Cavity Flow Research Articles

Influence of magnetic field on MHD mixed convection in lid-driven cavity with heated wavy bottom surface

This study investigates the influence of a rectangular heat source on magnetohydrodynamic hybrid convection flow in a lid-driven cavity. The effects of various parameters, such as the heat source size, magnetic field strength, and heat absorption/generation, are analyzed. The results show that increasing the heat source size decreases the average Nusselt number along the heated wall. The average Nusselt number also decreases with higher magnetic field strength and heat generation, while it increases with heat absorption. The major finding is to apply an important technique the Galerkin weighted residual technique of the finite element (FE) method to solve the non-dimensional equations and the associated boundary conditions. The isotherms are used to show the temperature distribution in a domain. Streamline present the flow field in the enclosure. However, it is easy to realize the direction and intensity of the heat transfer particularly in convection problems which the path of heat flux is perpendicular and the isotherm due to convection effect. Thus, the purpose of this research is to study the results of mixed convection. The effects of location and height of the partitions are considered for the various Richardson numbers. Fluid flow field, thermal field and heat transfer are presented through the streamlines and isotherms, respectively. Results are substantiated relating to the published work.

Comment on “Steady natural convection flows in a square cavity with linearly heated side wall(s)” [International Journal of Heat and Mass Transfer, 50 (2007) 766–775

The comment below addresses an inaccurate formulation in the calculation of the Nusselt number for linear heating as presented in the paper titled “Steady natural convection flows in a square cavity with linearly heated side wall(s)” by M. Sathiyamoorthy, T. Basak, S. Roy, and I. Pop, Int. J. Heat Mass Transfer 50 (2007) 766–775. Consequently, this analysis provides a mathematical reformulation for the local and mean Nusselt numbers of a linearly heated side wall. It regenerates a few quantitative results for a specific case solely intended for comparative purposes.

Convection heat transfer of MHD fluid flow in the circular cavity with various obstacles: Finite element approach

In the present research, a study has been conducted on a model to investigate magnetohydrodynamic (MHD) heat and mass transfer phenomena. In the geometry of this model, there is a circular cavity with a variable number of obstacles in each step. At each stage, some obstacles are heated, and its effect on fluid flow and heat transfer is investigated. Solving and developing partial differential equations is done using the finite element method. The effects of Rayleigh and Hartmann numbers on flow lines, isotherms, and equivalent concentrations have been investigated, and the output was displayed as contours and graphs. Finally, the Nusselt diagram is displayed. The main purpose of the present study is to evaluate the effect of changes in Rayleigh and Hartmann numbers in different geometries on its behavior. This particular flow configuration was chosen because of the fundamental role of magnetohydrodynamics and its widespread use in engineering, industry, and medicine. The findings of this research show that in almost all investigated geometries, the behavior of streamlines, isotherms, and isothermal concentrations is anti-symmetrical at X = 0.5. Also, with the heating of the upper obstacles, the total Nusselt number decreases, and with the heating of the lower obstacles, the total Nusselt number increases. The behavior of the total Nusselt number against the increase of the thermal radiation parameter is increasing, and as the number of obstacles inside the cavity increases, the total Nusselt number increases.

Large-eddy simulation of non-isothermal flow and heat transfer in an enclosed rotor–stator cavity

This paper presents a numerical study of non-isothermal flow and heat transfer in an enclosed rotor–stator disk cavity. Wall-resolved large-eddy simulation is implemented with attention focused on the Reynolds number effect (Reϕ=105 and 5×105) and non-isothermal effects, including different thermal Rossby numbers (βΔT=0.05–0.25) and heat convection types (axial heat convection, axial and radial heat convection). Verification and validation are implemented by comparing with available experimental data and examining the resolution of the present LES. Although the Batchelor flow type is unchanged, the non-isothermal effect is found to be responsible for the acceleration of flow in both disk boundary layers and cavity core. Temperature in the cavity is negatively correlated with the Rayleigh number. The radial inward temperature gradient is found to be responsible for destabilizing the flow near the cylinders, due to the effect of centrifugal buoyant force. Transition from laminar to turbulent is shown in the rotor boundary layer for Reϕ=5×105 conditions. The non-isothermal effect increases flow unsteadiness in both rotor and stator boundary layers, but it has little to no effect on the transition position, as well as the kinematic and thermal boundary layer thicknesses, which are mainly controlled by Reϕ. Spectral proper orthogonal decomposition is implemented to explore the Reynolds number effect. Analyzing the most energetic mode and its energy spectra provides some insights into the understanding of non-isothermal rotor–stator disk cavity flows.

Investigation of the effects of nasal surgery on nasal cavity flow using magnetic resonance velocimetry and computational fluid dynamics

The nasal cavity has the function of conditioning the air inhaled into the lungs by heating, humidifying, and filtering dust and virus-borne aerosols. Analyzing the flow field in the nasal cavity is vital because its function is strongly related to flow dynamics. Due to experimental limitations posed by the complex internal geometry of the nasal cavity, most previous studies have utilized Reynolds averaged Navier–Stokes based computational fluid dynamics (CFD) simulations. In this study, the flow field in a post-operative nasal cavity was evaluated using not only CFD simulations but also four-dimensional magnetic resonance velocimetry. The study was conducted under resting breathing conditions in pre- and post-operative models of a patient who received septoplasty and turbinoplasty. The experimental results confirmed balanced flow rates in the left and right nasal cavities after septoplasty and a decrease in velocity after turbinoplasty with a reduction in regions with vortices and reverse flow. Upon comparison, CFD results using the laminar, k–ω, and shear stress transport models were deemed to be consistent with the experimental results. However, there was a relatively large deviation observed with the k–ε model. Using the validated laminar CFD model, it was shown that the pressure and wall shear stress decreased after surgery.

Detached Eddy Simulations of Cavity-Store Interactions at Subsonic Turbulent Flow

Weapons bays have gained much attraction in the last decade, mainly in the context of next-generation aircraft. Although internal store carriage provides numerous advantages, aero-mechanical challenges still exist, particularly for safe store separation. Therefore, it is essential to gain fundamental knowledge of the flow field within weapons bays, which can be achieved by studying the flow within a more simplified geometry of a cavity. In this study, detached eddy simulations are performed using the Elastic-Zonal-Navier–Stokes-Solver (EZNSS) to characterize the unsteady turbulent flow within NASA’s benchmark rectangular cavity with a store model located at various positions. Simulations are performed at a Mach number of 0.4 and a Reynolds number of 7 million to form a transitional cavity flow, which is common in jet-fighter weapons bays. The numerical results are validated with experimental data for the empty cavity and cavity-with-store configurations. The effect of the store’s position on the cavity flow characteristics is analyzed and verified, as well as the aerodynamic loads exerted on the store. Results show a complex interaction between the store model and the cavity flow field, manifested by distortion of the wall pressure fluctuations and mean flow structures and large amplitude fluctuations of the loads exerted on the store. The insights reported herein can serve future development efforts of more accurate numerical frameworks for cavity-with-store configurations towards improving their applicability for weapons bays store separation in certification procedures.

РАСЧЁТ КОМБИНИРОВАННОЙ КОНСТРУКЦИИ ЖИДКОСТНОКОЛЬЦЕВОГО ВАКУУМНОГО НАСОСА

Liquid ring vacuum pumps are widely used in many areas of the agro-industrial complex, in particular for milking processes, storage of plant materials, their drying and extraction, as well as pneumatic transport. It has been revealed that one of the main disadvantages of liquid ring vacuum pumps - low efficiency (25-50%) is often caused by hydraulic losses during rotation of the liquid ring on a stationary body, as well as inaccurate physical prerequisites in the equations describing the movement of the liquid ring - a two-phase turbulent flow in the working pump cavity. As a consequence, the pump engineering calculation method leads to overestimated performance characteristics at the design stage. In this regard, a combined design of a liquid ring vacuum pump with a rotating casing has been proposed, in which rotation can be transmitted from the impeller blades to the casing blades (in the case of low and medium speed pump size), through involute engagement, or from the casing blades to the impeller blades (in in case of high and especially high speed of action). The basis for calculating the liquid ring is the continuity equation, the stability condition of the liquid ring and the threshold for the occurrence of cavitation phenomena, as well as a coefficient characterizing the drop in speed for turbulent motion in a bladeless space in areas (suction, maximum, compression, discharge). In this case, the mechanism of movement of the liquid ring in the working cavity of the pump is represented by physical processes in the form of the interaction of two power flows: the hydraulic flow of the working fluid and the thermodynamic flow of the gaseous medium. When calculating the main operating parameter of the pump - the actual speed of action - the evaporation of liquid droplets due to changes in the temperature of the liquid ring was taken into account. The forces acting on the rotating wheel and the rotating body of the combined design of a liquid ring vacuum pump are determined analytically.

Noise Prediction and Plasma-Based Control of Cavity Flows at a High Mach Number

Cavity flows are a prevalent phenomenon in aerospace engineering, known for their intricate structures and substantial pressure fluctuations arising from interactions among vortices. The primary objective of this research is to predict noise levels in high-speed cavity flows at Mach 4 for a rectangular cavity characterized by an aspect ratio of L/D = 7. Moreover, this study delves into the influence of the plasma actuator on noise control within the cavity flow regime. To comprehensively analyze acoustic characteristics and explore effective noise reduction strategies, a computational fluid dynamics technique with the combination of a delayed detached eddy simulation (DDES) and plasma phenomenological model is established. Remarkably, the calculated overall sound pressure level (OASPL) and plasma-induced velocity closely align with the experimental data, validating the reliability of the proposed approach. The results show that the dielectric barrier discharge (DBD) plasma actuator changes the movement range of a dominating vortex in the cavity to affect the OASPL at the point with the maximum noise level. The control of excitation voltage can reduce the cavity noise by 2.27 dB at most, while control of the excitation frequency can only reduce the cavity noise by 0.336 dB at most. Additionally, the increase in excitation frequency may result in high-frequency sound pressure, but the influence is weakened with the increase in the excitation frequency. The findings highlight the potential of the plasma actuator in reducing high-Mach-number cavity noise.

Closed-Loop Cavity Shear Layer Control Using Plasma Dielectric Barrier Discharge Actuators

The complex unsteady flow in cavities leads to the formation of large-scale disturbances in the shear layer. Natural closed-loop mechanisms provoke a dramatic increase in pressure pulsations and aerodynamic noise. This paper presents the experimental study of pressure fluctuations in closed-loop control in rectangular cavities using plasma dielectric barrier discharge. The flow velocity was 37 m/s, and the Reynolds number based on a cavity depth was approximately 120,000. The discharge ignition near the leading edge of the cavity provoked the shear layer restructuring. It was found that pressure fluctuations with an amplitude of 120 dB occur at frequencies 480 and 820 Hz. Frequency modulation of the discharge at resonant peaks was carried out by changing the phase shift of the power supply. The peak amplitude was reduced or increased by phase shifts from natural disturbances to forced ones. The optimum energy input was 50 W/m. This was three times less than the power consumption of the open-loop mode. The PIV visualization was organized in the phase-locked mode. The pressure spectrum corresponds to the magnitude of coherent structures in the shear layer of the cavity.

Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems

For linear and nonlinear systems arising from the discretization of PDEs, multiplicative Schwarz preconditioners can be defined based on subsets of the unknowns that derive from domain decomposition, field splitting, or other collections of conveniently solved subproblems, and are well established theoretically for nonoverlapping subsets. For overlapping subsets, establishing the equivalence of the preconditioned and original iterations is less trivial. We derive herein an explicit formulation for a variety of multiplicative Schwarz preconditioners including overlaps representative of interfacial and bulk coupling in multiphysics systems, thus extending theoretical support for the nonlinear multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm to these classes. For nonlinear multiplicative Schwarz preconditioners with overlaps, we illustrate the performance through numerical experiments involving applications such as a shocked duct flow and a natural convection cavity flow. We begin with a broad introduction to nonlinear preconditioning to set the context for those new to the technique.

Effects of various aftwall edge ramp on open cavities in a confined supersonic flow

An experimental study on the supersonic flow of Mach number 1.81 Over the rectangular cavity of L/D = 3 with different aft wall angles such as Baseline case 90° and aft wall edge ramp of 30°. Measurements of acoustic oscillations were carried out on the wall and floor of the cavity using unsteady pressure transducers. Schlieren flow visualization indicates the presence of a shear layer and the other shock features that are associated with the cavity flow field. In order to obtain the experimental results, data analysis was performed in the unsteady data Using statistical analytical techniques i.e., Fast Fourier Transform, Short Time Fourier Transform, and Coherence. After careful examination of the power spectra of the cavities, it is concluded that as the aft wall angle decreases by introducing the aft wall ramp, the amplitude decreases. It is clearly observed that the complete escape of vortices in Low angled cavity. From the correlation plot, the existence of the acoustic wave inside the cavity for all the cases is deduced. The maximum OASPL and static pressure values are observed at the aft wall. These results, the strength of the self-sustained oscillations and acoustic disturbance and mode switching were observed in the higher angled cavity 90°. Also, the mode switching co-existence was reduced in the aft wall edge ramp angle of 30°.

Fluid Structure Interaction Analysis of Natural Convective Flow and Heat Transfer in an L-Shaped Cavity

The primary objective of this research work is to perform a numerical study on the fluid-structure interaction (FSI) of flow and heat transfer characteristics within an L-shaped cavity. The investigation will focus on analyzing the effects of various key variables, namely the Rayleigh number and wall elasticity, on the observed results. To accomplish this, the COMSOL software, which utilizes the finite element method, will be employed as the numerical simulation tool. To ensure the reliability and credibility of the obtained results, the findings of this research were rigorously validated against previously published data available in the literature. The outcomes of this investigation were presented using various visualization techniques. Streamlines, temperature contours, and heat transfer enhancement will be among the visual representations used to illustrate the flow and temperature distribution within the L-shaped cavity. Anticipated results indicated that the calculations of the average Nusselt number exhibited a strong dependency on the Rayleigh number and the wall elasticity. As such, the average Nusselt number was higher for flexible wall compared to rigid wall model. Moreover, the average Nusselt number was found to increase with an increase in Rayleigh number. Young’s modulus was found to have a profound effect on the patterns of the streamlines. The average Nusselt number was found to decrease with an increase in the Young’s modulus. This study may provide valuable insights into optimizing heat transfer and designing efficient thermal management systems for various practical applications.

A mesoscopic model approach for polar fluid flow

In this paper we propose a mesoscale model for polar fluids and numerically investigate its validity by considering well known benchmark cases: the steady and unsteady Poiseuille and the low Reynolds lid-driven cavity flow. Analytical and numerical results are compared with our numerical results and a very good agreement is found. Then we consider not yet investigated high Reynolds lid-driven cavity flow cases, obtaining consistent and interesting results, which encourage to apply the proposed model to more complex cases.

Entropically damped artificial compressibility for the discretization corrected particle strength exchange method in incompressible fluid mechanics

We present a consistent mesh-free numerical scheme for solving the incompressible Navier–Stokes equations. Our method is based on entropically damped artificial compressibility for imposing the incompressibility constraint explicitly, and the Discretization-Corrected Particle Strength Exchange (DC-PSE) method to consistently discretize the differential operators on mesh-free particles. We further couple our scheme with Brinkman penalization to solve the Navier–Stokes equations in complex geometries. The method is validated using the 3D Taylor–Green vortex flow and the lid-driven cavity flow problem in 2D and 3D, where we also compare our method with hr-SPH and report better accuracy for DC-PSE. In order to validate DC-PSE Brinkman penalization, we study flow past obstacles, such as a cylinder, and report excellent agreement with previous studies.

Multiscale model reduction for incompressible flows

We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.

Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation

As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.

Natural convective Power law fluid flow in a crown cavity with heated cylinder: Application to energy transfer

The present study investigates heat transfer characteristics of power law fluid flow and energy transfer in a crown cavity with adjustment of the heated cylinder. The flow distribution is generated by the response of the heated cylinder. Additionally, the enclosure is partially adiabatic and the influence of cold interfaces is also taken. This whole setup generates a partial differential system in its mathematical translation. The numerical simulation is performed for the mathematical formulation by adopting the Galerkin Finite element method. The obtained results are analyzed against pertinent parameters of interest and presented via line graphs and contour maps for better explanation. The findings indicate that the K.E (energy motion) and Nu (Nusselt number) are higher for shear thinning While K.E energy motion) and Nu (Nusselt number) are higher is minimum for shear thickening.

An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

Natural convection of nanofluid flow in a porous medium in a right-angle trapezoidal enclosure: a Tiwari and Das’ nanofluid model

The study uses Tiwari and Das’ nanofluid model to present a study on free convective flows in a right-angled trapezoidal cavity that is saturated with a porous bed and filled with Cu-water nanofluid material. This investigation aims to enhance the characteristics of hybrid fuel cells and energy depository devices by analysing the cavity's heat expansion and fluid flow properties. In trapezoidal enclosures, the inclined and right wall portions are maintained at different isothermal temperatures at all times. Finite difference-based stream function-vorticity numerical simulations are employed to carry out this analysis. The outcomes have been presented for isotherms, streamlines, and Nusselt numbers concerning nanoparticle volume fraction, Darcy number, and various Rayleigh numbers. It is found that the inverse relationship between the thermal Rayleigh number and the nanofluid’s volume has a significant impact on the average Nusselt number.

Experimental investigation on tip vortex cavity deformation and flow dynamics using high-speed imaging and laser Doppler velocimetry measurements

Cavitation affects engineering applications relating to aquatic operations. Tip vortex cavitation (TVC) leads to several technical problems, such as efficiency loss and noise. Hence, there is a need for a comprehensive understanding of the formation mechanism, shape distortions, and underlying physical phenomena of TVC. The dispersion relation of inertial waves on inviscid cavitating vortices is a valuable tool for predicting various TVC shapes. This study explains the patterns of flow around the tip of an elliptical foil and the cavity shape deformations under different flow conditions through experimental analysis. Experiments are conducted using a National Advisory Committee for Aeronautics hydrofoil in the cavitation tunnel at Chungnam National University. The appearance, development, and shapes of vortex cavitation are closely examined using high-speed imaging technology. There is good agreement between the vortex cavity shapes captured by this high-speed imaging and those derived in previous studies. Using laser Doppler velocimetry (LDV) measurements and analysis through image processing of high-speed images, we compare the vortex core trajectories in cavitating and non-cavitating conditions. There is a good match between the two, demonstrating the feasibility of predicting the flow behaviors around vortex cavities using LDV data. As the noise from the TVC is considered a significant source of underwater radiated noise we also measured sound pressure level, which exhibits abrupt changes at specific cavitation numbers, supporting the occurrence of the singing vortex phenomenon and highlighting its sensitivity to small variations in flow conditions. Furthermore, we obtain precise measurements of the instantaneous TVC diameter under different cavitation numbers, allowing the physical functionality of distinct TVC shapes to be determined. Our results significantly extend the scientific understanding of the flow around TVC and the fundamental causes of TVC distortions.