New benchmark solutions for transient natural convection in partially porous annuli

Abstract

Purpose - The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro -ri . Moreover, several Darcy numbers have been considered. Design/methodology/approach - A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings - For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4 ? 106 for the 4:1 cavity and 3.4 ? 105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications - A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications - The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value - This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities

Influence of one porous layer insert on the transient heat transfer in a tall annulus in presence of large source terms

“…Few numerical works are available for the analysis of both steady [21][22][23][24] and transient [25][26][27] natural convection in partially porous annuli; the available time dependent solutions deal with open-ended [25], and with closed [26][27] vertical partially porous annuli with vertical porous inserts with variable properties and positions. These works focused on the stability of the flow in the cavity for high values of Darcy number, without providing any detailed sensitivity analysis of the influence of the porous layer on the transient heat transfer for low values of Da.…”

Transient Natural Convection in Partially Porous Vertical Annuli

“…The code has been successfully validated through a comparison with experimental data available in scientific literature for steady state and transient natural convection in porous cylindrical domain; details about code validation can be found in ref. [29].…”

“…For the fully discretized form of Eqs. (1)-(4) reader can refer to [29]. As the transient AC-CBS scheme presented here, employs a dual-time stepping technique in which each steadystate solution is derived with a fully explicit pseudo-time iterative procedure, an appropriate stability analysis is crucial for the definition of proper time-step values to avoid spurious oscillations.…”

“…As regards thermal analysis of partially porous cavities, while laminar free convection in partially porous square and rectangular domains has been extensively analyzed both in steady [16][17][18][19][20] and transient conditions [21][22][23], few works concerning natural convection in partially vertical cylindrical cavities are available in scientific literature [24][25][26][27][28][29]. Moreover, only few papers [28][29] did not overlook transient regime, despite many engineering applications of the enclosure problem are related to real systems operating in dynamic mode. In order to improve the knowledge of the transient behavior of vertical partially porous annuli where buoyancy-driven heat and fluid flow occur, the generalized porous medium model has been solved applying an operator-splitting technique, the Artificial Compressibility (AC)-Characteristic-Based Split (CBS) algorithm, based on Characteristic Galerkin approach.…”

“…Moreover, all these works are based on simplifying hypothesis; in fact, only few works referring to square cavities [14] or infinite domains [15] refer to very specific conditions, such as nonBoussinesq convection [14] or non-Newtonian viscoelastic fluids [15]. As regards thermal analysis of partially porous cavities, while laminar free convection in partially porous square and rectangular domains has been extensively analyzed both in steady [16][17][18][19][20] and transient conditions [21][22][23], few works concerning natural convection in partially vertical cylindrical cavities are available in scientific literature [24][25][26][27][28][29]. Moreover, only few papers [28][29] did not overlook transient regime, despite many engineering applications of the enclosure problem are related to real systems operating in dynamic mode.…”