Buoyancy-driven Cavity Research Articles

Directly irradiated liquid metal film in an ultra-high temperature solar cavity receiver. Part 2: Coupled CFD and radiation analysis

A novel solar cavity receiver was proposed in Part 1 to facilitate operation at ultra-high temperatures (>1300 K). The concept featured enclosing a directly irradiated liquid metal film inside a window-sealed cavity containing an inert protective fluid. The receiver’s technical performance was evaluated using a quasi-steady-state analysis based on various assumptions, which were used to enable analytical modelling of the involved energy transfer mechanisms. This paper describes a Computational Fluid Dynamics (CFD) solution developed to verify the conclusions of Part 1 and furtherly investigate the technical performance of the proposed receiver. The solution combined the Volume Of Fluid (VOF) and Discrete Ordinates Model (DOM) methods to simulate the volumetric radiation absorption by the liquid metal film while accounted for the transient flow developments of the gravity-driven film and buoyancy-driven cavity fluid. Analytical models were verified, showing improved performance for the absorptive cavity configuration. Film flow disintegration was mitigated by using surface corrugations, which were found to significantly influence the fluid dynamics and heat transfer performance of the receiver. Finally, a steady-state thermal analysis was presented for the proposed ceramic window, which indicated that active cooling is indispensable for protecting the window against thermo-mechanical fatigue.

A numerical study of the nanofluid mixtures inside a Buoyancy-driven cavity in the presence of a variable magnetic field

While magnetic flow applications have become a topic of great interest for decades, the coupling between fluid flow and electromagnetic forces is not straightforward. Therefore, the necessity of a robust guideline to simulate these types of problems has become apparent. Moreover, the heat transfer capabilities and the interaction between electromagnetic forces such as Lorentz and Kelvin require further investigation.In this regard, two objectives are pursued to address the noted issues. First, a robust and flexible solution framework using User-Defined-Functions (UDF)s is presented so that magnetic flow applications can be investigated without software limitations such as discretization scheme, solution setup, and simultaneous use of other advanced modules. Next, the impact of electromagnetic forces on streamlines and isotherms has been studied, and the forces’ area of influence is carefully investigated.Based on the results, the introduced framework has successfully predicted consistent results for three previous studies. Next, by considering a wide range of Rayleigh (Ra), Hartmann (Ha), and Magnetic (Mn) numbers, valuable revelations regarding the force interactions, thermofluidic properties, and force area of influence were revealed. Finally, the situations in which the Kelvin and Lorentz forces are influential are identified based on dimensional analysis.

Introducing compressibility with SIMPLE algorithm

A comparative assessment between SIMPLE and its variant SIMPLE-C is conducted based on two-dimensional (2-D) incompressible flows, using a cell-centered finite-volume Δ-formulation on a collocated grid. The SIMPLE-C (SIMPLE Compressibility) scheme additionally combines the concept of artificial compressibility (AC) with the pressure Poisson equation, provoking the diagonal dominance of influence coefficients. An improved nonlinear momentum interpolation scheme is employed at the cell face in discretizing the continuity equation to suppress pressure oscillations. The pseudo-time step Δti remains the same in both schemes to conserve an analogous scaling with momentum and scalar nodal influence coefficients. Numerical experiments in reference to buoyancy-driven cavity flow dictate that both contrivances execute a residual smoothing enhancement, facilitating an avoidance of the velocity/pressure under-relaxation (UR). However, compared with the SIMPLE approach, included benefits of the SIMPLE-C method are the use of larger Courant numbers, enhanced robustness and convergence. Excellent consistency is obtained between results available in the literature and numerical solutions obtained by both SIMPLE and SIMPLE-C solvers. The segregated SIMPLE algorithm is finally reformulated in conjunction with a new slope/flux limiter function to predict fluid flow at all speeds. Numerical results show that the compressible variant of SIMPLE replicates correct shock speed, well-resolved shock front, contact discontinuity and rarefaction waves when compared with analytical solutions. Compressible laminar flows are computed to further support the accuracy and robustness of proposed algorithm.

A Smoothed Particle Hydrodynamics approach for thermo-capillary flows

Interfacial-driven flows are important phenomena in many processes. In this article, we present a Smoothed Particle Hydrodynamics (SPH) model for thermo-capillary flow driven by gradients of the surface tension. The model is based on the continuum surface force (CSF) approach including Marangoni forces. An incompressible SPH approach using (i) density-invariant divergence-free (DIDF), (ii) corrected SPH and (iii) particle shifting approaches for multi-phase systems is used for accurate results.We carefully validate the proposed model using several test cases. First, we demonstrate the effects of corrected SPH and particle shifting approaches using Taylor-Green vortex. Then, we study single-phase flow problems to validate correct implementation of boundary conditions, momentum and energy balance using lid-driven cavity, diffusive transport problem, and buoyancy-driven cavity test cases.Afterward, we investigate different multi-phase flow problems to validate normal and tangential component of the surface tension. Finally, we apply the model to thermo-capillary rise of a droplet due to a temperature gradient. We present a convergence study and compare the results with their counterparts obtained from OpenFoam software as well as Finite Volume method (FVM) reference from literature. We demonstrate that the proposed model is very accurate for thermo-capillary flow. The simulation results of the current SPH approach will be available online for the community.

Lagrangian transport in a class of three-dimensional buoyancy-driven flows

The present study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as the archetypal configuration for natural-convection flows in which (contrary to the well-known Rayleigh–Bénard flow) gravity is perpendicular (instead of parallel) to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows, despite its relevance to observed flow phenomena as well as scalar transport, motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure and associated transport properties of the global streamline pattern (‘Lagrangian flow topology’) by both theoretical and computational analyses. The Grashof number$Gr$is the principal control parameter for the flow topology: limit$Gr=0$yields a trivial state of closed streamlines;$Gr>0$induces symmetry breaking by fluid inertia and buoyancy and thus causes formation of toroidal coherent structures (‘primary tori’) embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ‘smaller’$Gr$and gives behaviour that is dynamically entirely analogous to 3D lid-driven cavity flows. Buoyancy-induced bifurcation of the flow topology occurs for ‘larger’$Gr$and underlies the emergence of ‘secondary rolls’ observed in the literature and to date unreported secondary tori for ‘larger’ Prandtl numbers$Pr$. Key to these dynamics are stagnation points and corresponding heteroclinic manifold interactions.

An Alternative Strategy for the Solution of Heat and Incompressible Fluid Flow Problems via the Finite Volume Method

The characteristic-based split (CBS) method has been widely used in the finite element community to facilitate the numerical solution of Navier-Stokes (NS) equations. However, this computational algorithm has rarely been employed in the finite volume context and the stabilization of the numerical solution procedure has traditionally been addressed differently in volume-based numerical schemes. In this article, the CBS-based finite volume algorithm is employed to formulate and solve a number of laminar incompressible flow and convective heat transfer problems. Both explicit and implicit versions of the algorithm are first explained and validated in the context of the solution of a lid-driven cavity problem and a backward facing step (BFS) flow problem. The modified algorithm, capable of modelling the coupling between the momentum and energy balance equations, is then introduced and used to solve a buoyancy-driven cavity flow problem. Computational results show that the CBS finite volume algorithm can be reliably used in the solution of laminar incompressible heat and fluid flow problems.

Preconditioning Based on a Partially Implicit Implementation of Momentum Interpolation for Coupled Solvers

A new implicit and coupled algorithm for solving the Navier-Stokes equations is presented. A discretized Poisson-like equation for pressure is derived from the continuity equation by using expressions for the face velocities corrected with the momentum interpolation approach. A partially implicit implementation of this equation is proposed in order to achieve the coupling of velocity and pressure without increasing the size of the computational molecule. The ability of the algorithm to solve both constant- and variable-density flows is shown by presenting numerical results for the lid-driven cavity flow at moderate and high Reynolds numbers, and for the buoyancy-driven cavity flow with large temperature differences. A fully implicit scheme is used for discretizing the transient terms, and the efficiency and accuracy of the algorithm for unsteady flows is shown by solving the laminar vortex shedding over a square cylinder.

A NEW BENCHMARK QUALITY SOLUTION FOR THE BUOYANCY-DRIVEN CAVITY BY DISCRETE SINGULAR CONVOLUTION

This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.

MIXED CONVECTION IN CAVITIES WITH A LOCALLY HEATED LOWER WALL AND MOVING SIDEWALLS

A numerical study is conducted to investigate the transport mechanism of laminar mixed convection in a shear - and buoyancy-driven cavity having a locally heated lower wall and moving cooled sidewalls. Effort is focused on the interaction of forced convection with natural convection. Localized heating is simulated by a centrally located heat source on the bottom wall, and four different values of the dimensionless heat source length, epsilon, 1 / 5, 2 / 5, 3 / 5, and 4 / 5 of the nondimensional length of the bottom wall, are considered. Parametric studies on the effect of mixed convection parameter, Gr Re2 (also referred to as Richardson number, Ri), in the range 0.1 ? 10, on the fluid flow and heat transfer are performed for each epsilon. Local results are presented in the form of streamline and isotherm plots as well as the variation of local Nusselt number on the heated wall. Three different regimes are observed with increasing Gr Re2: forced convection (with negligible natural convection), mixed convection (comparable forced and natural convection), and natural convection (with negligible forced convection).

Development and validation of an advanced turbulence model for buoyancy driven flows in enclosures

A new buoyancy-modified turbulence model is developed on the basis of the four-equation model, k− ε− θ 2 − ε θ , of Hanjalic [K. Hanjalic, S. Kenjeres and F. Durst, Natural convection in partitioned two-dimensional enclosures at higher Rayleigh numbers, Int. J. Heat Mass Transfer 39(7) (1996) 1407–1427]. The strong anisotropy of Reynolds stresses due to buoyancy effects in the vertical boundary layers is considered by inclusion of the newly devised ‘return-to-isotropy’ concept in the pressure-strain correlation. The wall-reflection functions is also duly modified. The new model has been tested in buoyancy-driven cavity flows through comparison with published experimental data and the predictions from three other turbulence models [N. Z. Ince and B. E. Launder, On the computation of buoyancy-driven turbulent flows in rectangular enclosures, Int. J. Heat and Fluid Flow 10(2) (1998) 110–117; K. Hanjalic, S. Kenjeres and F. Durst, Natural convection in partitioned two-dimensional enclosures at higher Rayleigh numbers, Int. J. Heat Mass Transfer 39(7) (1996) 1407–1427]. It has demonstrated significant improvements in capturing the non-isotropy of Reynolds stresses and turbulent heat flux in vertical boundary layers.

Aiding and opposing mechanisms of mixed convection in a shear- and buoyancy-driven cavity

The present study was conducted to numerically investigate the transport mechanism of laminar combined convection in a shear- and buoyancy-driven cavity. The focus was on the interaction of the forced convection induced by the moving wall with the natural convection induced by the buoyancy. Two orientations of thermal boundary conditions at the cavity walls are considered in order to simulate the aiding and opposing buoyancy mechanisms. Velocity and temperature distributions of the flow are carried out through a stream function-vorticity transformation with a finite difference scheme. Parametric studies of the effect of the mixed convection parameter, Gr/Re 2, on the fluid flow and heat transfer have been performed. Calculations cover Re=100, Pr=0.71 and Gr/Re 2 the range of 0.01–100. Three different regimes are observed with increasing Forced convection (with Gr/Re 2 negligible natural convection), mixed convection (comparable forced and natural convection) and natural convection (with negligible forced convection). The code developed was carefully tested for the two limiting cases, the pure forced convection and the pure natural convection, for which experimental and numerical data are available.

Computation of turbulent buoyant flows in enclosures with low-Reynolds-number k-ω models

This work deals with the computation of turbulent buoyant convection flows with thermal stratification using the low-Reynoldsnumber (LRN) k-x model. When applying the k-e model to buoyancy-driven cavity flows induced by diAerentially heated side walls, a problem commonly encountered at moderate Rayleigh numbers (Raa 10 10 ‐1 0 12 ) is that the model is not capable of giving gridindependent predictions owing to the transition regime along the vertical walls. It was found that the buoyancy source term for the turbulence kinetic energy, Gk, exhibits strong grid sensitivity, as this term is modelled with the Standard Gradient DiAusion Hypothesis (SGDH). By introducing a damping function into this term, the above grid-dependence problem is eliminated and, additionally, the modelled Gk renders correct asymptotic behavior near the vertical wall. The mechanism held in the k-x model for describing the onset of transition is analyzed. The present approach is simple for practical use and gives reasonable predictions. ” 1999 Elsevier Science Inc. All rights reserved.

A fourth-order finite volume method with colocated variable arrangement

A finite volume solution method for the two-dimensional Navier-Stokes equations and temperature equation with 4th order discretization on cartesian grids is presented. The method uses colocated variable arrangement and the SIMPLE-kind of velocity-pressure coupling. The surface integrals (convection and diffusion fluxes through control volume faces) are approximated by Simpson's rule and polynomial interpolation, and the volume integrals (source terms) are approximated by fitting a fourth-order polynomial through nine points and integrating it analytically. Applications to the solution of a scalar transport on a known velocity field and to the lid-driven and buoyancy-driven cavity flows show superior accuracy as compared to the first and second order schemes. The approach can be readily extended to control volumes of arbitrary shape and unstructured grids.

A finite-element, parameter stepping solution procedure for the steady-state Boussinesq equations

In this paper we present a solution procedure for buoyancy-induced flows, based on a finite-element discretization and a continuation strategy. At each stage of the continuation procedure, the nonlinear discrete equations are linearized using the Newton-Raphson procedure and the resulting system of equations solved by a preconditioned biconjugate gradient algorithm. The solution procedure is tested on the buoyancy-driven cavity problem, and results obtained for a range of Rayleigh numbers. We prove that under appropriate conditions, the continuation strategy will converge to the true solution. The proof requires the assumption of the existence and uniqueness of solutions at each Rayleigh number; however, we finally prove the existence of weak solutions of the underlying continuous problem and give a sufficient condition for uniqueness of the solution.

An algorithm that accelerates convergence rates for incompressible Navier-Stokes problems

An algorithm, called the Algebraic Continuity Equations Solver (ACES), is developed based on the concept that two algebraic equations (three for 3D problems) can be generated from rearranging the discretized continuity equations. These rearranged equations are used to re-compute the two velocity components (three for 3D problems), whose values are already obtained from solving the momentum equations. When written in a Navier-Stokes computer code, this algorithm is equivalent to a fairly concise set of statements and can be implemented immediately after the computation of the continuity equation. In our analysis, ACES is used in conjunction with a grid having nodal velocity components at the vertices and the nodal pressure at the centre of each computational cell. With the aid of ACES, correction of velocity components during the iteration can be inexpensively made, leading to faster convergence rates or rendering otherwise divergent computations convergent. Test problems include benchmark problems such as lid-driven cavity flows and buoyancy-driven cavity flows of various parametric values and grid sizes. A 3D time-dependent flow in an irregular geometry is also investigated. Discussions are presented to clarify some relevant issues. A possible reason why we think ACES is capable of improving the convergence rates is also given.

Second-order corrections of the k- ε model to account for non-isotropic effects due to buoyancy

A new turbulence model which is a hybrid of the k- ε model and an algebraic Reynolds stress model (ASM) is developed. This model takes from an ASM that part of the non-isotropic Reynolds stress which is due to buoyancy, and the remaining part from the k- ε model. This concept is also applicable to flows with rotation where the Coriolis forces affect the turbulence by increasing its non-isotropy. The model is tested in a buoyancy-driven cavity flow. The contributions from the ASM corrections to the Reynolds stress and the turbulent heat flux are up to five and ten times, respectively, larger than those from the k- ε model.

A MULTILEVEL-MULTIGRID TECHNIQUE FOR RECIRCULATING FLOWS

A solution algorithm has been developed for the prediction of recirculating flows. Brandt's multilevel acceleration technique is used with Leonard's QUICK differencing scheme and a modified pressure implicit operator splitting scheme. Intermediate calculations enable a tau error distribution to be used for the identification of regions for local grid refinement, i.e., multigrid. The algorithm was tested for the prediction of laminar flow in a shear-driven and a buoyancy-driven cavity.

A Multilevel-Multigrid Technique for Recirculating Flows

A solution algorithm has been developed for the prediction of recirculating flows. Brandt's multilevel acceleration technique is used with Leonard's QUICK differencing scheme and a modified pressure implicit operator splitting scheme. Intermediate calculations enable a tau error distribution to be used for the identification of regions for local grid refinement, i.e., multigrid. The algorithm was tested for the prediction of laminar flow in a shear-driven and a buoyancy-driven cavity.