Cavity Flow Research Articles

Theoretical Developments for the Interpretation of Cavity Flow Permeability Tests Conducted on Intact Lac du Bonnet Granite

The permeability of intact geologic media features prominently in many geo-environmental endeavours. The laboratory estimation of permeability is an important adjunct to the field estimation of bulk permeability values, which involves a great deal of supplementary in situ investigations to correctly interpret field data. Laboratory permeability estimation is also a viable method if core samples are recovered from in situ geological mapping of the region under study. The basic methodologies for permeability estimation rely on either steady-state or transient tests of the geologic material depending on the anticipated permeability value. This paper presents a steady flow test conducted on a partially drilled cavity located on the axis of a cylindrical specimen. Certain compact theoretical relationships are proposed for the estimation of steady flow from a cavity of finite dimensions located along the axis of a cylindrical specimen. The relationships are used to estimate the permeability of a cylinder of Lac du Bonnet granite obtained from the western flank of the Canadian Shield. The results from the cavity flow permeability experiments are compared with other estimates for the permeability of granitic rocks reported in the literature.

Efficient Scale-Resolving Simulations of Open Cavity Flows for Straight and Sideslip Conditions

This study aims to facilitate a physical understanding of resonating cavity flows with efficient numerical treatments of turbulence. It reinforces the efficiency and affordability of scale-adaptive numerical techniques for simulating open cavity flows with a separated shear layer consisting of a wide range of flow scales. Visualization of the resonant modes occurring due to the acoustic feedback loop aids in a better understanding of large-scale flow oscillations. Under this scope, scale-adaptive simulation (SAS) based on the k-ω SST RANS model with different turbulence treatments has been studied for an open cavity configuration with a length-to-depth (L/D) ratio of 5.7 featuring Mach number (Ma) 0.8 and Reynolds number (Re) 12×106. It is shown that the essential cavity flow physics has been captured using the SAS approach with more than 90% improved computational efficiency compared to commonly used hybrid RANS-LES approaches. In addition, wall-modeled SAS when supplemented with an artificial forcing concept to trigger the model provides very good spectral estimates comparable with hybrid RANS-LES results. Following the validation of numerical approaches, the directional dependence of the cavity resonance is investigated under asymmetric flow conditions, and spanwise interference of waves due to the lateral walls of the cavity has been observed.

The convexity for compressible subsonic cavity flows

AbstractIn this paper, we first show that the flow velocity takes its maximum on the free boundary, provided that the nozzle wall and obstacle satisfy some corresponding geometric assumptions. Second, the convexity of the free boundary to the compressible subsonic cavity flows will be established. Finally, the optimal regularity of the free boundary at the detachment point is obtained.

Solution of conservative-form transport equations with physics-informed neural network

Physics-informed neural network (PINN) has recently gained significant attention in the field of scientific computing. This paper proposes a PINN framework for solving conservative-form transport equations (PINNforCTE). The PINNforCTE features an accelerated back-propagation in the neural network (NN) training due to low-order derivatives in the governing equations. We demonstrate the application of PINNforCTE in simulating a classical flow and heat transfer problem, i.e., the lid-driven cavity flow and heat transfer under three types of boundary conditions, and the simulation results are compared with those obtained from the traditional PINN and the finite element CFD method. The comparisons indicate that PINNforCTE can significantly accelerate the NN training and potentially shorten the solution time. For all cases considered, the training time of PINNforCTE is reduced by approximately ∼50% compared with the conventional PINN. Furthermore, PINNforCTE can accelerate the Adam optimization algorithm (L-BFGS-B optimization algorithm) by ∼100% (∼80%) compared to the traditional PINN. Additionally, PINNforCTE shows greater convenience in applying the Neumann and Robin boundary conditions directly and higher calculation accuracy than the conventional PINN. Finally, the ability of PINNforCTE to solve the inverse problems is confirmed with an example of 2D steady lid-driven cavity flow and heat transfer. PINNforCTE is an efficient NN solver for conservative-form transport equations (CTEs) that are ubiquitous in science and engineering.

Rotational Flows in Solar Coronal Flux Rope Cavities

We present a 2.5D magnetohydrodynamic simulation of a systematically rotating prominence inside its coronal cavity using the open-source MPI-AMRVAC code. Our simulation starts from a nonadiabatic, gravitationally stratified corona, permeated with a sheared arcade magnetic structure. The flux rope (FR) is formed through converging and shearing footpoints driving, simultaneously applying randomized heating at the bottom. The latter induces a left–right asymmetry of temperature and density distributions with respect to the polarity inversion line. This asymmetry drives flows along the loops before the FR formation, which gets converted to net rotational motions upon reconnection of the field lines. As the thermal instability within the FR develops, angular momentum conservation about its axis leads to a systematic rotation of both hot coronal and cold condensed plasma. The initial rotational velocity exceeds 60 km s−1. The synthesized images confirm the simultaneous rotations of the coronal plasma seen in 211 and 193 Å and condensations seen in 304 Å. Furthermore, the formation of the dark cavity is evident in 211 and 193 Å images. Our numerical experiment is inspired by observations of so-called giant solar prominence tornadoes and reveals that asymmetric FR formation can be crucial in triggering rotational motions. We reproduce observed spinning motions inside the coronal cavity, augmenting our understanding of the complex dynamics of rotating prominences.

Thermogravitational magnetonanofluid flow in a square cavity with isotropic heat flow field and viscous dissipation: A compact approach

In this paper, thermogravitational flow in a square enclosure filled with Cu-water nanofluid which is influenced by inclined magnetic induction, has been mathematically modelled. Isotropic heat flow field and viscous dissipation effects are introduced in the modelling as well. The vertical walls of the domain are subjected to finite temperature gradient while the horizontal walls are thermally insulated. The control equations subject to the flow physics of an incompressible, viscous and electrically conducting fluid are the Navier-Stokes equations along with energy equation. These governing equations are solved numerically by proposing a fourth order compact scheme. The influences of diverse effective parameters including Hartmann number, viscous dissipation parameter (Eckert number) and heat generation or absorption parameter on characteristic features of heat transfer and fluid flow with different concentration distributions of nanoparticles are analyzed and addressed in detail. Results show that the presence of viscous dissipation retards the thermal diffusion process. The average Nusselt number values are decreased with the increasing values of Eckert number. In addition, with the increasing values of Hartmann number, the thermal transport is decreased in spite of incorporation of isotropic heat flow.

An improved MRT-LBM and investigation to the transition and periodicity of 2D lid-driven cavity flow with high Reynolds numbers

An improved MRT-LBM and investigation to the transition and periodicity of 2D lid-driven cavity flow with high Reynolds numbers

Experimental investigation of passive control for cavity noise in high-speed flow using sawtooth spoiler

The aerodynamic noise from cavity flow poses an increased risk of fatigue fracture for structures in aeronautic engineering. To address this concern, a passive control device in the form of sawtooth spoiler was positioned at the leading edge of a rectangular cavity during wind tunnel tests at Ma 0.9 and 1.5. The results obtained by pressure measurements indicated maximum reductions in both the overall sound pressure level of 9.5 dB and 4.3 dB and the tonal amplitude of approximately 18 dB and 12 dB under the two test conditions. Through the implementation of the fluorescent oil flow technique, it was verified that the lifting of shear layer is still the dominant mechanism for the reduction of cavity noise in high-speed flow. Additionally, analysis of the oil flow images observed at Ma 1.5 revealed that the local separation on the bottom wall of the controlled cavity contributed to an increase in high-frequency tonal amplitudes. Moreover, the study delved into the effects of three sawtooth parameters, namely tooth angle, tooth height, and total height. The conclusive finding was that the total height emerged as the decisive parameter influencing the performance of the sawtooth spoiler in noise control.

Mean pressure gradient effects on the performance of ramjet cavity stabilized flames

Premixed cavity stabilized flames are experimentally investigated in a high-speed ramjet engine under the influence of varying mean pressure gradients. The ramjet cavity incorporates a backward facing step with an aft ramp for flame stabilization in high Reynolds number. The ramjet engine is subject to varying wall geometry to form converging, diverging, and nominal configurations in order to investigate the effects of mean pressure gradients on engine performance. High-speed particle image velocimetry (PIV) and chemiluminescence imaging diagnostics are simultaneously employed to capture the reacting flow fields and flame dynamics. Imposing a larger favorable pressure gradient is shown to shrink the recirculation zone and alter shear layer dynamics, which leads to increased drag on the cavity. Additionally, inducing a stronger favorable pressure gradient is shown to excite a shear layer instability mode, characterized by a Strouhal number of St=0.1. Proper orthogonal decomposition (POD) results reveal that the instability mode is comprised of large-scale oscillations that occupy the entire cavity flow region, indicating that the excited oscillations are the manifestation of a global vortex shedding instability that occurs under non-reacting conditions. The results demonstrate that the performance and stability of the ramjet cavity flame can be influenced by the mean pressure gradient, which is vital for the design of high-speed air-breathing propulsion systems such as dual-mode scramjets.

Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

A multi-degree-of-freedom (MDOF) kinetic model is developed to simulate three-dimensional nonequilibrium flows. By modifying collision term of Boltzmann model equation, a multi-scale molecular collision mechanism with translational, rotational and vibrational degrees of freedom is indicated by three coupled relaxation processes. Molecular vibration is modeled by harmonic oscillator. As a result, the degree of freedom of vibration may be directly related to temperature. Internal energy of various degrees of freedom are computed based on the equipartition theorem, and equilibrium distribution functions for each relaxation step are calculated. The present MDOF kinetic model is beneficial for assessing multi-scale evolutions of internal energy and molecular inelastic collisions. Several three-dimensional flow cases, including lid-driven cavity flow and hypersonic flows around a blunt cone at varying angles of attack, are simulated using the current MDOF technique. All numerical results were consistent with the reference data. It was shown that the proposed MDOF kinetic model well explains the vibration–rotation-translation energy exchange of polyatomic molecules in high-temperature gas, and that the current computational technique is a useful engineering tool for nonequilibrium aerodynamic research.

Application of Weighted Least Squares Meshless Method to Incompressible Flows

Meshless methods have been successfully applied to solve a large number of inviscid and viscous compressible flows in both two and three dimensional flow fields. However, the conventional methods of solution for compressible flow equations cannot be applied to incompressible flow equations. This is due to the basic difference in the nature of the pressure variable in the compressible and incompressible flows. Pressure acts as a thermodynamic variable in case of compressible flows and can be easily updated by using the equation of state. In contrast, in case of incompressible flows, the pressure is merely responsible for enforcing the incompressibility constraint and hence cannot be updated by the equation of state. This has led to the development of numerical methods based on Helmholtz Decomposition to solve for the fluid flows in the incompressible flow regimes. Here, we have applied weighted least squares meshless method to solve for the flows in the incompressible flow regime using the projection method based on Helmholtz Decomposition. The standard test cases of two dimensional lid driven cavity flow at Reynolds numbers of 100, 400 and 1000 have been solved using the weighted least squares meshless method. A good match between the results of the test case using the meshless methods and conventional CFD methods for the solution of the incompressible flows has been obtained.

Non-uniform Compact Schemes for Parallel Computing

Here, the performance of a sixth order accurate Non-Uniform Compact Scheme (NUCS6) in a parallel framework using the domain decomposition method is analyzed. Traditional compact schemes are used for uniform grids. However, study of flows involving complicated geometries requires transformation of computational domain onto a uniform grid. Compact schemes developed for physical plane computations eliminate the need for such grid transformations. The first successful implementation of uniform compact schemes on a parallelized framework with Schwartz domain decomposition demonstrated the effect of overlap points in eliminating spurious signals at inter-processor boundaries Sengupta et al. [Jour. Comp. Phy. 220 (2007)]. This paper presents the performance of a high order non-uniform compact scheme (NUCS6) in parallel computations with the domain decomposition method. The results of the benchmark problem of flow in a 2D square lid-driven cavity at post-Hopf bifurcation Reynolds number of 10000 is presented to show how the width of overlap region affects the growth and evolution of gyrating polygonal vortex at the centre of the cavity.

Natural convection and entropy generation in a trapezoidal region with hybrid nanoliquid under magnetic field

PurposeThis paper aims to study numerically the steady natural convective heat transfer of a hybrid nanosuspension (Ag-MgO/H2O) within a partially heated/cooled trapezoidal region with linear temperature profiles at inclined walls under an effect of uniform Lorentz force. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates.Design/methodology/approachThe governing equations formulated using the Oberbeck–Boussinesq approach and single-phase nanoliquid model are transformed to a non-dimensional form by using non-dimensional variables. The obtained equations with appropriate boundary conditions are resolved by the finite difference technique. The developed code has been validated comprehensively. Analysis has been performed for a wide range of governing parameters, including Rayleigh number (Ra = 105), Prandtl number (Pr = 6.82), Hartmann number (Ha = 0–100), magnetic field inclination angle (φ = 0–?/2) and nanoparticles volume fraction (φhnf = 0 and 2%).FindingsIt has been shown that inclined magnetic field can be used to manage the energy transport performance. An inclusion of nanoparticles without Lorentz force influence allows forming more stable convective regime with descending heat plume in the central zone, while such a regime was performed for clear fluid only for moderate and high Hartmann numbers. Moreover, the average overall entropy generation can be decreased with a growth of the Hartmann number, while an addition of hybrid nanoparticles allows reducing this parameter for Ha = 30 and 50. The average Nusselt number can be increased with a growth of the nanoparticles concentration for low values of the magnetic field intensity.Originality/valueGoverning equations written using the conservation laws and dimensionless non-primitive variables have been resolved by the finite difference approach. The created numerical code has been verified by applying the grid independence test and computational outcomes of other researchers. The comprehensive analysis for various key parameters has been performed.

Magnetic field impact on double diffusive mixed convective hybrid-nanofluid flow and irreversibility in porous cavity with vertical wavy walls and rotating solid cylinder

Mixed convective heat transfer due to rotating surface has sustainable importance in improving cooling efficiency of thermal engineering equipment. In this investigation, hydromagnetic double diffusive mixed convection in a wavy porous cavity filled with hybrid nanofluid having rotating heat source is numerically studied. A solid cylindrical rotating heat source is positioned at the center of the wavy cavity. The fluid domain inside the cavity is heated from the rotating heat source and partially heated bottom wall. The governing partial differential equations are simulated using finite element method. The computational technique is validated performing rational comparisons. The results indicate that the pattern of streamlines circulation, isotherms and local entropy generation are significantly influenced with the rotating heat source. The flow velocity is observed increasing rapidly with cylinder rotation speed which is maximized with increasing cavity porosity and permeability but minimized with magnetic field impact and amalgamating hybrid nanoparticles. Heat transfer enhancement is found increasing by 682.07% with rotating heat source for varying Darcy number (Da = 10−4 to 10−1) in absence of magnetic field (Ha = 0) which reduces to 504.02% in presence of magnetic field (Ha = 100). Moreover, 45.62% heat transfer enhancement is achieved for varying of cavity porosity (ε = 0.3 to 0.9) which declines to 22.83% in presence of magnetic field (Ha = 100). In addition, 90.04% more heat transfer enhancement is estimated in hybrid nanofluid of 5% volume fraction than base fluid water. The entropy generations components are affected significantly with higher values of physical parameters. The Bejan number is found declining for all influential parameters studied. Accordingly, the study has significant impact on the controlling and optimizing of fluid flow and heat transfer in hybrid nanofluid filled improved designing and is applicable in improving the performance of thermal equipment such as high-performance heat exchangers, electronic device cooling, energy storage systems, thermal mixing, space thermal management, crystal growth, float glass production, solidifications, solar technologies, and reactor safety devices, etc.

Active control of pressure fluctuations in an incompressible turbulent cavity flow

Large-eddy simulations of incompressible turbulent boundary layer flows over an open cavity are conducted to investigate the effects of wall-normal steady blowing on the suppression of pressure fluctuations on the cavity walls. The length (L) to depth (D) ratio (L/D) of the cavity is 2 and the Reynolds number based on the cavity depth (ReD) is 12,000. Wall-normal steady blowing is imposed through a limited transverse slot in an upstream region of the cavity leading edge while varying the momentum coefficient (Cμ). As the value of Cμ increases, the pressure fluctuations on the cavity walls decrease mostly due to weakened impingement of turbulent vortical structures residing in the shear layer on the aft wall by lifting effects, reaching a maximum reduction of −7.61% compared to a baseline when Cμ=0.015. However, as the value of Cμ increases further, the pressure fluctuations increase gradually, exceeding that of a baseline when Cμ>0.05. Because intensified turbulent vortical structures in the shear layer with an increase of Cμ lead to strong interactions of small-scale vortices with the cavity walls with an accompanying large motion of the primary recirculation zone within the cavity, additional pressure fluctuations generated on the cavity walls deteriorate the control performance due to the blowing.

Numerical Study of Natural Convection Flow in Rectangular Cavity with Viscous Dissipation and Internal Heat Generation for Different Aspect Ratios

Numerical simulations have been performed to investigate the influence of constant volumetric heat generation and viscous dissipation on the unsteady natural convection flow of an incompressible Newtonian fluid contained in a rectangular cavity. The left vertical wall of the cavity is cooled, while the right vertical wall is heated, and the bottom and top walls are adiabatic. A numerical technique based on the implicit finite difference method (IFDM), along with an upwind finite difference scheme and an iterative successive over relaxation (SOR) technique, is employed to solve the governing equations numerically. The effect of physical parameters, namely the modified Rayleigh number (103≤Ra≤107), aspect ratio (1≤A≤4), Prandtl number (Pr=0.7, 1.0, 6.2, 15), volumetric internal heat generation parameter (Qλ=0, 1), and Eckert number (0≤Ec≤10−6), on the streamlines and isotherms are discussed graphically. Variations of maximum stream function, as well as average and local Nusselt number, are also discussed. The results show that the increase in Eckert number from 0 to 10−4 causes the average heat transfer to decrease, while Pr=0.71, Ra=104, and Qλ=0. Additionally, the average heat transfer decreases as the cavity width increases from 1 to 4, while Pr=0.71, Ra = 5×104, Ec=10−6 and Qλ=1. The results of the numerical model used here are in excellent accord with earlier findings.

Numerical computation on MHD natural convective ternary nanofluid flow and heat transfer in a porous square cavity: Marker-and-cell technique

PurposeThe analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.Design/methodology/approachThe cavity inclination angle is fixed ω = 0 in case (I) and in case (II). The traditional fluid is water, and is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.FindingsThe average heat transfer rate is computed for four combinations of ternary nanofluids: and under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.Practical implicationsThe purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.Social implicationsThe current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.Originality/valueTo the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.

A numerical framework for low-speed flows with large thermal variations

In the numerical simulation of fluid dynamic problems there are situations in which low-speed flows exhibit a non-negligible density variation driven by thermal or compositional distributions. A new method for solving the Low Mach Number equations governing such flows is developed. The basis of the formulation is the semi-implicit scheme build on the Non-oscillatory Forward-in-Time integrator encompassing Multidimensional Positive Definite Advection Transport Algorithm and a robust Krylov solver. The spatial discretisation is constructed using the median dual finite volumes and the method is second-order-accurate in space and time. A collocated arrangement of all flow variables is implemented. The validity of the presented method is evaluated using the Differentially Heated Cavity flows. Three-dimensional simulations demonstrate its efficacy and ability to capture the Non-Oberbeck–Boussinesq effects. Ideally, a numerical method should be able to treat different flow regimes without strong limitations. When implemented, it is shown that in the limit of small density variations the new formulation correctly reproduces simulations of incompressible flows subject to the Oberbeck–Boussinesq approximation. Furthermore, the three-dimensional computations set to the quasi-two-dimensional cases are in excellent agreement with the established two-dimensional Differentially Heated Cavity benchmarks.

Numerical investigation of multistage cavity shedding around a cavitating hydrofoil based on different turbulence models

Multistage shedding in cavity flow processes is a challenging and crucial topic in cavitating flows. This paper employs three different turbulence models to obtain a more comprehensive understanding of the physical details of multistage shedding in compressible cavitating flows and compare the differences between the turbulence models. The study employs the Schnerr-Sauer cavitation model in combination with the volume of fluid (VOF) method to capture the details of the unsteady cavitating flow around NACA66. The results are compared to experimental data and validate the numerical method. The study reveals that the primary shedding process is dominated by the re-entrant jet mechanism, whereas the pressure wave mechanism dominates the second shedding process. The second shedding process generates multiple pressure waves that disrupt the stable vortex structure of the sheet cavity. Furthermore, wavelet analysis indicates that the higher-order coherent structure mainly originates from the second shedding stage, and the second shedding process is shorter than the primary shedding process. The study proposes the segmented dynamic mode decomposition (SDMD), which obtains the mode characteristics at different time scales within one cycle. Under the RANS model, the small-scale cavity collapse and vortex structure cannot be observed during the second shedding process. However, the LES model can predict more realistic multi-scale flow field information.

Study of a non-reacting hypersonic flow over an external cavity with flow injection using DSMC method

In the current study, a DSMC solver is utilized to study a rarefied external cavity flow. The main focus of this research is mainly on the properties of flow near the rear wall of the cavity. It is observed that the flow temperature near the wall increases by increasing the free stream Mach number. Also, the cavity length-to-depth (L/D) ratio affects the flow structure dramatically in a constant Mach number. Injection from the rear wall of the cavity is studied. Results show that injection does not affect cavity vortex location. Local density and x-velocity increase is observed at the point of injection. Nonmonotonic y-velocity behavior is seen as a result of cavity vortex interaction with low-momentum injection fluid. Dimensionless temperature is decreased significantly due to injection. So, it can be treated as a remedy to decrease surface heat transfer coefficient. No significant impact is seen on the wall pressure coefficient and friction coefficient due to injection. The average number flux is increased due to injection. Higher L/D ratios result in a higher average heat transfer coefficient while having lower gradients along the wall. Enhancing the injection velocity would decrease the heat transfer coefficient and promotes cooling effects. Cold-to-hot heat transfer occurs inside the cavity and heat flux lines show that injection, decreases the flow temperature inside the cavity near the rear wall in comparison with no injection case.