Turbulent Flows In Complex Geometries Research Articles

Quantum-inspired framework for computational fluid dynamics

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. However, the simulation of turbulent flows in complex geometries is a compute-power intensive task due to the vast vector dimensions required by discretized meshes. We present a complete and self-consistent full-stack method to solve incompressible fluids with memory and run time scaling logarithmically in the mesh size. Our framework is based on matrix-product states, a compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without passing through the expensive dense-vector representation. This framework lays the foundation for a generation of more efficient solvers of real-life fluid problems.

Turbulent Combustion Modelling and Experiments: Recent Trends and Developments

The development of better laser-based experimental methods and the fast rise in computer power has created an unprecedented shift in turbulent combustion research. The range of species and quantities measured and the advent of kHz-level planar diagnostics are now providing great insights in important phenomena and applications such as local and global extinction, pollutants, and spray combustion that were hitherto unavailable. In simulations, the shift to LES allows better representation of the turbulent flow in complex geometries, but despite the fact that the grid size is smaller than in RANS, the push towards realistic conditions and the need to include more detailed chemistry that includes very fast species and thin reaction zones emphasize the necessity of a sub-grid turbulent combustion model. The paper discusses examples from current research with experiments and modelling that focus on flame transients (self-excited oscillations, local extinction), sprays, soot emissions, and on practical applications. These demonstrate how current models are being validated by experimental data and the concerted efforts the community is taking to promote the modelling tools to industry. In addition, the various coordinated International Workshops on non-premixed, premixed, and spray flames, and on soot are discussed and some of their target flames are explored. These comprise flames that are relatively simple to describe from a fluid mechanics perspective but contain difficult-to-model combustion problems such as extinction, pollutants and multi-mode reaction zones. Recently, swirl spray flames, which are more representative of industrial devices, have been added to the target flames. Typically, good agreement is found with LES and some combustion models such as the progress variable - mixture fraction flamelet model, the Conditional Moment Closure, and the Transported PDF method, but predicting soot emissions and the condition of complete extinction in complex geometries is still elusive.

Numerical simulation to investigate the induced buoyant flow characteristics caused by intensive heat in complex curvilinear geometries

AbstractThe buoyancy‐induced turbulent flows in complex geometries with internal heat source have important application in enclosure fire dynamics, for example, smoke movement in the situation of fire in tunnels. The majority of computational works studying the fire‐induced hot air movement in such cases use a Cartesian coordinate system. Hence, to simulate curved geometries, the Cartesian grid should be refined so that it comparatively matches the geometry. In the present work, a three‐dimensional numerical method using nonorthogonal curvilinear coordinate system was developed. Numerical simulations were performed to study the flow structures and the heat transfer characteristics of fire‐induced buoyant flow and the effects of using curvilinear coordinates on the result's accuracy and the computational cost. Numerical results were compared with the available experimental data and the results obtained by fire dynamics simulator (FDS) software. The results of the present method showed better agreement with the experimental results when compared with the FDS results.

An improved k-ε turbulence model for FENE-P fluids capable to reach high drag reduction regime

An improved k-ε turbulence model for viscoelastic fluids is developed to predict turbulent flows in complex geometries, with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin constitutive model. The k-ε model is tested against a wide range of direct numerical simulation data, with different rheological parameters combinations, and is capable to capture the drag reduction for all regimes of low, intermediate and high, with good performance. Two main contributions are proposed, one through the viscoelastic closures present in the turbulent kinetic energy and dissipation equations, and the other, by modifying eddy viscosity model damping function to incorporate the viscoelastic effect close to the wall, especially at the buffer layer. In addition, improvements have been made to the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors present in the Reynolds-averaged transport equation for the conformation tensor. The main advantage is the capacity to predict all components of the tensor with good performance.

Large-eddy simulation of indoor air flow using an efficient finite-volume method

A numerical scheme for the large-eddy simulation of indoor air flows including heat transfer is presented. It is based on a finite-volume discretization of the Navier–Stokes equations for incompressible fluids on Cartesian grids. The governing equations are solved with a projection approach in combination with a direct Poisson solver for the pressure employing Fourier transformations. Complex boundaries are implemented by a variant of the immersed boundary method based on geometrical blocking of the fluid cells. The Boussinesq approximation is used to account for thermal buoyancy effects. The recently developed σ-subgrid scale model is utilized for the modeling of unresolved turbulent scales. Extensive validation of the code is carried out employing numerical and experimental reference data for laminar and turbulent flows in complex geometries including heat transfer. The computational speed is investigated for the flow in a model room including a heat source. It is shown that with the proposed numerical scheme real-time simulations of this configuration can be carried out with high accuracy at moderate numerical effort.

A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017

An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry

A sharp-interface Immersed Boundary Method (IBM) is developed to simulate density-stratified turbulent flows in complex geometry using a Cartesian grid. The basic numerical scheme corresponds to a central second-order finite difference method, third-order Runge–Kutta integration in time for the advective terms and an alternating direction implicit (ADI) scheme for the viscous and diffusive terms. The solver developed here allows for both direct numerical simulation (DNS) and large eddy simulation (LES) approaches. Methods to enhance the mass conservation and numerical stability of the solver to simulate high Reynolds number flows are discussed. Convergence with second-order accuracy is demonstrated in flow past a cylinder. The solver is validated against past laboratory and numerical results in flow past a sphere, and in channel flow with and without stratification. Since topographically generated internal waves are believed to result in a substantial fraction of turbulent mixing in the ocean, we are motivated to examine oscillating tidal flow over a triangular obstacle to assess the ability of this computational model to represent nonlinear internal waves and turbulence. Results in laboratory-scale (order of few meters) simulations show that the wave energy flux, mean flow properties and turbulent kinetic energy agree well with our previous results obtained using a body-fitted grid (BFG). The deviation of IBM results from BFG results is found to increase with increasing nonlinearity in the wave field that is associated with either increasing steepness of the topography relative to the internal wave propagation angle or with the amplitude of the oscillatory forcing. LES is performed on a large scale ridge, of the order of few kilometers in length, that has the same geometrical shape and same non-dimensional values for the governing flow and environmental parameters as the laboratory-scale topography, but significantly larger Reynolds number. A non-linear drag law is utilized in the large-scale application to parameterize turbulent losses due to bottom friction at high Reynolds number. The large scale problem exhibits qualitatively similar behavior to the laboratory scale problem with some differences: slightly larger intensification of the boundary flow and somewhat higher non-dimensional values for the energy fluxed away by the internal wave field. The phasing of wave breaking and turbulence exhibits little difference between small-scale and large-scale obstacles as long as the important non-dimensional parameters are kept the same. We conclude that IBM is a viable approach to the simulation of internal waves and turbulence in high Reynolds number stratified flows over topography.

On the suitability of the immersed boundary method for the simulation of high-Reynolds-number separated turbulent flows

Delayed detached eddy simulation based on the Spalart–Allmaras turbulence model is applied in conjunction with the immersed boundary method to high-Reynolds number turbulent flows in complex geometries. A fourth-order, finite-difference solver capable of discretely preserving the total kinetic energy in the limit of inviscid flow is adopted to solve the compressible Navier–Stokes equations and model-consistent, adaptive wall functions are employed to provide proper numerical boundary conditions at the fluid/solid interface. Numerical tests, performed for several configurations involving massively separated flows, demonstrate that computations at high Reynolds number typically occurring in flows of industrial relevance can be successfully carried out using the immersed boundary strategy, providing predictions whose accuracy is comparable to that of standard, body-fitted, structured and unstructured flow solvers.

Large Eddy Simulation Using Lattice Boltzmann Method Based on Sigma Model

The Lattice Boltzmann Method (LBM) is a novel method for simulating convection-diffusion type of problems. It has direct advantages over other available methods. One advantage of LBM is that it can be easily parallelized and hence can be used to simulate fluid flow in multi-core computers using parallel computing. In this paper we have used the Lattice Boltzmann Method to simulate turbulent flow in a channel using the Sigma Model for Large Eddy Simulation (LES). LES is widely used in simulating turbulent flows in industries because of its less computational needs compared to Direct Numerical Simulation (DNS) where the Kolmogorov Eddies have to be resolved. Unlike the static Smagorinsky Model this model has the potential to simulate turbulent flow in complex geometries. The eddy viscosity in the sigma model becomes zero at the boundary O(y3) and thus eliminates the use of artificial damping function that is used with the static Smagorinsky model. The sigma model also ensures a positive eddy viscosity which ensures that there are no numerical instabilities. The eddy viscosity also vanishes when the flow is two dimensional or axisymmetric.

A dynamic global-coefficient mixed subgrid-scale model for large-eddy simulation of turbulent flows

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.

Dynamic Global Model for Large Eddy Simulation in Complex Geometries

In the present study, the dynamic Vreman model based on the global equilibrium between the subgrid-scale dissipation and the viscous dissipation with a global model coefficient are applied to large eddy simulation of turbulent flow in complex geometries. Distributions of pressure, velocity and vorticity as well as some flow structure are gained, which is helpful to examine the performance of SGS model and understand the flow characters in complex geometries.

A high‐order finite difference method for numerical simulations of supersonic turbulent flows

AbstractThis paper describes a new class of three‐dimensional finite difference schemes for high‐speed turbulent flows in complex geometries based on the high‐order monotonicity‐preserving (MP) method. Simulations conducted for various 1D, 2D, and 3D problems indicate that the new high‐order MP schemes can preserve sharp changes in the flow variables without spurious oscillations and are able to capture the turbulence at the smallest computed scales. Our results also indicate that the MP method has less numerical dissipation and faster grid convergence than the weighted essentially non‐oscillatory method. However, both of these methods are computationally more demanding than the COMP method and are only used for the inviscid fluxes. To reduce the computational cost for reacting flows, the scalar equations are solved by the COMP method, which is shown to yield similar results to those obtained by the MP in supersonic turbulent flows with strong shock waves. Copyright © 2011 John Wiley & Sons, Ltd.

Large-eddy simulation of curved-geometry flows using contravariant components of velocity

The current large-eddy simulation (LES) research makes use of the contravariant components as the dependent variables on a staggered grid system for the discretisation of the governing equations in curvilinear coordinates. This technology provides a possibility to investigate efficiently turbulent flows in complex geometries. To test and validate the recently developed in-house LES code, LESSGA (Large-Eddy Simulation on a Staggered Grid Arrangement), numerical simulations were performed for turbulent flows in a concentric annular pipe and transitional flows past an airfoil. In this article, the computed results of flows in a concentric annular pipe with a radius ratio of a = R inner/Router = 0.5 at and flows past an SD7003 airfoil at Rec = 60,000 and angle of attack α = 4° are compared with available experimental and DNS data. Technical difficulties experienced are also discussed.

Turbulent flow simulation using LES with dynamical mixed one‐equation subgrid models in complex geometries

AbstractAn innovative computational model is presented for the large eddy simulation of multi‐dimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are (i) to better understand the structure of turbulent flows in complex geometry and (ii) to investigate the 3D characteristics of such complex fluid flow. The filtered Navier–Stokes equations are used to simulate large scales of the turbulence, while the energy transfer from large scales to subgrid‐scales (SGS) is simulated using dynamical mixed one‐equation subgrid models. In the proposed SGS model, the SGS kinetic energy, ksgs, is used for scaling the velocity for the eddy‐viscosity part of the model. The proposed SGS model contains not only some information on the small scales as described in traditional Smagorinsky model or Germano dynamical model but also includes additional scale‐similarity as that in the models of Ghosal et al. (J. Comput. Phys. 1995; 118:24–37) or Davidson (11th International Symposium on Turbulent Shear Flow, Grenoble, vol. 3, 1997; 26.1–26.6). The Navier–Stokes equations and the derived ksgs equation are solved using implicit finite‐volume method. The models have been applied to simulate the 3D flows over a backward‐facing step and in a strong 3D skew runner blade passage of a Francis hydro turbine, respectively. Good agreement between simulated results and experimental results as well as other numerical results was obtained. Copyright © 2009 John Wiley & Sons, Ltd.

Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion

Magnetic resonance velocimetry (MRV) is a non-invasive technique capable of measuring the three-component mean velocity field in complex three-dimensional geometries with either steady or periodic boundary conditions. The technique is based on the phenomenon of nuclear magnetic resonance (NMR) and works in conventional magnetic resonance imaging (MRI) magnets used for clinical imaging. Velocities can be measured along single lines, in planes, or in full 3D volumes with sub-millimeter resolution. No optical access or flow markers are required so measurements can be obtained in clear or opaque MR compatible flow models and fluids. Because of its versatility and the widespread availability of MRI scanners, MRV is seeing increasing application in both biological and engineering flows. MRV measurements typically image the hydrogen protons in liquid flows due to the relatively high intrinsic signal-to-noise ratio (SNR). Nonetheless, lower SNR applications such as fluorine gas flows are beginning to appear in the literature. MRV can be used in laminar and turbulent flows, single and multiphase flows, and even non-isothermal flows. In addition to measuring mean velocity, MRI techniques can measure turbulent velocities, diffusion coefficients and tensors, and temperature. This review surveys recent developments in MRI measurement techniques primarily in turbulent liquid and gas flows. A general description of MRV provides background for a discussion of its accuracy and limitations. Techniques for decreasing scan time such as parallel imaging and partial k-space sampling are discussed. MRV applications are reviewed in the areas of physiology, biology, and engineering. Included are measurements of arterial blood flow and gas flow in human lungs. Featured engineering applications include the scanning of turbulent flows in complex geometries for CFD validation, the rapid iterative design of complex internal flow passages, velocity and phase composition measurements in multiphase flows, and the scanning of flows through porous media. Temperature measurements using MR thermometry are discussed. Finally, post-processing methods are covered to demonstrate the utility of MRV data for calculating relative pressure fields and wall shear stresses.

A dynamic subgrid-scale eddy viscosity model with a global model coefficient

In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, turbulent channel flows at Reτ=180 and 590, flow over a circular cylinder at Red=3900, and flows over a sphere at Red=3700 and 104. The proposed dynamic model produces excellent performance for all flows considered. As shown in the present paper, the proposed model is robust and it can be readily applied to complex flows without homogeneous direction.

A multiblock joint PDF finite-volume hybrid algorithm for the computation of turbulent flows in complex geometries

A new hybrid joint probability density function (JPDF) solution algorithm for turbulent flows in complex 3D geometries is presented. The main focus is to demonstrate the applicability of JPDF methods for complex flows as observed in industrial applications. All elements of the algorithm are explained in detail and extensive validation studies are presented. A multiblock finite-volume solver, capable of handling globally unstructured, locally structured grids, was implemented together with a Lagrangian particle method. Efficient and robust particle management and accurate schemes for estimation and interpolation of particle statistics have been developed. For numerical efficiency particle sub-time stepping and an implicit finite-volume solver are applied. A fast coupling strategy was developed together with a multigrid method that allows very fast convergence on refined grids. Comparison with an established JPDF code for a bluff-body stabilized flow shows very good agreement. Furthermore, robustness and consistency of the algorithm for turbulent flow simulations with complex geometry is demonstrated.

Large eddy simulation of turbulent flows via domain decomposition techniques. Part 2: applications

The present paper discusses the application of large eddy simulation to incompressible turbulent flows in complex geometries. Algorithmic developments concerning the flow solver were provided in the companion paper, which addressed the development and validation of a multi-domain kernel suitable for the integration of the elliptic partial differential equations arising from the fractional step procedure applied to the incompressible Navier-Stokes equations

Large eddy simulation of turbulent flows via domain decomposition techniques. Part 1: theory

The present paper discusses large eddy simulations of incompressible turbulent flows in complex geometries. Attention is focused on the application of the Schur complement method for the solution of the elliptic equations arising from the fractional step procedure and/or the semi-implicit discretization of the momentum equations in velocity–pressure representation. Fast direct and iterative Poisson solvers are compared and their global efficiency evaluated both in serial and parallel architecture environments for model problems of physical relevance. Copyright © 2005 John Wiley & Sons, Ltd.

High order accurate solution of the incompressible Navier–Stokes equations

High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier–Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. The method is extended to three dimensions by a Fourier expansion. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.