Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNew methodology based on energy flux similarity for large-eddy simulation of transitional and turbulent flows
94
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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-diffusivity (TD) model has high similarity with the real energy flux. Then, we modify the modelled energy flux from the TD model and obtain uniform formulas of energy flux similarity corresponding to different filter widths and locations in the wall-bounded turbulence. To secure the robustness of simulation and the LES results similar to the real flow, we apply the energy flux similarity method (EFSM) to the Smagorinsky model in the LES of compressible turbulent channel flow, compressible flat-plate flow, and flow over a compressible ramp. The a posteriori tests show that, overall, EFSM can better predict these flows than other subgrid-scale models. In the simulation of turbulent channel flow, EFSM can accurately predict the mean stream-wise velocity, Reynolds stress, and affluent coherent structures. In LES of compressible flat-plate flow, EFSM could provide accurate simulation results of the onset of transition and transition peak, skin friction, and mean stream-wise velocity in cases with three different grid scales. Meanwhile, for flow over a compressible ramp, EFSM could correctly describe the process of bypass transition, locations of separation and reattachment in the corner region, and abundant coherent vortex structures, etc.
rate research
Read More
For wall-bounded turbulent flows, Townsends 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 $Re_tau = 1310$, 2430 and 3810. The instantaneous turbulence structures are sorted by width using an azimuthal Fourier decomposition, allowing us to create a set of average eddy velocity profiles by performing an azimuthal alignment process. The resulting eddy profiles exhibit geometric self-similar behavior in the $(r,theta)$-plane for eddies with spanwise length scales ($lambda_theta/R$) spanning from 1.03 to 0.175. The streamwise similarity is further investigated using two-point correlations between the two planes, where the structures exhibit a self-similar behaviour with length scales ($lambda_theta/R$) ranging from approximately $0.88$ to $0.203$. The candidate structures thereby establish full three-dimensional geometrically self-similarity for structures with a volumetric ratio of $1:80$. Beside the geometric similarity, the velocity magnitude also exhibit self-similarity within these ranges. However, the velocity scale depends on eddy size, and follow the trends based on the scaling arguments proposed by cite{Perry1986}.
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold Rt above which turbulence is uniform (featureless) and a lower threshold Rg below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, alternatively laminar and turbulent, and oriented obliquely with respect to the general flow direction. The final decay of the bands at Rg points to the relevance of directed percolation and criticality in the sense of statistical-physics phase transitions. The nature of the transition at Rt where bands form is still somewhat mysterious and does not easily fit the scheme holding for pattern-forming instabilities at increasing control parameter on a laminar background. In contrast, the bands arise at Rt out of a uniform turbulent background at a decreasing control parameter. Ingredients of a possible theory of laminar-turbulent patterning are discussed.
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 Direct Numerical Simulation. The main finding is that with a fixed cutoff wavenumber $k_c$, the performance of the Large-Eddy Simulation systematically improves as the regularization in the solution of the optimization problem is reduced and this is achieved with the optimal eddy viscosities exhibiting increasingly irregular behavior with rapid oscillations. Since the optimal eddy viscosities do not converge to a well-defined limit as the regularization vanishes, we conclude that the problem of finding an optimal eddy viscosity is not in fact well posed.
We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method inherits the advantages of both the EDG method and the HDG method to make itself well-suited for turbulence simulations. We propose a minimal residual Newton algorithm for solving the nonlinear system arising from the IEDG discretization of the Navier-Stokes equations. The preconditioned GMRES algorithm is based on a restricted additive Schwarz (RAS) preconditioner in conjunction with a block incomplete LU factorization at the subdomain level. The proposed approach is applied to the ILES of transitional turbulent flows over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both design and off-design conditions. The high-order ILES results show good agreement with a subgrid-scale LES model discretized with a second-order finite volume code while using significantly less degrees of freedom. This work shows that high-order accuracy is key for predicting transitional turbulent flows without a SGS model.
Parameter extension simulation (PES) as a mathematical method for simulating turbulent flows has been proposed in the study. It is defined as a calculation of the turbulent flow for the desired parameter values with the help of a reference solution. A typical PES calculation is composed of three consecutive steps: Set up the asymptotic relationship between the desired solution and the reference solution; Calculate the reference solution and the necessary asymptotic coefficients; Extend the reference solution to the desired parameter values. A controlled eddy simulation (CES) method has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special type of large eddy simulation (LES) method in which a weight coefficient and an artificial force distribution are used to model part of the turbulent motions. The artificial force distribution is modeled based on the eddy viscosity assumption. The reference weight coefficient and the asymptotic coefficients can be determined through a weight coefficient convergence study. The proposed PES/CES method has been used to simulate four types of turbulent flows. They are decaying homogeneous and isotropic turbulence, smooth wall channel flows, rough wall channel flows, and compressor blade cascade flows. The numerical results show that the 0-order PES solution (or the reference CES solution) has a similar accuracy as a traditional LES solution, while its computational cost is much lower. A higher order PES method has an even higher model accuracy.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
