Lid-driven Square Research Articles

Lid-Driven Square Cavity Flow: A Benchmark Solution With an 8192 × 8192 Grid

Abstract The incompressible steady-state fluid flow inside a lid-driven square cavity was simulated using the mass conservation and Navier–Stokes equations. This system of equations is solved for Reynolds numbers of up to 10,000 to the accuracy of the computational machine round-off error. The computational model used was the second-order accurate finite volume (FV) method. A stable solution is obtained using the iterative multigrid methodology with 8192 × 8192 volumes, while degree-10 interpolation and Richardson extrapolation were used to reduce the discretization error. The solution vector comprised five entries of velocities, pressure, and location. For comparison purposes, 65 different variables of interest were chosen, such as velocity profile, its extremum values and location, and extremum values and location of the stream function. The discretization error for each variable of interest was estimated using two types of estimators and their apparent order of accuracy. The variations of the 11 selected variables are shown across 38 Reynolds number values between 0.0001 and 10,000. In this study, we provide a more accurate determination of the Reynolds number value at which the upper secondary vortex appears. The results of this study were compared with those of several other studies in the literature. The current solution methodology was observed to produce the most accurate solution till date for a wide range of Reynolds numbers.

Numerical Simulation of Hybrid Nanofluid Mixed Convection in a Lid-Driven Square Cavity with Magnetic Field Using High-Order Compact Scheme.

In this study, the energy transference of a hybrid Al2O3-Cu-H2O nanosuspension within a lid-driven heated square chamber is simulated. The domain is affected by a horizontal magnetic field. The vertical sidewalls are insulated and the horizontal borders of the chamber are held at different fixed temperatures. A fourth-order accuracy compact method is applied to work out the vorticity-stream function view of incompressible Oberbeck–Boussinesq equations. The method used is validated against previous numerical and experimental works and good agreement is shown. The flow patterns, Nusselt numbers, and velocity profiles are studied for different Richardson numbers, Hartmann numbers, and the solid volume fraction of hybrid nanoparticles. Flow field and heat convection are highly affected by the magnetic field and volume fraction of each type of nanoparticles in a hybrid nanofluid. The results show an improvement of heat transfer using nanoparticles. To achieve a higher heat transmission rate by using the hybrid nanofluid, flow parameters like Richardson number and Hartmann number should be considered.

Solving steady-state lid-driven square cavity flows at high Reynolds numbers via a coupled improved element-free Galerkin–reduced integration penalty method

Steady-state two-dimensional lid-driven square cavity flows at high Reynolds numbers are solved in this communication using a velocity-based formulation developed in the context of the improved element-free Galerkin–reduced integration penalty method (IEFG–RIPM). The analyses based on the IEFG–RIPM are performed under a standard Galerkin weak-formulation, i.e. without the need of introducing streamline-upwind or pressure stabilizing terms in order to suppress the appearance of non-physical oscillations. Solutions in a wide range of high Reynolds numbers are successfully achieved, and the results obtained have exhibited an excellent agreement with mesh-based solutions reported in the literature. The numerical performance of the proposed IEFG–RIPM in the solution of such benchmark problem has been analysed in terms of velocity distribution, streamline patterns, vorticity and pressure contours, and also in terms of the properties of primary and secondary vortices. The outcomes of this study demonstrate the potential of the IEFG–RIPM as a feasible and reliable numerical technique for the analysis of lid-driven square cavity flows at high Reynolds numbers, allowing the fulfilment of accuracy and stability numerical requirements demanded in the solution of this benchmark problem in a remarkably simple manner.

Dynamics of a pair of neutrally buoyant circular particles with different sizes in a lid-driven square cavity

The solid particles with different sizes exist widely, like cell separation, food processing, water treatment, thus, investigating the motion of the solid particles with different sizes is important. This study investigates the motion of a pair of neutrally buoyant circular particles with different sizes in a lid-driven square cavity using the lattice Boltzmann method. The motion of the circular particles with different sizes and that of the circular particles with identical sizes are quite different. The steady trajectories of the circular particles with identical sizes are identical, which is not affected by the Reynolds number. Differently, the circular particles with different sizes orbit along different steady trajectories, namely, the steady trajectory of the small particle is closer to the walls of the square cavity, while that of the large particle shrinks toward the center of the square cavity, which may provide us a possible method to separate them. However, it is not always effective, if the Reynolds number is low, the velocity difference between the circular particles with different sizes is small, which may fail to separate them completely.

Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

The present paper investigates the mixed convection in a two-sided and four-sided lid-driven square cavity in porous media. In the two-sided porous cavity, the left and right walls of the enclosure are maintained at constant but different temperatures, while the top and bottom walls are adiabatic. The top and the bottom walls of the enclosure move with a constant speed from left to right. In the four-sided porous cavity, the top and the bottom walls of the enclosure move from left to right and right to left, respectively, while the left and the right walls move from top to bottom and bottom to top, respectively, with a constant speed. The left and right walls of the enclosure are maintained at different heat fluxes, while the top and bottom walls are maintained at hot and cold temperatures, respectively. The governing equations are discretized by the fully implicit finite difference method, namely, Alternating-Direction-Implicit (ADI) method. The numerical results are analyzed for the effect of Darcy number (Da = 0.001, 0.01), Prandtl number (Pr = 7), Grashof number (Gr = 50,000), porosity (ε = 0.2) and viscosity ratio (Λ = 1, 3). The stability and convergence of the considered problem have been proved using the Matrix method.

Mixed convective heat transfer and heat generation simulation in lid-driven enclosure filled with porous medium

Researchers in heat transfer field always attempt to find new solutions to optimize the performance of energy devices through heat transfer enhancement. Among various methods which are implemented to reinforce the thermal performance of energy systems, one is utilizing porous media in heat exchangers. In this study, characteristics of laminar mixed convection in a porous two-sided lid-driven square cavity induced by an internal heat generation at the bottom wall have been carried out by using a numerical methodology based on the finite volume method and the full multigrid acceleration. The two-sided and top walls of the enclosure are assumed to have cold temperature while the remaining walls of the bottom wall are insulated. The working fluid is air so that the Prandtl number equates 0.71. The behavior of different physical parameters is shown graphically so that computations have been conducted over a wide range of pertinent parameters; (10[Formula: see text] Ri [Formula: see text]), Darcy number ([Formula: see text] Da [Formula: see text]), internal Rayleigh number ([Formula: see text] Ra[Formula: see text]), the porosity ([Formula: see text]) and the Grashof number (10[Formula: see text] Gr [Formula: see text]). Results revealed that heat transfer mechanism and the flow characteristics inside the enclosure are strongly dependent on the Grashof number. For instance, the best heat transfer rates at the considered values of internal Rayleigh numbers are obtained for a high Grashof number. Furthermore, an increase of internal heat generation (RaI) leads to a higher flow and temperature intensities for Grashof numbers ranging from [Formula: see text] to [Formula: see text] and a specific Richardson number value. Besides, an increase in porosity values ([Formula: see text]) leads to an obvious decrease in the average Nusselt number. Maximum temperature [Formula: see text] is optimal for high ([Formula: see text]) value. A correlation expression for the average Nusselt number relative to the internal heat source was established in function of two control parameters such as Darcy and Richardson numbers.

Computational Fluid Dynamics Analysis of Mixed Convection Heat Transfer and Fluid Flow in a Lid-driven Square Cavity Subjected to Different Heating Conditions

The present study investigates mixed convective and fluid flow characteristics in a lid-driven enclosure filled with air and its walls subjected to various heating conditions. The vertical (left and right) walls of the enclosure are cooled (Tc), and the bottom wall is heated to (Th) while the horizontal lid-driven upper wall is subjected to sinusoidal heating. The dimensionless governing equations (continuity, momentum, and energy transport) were implemented in COMSOL Multiphysics 5.4 software. The influences of Grashof number (103 ⩽ Gr ⩽ 105 ) and Reynold number in the interval of 1 ⩽ Re ⩽ 100 on the average Nusselt number ( NU ) for all walls of the cavity was examined. Furthermore, the results presented in the form of isotherms, streamlines, and the local and average Nusselt numbers in the enclosure for Re ⩽ 100 and Gr in the range of 103 ⩽ Gr ⩽ 105 . The results indicated the highest and lowest average rate of heat transfer at the bottom and top walls of the cavity respectively. The top wall region presented a higher velocity as confirmed by the velocity contour plots.

Natural and Mixed Convection Study of Isothermally Heated Cylinder in a Lid-Driven Square Enclosure Filled with Nanofluid

A computational study of an isothermally heated circular cylinder which has been locomoted at different locations within a square enclosure is investigated numerically using finite volume method. The numerical work is conducted to acquire the heat transfer details through steady, laminar, natural and mixed convection in the enclosure filled with pure water and Al2O3–water nanofluid. The study is performed for different restraints such as cylinder position (CP1–CP9), nanoparticles volume fractions (0 ≤ ϕ ≤ 0.05), Richardson number (Ri = 0.1–10) and Rayleigh number (105–107). The results are exhibited qualitatively in terms of streamlines and isotherms however quantitatively by local and average Nusselt number for various constraints. The results unfolded from investigation that the average Nusselt number is significantly changed with the cylinder locations and is found maximal at the cylinder position CP2. The investigation is further explored at this position of cylinder. It is found that the average Nusselt number enhances in addition, with the increment of nanoparticle concentrations, for lower value of Richardson number and higher values of Rayleigh number.

Numerical Assessment of Turbulent Flow Driving in a Two-Sided Lid-Driven Cavity with Antiparallel Wall Motion

In this paper, the case of the steady two-dimensional flow in a two-sided lid-driven square cavity is numerically investigated by the finite volume method (FVM). The flow motion is due to the top and bottom horizontal walls sliding symmetrically in the opposite direction with equal velocities, UT and UB, obtained through three respective Reynolds numbers, Re1,2=10000, 15000, and 20000. Due to the lack of availability of experimental results in this Reynolds number margin for this type of flow, the problem is first examined by considering that the flow is turbulent with the inclusion of four commonly used RANS turbulence models: Omega RSM, SST k-ω, RNG k-ε and Spalart-Allmaras (SA). Next, the regime is considered being laminar in the same range of Reynolds numbers. A systematic evaluation of the flow characteristics is performed in terms of stream-function contour, velocity profiles, and secondary vortices depth. Examination of the calculation results reveals the existence of a great similarity of the predicted flow structures between the Omega RSM model and those from the laminar flow assumption. On the other hand, the computed flow with the SST k-ω model, the RNG k-ε model, and the SA model reveals a remarkable under-prediction which appears clearly in the size and number of secondary vortices in the near-wall regions. Various benchmarking results are presented in this study.

Mixed Convection in a Two-Sided Lid-Driven Square Cavity Filled with Different Types of Nanoparticles: A Comparative Study Assuming Nanoparticles with Different Shapes

Mixed Convection in a Two-Sided Lid-Driven Square Cavity Filled with Different Types of Nanoparticles: A Comparative Study Assuming Nanoparticles with Different Shapes

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

Lattice Boltzmann Simulations of Coupled Mixed Convection and Radiation Effect in a Two-Sided Lid-Driven Enclosure

Using Lattice Boltzmann Method (LBM), the mixed convection and surface radiation effect in a two-sided lid-driven square cavity is studied numerically with air as a working fluid. The numerical code is validated against results available in the literature. The parameters governing the problem are the emissivity of the walls, the Reynolds number and the Richardson number that was varied through the Grashof number. The results obtained show significant effects of the Richardson number and surface radiation on the overall structure of the flow and heat transfer characteristics. The contribution of radiation component to the total Nusselt number outclasses that of convection for high emissive walls at some threshold value of Richardson number.

타원형 실린더의 종횡비의 변화가 Lid-driven 사각 밀폐계의 혼합 대류에 미치는 영향

타원형 실린더의 종횡비의 변화가 Lid-driven 사각 밀폐계의 혼합 대류에 미치는 영향

Numerical simulation of mixed convection in a two-sided lid-driven square cavity with four inner cylinders based on diamond arrays

The hydrodynamics and thermal characteristics due to mixed convection in a vertical two-sided lid-driven differentially square cavity containing four hot cylinders in a diamond array are investigated by the lattice Boltzmann equation model. The moving walls of the cavity are cold while the others are adiabatic. The flow in the cavity is driven by both the temperature difference and the moving vertical walls. The influence of different flow governing parameters, including the direction of the moving walls (the left wall moves up and the right wall moves down (Case I), both the left and right walls are moving upward (Case II), both the left and right walls are moving downwards (Case III)), the distance between neighboring cylinders [Formula: see text] ([Formula: see text]), and the Richardson number [Formula: see text] ([Formula: see text]) on the fluid flow and heat transfer are investigated with the Reynolds number in the range of [Formula: see text], the Grashof number of [Formula: see text] and the Prandtl number of [Formula: see text]. Flow and thermal performances in the cavity are analyzed in detail by considering the streamlines and isotherms profiles, the average Nusselt number, as well as the total Nusselt number. It is found that the heat transfer efficiency is highest when [Formula: see text] for the cases of the walls moving in the opposite direction. When the walls move in the same directions, the heat transfer efficiency obtained by [Formula: see text] is maximum among the considered values of [Formula: see text]. On the other hand, compared with the cases of [Formula: see text] and [Formula: see text], the cylinder positions corresponding to the largest and the smallest Nusselt numbers are very sensitive to the moving direction of the walls for [Formula: see text]. Moreover, the results also show that in terms of the value of Nusselt number and the stability the case of both walls moving downwards works well. Besides, the effect of the distance between neighboring cylinders is also discussed, it is found that increasing or decreasing the spacing between cylinders could enhance heat transfer to different degrees for the range of [Formula: see text] number considered. Finally, the empirical relationships among [Formula: see text], [Formula: see text], and the spacing between the cylinders ([Formula: see text]) are given, and predictive results match with the computed values very well.

Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation

This study presents the mixed convection inside a four-sided lid-driven square porous cavity whose right wall is maintained at a sinusoidal temperature condition, the left wall of the cavity is maintained at a cold temperature, while the top and the bottom walls are adiabatic. We have discussed two different cases depending upon the direction of the moving walls. Brinkmann-extended Darcy model is represented in terms of $$\psi $$ and $$\xi $$ using the stream function-vorticity formulation to simulate the momentum transfer in the porous medium. This formulation is used to solve the governing equations as a coupled system of equations which consists of the field variables, vorticity $$(\xi )$$ , stream function $$(\psi )$$ , and temperature (T). The velocity components (u, v) are derived from the stream function $$(\psi )$$ whereas the average Nusselt number is derived from temperature. The stability and consistency of the applied numerical scheme to the considered problem has been proven by matrix method. The numerical results are investigated by ranging the various dimensionless numbers such as Grashof number $$(10^3 \le { {Gr}} \le 10^5)$$ , Darcy number $$(10^{-1} \le { {Da}} \le 10^{-5})$$ , Reynolds number $$(10 \le { {Re}} \le 1000)$$ and keeping the Prandtl number $$({ {Pr}}=0.7)$$ fixed.

Assessment of multiple relaxation time-lattice Boltzmann method framework for non-Newtonian fluid flow simulations

A kinetic-theory based approach known as the lattice Boltzmann method (LBM) with multiple-relaxation-time (MRT) collision is employed to assess the non-Newtonian fluid models for standard two-dimensional benchmarks flow configurations. A two-dimensional nine-velocity square lattice (D2Q9) is used as a basic space-microscopic-velocity coupled LBM structure. The MRT-LBM formulation for the non-Newtonian fluids is validated for flow inside a lid-driven cavity. The non-Newtonian fluid viscosity is estimated using standard models as, Power-law, Carreau, Carreau–Yasuda, and Cross. These models are incorporated in the MRT-LBM framework to solve four standard benchmark flow configurations, namely, (a) lid-driven square cavity flow; (b) flow over a circular cylinder placed inside the lid-driven square cavity; (c) flow through two parallel plates, i.e. through a straight channel; and (d) flow over an asymmetrically placed circular cylinder in a straight channel. The simulation results for various benchmark cases found to be comparable with the earlier published data.

Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

Visualization Analysis of Numerical Solution With 32x32 and 64x64 Mesh Grid Lid-Driven Square Cavity Flow

In this paper, the flow problem of constant velocity of a square cavity whose lid is solved and obtained a numerical solution on 2 grid levels, having 32x32 and 64x64 cells. Reynolds number of 1x102 , 1x103 was selected for laminar flow and 8x103 was selected for turbulent flow. The problem is identified in NavierStokes equations. The finite volume discretization is based on the numerical model. The simulated results are in valid agreement with those that are available in the given report. The numerical solution of these works are accurately obtained for this problem.

Motion of a neutrally buoyant elliptical particle in a lid-driven square cavity

The motion of the solid particles in the enclosed cavity is important, to investigate the interaction between the motion of the solid particles and the fluid flow, the motion of a neutrally buoyant elliptical particle in a lid-driven square cavity is studied with the lattice Boltzmann method. To understand, predict and control the motion of the elliptical particle, the effects of the aspect ratio, initial orientation, initial position, particle size and Reynolds number are studied. The obvious characteristic of the motion of the elliptical particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the elliptical particle, confinement of the boundaries of the square cavity and vortex behavior. Compared with the circular particle, with the increase of the aspect ratio, the roundness of the limit cycle decreases, namely, the limit cycle becomes flatter. Especially, the limit cycle is insensitive to the initial orientation and position, namely, the limit cycle is the same no matter where the elliptical particle is placed initially. With the increase of the particle size, the confinement of the boundaries becomes stronger, and the limit cycle is squeezed toward the center of the square cavity. Finally, with the increase of the Reynolds number, the vortex at the top left corner develops, and the limit cycle is pushed toward the bottom right corner of the square cavity.

Finite element analysis of hybrid nanofluid flow and heat transfer in a split lid-driven square cavity with Y-shaped obstacle

The constructal design-based model is reported to analyze the thermal control and heat augmentation inside a split lid-driven square cavity. A Y-shaped obstacle is placed within the cavity, which is filled with Al2O3–Cu–water hybrid nanofluids. The concept of the split-lid-driven cavity is utilized for the first time. The governing flow mathematical structure is obtained in terms of a system of partial differential equations and converted to a non-dimensional form through dimensionless variables. The numerical experiments are performed by employing a Galerkin finite element scheme for different values of involved physical parameters. The effects of pertinent parameters on the streamlines, isotherms, dimensionless temperature, and Nusselt numbers are investigated for different values of the Richardson number. Due to the simultaneous motion of the split-lids, the streamlines and isotherms show symmetrical distribution. The local Nusselt number increases with the moving split-lids and attains the maximum value when both lids meet. The average Nusselt number decreases with an increase in the Richardson number. It is important to note that the Y-shaped obstacle enhances the heat transfer rate in the cavity.