Cavity Flow Research Articles

Unsteady, two-dimensional magnetohydrodynamic (MHD) analysis of Casson fluid flow in a porous cavity with heated cylindrical obstacles

This research presents an analysis of entropy generation during natural convection in a porous medium using triangular heated cylindrical obstacles with equal spacing. The study consists of three cylindrical obstacles arranged in a triangular pattern. Each cylinder is uniformly spaced from its neighboring cylinders, creating equilateral triangles throughout the arrangement. All of these cylindrical obstacles are heated. The triangular arrangement guarantees an even distribution of obstacles across the experimental space. The governing equations, with entropy, are numerically solved using the finite element method. The study aims to investigate the interactions between several key elements in fluid dynamics: Casson fluid, magnetohydrodynamics, the Darcy–Forchheimer model, entropy, and natural convection. The goal is to gain insights into the individual behaviors of these elements and their interactions in combined systems. The results indicate that the Casson fluid parameter has an impact on the flow and heat transfer characteristics, while the Hartmann and Nusselt numbers exhibit control mechanisms for the intensity of natural convection and affect the patterns of isotherms, streamlines, and entropy.

The role of permeability in lid-driven cavity flow containing a cluster of hot solids

The flow behavior of particle clusters with thermal convection in confined fluid flow has garnered considerable attention. One of the remaining challenges is to understand the role of a porous structure of particle clusters in the confined thermal fluid flow. In present work, a numerical study based on a double distribution function lattice Boltzmann model has been conducted to unveil the two-sided lid-driven cavity flow containing a hot cluster formed by an array of center-placed solids. First, we investigated the heat transfer by varying the Richardson number (Ri, from 0.01 to 1.0) and the solid fraction of the cluster (ϕ, from 0.0143 to 0.6734) with fixed cavity Reynolds number (Re=1000) and Prandtl number (Pr=0.7). The increase in Ri would lead to the formation of non-centrosymmetric streamlines and isotherms and an increase in the total averaged Nusselt number Nu¯a, in which several vortex structures being identified at high Ri and ϕ. Then, we explored the influence of permeability, quantified by the Darcy number (Da), by changing the porous structure of cluster via rearranging the array of solids. It is found that a higher permeability could enhance heat transfer of particle cluster due to the increase in convection, but the smaller surface area of solid particles would limit heat transfer. A correlation of Nu¯a with respect to Ri and Da could be developed based on our two-dimensional simulation results, allowing the evaluation of involved interplay between the porous structure of particle cluster and thermal convection in confined flow via a simple yet effective way.

Editorial: Comment on “MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall”

Editorial: Comment on “MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall”

Role of three-dimensional vortex motions on horizontal eddies in an open-channel cavity

AbstractLateral cavities are a popular object of study in hydraulic research as they are widely found in rivers and hydraulic facilities and significantly impact flow patterns, sediment transport, and water quality in aquatic ecosystems. While the effects of open-channel cavities on various aspects including characteristics of three-dimensional structures have been extensively studied, the role of vertical flow structures in the cavity has not been focused on. This study examines the relationship between the shallowness parameter and the three-dimensional flow effects on the dynamics of an open-channel lateral cavity flow with horizontal vortex motion, comparing the conventional two-dimensional model (2DC), advanced depth-integrated models including general bottom velocity calculation method (GBVC) with the ability to consider vertical flow structures, simplified bottom velocity calculation method with the shallow water assumption (SBVC), a three-dimensional model (3DC), and experimental data. The comparison results demonstrate that the three-dimensional flow effect significantly impacts the velocity distribution and vortex evolution in the cavity. The GBVC model demonstrates a good agreement with the flow patterns by the 3DC model and experimental results in the cavity, whereas the 2DC and SBVC models are unsuitable for deep-water conditions.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

Correcting model misspecification in physics-informed neural networks (PINNs)

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed neural networks (PINNs) have also been employed to learn governing equations given data across diverse scientific disciplines, e.g., in biology and fluid dynamics. Despite the effectiveness of PINNs for discovering governing equations, the physical models encoded in PINNs may be misspecified in complex systems as some of the physical processes may not be fully understood, leading to the poor accuracy of PINN predictions. In this work, we present a general approach to correct the misspecified physical models in PINNs for discovering governing equations, given some sparse and/or noisy data. Specifically, we first encode the assumed physical models, which may be misspecified in PINNs, and then employ other deep neural networks (DNNs) to model the discrepancy between the imperfect models and the observational data. Due to the expressivity of DNNs, the proposed method is capable of reducing the computational errors caused by the model misspecification and thus enables the applications of PINNs in complex systems where the physical processes are not exactly known. Furthermore, we utilize the Bayesian physics-informed neural networks (B-PINNs) and/or ensemble PINNs to quantify uncertainties arising from noisy and/or gappy data in the discovered governing equations. A series of numerical examples including reaction-diffusion systems and non-Newtonian channel and cavity flows demonstrate that the added DNNs are capable of correcting the model misspecification in PINNs and thus reduce the discrepancy between the physical models encoded in PINNs and the observational data. In addition, the B-PINNs and ensemble PINNs can provide reasonable uncertainty bounds in the discovered physical models, which makes the predictions more reliable. We also demonstrate that we can seamlessly combine the present approach with the symbolic regression to obtain the explicit governing equations upon the training of PINNs. We envision that the proposed approach will extend the applications of PINNs for discovering governing equations in problems where the physico-chemical or biological processes are not well understood.

Combustion of a nanoparticles-laden chemical in a vented cavity

Mixed convective characteristics of the combustion of a nanoparticles-laden fuel (n-butanol nanofluid) in a vented cavity are investigated. The nanofluid and the oxidizer enter the cavity through the inlets on the left and right vertical walls, respectively. However, the resulting product produced from the oxidation process of the fuel exits the cavity through the outlet at the bottom wall. Heat generated from the oxidation process causes natural convection within the cavity. The conjugate effect of natural and forced convection finally gives rise to mixed convection phenomena. In this regard, a mathematical model for mixed convection flow in a vented cavity is formulated with no-slip and isothermal boundary conditions. Having transformed the model into a dimensionless form, the stream function-vorticity formulation is used. The resulting equations are then solved numerically using the finite difference method. Numerical results are illustrated with the streamlines, isotherms, and isolines of fuel and oxidizer concentrations. The maximum values of the stream function (ψmax) and the temperature (θmax) are found to increase with an increase in the Frank–Kamenetskii number (Λ), volume fraction of nanoparticles (φ), and stoichiometric ratio (χ). On the contrary, they decrease with the increase in the Reynolds number (Re). When the Grashof number (Gr) is increased, ψmax increases and θmax decreases. The remaining concentrations of fuel, (CF)min, and oxidizer, (CO)min, are higher for an increase in Gr, whereas the opposite is recognized for increasing Λ. With the increase in Gr and Λ, the steady-state flow in the cavity tends to be oscillating and then chaotic.

Intelligent prediction of non-Newtonian hybrid nanoparticle-enhanced fluid flow and heat transfer behaviours in a trapezoidal enclosure: Integrated simulation approach

This study investigates the utilization of a trapezoidal cavity with a corrugated bottom wall containing a Carreau hybrid nanofluid composed of water, aluminum, and copper nanoparticles. A heated, rotating cylinder is placed at the center of the enclosure in the presence of an external magnetic field. The impact of Forchheimer and Brinkman porous medium models on the hybrid nanofluid is examined. Three different inlet–outlet placement configurations are considered to investigate their influence on heat transfer. The governing equations for fluid flow and heat transfer are solved numerically. Through simulations, a range of flow-controlling variables is systematically adjusted, including the Darcy number, Reynolds number, Hartmann number, nanoparticle volume fraction, undulation on the hot bottom wall, power law index, and rotational speed of the inner heated cylinder. The results demonstrate that the hybrid nanofluid and rotating cylinder significantly enhance heat transfer within the trapezoidal cavity. Higher values of the Darcy number, Reynolds number, and nanoparticle volume fraction lead to increased heat transfer rates. The placement configuration of the inlet and outlet ports also affects heat transfer performance, with the bottom-top configuration yielding the best results. Furthermore, a comparative analysis of flow profiles and heat distribution is conducted using the multiple expression programing technique. The proposed model accurately predicts the flow and heat transfer characteristics in the trapezoidal cavity, as validated through comparison with provided data sets.

Vertical water entry of a cylinder considering wind and linearly sheared flow effect: A numerical investigation

Objects entering water is a complex multiphase flow event that exhibits nonlinear and transient characteristics. This study examines the impact cavities, multiphase flow characteristics, and motion behaviors of a cylinder during vertical water entry, considering different flow and entry velocities. A three-dimensional model was carried out using OpenFOAM® framework, taking into account the effects of wind and linearly sheared flow through newly customized initial and boundary conditions. The overset mesh technique was applied to capture the water entry trajectories of the moving cylinder. Numerical results for the cavity evolution and cylinder motion behaviors were validated against published laboratory tests. The cavity closure patterns were classified into four categories based on the evolution characteristics, which were found to be more complex than those observed under calm water and uniform current conditions. Furthermore, the rapid closure of the splash dome results in a unique cavity flow phenomenon, which creates a suction air channel. The velocities of the flow and water entry have a noticeable impact on the closure modes and time of the cavity. This, accordingly, affects the motion characteristics of the cylinder, as well as the evolution of the velocity field, pressure field, and vortex structures.

Mixed convection of a viscoplastic fluid with a variable yield stress in a lid-driven cavity

This study is a numerical investigation on heat and momentum transfer in viscoplastic fluids that exhibit a variable yield stress. Viscoplastic fluids are recognized for transitioning from solid to liquid under flow-induced shear-rate. However, these materials exhibit intricate rheological behaviors beyond this fundamental characteristic, often linked to thixotropy. Thixotropy delineates reversible, time-dependent alterations in a fluid's viscosity at a specific shear-rate. The temporal changes in viscosity stem from variations in the fluid's microstructure, responsive to the induced shear-rate. When subjected to shear, the fluid's microstructure breaks down into smaller units, countered by Brownian motion, resulting in a rearrangement of the microstructure due to attractive forces between microconstituents. These microstructural variations are thus reversible. Notably, these changes affect not only viscosity but also the yield stress of the fluid, categorizing it as a non-ideal yield-stress fluid with yield-stress variations linked to microstructure, termed isotropic hardening. This study aims to explore how variations in yield-stress fluid microstructure impact heat and momentum transfer. As a starting point, this study considers the lid-driven cavity flow with differentially heated walls in the presence of an external magnetic field. Addressing the yield-stress fluid microstructure variations involves utilizing the Houska–Papanastasiou model, a regularized model capturing thixotropy and isotropic hardening. The resulting governing equations are made dimensionless and numerically solved through the finite-element method. The findings indicate that a more pronounced breakdown of the fluid's microstructure correlates with a higher Nusselt number at the hot wall. Additionally, variations in fluid microstructure influence both the size and location of unyielded zones.

Numerical simulation of heat transfer and entropy generation due to the nanofluid natural convection with viscous dissipation in an inclined square cavity

In this work, the effects of viscous dissipation on heat transfer and entropy generation of the nanofluid natural convection in an inclined square cavity are numerically investigated. A fractional-step semiimplicit finite difference algorithm based on the projection method on a staggered grid is proposed to solve the laminar natural convection problem, which has the advantage of larger time steps. The square cavity is filled with a nanofluid composed of (Cu) copper nanoparticles and water. and the viscous dissipative behavior of the mixture flow is not negligible. The studied parameters are Rayleigh number Ra ( 10 4 and 10 5 ), Eckert number Ec ( 0 − 2 ), the volume fraction of solid particles ϕ ( 0 − 0.06 ), and inclination angle of square cavity α ( 0 − π / 2 ). The Prandtl number is fixed to Pr = 6.2 . The results show that at any inclination angle, the increase in viscous dissipation leads to weakened heat transfer on the hot wall, enhanced heat transfer on the cold wall, and weakened flow in the square cavity. For the base solution without nanoparticles, the Eckert number has the greatest impact, with its effects on the average Nusselt number on the hot wall, maximum streamfunction, and average Nusselt number on the cold wall being ∼13, 0.15, 18.69%, and at Ra = 10 4 , and 12, 0.5, 28.87% at Ra = 10 5 , respectively. Research on entropy generation shows that as Eckert number increases, the entropy generation due to heat transfer increases, while due to fluid friction decreases. As the Rayleigh number increases, the effect of viscous dissipation increases. As the inclination angle increases, the effects of volume fraction and Eckert number weaken. Adding solid particles can effectively weaken the effect of viscous dissipation.

Study of Bejan number and entropy generation for mixed convection of nanofluid flow inside a chamber under an inclined magnetic field

Examination of the efficiency and losses in heat exchange devices is pivotal. Therefore, the entropy generation (EYG) and Bejan number (Be) of mixed convective heat transfer of nanofluid flow in a rectangular cavity (RCY) are evaluated in this study. Five baffles are placed at the lower hot wall of the RCY. The cold upper wall moves and causes forced convection flow of nanofluid. The magnetic field (MFD) at different angles affects the nanofluid when the Hartmann number (Ha) changes from 10 to 40. The length of stepped baffles is changed, and the values of frictional EYG, thermal EYG, and total EYG are estimated. The simulations are done using the LBM and an in-house code. The results demonstrate that the improvement in Ha decreases the amount of frictional EYG, thermal EYG, total EYG, and Be. The total EYG and Be also increase as the MFD angle is increased. The increment in the Richardson number (Ri) reduces the frictional EYG and total EYG (61.8 %) and increases the value of thermal EYG. Enhancing the length of the baffles intensifies the amount of Be and total EYG (3.4 %) and thermal EYG, but decreases the frictional EYG.

Effects of vegetation density on flow, mass exchange and sediment transport in lateral cavities

Large-Eddy Simulations (LES) were used to investigate the hydrodynamics and mass transfer between the flow in the main channel and a vegetated lateral cavity. Fourteen vegetation densities (0 to 10.65 %) were tested, revealing two distinct hydrodynamic patterns. For cavities with low vegetation density (a < 3.99 %), one primary gyre in contact with the interface between main channel and cavity with high velocity was formed; the thickness of the mixing layer grew longitudinally along the interface, and regions with high vorticity and turbulence kinetic energy appeared at the interface and inside the cavity. For cavities with high vegetation density (a > 3.99 %), two gyres in contact with the interface with low velocity were formed, the thickness of the mixing layer did not grow, and the vorticity and turbulence kinetic energy were low inside the cavity. The mass transport presented the same threshold value as the hydrodynamics (a = 3.99 %). For cavities with low vegetation density, a fast mass transfer occurred through the interface between the main channel and cavity and inside the cavity, while the opposite was observed for cavities with high vegetation density. Finally, the modelled hydrodynamics was used to infer possible sediment deposition patterns and flow resistance.

Modal analysis for incompressible fluid flow

This paper presents a numerical method for incompressible fluid flow. A difficulty in analyzing incompressible fluid flow is that the continuity equation has no time evolution term. In the marker and cell (MAC) method, Poisson’s equation is solved iteratively, which takes most of the computation time, and in the artificial compressibility method (ACM), pseudo-time iteration is necessary to solve for unsteady solutions. Here, modal analysis that uses the velocity eigenvectors corresponding to zero eigenvalues is proposed for analyzing two-dimensional incompressible fluid flow. The proposed method involves only about one third of the number of variables needed in the MAC method and the ACM, and it does not require iterative calculation of Poisson’s equation or pseudo-time iteration. Numerical results for a simple flow system and a cavity flow obtained using the proposed method are compared with those obtained using the ACM and the simplified MAC method. The results agree well, thereby validating the proposed modal analysis.

Heat transfer and fluid flow in nano-encapsulated PCM-filled undulated cavity

This article discusses the heat transfer characteristics of the mixed convection of NEPCM-fluid (Polyurethane/ Nonadecane dispersed in water) contained within a wavy-sided walls cavity. Mixed convection is caused by an adiabatic rotating cylinder located in the cavity center, while natural convection results from deferential heating of side walls. The upper and lower walls of the cavity are insulated. The Galerkin finite element method (GFEM) implemented in COMSOL CFD package is employed to solve the governing equations. The influence of the nanoparticles volume fraction (Ø = 0.02, and 0.05), cylinder radius (R = 0.05, 0.15, and 0.25), cylinder rotating speed (Ω = 100, −500, 500, and 1000), the dimensionless fusion temperature (θfu = 0.1, 0.25, and 0.5), wavy side walls undulation peaks number (N = 1 to 4) on the flow pattern and temperature field are presented. The results revealed that the heat transfer enhances by increasing the angular speed of the cylinder and its radius, also an enhancement in heat transfer is obtained by upgrading the volume fraction of NEPCM, however, it was noticed that for small cylinders, the counterclockwise rotation of the cylinder reduced the heat transfer rate as the rotation opposed the direction of natural heat convection. In addition, the waviness pattern has a specific impact on each case, for example, N = 4 denotes the best result for only the cases Ω = -500 or 500 when R = 0.25 and Ø = 0.05, while the heat transfer is negatively affected by increasing N for the other cases. On another hand, the impact of θfu on the heat transfer rate was found to be insignificant. Globally, at the biggest cylinder radius, higher Ø and highest angular speed an enhancement by more than 900 % can be achieved.

Entropy generation in a partially heated hybrid nanofluid saturated wavy porous cavity

PurposeA porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.Design/methodology/approachThe governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 102, 103), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.FindingsA thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 103, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 102.Originality/valueTo the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

The influence of ring clearance on the performance of a double-suction centrifugal pump

Due to the complex structure of a double-suction pump's suction chamber, the flow in the pump's cavity is often ignored in numerical simulations because of difficulties in structured hexahedral meshing. However, the wear ring clearance interlinking the pump chamber leads the fluid at the impeller inlet directly to the impeller area. This significantly impacts the pump's internal flow field, so the influence of the clearance on the internal flow of a double-suction pump cannot be ignored. This paper develops four three-dimensional double-suction pump models with different wear ring clearances to investigate their influence on pump performance, and structured hexahedral meshes were used for all the computational domains. The clearances varied from 0.2 to 0.5 mm in 0.1 mm increments. The influences of the clearance on the energy loss, external characteristics, and internal flow field distribution of the pump were simulated via a verified computational fluid dynamics method. The results show that the wear ring leakage decreases with the flow rate and increases with wear ring clearance. The increase in backflow leads to an internal flow disorder inside the impeller, resulting in a decreased head and efficiency. Energy loss is mainly caused by increasing the turbulence entropy production with an increasing wear ring clearance. Also, the low-pressure region in the pump cavity expands to the volute with increasing clearance, and the impeller outlet pressure decreases. This study's research on wear ring clearance provides a reference for the design and application of double-suction centrifugal pumps.

Physics-informed neural networks with domain decomposition for the incompressible Navier–Stokes equations

Physics-informed neural network (PINN) has emerged as a promising approach for solving differential equations in recent years. However, their application to large-scale complex problems has faced challenges regarding accuracy and efficiency. To address these limitations, domain decomposition has gained popularity as an effective strategy. This paper studies a domain decomposition PINN method for solving incompressible Navier–Stokes equations. We assess the method's predicted accuracy, convergence, and the impact of different strategies on performance. In the domain decomposition PINN method, individual PINN is employed for each subdomain to compute local solutions, which are seamlessly connected by enforcing additional continuity conditions at the interfaces. To improve the method's performance, we investigate various continuity conditions at the interfaces and analyze their influence on the predictive accuracy and interface continuity. Furthermore, we introduce two approaches: the dynamic weight method and a novel neural network architecture incorporating attention mechanisms, both aimed at mitigating gradient pathologies commonly encountered in PINN methods. To demonstrate the effectiveness of the proposed method, we apply it to a range of forward and inverse problems involving diverse incompressible Navier–Stokes flow scenarios. This includes solving benchmark problems such as the two-dimensional (2D) Kovasznay flow, the three-dimensional (3D) Beltrami flow, the 2D lid-driven cavity flow, and the 2D cylinder wake. Additionally, we conduct 3D blood flow simulations for synthetic flow geometries and real blood vessels. The experimental results demonstrate the capability and versatility of the domain decomposition PINN method in accurately solving incompressible Navier–Stokes flow problems.

Grad's 13 moments-based gas kinetic flux solver with triangle unstructured meshes for simulating continuum and rarefied fluid flows

A numerical framework based on the gas kinetic flux solver (GKFS) with unstructured meshes of triangle cells has been proposed and assessed in this work. Like conventional GKFS, the present scheme only updates the cell-average macroscopic conservative variables in time, thereby saving computational costs. At each cell interface, the numerical normal flux is computed with the GKFS scheme proposed by Liu et al. [J. Comput. Phys. 415, 109548 (2020)], in which the distribution functions at the surrounding points are reconstructed with the Grad's 13 moments (G13). Additionally, a solid wall boundary condition treatment has been proposed in the present G13-GKFS framework, which allows one to model from purely specular to perfectly thermalized solid walls. The present framework has been validated with the steady cylindrical Couette flow, the lid-driven cavity flow, the unsteady Rayleigh flow, and the rarefied flow around the NACA0012 airfoil test-cases, where good agreements are found with references for a quite wide range of flow regimes, from continuum to transitional flow regimes.

The Rossiter equation: Improving the fractional vortex speed and defining an effective length to depth ratio for cavity flows

This paper first reviews well known analytical techniques for predicting the Rossiter modes of a cavity in compressible flow. We combine existing methods to improve the performance in compressible flow. Second, we introduce a method based on an effective length to depth ratio of the cavity from experimental results for predicting frequencies across Mach numbers. Finally, the fractional vortex speed used in the Rossiter equation and its derivatives is calculated from high subsonic (M 0.55) to supersonic (M 2.3) for use in future cavity mode prediction.