Computation Of Turbulent Flows Research Articles

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) 1). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) 12. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization

We study mathematical and physical properties of a family of recently introduced, reduced-order approximate deconvolution models. We first show a connection between these models and the NS-Voigt model, and that NS-Voigt can be re-derived in the approximate deconvolution framework. We then study the energy balance and spectra of the model, and provide results of some turbulent flow computations that backs up the theory. Analysis of global attractors for the model is also provided, as is a detailed analysis of the Voigt model's treatment of pulsatile flow.

High-order compact difference algorithm on half-staggered meshes for low Mach number flows

The paper presents a solution algorithm for variable density non-isothermal flows based on a high-order compact difference approximation combined with the projection method formulated on half-staggered meshes. In contrast to full-staggered grid arrangement, with the pressure and all scalar variables located in the cell centers, we shift only the pressure nodes while we keep the scalars and velocity components in the same nodes. This greatly simplifies the solution procedure as the interpolation between the nodes takes place only within the projection method. Derivative approximations and interpolation formulas are discretized using the high-order compact difference schemes up to 10th order in the central nodes and third/fourth order schemes near domain boundaries. The proposed algorithm is first verified in natural convection problems in square and rectangular wall bounded cavities for Rayleigh numbers Ra=3.4×105 and Ra=1.0×106 with maximal density ratio equals nine. The results are compared with published data for both steady and unsteady flow regimes. The performed simulations reveal that achievement of accurate results is conditioned by a mesh resolution in thermal boundary layers near the walls, and a way in which the governing equations are formulated, i.e., the conservative or non-conservative form. This turns out more important than a formal order of discretization method. Robustness of the proposed algorithm for the computations of turbulent flow is demonstrated based on the flow in a periodic channel at Reynolds number Reτ=200 with density ratio equal to two. In this case the profiles of mean velocity, temperature and their fluctuations are analyzed and they agree quite well with literature data. In all presented test cases the obtained pressure fields are smooth and without any oscillations observed when the collocated meshes are employed.

Convective Thermal Analysis of a Turbulent Flow in a Pipe with Two and Three Corrugated Baffles Arranged in Overlap

The present work is a numerical computation of steady turbulent forced convection flow and pressure drop characteristics in a two-dimensional horizontal rectangular cross section channel with isothermal walls and with two and three transverse waved baffles disposed overlapping in a channel. The fluid is considered as Newtonian, incompressible with constant properties. The governing equations are solved by the method of finite volume using the SIMPLE-algorithm, in two-dimensions with the k-e Realizable model to describe the turbulence phenomena. Air is the working fluid with the flow rate in terms of Reynolds numbers ranging from 5.000 to 20.000. The effects of baffle shape geometries as well as Reynolds numbers on the flow patterns and heat transfer performances are investigated. To understand the characteristics of thermal enhancements, the friction factors are also computed. The numerical results are validated with available flat rectangular-shaped baffle measured data and found to agree well with measurement. The computational results reveal essentially, that the shape of the baffles can alter substantially the flow and heat transfer characteristics. In general, an increase in the flow Reynolds number causes a substantial increase in the convective Nusselt number other than the pressure loss is also very important. The detailed knowledge on the flow and heat transfer distribution in this computation provides the basis for further optimization of shell-and-tube heat exchangers.

Large Eddy Simulation of Flows Around a Kite Used as an Auxiliary Propulsion System

The aerodynamic forces acting on a kite proposed for propelling marine shipping are investigated using computational and experimental means. Attention is given to the kite's positions as perpendicular or nearly perpendicular to the air flow that still possess potential for thrust generation but cannot be analysed using finite wing models applicable for kites at low angles of attack. Good agreement is achieved in the prediction of the time-averaged drag coefficient between the large eddy simulations (LESs) of a full scale kite and wind tunnel measurements of a small scale kite model. At zero-yaw conditions both the time-averaged drag and lift (side) forces show behavior similar to the literature-reported empirical relations for flat plates of the same aspect ratio (AR), but with differences of up to 20% in the coefficients’ values. Thus, the plate’s known empirical formulae for aerodynamic forces at zero yaw angles may be used as fast low-accuracy prediction tools before engaging with the more costly turbulent flow computations and wind tunnel tests. Yawing moderately the kite can actually increase mildly the drag but further yawing or pitching it reduces the dominant drag force. Both the drag and lift show unsteady components that are related to the large turbulent wake behind the kite and vortical shedding from the kite's ends. Power spectra of the aerodynamic forces’ coefficients are presented and analysed.

Computational Fluid Dynamics Computations Using a Preconditioned Krylov Solver on Graphical Processing Units

Graphical processing unit (GPU) computation in recent years has seen extensive growth due to advancement in both hardware and software stack. This has led to increase in the use of GPUs as accelerators across a broad spectrum of applications. This work deals with the use of general purpose GPUs for performing computational fluid dynamics (CFD) computations. The paper discusses strategies and findings on porting a large multifunctional CFD code to the GPU architecture. Within this framework, the most compute intensive segment of the software, the BiCGStab linear solver using additive Schwarz block preconditioners with point Jacobi iterative smoothing is optimized for the GPU platform using various techniques in CUDA Fortran. Representative turbulent channel and pipe flow are investigated for validation and benchmarking purposes. Both single and double precision calculations are highlighted. For a modest single block grid of 64 × 64 × 64, the turbulent channel flow computations showed a speedup of about eightfold in double precision and more than 13-fold for single precision on the NVIDIA Tesla GPU over a serial run on an Intel central processing unit (CPU). For the pipe flow consisting of 1.78 × 106 grid cells distributed over 36 mesh blocks, the gains were more modest at 4.5 and 6.5 for double and single precision, respectively.

Stochastic separated flow models with applications in numerical computations of supersonic particle-laden turbulent flows

In this article, three stochastic separated flow models were applied to predict the dispersion of inertial fuel particles in the supersonic turbulent flows. The flow field of continuous phase was simulated by means of Reynolds-averaged Navier–Stokes method with a two-equation turbulence model. Clift’s expression was used to modify the drag force on the particle considering the compressibility effects. The particle-phase statistics were obtained by a secondary-order time-weighed Eulerian method. The ability of those stochastic separated flow models was then compared for predicting the mean particle velocity and the particle dispersion. For obtaining a statistically stationary solution, the stochastic separated flow model required the largest number of computational particles, whereas the improved stochastic separated flow model was found to need the least. The time-series stochastic separation flow model lay in-between. Compared with the other two models, the particle dispersion was over-predicted by the stochastic separated flow model in the supersonic particle-laden boundary layer flow, while the improved stochastic separated flow model was less predictable for the particle spatial distribution in the particle-laden strut-injection flow. Three models could well predict the mean velocities of the particle phase. This study is valuable for selecting a validated model used for predicting the particle dispersion in supersonic turbulent flows.

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

In this paper, the ability of high-order flux reconstruction numerical schemes to perform accurate and stable computations of compressible turbulent flows on coarse meshes is investigated. Two new flux reconstruction schemes, which are optimized for wave dissipation and dispersion properties, are compared to the nodal discontinuous Galerkin and spectral difference methods recovered via the energy-stable flux reconstruction method. The Taylor–Green vortex benchmark problem at is used as a simple a priori test of the numerics. Dissipation rates computed from kinetic energy, vorticity, and pressure dilatation are plotted against reference solutions. Results show that, at low mesh resolution, the flux reconstruction schemes are highly accurate across a range of orders of accuracy, although oscillations can appear in the solution at orders of six and above. Although the flux reconstruction method has a built-in stabilization mechanism, an additional means of damping these instabilities is required. The schemes vary in the amount of numerical dissipation and resolution of the turbulent spectrum. One of the optimized flux reconstruction schemes (the optimized flux reconstruction scheme) is shown to have greater spectral accuracy than any of the others tested, motivating its future usage for high-order high-fidelity computational fluid dynamics.

Numerical simulation of turbulent flow in the throttle of the MBIR reactor’s low-pressure chamber

This work in devoted to numerical calculation of turbulent flow in a labyrinth-type throttle. A system of such throttles is installed at the inlet to the MBIR reactor’s low-pressure chamber and serves for setting up the required pressure difference and coolant flow rate. MBIR is a multipurpose fourthgeneration fast-neutron research reactor intended for investigating new kinds of nuclear fuel, structural materials, and coolants. The aim of this work is to develop a verified procedure for carrying out 3D calculation of the throttle using CFD modeling techniques. The investigations on determining the throttle hydraulic friction coefficient were carried out in the range of Reynolds numbers Re = 52000–136000. The reactor coolant (liquid sodium) was modeled by tap water. The calculations were carried out using high-Reynolds-number turbulence models with the near-wall functions k-ɛ and RNG k-ɛ, where k is the turbulent pulsation kinetic energy and ɛ is the turbulence kinetic energy dissipation rate. The obtained results have shown that the calculated value of hydraulic friction coefficient differs from its experimental value by no more than 10%. The developed procedure can be applied in determining the hydraulic friction coefficient of a modified labyrinth throttle design. The use of such calculation will make it possible to predict an experiment with the preset accuracy.

A finite element variational multiscale method for computations of turbulent flow over an aerofoil

Numerical simulation of turbulent flows over different aerofoil configurations are presented in this paper. The incompressible fluid flow is described by the time-dependent incompressible Navier–Stokes equations. Further, a finite element variational multiscale method is used to simulate the turbulent flows. Computation over a cylinder and different variants of aerofoils are presented. The obtained numerical results demonstrate the capabilities of variational multiscale methods.

Feasibility of Ceiling-Mounted Assist Device of Air-Purifier for Removal of Airborne Allergic Pollen Grains

Feasibility of a ceiling-mounted assist device of the air-purifier for removal of airborne allergenic pollen grains is investigated by both turbulent flow and particle-tracking calculations. The device is mounted straight above the air-purifier and it collects suspended pollen grains in the exhaust flow of the air-purifier. It is found from the turbulent flow calculation that the flow rate of the assist device should be larger than that of the air-purifier. Otherwise the upward air flows around the assist device, and pollen grains move along the surrounding flow; they are never removed from the air. We also found about 40% improvement of the pollen removal efficiency by installing the assist device.

Investigation on the relative performance of various low-Reynolds number turbulence models for buoyancy-driven flow in a tall cavity

The present study deals with the numerical investigation of turbulent buoyancy driven flow in a differentially heated rectangular cavity with adiabatic horizontal walls. The aspect ratio of cavity is 5 and the Rayleigh number based on the cavity height is 4.56 × 1010. The computations have been carried out using the finite volume method on a staggered grid and SIMPLEC algorithm for pressure–velocity coupling. The low-Reynolds number \(k-\epsilon\) model proposed by Yang and Shih (YS), low-Reynolds number \(k-\omega\) model proposed by Wilcox, and \(k-\omega\) shear stress transport (SST) model of Menter have been applied for turbulence closure. The performance comparison of different models have been carried out using the experimental, LES and various RANS results available in the literature. The computation of turbulent natural convection flow is numerically challenging due to complex flow involving laminar, transition and turbulent regions, coupling of velocity with the energy equation, and some other problems reported in literature e.g. grid dependency of solution, numerical stability problem, etc. The flux Richardson number is calculated to get an estimate of relative importance of buoyancy and shear force in different regions of flow. The shearing and swirling zones have been identified in the entire flow domain using the \(\lambda _{2}\) criterion. Based on the comparison of mean flow, heat transfer and turbulence characteristics with the available results, it has been found that YS model performs better. The better performance obtained from YS model may be due to peculiarity of model that takes into account the Kolmogorov time scale near the wall and the conventional time scale \((k/\epsilon )\) away from the wall.

A pencil distributed finite difference code for strongly turbulent wall-bounded flows

We present a numerical scheme geared for high performance computation of wall-bounded turbulent flows. The number of all-to-all communications is decreased to only six instances by using a two-dimensional (pencil) domain decomposition and utilizing the favourable scaling of the CFL time-step constraint as compared to the diffusive time-step constraint. As the CFL condition is more restrictive at high driving, implicit time integration of the viscous terms in the wall-parallel directions is no longer required. This avoids the communication of non-local information to a process for the computation of implicit derivatives in these directions. We explain in detail the numerical scheme used for the integration of the equations, and the underlying parallelization. The code is shown to have very good strong and weak scaling to at least 64K cores.

High-Order Discontinuous Galerkin Method for Computation of Turbulent Flows

This paper presents a high-order discontinuous Galerkin method for computation of compressible turbulent flows in three space dimensions. A modified Spalart-and-Allmaras turbulence model is implemented and discretized to the same order of accuracy as that for the Reynolds-averaged Navier–Stokes equations. The creation of curvilinear meshes for arbitrary three-dimensional configurations is achieved through the aid of a computational analysis programming interface, which enables direct communications with the computer-aided design module to determine the true positions of surface quadrature points for high-order geometric representations. A modified linear elasticity approach is used sequentially and is of crucial importance for reshaping the interior mesh to allow high-aspect-ratio curved elements in turbulent boundary layers. Requirements of the mesh parameters, including the wall spacing and viscous stretching factor, are studied; and it is concluded that, for attached turbulent flows, the conventional settings often used in low-order methods should be less stringent when a higher-order method is considered. Several other numerical examples, including a direct numerical simulation of the Taylor–Green vortex and turbulent flow over an ONERA M6 wing, are considered to assess the solution accuracy and to demonstrate the performance of high-order discontinuous Galerkin methods in capturing transitional and turbulent flow phenomena.

Detached eddy simulation of turbulent flow in isolated street canyons of different aspect ratios

Air quality management in urban areas requires the use of advanced modeling tools, able to predict and evaluate the pollution level under different traffic and meteorological conditions. In the present paper, the Artificial Compressibility version of the Characteristic Based Split algorithm (AC–CBS) was used to assess the performance of the Spalart–Allmaras based Detached Eddy Simulation (SA–DES) model, for the calculation of incompressible turbulent flow in different urban street canyon configurations. To our knowledge, the DES version of the SA turbulence model was applied in this work for the first time for the simulation of turbulent flow in a street canyon. The proposed DES model was able to accurately reproduce the turbulent characteristics of the flow compared with results from real street canyon experiments, wind tunnel experiments, and also to that obtained with RANS simulations. These results are very similar to the ones obtained from Large Eddy Simulation (LES) of street canyons flow reported in some recent publications, but with the potential characteristic of reduced computational costs. The DES approach is very promising for the simulation of transient turbulent flows in urban areas when complex three–dimensional domains are considered. The performance of the DES model evaluated for the mean dimensionless streamwise velocity profiles was comparable to that of Reynolds–Averaged Navier–Stokes RANS approach if referred to Hit Rate (HR) validation metric, and even better if referred to Factor of two observation (FAC2) validation metric. An accurate reproduction of the turbulent flow is crucial for urban pollutant dispersion simulations, since the distribution of the pollutant concentrations could differ by order of magnitude in the different points of the street canyon. DES approach results were able to accurately predict the unsteadiness characteristic of the flow, and to reproduce some minor vortex structures, which were not observed in the RANS cases, that will lead to a more accurate reproduction of the pollutant concentrations.

Modelling of turbulent flow in a radial reactor with fixed bed

The data of the computation of turbulent flow in the CF-π and CP-π configurations of the radial reactor with a fixed bed are presented. The Reynolds motion equations have been solved jointly with the k-ɛ turbulence model. To couple the parameters of flows at the interface free part-fixed bed the classical continuity equations were used. The computational data are obtained for the averaged and turbulent characteristics, and it is shown that the flow in the fixed bed causes the generation of the turbulence kinetic energy and its dissipation rate; the flow in the CF-π configuration is distributed more uniformly as compared to the CP-π configuration of the radial reactor. Computed data are compared with the experimental ones.

Utilization of high order DRP-type schemes and large eddy simulation based on relaxation filtering for turbulent gas flow computations in the case of Taylor-Green vortex breakdown

The paper considers Large Eddy Simulation based on the relaxation filtering technique (LES-RF) and implemented by high order DRP-type schemes. This technique is an alternative to the classical eddy-viscosity-type methods. It can be expressed as the composition of a high-order and high-resolution numerical scheme and an explicit selective filtering, which dissipates the energy from small scales poorly resolved by the scheme. With this technique, simulations of the Taylor-Green vortex breakdown problem have been performed for Reynolds numbers 1600 and 3000 and different computational meshes varying from 643to 2563cells. The problem of periodic three-dimensional flow decaying to small-scale turbulent structures because of the inherent instability has been studied. The simulation employs a compressible formulation at small Mach number (Ma = 0.09) for minimization of compressibility effects. Filter strength, the only free parameter in the scheme, is varied as well. The obtained results are in good agreement with the Direct Numerical Simulations performed by other authors. It has been found that the filter strength, if taken sufficiently high and at a fixed time step size chosen from the condition CFL ~ 0.45, has no marked effect on the results. However, the quality of the results begins to degrade if the time step size decreases significantly. This indicates the need for modification of the scheme for practical applications.

Computation of turbulent flow in a mixed compression intake

Turbulent flow in a mixed compression intake is investigated. The unsteady compressible Navier–Stokes equations are solved using a stabilized finite element method with 6-noded triangular element. The Spalart–Allmaras model is used for turbulence closure. For comparison, the laminar flow is studied as well. A bleed of 6 % is utilized to overcome the start-up problem of the intake. The effect of back pressure on the performance of the intake is studied via the total pressure recovery and distortion index. Total pressure recovery is relatively lower while distortion index is higher for turbulent flow compared to laminar flow. The critical back pressure ratio, for unstart of the intake, for turbulent flow is higher compared to laminar flow. The effect of bleed on the performance of the intake is studied.

Numerical investigation of the vortex core precession in a model hydro turbine with the aid of hybrid methods for computation of turbulent flows

Numerical modeling of the unsteady flow in the draft tube of the test bench hydro turbine is conducted. The hybrid RANS-LES methods for modeling turbulent flows are compared. The intensity and frequency of pressure fluctuations, which are induced by the vortex core precession under the runner, and the integral characteristics are considered. An analysis of the synchronous and asynchronous parts of pressure fluctuations is done; the generating and influence of the synchronous component of fluctuations are considered. The vortex core interaction with the draft tube elbow is considered.

Influence of setting angle of the airfoil cascade on the flow «choking» regimes in the blade channel

The emergence of “choking” regimes of last stages leads to the stall in the blade rows of first stages, appearance of rotating stall and surge, and is one of the main causes of reduced GTE effectiveness on the off-design operating conditions. The paper deals with investigating the impact of setting angle in the airfoil cascade at the critical flow regime. To solve this problem, a series of gas-dynamic calculations for compressor airfoil cascade with different setting angles γ=30º, γ=40º, γ=50º, γ=60º, γ=70º was carried out. The computational domain for this problem consists of one blade and one blade channel. To solve this problem, irregular adaptive grid was selected. The turbulent gas flow calculation was performed by numerical solution of the averaged Navier-Stokes equations (Reynolds equations). To close the Navier-Stokes equations, the Menter's SST turbulence model was chosen. The second-order design scheme with the local use of the first-order design scheme was used for the calculation. Comparison of theoretical and experimental research results have shown that the flow nature in the blade channels and boundary layer formation depend strongly on the airfoil setting angle. With a decrease in the airfoil setting angle there is a significant decrease in the relative value of the minimum actual flow area of blade channels (described in aerodynamics as free area), which leads to a decrease in the Mach number value at the cascade entrance, at which the flow “choking” regime in blade channels by air flow occurs. These features should be taken into account in “choking” regime calculations. The obtained generalized characteristics of “choking” regimes of compressor cascades can be used in calculating “choking” regimes of the axial flow compressor stages and determining the boundaries of gas-dynamic stability of multistage axial flow compressors.