Rectangular Cavity Flow Research Articles

Evolution of tornado-like vortices in three-dimensional compressible rectangular cavity flows

The spatial structure and time evolution of tornado-like vortices in a three-dimensional cavity are studied by topological analysis and numerical simulation. The topology theory of the unsteady vortex in the rectangular coordinate system (Zhang, Zhang & Shu, J. Fluid Mech., vol. 639, 2009, pp. 343–372) is generalized to the curvilinear coordinate system. Two functions $\lambda (q_1,t)$ and $q(q_1,t)$ are obtained to determine the topology structure of the sectional streamline pattern in the cross-section perpendicular to the vortex axis and the meridional plane, respectively. The spiral direction of the sectional streamlines in the cross-section perpendicular to the vortex axis depends on the sign of $\lambda (q_1,t)$ . The types of critical points in the meridional plane depend on the sign of $q(q_1,t)$ . The relation between the critical points of the streamline pattern in the meridional plane and that in the cross-section perpendicular to the vortex axis is set up. The flow in a three-dimensional rectangular cavity is numerically simulated by solving the three-dimensional Navier–Stokes equations using high-order numerical methods. The spatial structures and the time evolutions of the tornado-like vortices in the cavity are analysed with our topology theory. Both the bubble type and spiral type of vortex breakdown are observed. They have a close relationship with the vortex structure in the cross-section perpendicular to the vortex axis. The bubble-type breakdown has a conical core and the core is non-axisymmetric in the sense of topology. A criterion for the bubble type and the spiral type based on the spatial structure characteristic of the two breakdown types is provided.

Effect of interface dynamic deformations on instabilities of buoyancy-thermocapillary convection in a two-fluid two-layer system

The effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The relation between interface deformations and the Boussinesq approximation is discussed. It is shown that including interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either a destabilizing, or a stabilizing effect.

Solution of Navier-Stokes equations for fluids with magnetorheological compensation used in structures with energy dissipaters

The fixed-wall rectangular cavity flow problem is a classic problem that has been studied since the beginning of computational fluid mechanics. The present work aims to provide a numerical and computational solution of the Navier-Stokes equations using the finite difference method, applied to model the problem of a magnetorheological fluid in a rectangular cavity with a fixed wall in shock absorbers devices, used in civil structures that use energy dissipators.

Analogy between Thermodynamic Phase Transitions and Creeping Flows in Rectangular Cavities

An analogy is found between the streamline function corresponding to Stokes flows in rectangular cavities and the thermodynamics of phase transitions and critical points. In a rectangular cavity flow, with no-slip boundary conditions at the walls, the corners are fixed points. The corners defined by a stationary and a moving wall, are found to be analogous to a thermodynamic first-order transition point. In contrast, the corners defined by two stationary walls correspond to thermodynamic critical points. Here, flow structures, also known as Moffatt eddies, form and act as stagnation regions where mixing is impeded. A third stationary point occurs in the middle region of the channel and it is analogous to a high temperature thermodynamic fixed point. The numerical results of the fluid flow modeling are correlated with analytical work in the proximity of the fixed points.

Application of Lattice Boltzmann Method for fluid flow modelling of FSLDR domain

Abstract In this work Lattice Boltzmann method is used to solve the Four Sided lid-driven rectangular cavity flow (FSLDR) problem. The fluid is considered as incompressible. In the present problem all the four walls moves with a constant velocity. The left wall moves in positive y-direction, the right wall moves in negative y-direction. The top wall moves in positive x-direction and the bottom wall moves in negative x-direction. The aspect ratio of the cavity taken is 0.50. The present code is validated for single lid-driven cavity flow problem. Next, the study is extended to FSLSR problem. The position of vortex obtained are studied at Reynolds number Re=50, 100, 500, 1000. In addition to the primary vortex, two secondary vortices are also obtained. Thus, the present study shows that Lattice Boltzmann Method can be used to capture the details of vortex dynamics

Effect of three modes of linear thermal forcing on convective flow and heat transfer in rectangular cavities

The convective flow in rectangular cavities with different linear thermal forcing at the sidewalls is investigated by DNS (direct numerical simulation) in the present study. A non-finned cavity and a cavity with an adiabatic horizontal thin fin attached to the middle of both sidewalls are modelled. Three heating modes are considered and calculated, i.e. s < 0, s = 0 and s > 0 thermal forcing respectively and six Rayleigh numbers ranging from 1.15 × 108 to 3.68 × 109 are examined. It demonstrates that compared to the s = 0 case, which is the classic homogenously heating problem, the thermal boundary layer flow as well as the convective flow in the cavities is strengthened for the s < 0 heating mode and weakened for the s > 0 heating mode. It is found from the finned cavity calculation that, for all the three thermal forcing considered, significant flow oscillation is observed on top the thin fin which in turn causes strong disturbances in its downstream flow adjacent to the sidewalls. The present results suggest that compared to simply increasing the Rayleigh number of the flow, switching the heating mode to s < 0 is potentially a shortcut for the purposes of promoting the flow. However, it is further revealed that due to the existence of the so called neutral buoyant effect at the sidewalls, the heat transfer associated with the s < 0 scenario is lower than the other two heating modes.

Effects of an inserted circular cylinder on a steady lid-driven rectangular cavity flow

This paper provides numerical investigations of flow in a steady lid-driven cavity of depth to width ratio 1/3 containing a circular cylinder. The inner cylinder is treated using a direct-forcing immersed boundary method, and a project method is applied to solve the incompressible Navier-Stokes equations. Three different Reynolds numbers and positions of the cylinder are considered; for a lower Reynolds number, flow structures are weakly affected by the cylinder near the left wall while two clockwise vortices attached to the cylinder are formed as the cylinder moves rightwards; for a moderate Reynolds number, an anticlockwise bottom vortex is formed for the cylinder near the left wall, and it disappears as the cylinder is shifted rightwards; for the largest Reynolds number, two anti-clockwise vortices attached the cylinder are formed for the cylinder close to the left wall, and as the cylinder moves gradually closer to the left wall a bottom vortex is formed and disappears together with the clockwise vortex to the right side of the cylinder.

An efficient Legendre–Galerkin spectral element method for the steady flows in rectangular cavities

An efficient Legendre–Galerkin spectral element method for the steady flows in rectangular cavities is proposed in this paper. Firstly, we eliminate the singularity of biharmonic equation in rectangular cavity at the corner by the singularity substraction technique. Then we construct some appropriate interior basis functions and interface basis functions which maintain -continuity. Consequently, the discrete variational formulation is reduced to a linear system with block diagonal and well-conditioned coefficient matrix, which can be efficiently solved by the conjugate gradient iteration method. Finally, several numerical examples are given to show the effectiveness of our numerical method. The present method is used to solve the creeping flows in rectangular cavities, the numerical results are compared well with the benchmark steady solutions provided by the finite difference method.

Lattice Boltzmann computation of multiple solutions in a double-sided square and rectangular cavity flows

This paper uses Lattice Boltzmann computation to obtain multiple fluid flow solutions in square and rectangular cavity that involves movement of the facing and non-facing walls. For some aspect ratios the double-sided lid-driven cavity problem has multiple steady fluid flow solutions. In double-sided rectangular cavities, a single-relaxation-time model is used to over out Lattice Boltzmann computations in order to receive multiple fluid flow solutions. Three numerical examples are taken into consideration on this work. First one is double-sided square cavity with parallel wall movement, double-sided non-facing rectangular lid-driven cavity with parallel wall movement and the final one is the double-sided lid-driven rectangular cavity with antiparallel wall movement. When the walls move in pairs, multiple fluid flow solutions exist above critical Reynolds numbers. In the present work, five multiple solutions of parallel wall movement and seven multiple solutions of antiparallel wall movement is acquired. The boundary conditions used are stable and also correct. It might be inferred that the present mesoscopic Lattice Boltzmann study produces comes about that are in phenomenal similarity with prior customary numerical perceptions.

The three-dimensional characteristics of the unsteady wall-pressure in a low-Mach-number rectangular cavity flow with Rossiter model oscillation

This study is focused on examining the three-dimensional characteristics of the unsteady wall-pressure in a low-Mach-number rectangular cavity with Rossiter model oscillation. The effect of cavity width on the resonance is investigated as well. It is observed that not only the resonance magnitude but also the resonance frequency could be altered when the cavity width changes. As the cavity becomes narrow to W/L ≈1, the resonance frequency decreases substantially comparing to that for W/L >1. While for the narrowest cavity with W/L <1, the resonance frequency is the same as that for the wide cavity. Low-frequency disturbances grow stronger as approaching to the side walls. Instantaneous velocity magnitude measurement simultaneously with the unsteady wall-pressure shows the propagation of flow disturbances highly correlated with the pressure resonance. It is observed that for the cavity with W/L ≈1, the pressure resonance is highly correlated with a local propagation of disturbances near the cavity aft wall. The downstream convecting disturbances in the shear layer are found to be weaken in the cases of W/L ≈1. Meanwhile the convection velocity of shear-layer disturbances is decreased, which results in a decrease of the resonance frequency.

Characteristics of cylindrical cavities in a compressible turbulent flow

The characteristics of flow over rectangular cavities have been well documented. However, few studies have considered cylindrical cavity flows. For compressible cylindrical cavity flows, the type of cavity flowfield is dependent on the diameter-to-depth ratio (D/H), which is similar to the length-to-depth ratio for a rectangular cavity flow. For an open-type cavity flow (D/H≤6.14), there is a slight upstream influence and uniform static pressure distributions are observed inside the cavity; a small adverse pressure gradient ahead of the rear face and a downstream expansion. The leading- and rear-edge expansions are more significant for transitional- (D/H=8.60–21.00) and closed-type (D/H=43.00) cavities. The amplitude of surface pressure fluctuations increases toward the rear face, for all of the test cases, whereas an additional peak near the middle of cavity floor is observed for a closed-type cavity. Notably, the effect of freestream Mach number is pronounced only on the amplitude of peak pressure fluctuations near the rear wall. Similarities between a cylindrical cavity and a rectangular cavity for a compressible flow are also highlighted in this study.

The Effect of Yaw Angle on a Compressible Rectangular Cavity Flow

Experiments are performed to determine the characteristics of a compressible flow over yawed rectangular cavities for Mach numbers of 0.64, 0.70, and 0.83. The cavity’s length-to-depth ratio varies from 4.43 to 21.50 and the length-to-width ratio is unity. The yaw angle is 0°–45°. The upstream compression and downstream expansion near the front and rear corners of a cavity decrease when the value of the yaw angle increases. The amplitude of the fluctuating pressure is a maximum for an open cavity with a yaw angle of 15°. An increase in the yaw angle results in a reduction in the pressure fluctuations for both open and transitional cavities. In the span-wise direction, variations in the mean and fluctuating pressure are less significant than those in the chord-wise direction. The oscillating frequency of resonance varies slightly with the yaw angle, but the amplitudes for the power spectral density are significantly reduced when the yaw angle is larger than 30°. For lower Mach numbers, the lower mode plays an important role in self-sustained oscillations for an open cavity when there is an increase in the yaw angle.

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two- (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of $L/D=6$ is analyzed at a free stream Mach number of $M_\infty=0.6$ and depth-based Reynolds number of $Re_D=502$. In this study, we closely examine the influence of three-dimensionality on the wake-mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the instability characteristics of the wake-mode. Using the bi-global stability analysis with the time-average flow as the base state, we capture the global stability properties of the wake-mode at a spanwise wavenumber of $\beta=0$. To uncover spanwise effects on the 2D wake-mode, 3D DNS are performed with cavity width-to-depth ratio of $W/D=1$ and $2$. We find that the 2D wake-mode is not present in the 3D cavity flow for a wider spanwise setting with $W/D=2$, in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of $\lambda/D=0.5-2.0$ to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake-mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.

Use of an HOC scheme to determine the existence of multiple steady states in the antiparallel lid-driven flow in a two-sided square cavity

Though the existence of multiple steady states for the antiparallel lid motion is known only for two-sided rectangular cavity flows, this work demonstrates for the first time that such solutions exist for a square cavity as well if the Reynolds number (Re) exceeds the threshold value of 3202. To obtain accurate results a higher-order compact (HOC) scheme of spatially fourth- and temporally second-order accuracy is used. It is also known that multiple solutions exist at all aspect ratios for the parallel motion in a two-sided cavity above a certain Re value. Earlier computations for parallel and antiparallel lid motion have been carried out using non-compact schemes. In this work much care has been observed to carry out highly accurate computations using the HOC scheme to re-examine these cases as well. Tabulated values of various parameters serve as a means of comparison to determine the accuracy of other solution methods.

Numerical simulation with a Reynolds stress turbulence model of flow and heat transfer in rectangular cavities with different aspect ratios

Numerical simulation with a Reynolds stress turbulence model of flow and heat transfer in rectangular cavities with different aspect ratios

Scale effects on the performance of sawtooth spoilers in transonic rectangular cavity flow

An experimental study was conducted on the effectiveness of sawtooth spoilers at suppressing acoustic tones within a rectangular cavity with a length-to-depth ratio of five and a width-to-depth ratio of two, operating at a freestream Mach number of 0.71. Whereas previous research has focussed on the ratio of spoiler height to boundary-layer thickness (h/δ), this study also considers the effect of the ratio of cavity length to boundary-layer thickness (L/δ). Using a combination of unsteady pressure measurements and particle image velocimetry, it was established that consideration of the magnitude of both parameters is important when designing passive control methods for transonic cavities. A correlation was developed which suggests that in order to suppress fully the cavity tones, a critical spoiler height, hcr, is defined such that hcr/δ = 0.065 ≤ L/δ ≤ 0.082.

Effects of circular corners and aspect-ratio on entropy generation due to natural convection of nanofluid flows in rectangular cavities

In this paper, entropy generation induced by natural convection of cu-water nanofluid in rectangular cavities with different circular corners and different aspect-ratios were numerically investigated. The governing equations were solved using a finite volume approach and the SIMPLE algorithm was used to couple the pressure and velocity fields. The results showed that the total entropy generation increased with the increase of Rayleigh number, irreversibility coefficient, aspect ratio or solid volume fraction while it decreased with the increase of the corner radius. It should be noted that the best way for minimizing entropy generation is decreasing Rayleigh number. This is the first priority for minimizing entropy generation. The other parameters such as radius, volume fraction, etc are placed on the second priority. However, Bejan number had an inverse trend compared with total entropy generation. As an exception, Bejan number and total entropy number had the same trend whenever solid volume fraction increased. Moreover, Nusselt number increased as Rayleigh number, solid volume fraction or aspect ratio increased whereas it decreases with the increase of corner radius.

Oil Film Flow-State Analysis of Hydrostatic Vertical Guideway of CNC Vertical Lathe Rail Head

Hydrostatic lubricated vertical guideway is commonly used as a form of rail head bearing lubrication in CNC vertical lathe lubricated bearing. In order to improve the cutting performance of CNC equipment during machining, we have studied the hydrostatic vertical guideway with inner slide during the process of ram feed moving in this paper. The single rectangular cavity flow equation and velocity equation are derived. Numerical simulation of taking limit working conditions that the cutting force is taken byis studied by the Finite Volume Method (FVM). The flow field and velocity distribution of X direction and Y direction of hydrostatic vertical guideway are obtained by using quantitative method and supplying oil with a single chamber, with the inlet flow of 0.52L/min, with the film thickness of 0.023mm and the depth of oil cavity of . The mathematical model by theoretical derivation and the flow state regularity in limit working conditions are verified and revealed. The results of study above in this paper provide valuable theoretical basis for hydrostatic guideway design in practical projects.

Nonlinear Feedback Mechanisms Inside a Rectangular Cavity

An examination of a rectangular cavity with a length-to-depth ratio of 5.67 was tested at Mach 0.7 and 1.5 with corresponding Reynolds numbers of and , respectively. High-speed shadowgraph movies were simultaneously sampled with dynamic pressure sensors at 75 kHz. From the high-speed shadowgraph movies, observations of the cavity flowfield indicate that linear models like Rossiter’s equation and Helmholtz resonance may be too simplistic to correctly model rectangular cavity flow physics. Some of the observations are as follows. In the cavity’s shear layer, large-scale vortices have been found to be nonperiodic. The shear-layer convection velocity was determined to be at both Mach numbers, which is significantly higher than Rossiter’s equation predicts for correct peak frequency matching. Shear-layer entrainment of freestream flow starts and feeds the acoustic cycle inside the cavity. There are more acoustic wave in the cavity at any one time than has been considered before, which produce the discrete acoustic tones throughout the frequency spectrum.

Modal analysis of confined square and rectangular cavity flows

Particle image velocimetry (PIV) and common-base proper orthogonal decomposition (CPOD) were used to quantify the velocity field within the separated region of confined square and rectangular cavities with streamwise aspect ratios of one and two, respectively. For a constant Reynolds number of 60,000, the flow structure within the entire domain of the square cavity is dominated by a nominally two-dimensional primary vortex. The flow unsteadiness here is manifested in the rms distributions, which reveal significant contributions from the pseudo-fluctuations due to the meandering of the primary vortex core and from random unsteadiness. Comparisons were made to the backward-facing step geometry, and in contrast, for the rectangular cavity and backward-facing step, large-scale unsteady flow patterns, three-dimensional in character, are present in the velocity field. The formation of these unsteady events was identified through the realization of instantaneous velocity fields. In contrast to the square cavity, the CPOD analysis reveals the presence of a “shift mode” for the rectangular cavity, which results in spanwise variation throughout the entire flow field. As a conclusion, the unsteady behavior observed for both the rectangular-cavity and backward-facing-step flows is absent for the square cavity, which can be attributed to the strong coupling effect of the two vertical cavity boundaries at low streamwise aspect ratios. Furthermore, the spatio-temporal character of the rectangular cavity is shown to be more closely related to the backward-facing step than the square cavity.