysis of dominant coherent structures, such as the von Kármán vortex street and the global spiral mode associated with the vortex breakdown of swirling jets. In recent years, linear stability analysis has been applied successfully to turbulent time-mean flows, instead of laminar base-flows, \textcolor{black}{which requires turbulent models that account for the interaction of the turbulent field with the coherent structures. To retain the stability equations of laminar flows, the Boussinesq approximation with a spatially nonunif…
In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains simultaneously, i.e. in one domain a turbulent Atmospheric Boundary Layer (ABL) without wind turbines is simulated in order to generate the turbulent inflow conditions for a second domain in which the wind turbines are placed. The benefit of this approach is that a) it avoids the need for large databases in which the turbulent inflow conditions are stored and the corre…
Predicting the behavior of turbulent flows using large-eddy simulation requires modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD-Bardina model. In order to also obtain a physics-conform…
In this work, a discontinuous Galerkin scheme is employed to perform LES simulations of supersonic jet flows. A total of four simulations are performed with different meshes and order of accuracy. The number of degrees of freedom from the simulations varies from 50 x 106 to 400 x 106. The results indicate that by increasing the resolution of simulation, in general, the results got closer to experimental data. The jet lipline is the only region in which this behavior is not observed. It investigated a procedure of using lower-order simulations to initialize high-order simulations and consequent…
