Rectangular Cavity Flow Research Articles

Geometric Effect on Compressible Rectangular Cavity Flows.

Experiments were performed to study the geometric effects on the compressible rectangular cavity flows at Mach 0.33, 0.62, and 0.82. Typical characteristics of mean surface pressure distributions show a slight pressure variation near the front face, a local peak surface pressure ahead of the rear corner, and a low pressure immediately downstream of the cavity. The length-to-width ratio of a cavity has a strong effect on the recompression and downstream expansion near the rear face, and the Mach number effect is minimized. Surface pressure fluctuation distributions show a damping near the leading edge at a higher freestream Mach number, a minor peak near the middle of the cavity floor, an increase toward the cavity rear face, and a peak value immediately downstream of the cavity. The amplitude of the pressure fluctuations ahead of the rear face increases with the length-to-width ratio for transitional- and closed-type cavity flows, and the maximum of peak pressure fluctuations rises rapidly for the transitional cavity flows at higher length-to-width ratio.

Three-dimensional effect on transonic rectangular cavity flows

Experiments are performed to study the characteristics of rectangular cavity flows. Mean and fluctuating surface pressures in a Mach 1.28 turbulent flow past rectangular cavities are obtained. The cavity length-to-depth ratio (L/D) is varied from 2.43 to 43.00, while the length-to-width ratio (L/W) is 0.5, 1.0 and 2.0. The three-dimensional effect is significant on the trailing edge vortex, which affects the peak pressure ahead of the rear face, pressure gradient and levels of pressure fluctuation near the trailing edge, particularly for closed and transitional cavity flows. L/W and Mach number are important for the definition of critical L/D for the cavity flowfield models.

Multiplicity of Steady Two-Dimensional Flows in Two-Sided Lid-Driven Cavities

The two-dimensional steady incompressible flow in rectangular cavities is calculated numerically by a finite volume method. The flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves. Depending on the cavity aspect ratio and the two side-wall Reynolds numbers different flow states exist. Their range of existence and the bifurcations between different states are investigated by a continuation method accurately locating the bifurcation points. When both side walls move in opposite directions up to seven solutions are found to exist for the same set of parameters. Three of these are point-symmetric and four are asymmetric with respect to the center of the cavity, if the side-wall Reynolds numbers have the same magnitude. When the walls move in the same direction, up to five different flow states are found. In this case only a single mirror symmetric solution exists for equal Reynolds numbers.

505 軸流中の円筒上キャビティ内流れの実験 : 平均速度場とせん断層の振動特性(OS1 複雑流れの計測と解析)

505 軸流中の円筒上キャビティ内流れの実験 : 平均速度場とせん断層の振動特性(OS1 複雑流れの計測と解析)

QSIスキームを用いた流体解析法の適用性について

A computational method has been proposed for viscous incompressible flows with QSI (quintic spline interpolation) scheme. This method is based on general curvilinear coordinates and collocated grid arrangement, which allows us to deal with moving boundary problems. In order to confirm the validity of this computational method, it was was applied to the rectangular and polar cavity flows. In addition, it was also applied to small amplitude standing waves and free-surface flows within a cavity. As a result, it has been shown that the predicted results are in good agreement with the theory and other computational results and that the QSI scheme is effective to predict various fluid flows with sufficient accuracy.

EFFECTS OF LID-DRIVEN CAVITY SHAPE ON THE FLOW ESTABLISHMENT PHASE

Experiments are carried out to study the flow establishment phase inside closed cavities submitted to the impulsive translation from rest, of one of their walls at a Reynolds number of 1000. Three standard industrially machined or molded cylindrical cavity shapes are studied and are compared with respect to the efficiency of mixing process: square, rectangular and semi-circular of length-to-width ratio of 2:1. The flow structures in the mid-cross-section are analysed by means of fine topological and kinematic visualization series using two complementary techniques: continuous dye filament and discrete solid tracers both coupled with a laser sheet illumination. Particular attention is given to vorticity propagation and primary/secondary eddy formations. Although a roughly similar vortex generation is observed in all examined cavities, important differences appear with time. The semi-circular cavity flow results in a much more homogeneous and uniform recirculation with no secondary flow recirculation zone. On the contrary, the square and rectangular cavity flows develop a better flow mass dispersion and, respectively, one and two secondary eddies. At the final time of observation (t*=12), both semi-circular and rectangular cavity flows seem to reach their steady state whereas the square one continues to evolve. Comparisons with 2-D computational results of other authors illustrate the three-dimensional flow aspect present in experiments.

Pressure Fluctuations in Rectangular Cavity Flows

AbstractExperiments are performed to study the unsteadiness of rectangular cavity flows at Mach 0.325, 0.620 and 0.818. Typical characteristics of mean surface pressure distributions show a slight pressure variation near the front face, a local peak surface pressure ahead of the rear corner and a low pressure at immediate downstream of the cavity. Larger peak pressure and pressure variation near the cavity rear face are observed as the length-to-depth ratio increases. Surface pressure fluctuation distribution shows an increase toward the cavity rear face and reaches a peak value. At further downstream locations, the level of surface pressure fluctuation approaches the value of incoming flow. The amplitude of peak surface pressure fluctuation is associated with length-to-depth ratio and reaches the maximum at length-to-depth ratio of 8.60. This is considered due to intermittent switching between open- and closed-cavity flows. Higher moments of surface pressure signal at immediate downstream of the cavity show a similar trend. More negative skewness coefficient and larger deviation of flatness coefficient indicate the presence of more large negative events, which is mainly corresponding to mass removal process (breath-out phase). This unsteady mass flow is more pronounced at higher Mach number.

Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures

The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.

NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN GENERALIZED NON-ORTHOGONAL CURVILINEAR CO-ORDINATES

A method based on the vorticity stream function formulation is used for the solution of the unsteady incompressible two-dimensional laminar viscous flow problems. Vorticity transport and stream function equations are written in generalized curvilinear non-orthogonal coordinate system, and discretized using an implicit finite difference approximation. A second order accurate scheme with a stabilizing correction splitting method as an ADI technique is used. Both conservative and non-conservative forms of the vorticity transport equation are considered and the problems associated with different treatments of boundary conditions are addressed. Several test cases, including rectangular cavity flow problem, flow around circular cylinder and flow past an isolated airfoil at moderate angles of attack, are illustrated.

Effects of bottom injection on heat transfer and fluid flow in rectangular cavities

A numerical study is performed for investigating the effects of bottom injection on the heat transfer in a cavity. The Reynolds number (based on the cavity height and bulk mean velocity over the cavity) ranges in value from 100 to 1000. The cavity aspect ratios W/D investigated are 1, 6, and 10. The injection flow rate varies between 2-20% of the bulk flow rate. With the injectant temperature maintained the same as the cavity wall temperature, the effects of injection-reduced cavity heat transfer are strongly dependent on all the parameters aforementioned. For given injection rate and Reynolds number, the degree of heat-transfer reduction increases with a decrease of cavity aspect ratio. In addition, the current results suggest that the heat-transfer correlations presented in previous studies for cavities with aspect ratio of unity overestimate the extent of heat-transfer reduction for wider cavities.

LATTICE GAS SIMULATION OF VISCOUS FLOW IN A CAVITY

Two-dimensional rectangular cavity flows are studied using a 7-bit lattice gas automaton model. The uniform velocity boundary and wall-driven boundary are applied to the upper boundary or both the upper and lower boundaries to simulate different cavity flows. The comparison of the velocity distribution of this calculation with experimental data and other numerical results is encouraging.

Fluctuations in cavities in a supersonic gas flow

Numerical calculations are carried out within the framework of the ideal compressible gas model for the unsteady flows in rectangular cavities exposed to a supersonic external stream. The Euler equations are integrated by means of Godunov's finite-difference method [6]. On the basis of an analysis of the calculation results an expression is proposed for determining the possible frequencies of the flow rate oscillations in the cavity as a function of the free-stream Mach number M∞ and the geometry of the cavity. The results obtained are compared with the experimental data and calculations of other authors.

Recirculating mixed convection flows in rectangular cavities

A numerical investigation is carried out to determine the flow and thermal structures of mixed convective flow in a rectangular cavity. The effect of aiding and opposing buoyancy on the flow in a vertical downward laminar jet is studied for Re < 200, -1.0 < 'Ri < 0.5, and 0.5 < A < 5.0. Such flow situations occur in enclosure fires, energy storage, and ventilation systems. Results of the velocity profile, temperature distribution, local friction factor, and heat-transfer coefficient are presented for both hot and cold jets. The flow configuration is found to be strongly affected by the positive and negative buoyancy and also by the aspect ratio of the cavity.

Creeping flows in rectangular cavities with translating top and bottom walls: Numerical study and flow visualization

The recirculating flow patterns in the creeping flow range of an incompressible fluid in rec-tangular cavities with translating top and bottom walls were obtained numerically and by visualization, then were compared with each other. The aspect ratio was put to be either one or two.

Numerical solution of recirculating flow by a simple finite element recursion relation

A time-split finite element recursion relation, based on linear basis function, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.

Numerical Simulation of Natural Convection in Closed Containers by a Fully Implicit Method

Abstract Numerical solutions have been obtained for two-dimensional free convective flow in rectangular and annular cavities by the strongly implicit procedure (SIP) and the cyclic reduction-fast Fourier transform (CR-FFT) technique. Rayleigh numbers range from 104 to 106, Prandtl numbers from 0.713 to 103, radius ratios from 1 to 3 (annular cavities), and aspect ratios (height/width) from 1 to 15. Motion is generated by either uniformly heating the bottom wall or heating a vertical wall and cooling the opposite wall. Both time-dependent and steady-state solutions confirm results previously obtained by others. Because SIP uses a common set of matrix algorithms, the governing equations of motion can be solved simultaneously without major modification to the method for each equation.

Numerical Study of Transient and Steady Induced Symmetric Flows in Rectangular Cavities

Symmetric flows induced in rectangular cavities by a pair of moving walls are studied numerically. Solutions are obtained by solving the coupled transient vorticity transport and stream function relations using the alternating direction implicit method. Steady state solutions are obtained as limiting cases of the transients. The study covers Reynolds numbers of 1 100 and 1000 for cavities having aspect ratios of 0.5 and 1.0.

Glass bead-filled polypropylene part II: Mold-filling studies during injection molding

Five glass bead-filled polypropylene composites, which had been rheologically characterized, were used in mold-filling studies to investigate the influence of rigid beads (0 to 26 vol percent) in complex flow fields. The two basic flows studied were simple shear flow in an edge-gated, rectangular cavity and stagnation flow leading to diverging radial flow in a center-gated, rectangular cavity. Pigmented tracer elements were used to illustrate flow patterns and to distinguish the skin-core structure which is a consequence of the injection molding process. Despite the strong dependence of the rheological properties (both viscous and elastic) and physical properties (density, thermal conductivity, etc.) on bead volume fraction, the basic character of the polymer dominated the flow behavior of each composite and the flow patterns were unaffected by the beads. Injection pressures were increased with increasing bead fraction to maintain the same, constant volumetric flow rate (2.21 in.3/min) for each composite. Relative injection forces follow closely the relative viscosit trend.

Unsteady Cavity Flows: Oscillatory Flat Box Flows

The oscillatory cavity flows reported here are extensions of previously studied steady closed rectangular cavity flows (box flows). The periodic laminar incompressible flows are characterized by three numerical parameters, peak Reynolds number, a reduced frequency (or Stokes number) and the height-to-length ratio of the cavity. Depending on the height-to-length ratio, flow fields are obtained by finite-difference solutions or analytic solutions of the Navier-Stokes equation. The central portion of a flat cavity contains an oscillatory parallel flow. Experimental measurements corroborate the theory. Stokes number dependency and particularly differences from the corresponding steady flow (whose Stokes number is zero) are illustrated.

Steady flows in rectangular cavities

This paper deals with the steady flow in a rectangular cavity where the motion is driven by the uniform translation of the top wall. Creeping flow solutions for cavities having aspect ratios from ¼ to 5 were obtained numerically by a relaxation technique and were shown to compare favourably with Dean &amp; Montagnon's (1949) similarity solution, as extended by Moffatt (1964), in the region near the bottom corners of a square cavity as well as throughout the major portion of a cavity with aspect ratio equal to 5. In addition, for a Reynolds number range from 20 to 4000, flow patterns were determined experimentally by means of a photographic technique for finite cavities, as well as for cavities of effectively infinite depth. These experimental results suggest that, within finite cavities, the high Reynolds number steady flow should consist essentially of a single inviscid core of uniform vorticity with viscous effects being confined to thin shear layers near the boundaries, while, for cavities of infinite depth, the viscous and inertia forces should remain of comparable magnitude throughout the whole domain even in the limit of very large Reynolds number R.