Three-dimensional Cavity Flow Research Articles

A conservative finite element solver for the induction equation of resistive MHD: Vector potential method and constraint preconditioning

A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented. The solver utilizes magnetic vector potential and current density as solution variables, which are discretized by H(curl)-conforming edge-element and H(div)-conforming face element respectively. As a result, the divergence-free constraints of discrete current density and magnetic induction are both satisfied. Moreover the solutions also preserve the total magnetic helicity. The generated linear algebraic equation is a typical dual saddle-point problem that is ill-conditioned and indefinite. To efficiently solve it, we develop a block preconditioner based on constraint preconditioning framework and devise a preconditioned FGMRES solver. Numerical experiments verify the conservative properties, the convergence rate of the discrete solutions and the robustness of the preconditioner. Simulation of three-dimensional driven cavity flow problem using full MHD solver is also conducted.

Waves model of three-dimensional cavity flow and its oscillation mode evolution

The high-speed flow passing through an open cavity will generate complex wave structures. The propagation and evolution of these waves can lead to the self-sustained oscillation of the cavity flow and cause strong noise. The cavity noise may contain multiple acoustic modes with discrete frequencies in the spectrum. A clear understanding of the evolution of the oscillation mode will provide a theoretical basis for the study of the noise control method. By analyzing the waves scattering process at both ends of the cavity at subsonic speed and supersonic speed and considering the three-dimensional spanwise flow, the three-dimensional wave model for subsonic cavity flow and supersonic cavity flow are established respectively. The model involves the nonlinear interaction between different waves in the cavity, which may produce other components different from the Rossiter mode. Based on the pressure signal data measured from the experiments on cavity flow for Mach numbers 0.9 and 1.5, the parameters in the model are linearly estimated. The pressure signals are analyzed by using FFT, bispectral analysis, and continuous wavelet transform. The results show that there are nonlinear interactions between the main oscillation modes, thus producing strong harmonics. The mode-switch phenomenon is observed in both the subsonic case and the supersonic case. The mode-switching exhibits low-frequency behavior and shows randomness as a whole.

Research on 3D Hydrodynamic Model Based on Adaptive Mesh

In this paper, a three-dimensional hydrodynamic model based on adaptive mesh was established. The cubic mesh based on octree structure was adopted to solve the three-dimensional Navier-Stokes equation by the step-by-step pressure decomposition method, which realized the automatically encryption and coarsening of the grid. The calculation of three-dimensional square cavity flow showed that the calculation results of this model are in perfect agreement with those of Chen, and the calculation accuracy is high. Through the calculation of three-dimensional flow around a cylinder, the model can automatically encrypt the grid near the complex boundary, and can refine and coarsen the grid reasonably through the vorticity field. Meanwhile, it can also reduce the calculation amount and improve the calculation speed while maintaining the calculation accuracy.

Topological equivalence between two classes of three-dimensional steady cavity flows: A numerical-experimental analysis

The present study concerns Lagrangian transport and (chaotic) advection in three-dimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end, we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow vs fluid inertia (increasing Re) and single- or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms, and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry and 3D particle-tracking velocimetry.

Spatial-temporal patterns of three-dimensional subsonic turbulent cavity flow

Three-dimensional, high Reynolds number cavity flow is investigated. The cavity was exposed to a free-stream Mach number of 0.40 and a Reynolds number (based on cavity depth) of 1.6 × 106, with a thick incoming turbulent boundary-layer. Dominant modes and structures were studied by conducting unsteady numerical flow simulations (CFD), and applying Proper-Orthogonal-Decomposition (POD) in both two and three-dimensions. Fully three-dimensional POD analysis of cavity flow has been rarely conducted in other studies, and it is demonstrated that two-dimensional POD analysis is valid in order to emphasize patterns which are limited in space, but could be misleading without the comparison with the three-dimensional POD analysis. The analysis sheds new light on three-dimensional cavity flow by disclosing novel non-intuitive dominant structures and modes. Stretched streamwise vortices were found to be dominant, at least as the spanwise structures that originate from the classical two-dimensional shear-layer instability. Furthermore, the effect of symmetry plane assumption, which is usually disregarded, was studied rigorously for the first time. POD decomposition of symmetric and anti-symmetric flow modes revealed that anti-symmetric modes contain a significant portion of the total energy; however, they only interact weakly with the symmetric modes.

Successive bifurcations in a fully three-dimensional open cavity flow

The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.

Steady-state Analysis of Supersonic Mixing Enhanced by a Three-dimensional Cavity Flow

Steady-state Analysis of Supersonic Mixing Enhanced by a Three-dimensional Cavity Flow

Numerical Study of Different Closure Approaches for Prediction of Forced Convective Turbulent Cylindrical Cavity Flows

The present work exhibits a numerical study comparing the fluid dynamic and thermal fields of turbulent, three-dimensional forced convective cylindrical cavity flows obtained with Large Eddy Simulation (LES) and Reynolds-Averaged Navier Stokes (RANS). In the latter approach, three different closure models are employed: Reynolds Stress Model (RSM), standard k – ε and standard k - ω. It is considered a three-dimensional, incompressible, turbulent fluid flow at the steady state with ReD = 22,000 and Pr = 0.71. The main purpose is to investigate whether discrepancies are noticed in time-averaged and statistics of turbulent flows between LES and RANS predictions. Differences in time-averaged and statistical fields can be important for evaluation of convective fluxes in turbulent flows and combined convective and radiative transfer in participant media, i.e., for study of Turbulence-Radiation Interactions (TRI). The spatially-filtered and time-averaged conservation equations of mass, momentum and energy are solved with the Finite Volume Method (FVM). Results showed that time-averaged and RMS thermal fields obtained with LES and RANS presented reasonable discrepancies in regions near the cavity surfaces, which affects the convective fluxes in this region. For the highest temperature region of the cavity (near its inlet) the predictions obtained with LES and RANS are similar, which can led to similar predictions in heat exchange when thermal radiation is taken into account in optically thin participant media. For optically thick media, where local differences increase their importance, the employment of RANS is not recommended.

Scalable multi-relaxation-time lattice Boltzmann simulations on multi-GPU cluster

In this paper, the D3Q19 multi-relaxation-time lattice Boltzmann model is adopted to simulate three-dimensional cavity flows using graphic processing units (GPUs). For single GPU computations, utilizing on-chip memory generates three to five times speedup over adopting global memory alone. Also, streaming using offset reading attains another two times speedup over employing offset writing. For Message Passing Interface (MPI) based multi-GPU computations, overlapping communication and computation can achieve 38% improvement and provide an efficient scheme to improve the scalability and its performance. Numerical experiments show that 12TeslaTM M2070 GPUs produce around 5500 million lattices updates per second (MLUPS) using 5763 grid. On the other hand, three GTX Titans deliver 5000 MLUPS for 1923 grids, while 12Tesla attain half performance.

Reduced-order modeling of three-dimensional unsteady partial cavity flows

An efficient reduced-order modeling to analyze three-dimensional unsteady partial cavity flows is proposed. The proposed approach is based on the boundary element method along with the potential flow assumption. To this end, a novel non-iterative method based on the flow eigenmodes of three-dimensional partial cavity flows is applied. Eigenanalysis and reduced-order modeling for unsteady flows over a three-dimensional hydrofoil with various sections are performed. The results obtained from the present analysis are compared with those reported in the literature to verify the strength of the proposed approach. In order to examine the performance of the introduced algorithm for unsteady cavitating flows, various simulations for several reduced frequencies, hydrofoil geometries and different cavitation numbers are also investigated. Comparison between the obtained results using the novel and conventional methods indicates that the present algorithm works very well with sufficient accuracy. Moreover, it is shown that the proposed method is computationally more efficient than the conventional ones for unsteady sheet cavitation analysis on three-dimensional hydrofoils.

Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations.

We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.

Three-dimensional flow within shallow, narrow cavities

AbstractThe three-dimensional structure of incompressible flow in a narrow, open rectangular cavity in a flat plate was investigated with a focus on the flow topology of the time-averaged flow. The ratio of cavity length (in the direction of the flow) to width to depth was $l{: }w{: }d= 6{: }2{: }1$. Experimental surface pressure data (in air) and particle image velocimetry data (in water) were obtained at low speed with free-stream Reynolds numbers of ${\mathit{Re}}_{l} = 3. 4\times 1{0}^{5} $ in air and ${\mathit{Re}}_{l} = 4. 3\times 1{0}^{4} $ in water. The experimental results show that the three-dimensional cavity flow is of the ‘open’ type, with an overall flow structure that bears some similarity to the structure observed in nominally two-dimensional cavities, but with a high degree of three-dimensionality both in the flow near the walls and in the unsteady behaviour. The defining features of an open-type cavity flow include a shear layer that traverses the entire cavity opening ultimately impinging on the back surface of the cavity, and a large recirculation zone within the cavity itself. Other flow features that have been identified in the current study include two vortices at the back of the cavity, of which one is barely visible, a weak vortex at the front of the cavity, and a pair of counter-rotating streamwise vortices along the sides of the cavity near the cavity opening. These vortices are generally symmetric about the cavity centre-plane. However, the discovery of a single tornado vortex, located near the cavity centreline at the front of the cavity, indicated that the flow within the cavity is asymmetric. It is postulated that the observed asymmetry in the time-averaged flow field is due to the asymmetry in the instantaneous flow field, which switches between two extremes at large time scales.

Numerical Simulation on Ventilated Cavity Flow with Different Turbulence Models

The gas leakage and capabilities in cavity tail-part can affect the characteristics of ventilated cavity shape, while turbulence models influence directly the function of turbulence and gas-leakage mode in cavity tail-part. To compare the impact of two turbulent models (large eddy simulation (LES) and Renormalization Group (RNG) k-ε) on ventilated cavity shape, FLUENT6.2 software was used to simulate the three-dimensional ventilated cavity flow, taking into account gravity effects, the cavity transient image and pressure distributions along model surface under two turbulence models were also presented. The results show that the results of LES are more consistent with the transient characteristics of ventilated cavity, and are more suitable for simulations of ventilated cavity flow than RNG k-ε model.

The proposal and realization on more exact modeling of COIL performance

AbstractThe chemical oxygen–iodine laser (COIL) is the shortest-wavelength high-power chemical laser that has been demonstrated. The characteristics, such as good atmospheric propagation, short wavelength and excellent transmission through optical fibers, make the COIL a good candidate for high-power laser application. To model the complete COIL lasing interaction, a three-dimensional formulation of the fluid dynamics, species continuity and radiation transport equations is necessary. The computational effort to calculate the flow field over the entire nozzle bank with a grid fine enough to resolve the injection holes is so large as to preclude doing the calculation. The approach to modeling chemical lasers then has been to reduce the complexity of the model to correspond to the available computational capability, adding details as computing power increased. The modeling of lasing in the COIL medium is proposed, which is coupling with the effects induced by transverse injection of secondary gases, non-equilibrium chemical reactions, nozzle tail flow and boundary layer. The coupled steady solutions of the fluid dynamics and optics in a COIL complex three-dimensional cavity flow field are obtained following the proposal. The modeling results show that these effects have some influence on the lasing properties. A feasible methodology and a theoretical tool are offered to predict the beam quality for large-scale COIL devices.

Simulations of Three-dimensional Cavity Flows with Multi Relaxation Time Lattice Boltzmann Method and Graphic Processing Units

Three-dimensional square cavity flows are simulated using multi-relaxation lattice Boltzmann method and graphic processing units. It was found that transition takes place between 1700 < Re < 2000. Parallel computations are conducted on a single node multi graphic processing unit (GPU) system, consisting of three nVIDIA M2070 or GTX560 devices using OpenMP. Results show that the speedup performance is strongly dependent on problem size and the precision adopted. For single precision computation with 2403 grid density, about 159 times speedup can be obtained, while for double precision computation, this is slightly degraded to 112. Both are achieved with three Tesla M2070.

Dependence on the Aspect Ratio of Streamline Patterns in Three-Dimensional Cavity Flows

Dependence on the Aspect Ratio of Streamline Patterns in Three-Dimensional Cavity Flows

A numerical study of secondary flow and large eddies in a driven cavity

This paper reports on the application of a newly developed LES flow solver to compute a true three-dimensional flow. The research also investigates the behavior of turbulence statistics by comparing transient simulation results to available data based on experiments and simulations. An extensive discussion on the results such as energy spectrum, velocity profiles and time trace of velocities is carried out in the research as well. Based on the results obtained, the application of the flow solver for a turbulent three-dimensional driven cavity flow by using three grids with varying densities is proven. In addition, the research successfully verifies that in many instances computational results agreed reasonably well with the reference data, and the changes in the statistical properties of turbulence with respect to time are closely related to the changes in the flow structure and strength of vortices. The focus of this study is on the prediction of a subgrid scale Reynolds shear stress profiles, and the results show that the standard model is able to reproduce general trends measured from experiments. Furthermore, in certain areas inside the cavity the computed shear stress values are in close agreement with experimental data.

Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows

Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy.

Transition of Streamline Patterns in Three-Dimensional Cavity Flows

Transition of Streamline Patterns in Three-Dimensional Cavity Flows

Implementation of Logistic Parallelization in Arbitrary Lagrangian Eulerian Framework for Incompressible Flows

A logistic parallelization is implemented in the Arbitrary Lagrangian Eulerian framework with an operator splitting technique for incompressible flows. The logistic parallelization adopts superposition-based data structure, follows the global structure of serial computation, and reduces communications by careful arrangement of data and filtering. Logistic parallelization is simple to implement. A three-dimensional pulsatile flow, a three-dimensional cavity flow, and a two-dimensional free-surface capillary wave are calculated. Numerical results demonstrate moderate efficiency of the logistic parallelization.