Three-dimensional Cavity Flow Research Articles

Three-dimensional effects of supersonic cavity flow due to the variation of cavity aspect and width ratios

Unlike the steady closed-type supersonic cavity flow, open-type cavity flow is divided into internal and external flows by turbulent shear layer. The cavity flow may cause resonance phenomena due to pressure oscillation, depending on the cavity geometry and the flow conditions. These phenomena may induce noise generation, structural damage, and aerodynamic instability. In this research, the flow characteristics of three-dimensional supersonic cavity flow of Mach number 1.5 were analyzed with the variations of aspect ratio and width ratio. Three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes (RANS) equations were used with a turbulence model. For numerical calculations, the 4th-order Runge-Kutta method and the FVS method with van Leer’s flux limiter were applied. The numerical calculations were performed by using a parallel processing program with 16 CPUs. The sound pressure level (SPL) spectra of pressure variations were analyzed at the point of cavity leading edge. The correlation of pressure distribution (CPD) was also analyzed for the propagation of dominant oscillation pressure waves with respect to the reference point of the cavity leading edge. The dominant oscillation frequency was compared with the oscillation modes of Rossiter’s formula. Oscillation Mode 2 appeared as a dominant oscillation frequency regardless of the aspect ratio of cavity in the two-dimensional flow. Oscillation Modes1 and 2 appeared in three-dimensional cavities of small aspect ratios. However, as the aspect or the width ratio increases, only the mode 2 or 3 frequency appeared as a dominant oscillation frequency.

Experimental/Numerical Analysis of Chaotic Advection in a Three-dimensional Cavity Flow

Abstract Advection of material volumes in a three-dimensional cavity flow is analyzed by using an experimental setup and a collection of computational tools. The experimental setup for the lid-driven cavity flow makes it possible to study the advection of drops for a wide range of flow parameters. The location of unmixed regions for a specific mixing protocol is predicted by means of the mapping method, which are then used to determine the initial location of the dyed drops in the experiments. Finally, an adaptive front tracking method is used to computationally follow the drops during flow in a precise way. In most cases, a qualitative comparison between the experiments and the simulations is found. In addition, the mapping method proves to be well suited to quickly predict unmixed regions in mixers.

F212 三次元キャビティ内流れの数値解析(一般セッション 数値解析)

F212 三次元キャビティ内流れの数値解析(一般セッション 数値解析)

Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number

Large-eddy simulations of a subsonic three-dimensional cavity flow with self-sustaining oscillations are carried out for a Reynolds number based on the length of the cavity equal to . Meticulous comparisons with available experimental data corresponding to the same configuration demonstrate a high level of accuracy. Special attention is paid to the mixing layer that develops over the cavity and two different zones are identified. The first one is dominated by Kelvin–Helmholtz instability, and the linear as well as quadratic energy transfers leading to the filling of velocity spectra are described. The Kelvin–Helmholtz instability also appears to be forced near the origin of the layer, and it is postulated that the small recirculation bubble located in this area is responsible for the forcing. Downstream of the first zone and up to the vicinity of the aft wall, the layer behaves very similarly to a free mixing layer by exhibiting a linear spreading. An influence of the recirculating flow inside the cavity upon the growth of the layer is nevertheless observed at downstream stations. Analysis of the pressure on the floor of the cavity reveals that the self-sustaining oscillation-related pressure modes (Rossiter modes) are independent of their spanwise location inside the cavity. On the contrary, Rossiter modes exhibit streamwise modulations and it is demonstrated that a very simple two-wave model is able to reproduce the spatial shape of the modes. Nonlinear interactions between Rossiter modes are encountered, as well as nonlinear interactions with low-frequency components. A joint time–frequency analysis shows a temporal modulation of the Rossiter mode levels at similar low frequencies, resulting in a special form of intermittency with competitive energy exchanges between modes.

Molecular study of turbulence in three-dimensional cavity flow

Three-dimensional molecular cavity problems are formulated and solved numerically. The fluid considered is water at 15°C. The turbulent flows generated are characterized by strong cross-currents over the usual primary vortex direction.

Numerical solution of three-dimensional Navier-Stokes equations by a velocity-vorticity method

A finite difference method for solving the incompressible viscous flow in velocity–vorticity form is presented. A staggered mesh is employed to ensure continuity. To enforce the zero divergence of the vorticity, the computed vorticity is replaced at each time step with . An explicit three-level backward scheme is used to update the vorticity transport equation for the vorticity at the next time level. To solve the Poisson equations for velocity, a restarted version of the Generalized Minimal Residual method (GMRES) implemented with incomplete lower–upper (ILU) decompositions preconditioner has been adopted. Two- and three-dimensional driven cavity flows with impulsively started and oscillating lids are used to test the method. Detailed results and comparisons with the numerical literature data show that the proposed method is accurate and efficient. Copyright © 2001 John Wiley & Sons, Ltd.

Mixing of non-Newtonian fluids in time-periodic cavity flows

Fluid mixing in two- and three-dimensional time-periodic cavity flows as a function of rheological fluid parameters is studied. Computational methods are applied to obtain accurate descriptions of the velocity fields, which form the basis of the mixing analysis. In addition to some classical techniques, like Poincaré maps and the analysis of periodic points, a recently developed mapping method is used to determine mixing efficiency over a wide range of different flow parameters. Within this framework, different mixing protocols can be evaluated with respect to their long term mixing behaviour and compared quantitatively. It is shown that local ‘optimal’ parameter settings for mixing of Newtonian fluids can result in a considerable worse mixing behaviour for non-Newtonian fluids, and vice versa, illustrating the importance of taking the rheology of the fluid into account.

Analysis of mixing in three-dimensional time-periodic cavity flows

A method to locate periodic structures in general three-dimensional Stokes flows with time-periodic boundary conditions is presented and applied to mixing cavity flows. Numerically obtained velocity fields and particle tracking schemes are used to provide displacement and stretching fields. From these the location and identification of periodic points can be derived. The presence or absence of these periodic points allows a judgement on the quality of the mixing process. The technique is general and efficient, and applicable to mixing flows for which no analytical velocity field is available (the case for all three-dimensional flows considered in this paper). Results are presented for three different mixing protocols in a three-dimensional time-periodic cavity flow, serving as an accessible test case for the methods developed. A major result is that periodic lines are obtained for these three-dimensional flows. These lines can be complex in geometry and their nature can change along a line from hyperbolic to elliptic. They can serve as practical criteria in the optimization of three-dimensional mixing processes.

The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier-Stokes equations

This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier–Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.

Numerical Analysis of a Three-Dimensional Cavity Flow Field in a Supersonic Duct.

The flow field in a cavity that is attached to a supersonic duct at M=1.83 is computationally simulated. The basic characteristics of the cavity flow field and the effect of cavity dimensions (the length to depth ratio) are discussed. The computational results show good agreement with the experimental ones. From the numerical and the experimental results, time-averaged characteristics of the cavity flow fields are clarified. In the case of a longer cavity, the flow field is highly three-dimensional due to the effect of sidewalls. In the case of a shorter cavity, the flow field is essentially two-dimensional. The flow-in and flow-out mechanisms of the cavity are also clarified.

A Large-Eddy Simulation of the Shear-Driven Cavity Flow Using Dynamic Modeling

A large-eddy simulation of the three-dimensional shear-driven cavity flow was carried out at a high Reynolds number where the subgrid scale turbulence was represented by a dynamic model. Lilly's expression was tested for determining Smagorinsky's coefficient in the model without ad hoc measures such as ensemble-averaging or filtering. However, zero cut-off of negative total viscosity was necessary to maintain stable solutions. A discretized filter function is derived for the test filter. Good qualitative and quantitative agreement with published experimental data was obtained indicating that the dynamic model performed quite well. The cavity flow at Reynolds number of 104 is transitional. The highest turbulent production levels not only occurred within the downstream eddy region of the cavity, but also along the upper half of the downstream wall.

On the Unsteady and Turbulent Characteristics of the Three-Dimensional Shear-Driven Cavity Flow

The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of 5000 and 10000. This investigation focuses on the unsteadiness and turbulent characteristics of the flow. At the moderate Reynolds number (Re = 5000) where the cavity flow is fully laminar, a direct numerical simulation (DNS) is used whereas large-eddy simulation (LES) methodology is adopted to predict the cavity flow at the higher Reynolds number (Re = 10000). Establishing a suitable form for the subgrid scale (SGS) turbulence model in this complex flow is guided by the DNS results at Re = 5000. Additionally, the SGS model is verified against DNS results at Re = 7500 where the cavity flow is known through experimentation to be locally transitional. The LES results verify the published experimental evidence as well as uncover new flow features within the cavity.

APPLICATION OF THE PIECEWISE PARABOLIC FINITE ANALYTIC METHOD TO THE THREE-DIMENSIONAL CAVITY FLOW

Abstract The three-dimensional piecewise parabolic finite analytic method (PPFAM3D), with vector potential and vorticity as dependent variables, was used to solve the steady three-dimensional (3-D) laminar cavity flow. Predictions were obtained for Reynolds numbers between 100 and 2000. Results for Re = 100, 400, and 1000 are compared with those available in the literature. The overall agreement is excellent. Results are also compared with the two-dimensional PPFAM cavity flow, showing the effect of three-dimensionality on the velocity predictions at the symmetry plane. The PPFAM3D is a robust numerical algorithm requiring no relaxation to produce physically meaningful and numerically converged solutions. It is a promising tool for solving a variety of flow phenomena governed by unsteady second-order partial differential convection-diffusion equations

Experimental numerical studies on a supercomputer of natural convection in an enclosure with localized heating

We present particle simulations of natural convection of a symmetrical, nonlinear, three-dimensional cavity flow problem. Qualitative studies are made in an enclosure with localized heating. The assumption is that particles interact locally by means of a compensating Lennard-Jones type force F, whose magnitude is given by − G/ r p + H/ r q . In this formula, the parameters G, H, p, q depend upon the nature of the interacting particles and r is the distance between two particles. We also consider the system to be under the influence of gravity. Assuming that there are n particles, the equations relating position, velocity and acceleration at time t k = kΔt, k = 0, 1, 2, …, are solved simultaneously using the “leap-frog” formulas. The basic formulas relating force and acceleration are Newton's dynamical equations F i,k = m i a i,k, i = 1, 2, 3, …, n , where m i is the mass of the ith particle. Extensive and varied computations on a CRAY X - MP/24 are described and discussed, and comparisons are made with the results of others.

Numerical simulation of three-dimensional flow structure in a driven cavity

Investigations have been made of three-dimensional flows of an incompressible viscous fluid in a square cubic cavity. The flows are driven by the sliding upper surface of the cavity. Numerical solutions are obtained by directly integrating the full, three-dimensional, time-dependent Navier-Stokes equations. The three-dimensional flow structure is examined in detail over a wide range of the Reynolds number Re. One primary finding of these three-dimensional numerical simulations indicates that steady solutions are attained at lower values of Re, but the flow becomes unsteady at higher values, say, when Re exceeds approximately 2000. Due to the profound influence of the endwall effects, three-dimensional flows show substantial differences from two-dimensional solutions: for two-dimensional flow situations, steady solutions are known to exist for up to Re = 10000. The three-dimensional flow structure displays qualitatively distinct features in the low-Re and high-Re regimes. The demarcation separating these two regimes appears to lie in the neighborhood of Re = 2000–3000. One principal characteristic is that the Taylor-Görtler-like vortices are discernible for the high-Re regimes, although these have not been clearly captured in the numerical results for the low-Re regimes. Critical assessments of the present numerical results have been made by cross-checking the data with the available experimental measurements for three-dimensional cavity flows. The comparisons demonstrate broad qualitative agreement between the present numerical computational results and the laboratory measurement data.

Parallel Algorithms for Fluid Dynamics Problems

The recent trend toward increased parallelism in supercomputer architectures, together with the need to use existing supercomputer resources more efficiently, has motivated this study of parallel algorithms designed specifically for implementation on parallel machines. Users of parallel machines like the ICL Distributed Array Processor (DAP) are all too familiar with the problem of having to reformulate their algorithms to incorporate the inherent parallelism of the DAP architecture. The individual processing elements of the DAP are comparatively slow, and the full potential of such a machine is only realized if the algorithm used is highly parallel. The very fast processing capabilities of pipeline machines like the Cray-1 or the Cyber 205 tend to obscure this point somewhat, and in fact most users of these machines are content with using existing codes, vectorized where possible. Such a strategy, however, is not appropriate for the parallel processors like the ICL DAP, AMT DAP, the Goodyear MPP, GEC GRID, etc.The application of parallel algorithms to the solution of fluid dynamics problems is considered. Most of the work concerns the solution of the two- and three-dimensional incompressible Navier-Stokes equations, steady and unsteady. The results are relevant for the above-mentioned parallel machines, but the methods can be adapted for use on vector machines.Concerning parallel algorithms, the easiest and possibly those with the widest potential application are relaxation techniques based on red-black (R-B) ordering. The use of R-B successive overrelaxation, R-B LSOR, etc., on two- and three-dimensional cavity flows, unsteady channel, and boundary layer flows at high Reynolds numbers is considered. While these methods are extremely problem dependent, in the favorable cases they can be as competitive as more sophisticated serial “vectorized” algorithms. As far as parallel algorithms are concerned, the most important criteria are what is the cost per iteration, and how fast do they converge. For application on serial machines, the latter factor seems to dominate.

A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations

A new Chebyshev pseudospectral technique (based on the projection method that was previously applied by the authors to the solution of two-dimensional incompressible Navier-Stokes equations in primitive variables for nonperiodic boundary conditions) is extended to solve the three-dimensional Navier-Stokes equations. The crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain, on the boundaries as well as in the interior. The key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure Poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition. The method was tested on a two-dimensional driven cavity flow and the results were compared with those of the most accurate finite-difference calculation. The three-dimensional driven cavity flow was then calculated at the same Reynolds numbers as the two-dimensional cases, i.e., Re = 100, 400, and 1000. In the calculated results, three-dimensional boundary effects were observed in all cases and became more apparent with increasing Reynolds number.

Singularity Representations of Perturbed Flow and Unsteady Characteristics for Oscillating Hydrofoils of Finite Cavity : 2nd Report, Three-Dimensional Unsteady Cavity Flow Model

オイラーの運動方程式に基づいて,有限長さの超空どうを伴う三次元振動翼による非定常流れを特異点表示し,非定常随伴うずの発生が三次元性の特徴であることを示した.ついで,境界条件から得られた基礎式の近似化をはかり,局所有効迎え角に関する二次元性の成立を利用して見とおしのよい特性解析法が提示された.実験値との比較から,既存理論に比し,新しい三次元非定常空どう模型に基づく本解析法の妥当性が立証された.

A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows

A numerical algorithm for solving two- or three-dimensional incompressible viscous Navier-Stokes equations is presented. The technique presented here is based on a simple variant of the Chorin method and is related to the MAC method. Auxiliary velocity fields are introduced, which are calculated by the use of a fractional-step procedure for the convective and diffusive part of the solution. For the pressure resolution, a triple sweep is used to obtain the fluid pressure. By these fractional techniques, the three-dimensional equations are separated into only one-dimensional forms. Thus, this saves more computation time and makes algorithm simple. Some numerical computations are made on flows within square and cubic cavities, and some comparisons are made in regard to boundary effects in three-dimensional flows. Further, some discussions are made on primary and secondary eddies generated in a cubic cavity, and comparisons with those in a square cavity are also made. It was found that boundary effects mainly locate near a side wall, but these are not negligibly small in a central region in a cubic cavity.

A criterion for the transition between flow regimes in turbulent cavity flow.

Pressure coefficient criterion for transition between two- and three-dimensional turbulent cavity flow