A comparative study of turbulence models performance for separating flow in a planar asymmetric diffuser

This paper presents a computational study of the separated flow in a planar asymmetric diffuser. The steady RANS equations for turbulent incompressible fluid flow and six turbulence closures are used in the present study. The commercial software code, FLUENT 6.3.26, was used for solving the set of governing equations using various turbulence models. Five of the used turbulence models are available directly in the code while the v²–f turbulence model was implemented via user defined scalars (UDS) and user defined functions (UDF). A series of computational analysis is performed to assess the performance of turbulence models at different grid density. The results show that the standard k–ω, SST k–ω and v²–f models clearly performed better than other models when an adverse pressure gradient was present. The RSM model shows an acceptable agreement with the velocity and turbulent kinetic energy profiles but it failed to predict the location of separation and attachment points. The standard k–ε and the low-Re k–ε delivered very poor results.     

Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model

In this study, a newly developed two-equation transitional model was employed for the prediction of blood flow patterns in a thoracic aortic aneurysm (TAA) where the growth and progression are closely linked to low and oscillating wall shear stresses. Laminar–turbulent transition in the dilated vessel can alter the flow structure, shear stress and pressure distribution within the aneurysm. A patient-specific TAA model was reconstructed from magnetic-resonance (MR) images and measured velocity waveform was used as the inflow condition. Laminar flow and a correlation-based transitional version of Menter’s hybrid k ? ?/k ? ω Shear Stress Transport (SST Tran) model were implemented in pulsatile simulations from which WSS distribution was obtained throughout a cardiac cycle and velocity profiles were compared with MR measurements. The correlation-based transitional model was found to produce results in closer agreement with the MR data than the laminar flow simulation.     

Hexagon-based all-quadrilateral mesh generation with guaranteed angle bounds

In this paper, we present a novel hexagon-based mesh generation method which creates all-quadrilateral (all-quad) meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains. Given any planar curves, an adaptive hexagon-tree structure is constructed by using the curvature of the boundaries and narrow regions. Then a buffer zone and a hexagonal core mesh are created by removing elements outside or around the boundary. To guarantee the mesh quality, boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary, and two layers of quad elements are inserted in the buffer zone. For any curve with sharp features, a corresponding smooth curve is firstly constructed and meshed, and then another layer of elements is inserted to match the smooth curve with the original one. It is proved that for any planar smooth curve all the element angles are within [60° ? ε, 120° + ε] (ε ? 5°). We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin (60° ? ε),  sin 90°], or [0.82, 1.0]. The same angle range can be guaranteed for curves with sharp features, with the exception of small angles in the input curve. Furthermore, an approach is introduced to match the generated interior and exterior meshes with a relaxed angle range, [30°, 150°]. We have applied our algorithm to a set of complicated geometries, including the China map, the Lake Superior map, and a three-component air foil with sharp features. In addition, all the elements in the final mesh are grouped into five types, and most elements only need a few flops to construct the stiffness matrix for finite element analysis. This will significantly reduce the computational time and the required memory during the stiffness matrix construction.     

Guaranteed-quality all-quadrilateral mesh generation with feature preservation

In this paper, a quadtree-based mesh generation method is described to create guaranteed-quality, geometry-adapted all-quadrilateral (all-quad) meshes with feature preservation for arbitrary planar domains. Given point cloud, our method generates all-quad meshes with these points as vertices and all the angles are within [45°, 135°]. For given planar curves, quadtree-based spatial decomposition is governed by the curvature of the boundaries and narrow regions. 2-refinement templates are chosen for local mesh refinement without creating any hanging nodes. A buffer zone is created by removing elements around the boundary. To guarantee the mesh quality, the angles facing the boundary are improved via template implementation, and two buffer layers are inserted in the buffer zone. It is proved that all the elements of the final mesh are quads with angles between 45° ± ε and 135° ± ε (ε ≤ 5°) with the exception of badly shaped elements that may be required by the sharp angles in the input geometry. We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin(45° ? ε), sin90°], or [0.64, 1.0]. Furthermore, sharp features and narrow regions are detected and preserved automatically. Boundary layer meshes are generated by splitting elements of the second buffer layer. We have applied our algorithm to a set of complicated geometries, including the Lake Superior map and the air foil with multiple components.     

Numerical simulation of three-dimensional turbulent separated and reattaching flows using a modified turbulence model

A modified version of k-ε model is proposed through modification of the damping function of eddy viscosity that incorporates the effect of wall proximity in the near the wall region and the effect of non-equilibrium away from the wall together with the simple model functions in the ε equation. The proposed turbulence model is validated with the available experimental data of reattachment length, mean streamwise velocity distribution, turbulence intensity profile, and wall static pressure coefficient in the turbulent backward-facing step flows. The predicted results with the present model are in good agreement with the experiments. Computed results reveal that the reattachment length (recirculation zone) and the wall static pressure are decreased with increasing inlet velocity. And the asymmetric distributions of the reattachment point, cross-section view of velocity vector, streamwise skin friction coefficient, and turbulent kinetic energy demonstrate the important three-dimensional side-wall effect in an insufficient aspect ratio channel flow.     

Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook–White equation, is presented. An extensive comparison test was established on the 20 × 500 grid, for a wide range of relative roughness (ε/D) and Reynolds number (R) values (1 × 10^?6 ? ε/D ? 5 × 10^?2; 4 × 10³ ? R ? 10⁸), covering a large portion of turbulent flow zone in Moody’s diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of ε/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 5 × 10^?4, a maximum absolute error of 4 × 10^?3 whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of ε/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of ε/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.     

Improved parameterisation for the numerical modelling of air pollution within an urban street canyon

Numerical modelling for application to wind flow and dispersion in urban environments has noticeably progressed in recent years, to currently represent a widely used tool for simulating mechanical processes governing air pollution in complex geometries. In particular, Computational Fluid Dynamic (CFD) techniques based on RANS (Reynolds-Averaged Navier–Stokes equations) models, are extensively used to produce detailed simulations of the wind flow and turbulence in the urban canopy. However, several studies have indicated that RANS models, and in particular the widely used standard k–? turbulence model, are sensitive to the particular form of inlet profiles for turbulence and velocity. In the present study, simulations of the wind flow and dispersion within an idealised street canyon were carried out using the standard k–? turbulence model provided by the commercial software FLUENT. The aim of this study was to improve the standard k–? model performance by modifying the model parameters according to the chosen form of inlet profiles for velocity and turbulence. Capability of the model to reproduce real wind flow fields, turbulence and concentration patterns was evaluated by comparing the model results against recently published wind tunnel data. Results for turbulent kinetic energy and concentration showed that the redefinition of the default dispersive parameters can significantly enhance the model performance. The newly proposed parameterisations of the standard k–? turbulence model can be readily implemented within commercial CFD software packages, offering a reliable modelling tool for application to urban air pollution and other environmental studies.     

履带式两栖运输设备多湍流模型的研究

关于履带式两栖运输设备精确建模问题,针对履带式两栖运输设备水上受湍流影响大,但湍流模型难于选择的问题,为达到使用恰当湍流模型提高仿真精度的目的,采用对比阻力系数和绕流场云图的方法进行湍流模型适用性的研究,明确各种湍流模型的特性。以某型履带式两栖运输设备水下绕流场为计算对象,基于RANS方程的求解,分别采用Spalart-All-maras、标准k-ε、RNG k-ε、Realizable k-ε、标准k-ω、SST k-ω湍流模型。对比多组仿真结果,表明Realizable k-ε、SSTk-ω模型计算得到的总阻力相对误差最小,RNG k-ε模型对复杂形体周围流场描绘最详细,Spalart-Allmaras模型也有较好的计算精度。     

Performance of a bend-diffuser system: Experimental and numerical studies

The turbulent flow inside a combined bend-diffuser configuration with a rectangular cross section is experimentally and numerically studied. The experimental study includes the outer and inner-wall-pressure measurements and the overall system/diffuser loss determination. Simulation is performed using the high-Reynolds number k-ε turbulence model improved by the low-Reynolds number k-ε turbulence model near the walls, because of its success to predict the flow with strong adverse pressure gradient. So the present paper provides a numerical procedure for the calculation of turbulent flow in a sequence curved, expanding passages, with emphasis on the bend-diffuser configuration system consisting of a 90° bend followed by a diffuser with different expanding angles ranges from 2θ = 6-30° at different inflow Reynolds numbers. Satisfied comparisons with reported experimental data in the literature as well as that carried out by the present authors at the heat engine laboratory of Menoufiya university show that the numerical method with the utilized closure turbulence model reproduces the essential features of upstream curved flow effects on the diffuser performance. The effect of spacer length (between the bend and diffuser) is also experimentally and numerically included. The results show that there is an optimum diffuser angle which depends on the inflow Reynolds number and produces the minimum pressure loss and hence good performance of such complex geometry is obtained.     

Comparison of the lattice Boltzmann and pseudo-spectral methods for decaying turbulence: Low-order statistics

We conduct a detailed comparison of the lattice Boltzmann equation (LBE) and the pseudo-spectral (PS) methods for direct numerical simulations (DNS) of the decaying homogeneous isotropic turbulence in a three-dimensional periodic cube. We use a mesh size of N³=128³ and the Taylor micro-scale Reynolds number 24.35?Re_λ?72.37, and carry out all simulations to t≈30τ₀, where τ₀ is the turbulence turnover time. In the PS method, the second-order Adam-Bashforth scheme is used to numerically integrate the nonlinear term while the viscous term is treated exactly. We compare the following quantities computed by the LBE and PS methods: instantaneous velocity u and vorticity ω fields, and statistical quantities such as, the total energy K(t) and the energy spectrum E(k,t), the dissipation rate ε(t), the root-mean-squared (rms) pressure fluctuation δp(t) and the pressure spectrum P(k,t), and the skewness and flatness of the velocity derivative. Our results show that the LBE method performs very well when compared to the PS method in terms of accuracy and efficiency: the instantaneous flow fields, u and ω, and all the statistical quantities — except the rms pressure fluctuation δp(t) and the pressure spectrum P(k,t) — computed from the LBE and PS methods agree well with each other, provided that the initial flow field is adequately resolved by both methods. We note that δp(t) and P(k,t) computed from the two methods agree with each other in a period of time much shorter than that for other quantities, indicating that the pressure field p computed by using the LBE method is less accurate than other quantities. The skewness and flatness computed from the LBE method contain high-frequency oscillations due to acoustic waves in the system, which are absent in PS methods. Our results indicate that the resolution requirement for the LBE method is δx/η₀?1.0, approximately twice of the requirement for PS methods, where δx and η₀ are the grid spacing and the initial Kolmogorov length, respectively. Overall, the LBE method is shown to be a reliable and accurate method for the DNS of decaying turbulence.     

Airflow patterns inside slotted obstacles in a ventilated enclosure

Laser Doppler measurements and CFD predictions were carried out to characterize air flow pattern, mean velocities and turbulence structure inside slotted boxes stacked within a slot ventilated enclosure. Special attention was paid to the strong aerodynamic interactions observed on the top faces of the slotted boxes, between the external main flow and the return flow which predominate inside the boxes. Numerical and experimental data make it possible to evaluate the air ventilation levels and their heterogeneity for the different boxes. The two turbulence models used, RSM and k-ε, give quite similar results for the velocity levels in the load and show qualitative agreement with experiments.     

Modal analysis and modified cascade neural networks in identification of geometrical parameters of circular arches

A hybrid computational system, composed of the finite element method (FEM) and cascade neural network system (CNNs), is applied to the identification of three geometrical parameters of elastic arches, i.e. span l, height f and cross-sectional thickness h. FEM is used in the direct (forward) analysis, which corresponds to the mapping α = {l, f, h} → {ω_j}, where: α – vector of control parameters, ω_j – arch eigenfrequencies. The reverse analysis is related to the identification procedure in which the reverse mapping is performed {ω_j} → {α_i}. For the identification purposes a recurrent, three level CNNs of structure (D^k-H^k-1)_s was formulated, where: k – recurrence step, s = I, II, III-levels of cascade system. The Semi-Bayesian approach is introduced for the design of CNNs applying the MML Maximum Marginal Likelihood) criterion. The computation of hyperparameters is performed by means of the Bayesian procedure evidence. The numerical analysis proves a great numerical efficiency of the proposed hybrid approach for both the perfect (noiseless) values of eigenfrequencies and noisy ones simulated by an added artificial noise.     

A vorticity based aeroacoustic prediction for the noise emission of a low-speed turbulent internal flow

Turbulent internal flows are known to generate intense noise as well as surface pressure fluctuations. Numerically predicting the noise emission near the prescribed boundaries requires that the sound-generating turbulent flow be adequately represented and described. The k-ε method provides a promising tool for obtaining the unsteady characteristics of a realistic turbulent flow interacting with a rectangular flat plate undergoing “ground effect”. The far-field acoustic calculation is facilitated by the Kambe model (from Lighthill’s theory) and an original post-processor has been developed to determine the far-field spectra and the source term characteristics. In pre-processed turbulent confined flows inside a rectangular enclosure, computations using the k-ε method, coupled with a convenient post-processor, is used to predict noise radiation over a wide range of frequencies and geometrical configurations. The portability and effectiveness of the present method, however, start to be less evident when the turbulent flow has very chaotic internal features; these suggest the need for a wider computational aeroacoustic domain and a new procedure suitable for the turbulent flow representation.     

Embedding meshes into twisted-cubes

The n-dimensional twisted-cube, TN_n, is a variation of the hypercube. In this paper, we study embedding of meshes into TN_n. We prove three major results in this paper: (1) For any integer n ? 1, a 2 × 2ⁿ⁻¹ mesh can be embedded into TN_n with dilation 1 and expansion 1. (2) For any integer n ? 4, an m × k(m ? 3, k ? 3) mesh cannot be embedded into TN_n with dilation 1. (3) For any integer n ? 4, two node-disjoint 4 × 2ⁿ⁻³ meshes can be embedded into TN_n with dilation 2 and expansion 1.     

A computational study of the effect of angles of attack on a double-cone type supersonic inlet with a bleeding system

The flow characteristics of a supersonic inlet with a bleeding system under varying angles of attack are studied by computational 3D turbulent flow analysis. A compressible upwind flux difference-splitting Navier–Stokes method with the k–ω turbulence model is used to analyze the super inlet flowfields. The bleeding system successfully removes the low energy flow from the boundary layer near the throat. The bleeding system enables the supply of more uniform flow at the engine face compared to a supersonic inlet without a bleeding system at the expense of mass flow. More non-uniform flowfields are seen at the Aerodynamic Interface Plane when the angle of attack increases. These non-uniform flowfields at the supersonic engine face degrade engine performance.     

Embedding a family of disjoint multi-dimensional meshes into a crossed cube

Crossed cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint multi-dimensional meshes into a crossed cube. We prove that for n?4 and 1?m?⌊n/2⌋−1, a family of m² disjoint k-dimensional meshes of size t₁²×t₂²×?×tk² each can be embedded in an n-dimensional crossed cube with unit dilation, where and max1?i?k{ti}?n−2m−1. This result means that a family of mesh-structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel. Our work extends some recently obtained results.     

Parameterizing cut sets in a graph by the number of their components

For a connected graph G=(V,E), a subset U⊆V is a disconnected cut if U disconnects G and the subgraph G[U] induced by U is disconnected as well. A cut U is a k-cut if G[U] contains exactly k(≥1) components. More specifically, a k-cut U is a (k,?)-cut if V?U induces a subgraph with exactly ?(≥2) components. The Disconnected Cut problem is to test whether a graph has a disconnected cut and is known to be NP-complete. The problems k-Cut and (k,?)-Cut are to test whether a graph has a k-cut or (k,?)-cut, respectively. By pinpointing a close relationship to graph contractibility problems we show that (k,?)-Cut is in P for k=1 and any fixed constant ?≥2, while it is NP-complete for any fixed pair k,?≥2. We then prove that k-Cut is in P for k=1 and NP-complete for any fixed k≥2. On the other hand, for every fixed integer g≥0, we present an FPT algorithm that solves (k,?)-Cut on graphs of Euler genus at most g when parameterized by k+?. By modifying this algorithm we can also show that k-Cut is in FPT for this graph class when parameterized by k. Finally, we show that Disconnected Cut is solvable in polynomial time for minor-closed classes of graphs excluding some apex graph.     

The data from the numerical investigation of turbulent combustion in jet flows

The data from the numerical calculations are represented for free subsonic and supersonic turbulent jets subject to chemical reactions (combustion) of the flowing components. The calculations are carried out using averaged Navier–Stokes equations with various turbulent-viscosity models (k–ε, SST, Secundov model) and the large eddy simulation (LES). The Magnussen model and the Zeldovich model are regarded as turbulent combustion models. The calculation data are compared with the experimental data.     

A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n ? 6 and 1 ? m ? ⌈n/2⌉ − 1, a family of 2^m disjoint k-dimensional tori of size 2^s₁×2^s₂×?×2^s_k each can be embedded in an n-dimensional crossed cube with unit dilation, where each s_i ? 2, , and max_1?i?k{s_i} ? 3 if n is odd and ; otherwise, max_1?i?k{s_i} ? n − 2m − 1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.     

A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows

In this paper we introduce and analyze new mixed finite element schemes for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. The methods are based on a non-standard mixed approach in which the velocity, the pressure, and the pseudostress are the original unknowns. However, we use the incompressibility condition to eliminate the pressure, and set the velocity gradient as an auxiliary unknown, which yields a twofold saddle point operator equation as the resulting dual-mixed variational formulation. In addition, a suitable augmented version of the latter showing a single saddle point structure is also considered. We apply known results from nonlinear functional analysis to prove that the corresponding continuous and discrete schemes are well-posed. In particular, we show that Raviart–Thomas elements of order k ? 0 for the pseudostress, and piecewise polynomials of degree k for the velocity and its gradient, ensure the well-posedness of the associated Galerkin schemes. Moreover, we prove that any finite element subspace of the square integrable tensors can be employed to approximate the velocity gradient in the case of the augmented formulation. Then, we derive a reliable and efficient residual-based a posteriori error estimator for each scheme. Finally, we provide several numerical results illustrating the good performance of the resulting mixed finite element methods, confirming the theoretical properties of the estimator, and showing the behaviour of the associated adaptive algorithms.