Numerical investigation on flow and heat transfer from porous bluff bodies using lattice boitzmann method

Abstract

The remarkable development in miniaturisation and performances of thermal devices and increasing use of Multi-Chip-Module (MCM) in electronics demand reliable thermal control methods. The temperature regulation has become indispensable in order to guarantee the optimum performance of a system for a stipulated period of time. Several active and passive approaches have been suggested and implemented for enhancing the heat transfer characteristics [1]. Amongst various passive techniques for augmenting heat dissipation, employing higher thermal conductivity fluids (nanofluids), increasing the surface area of the component and utilizing porous medium are popular. Numerous studies related to porous medium [2–4] suggest that the heat transfer performance of a system can be extensively improved by using porous material with higher thermal conductivity. The utilization of intrinsic feature of the porous medium is being widely used in many environmental and engineering applications such as packed bed heat exchangers, drying technology, catalytic reactors, thermal insulation, petroleum industries, tissue engineering and electronic cooling [5, 6]. On the other hand, a complex system with numerous elements arranged orderly can be considered as a single porous body [7]. This empowers the researchers and/or engineers to discover experimentally unapproachable problems with significant computational economy. Few relevant examples are arrangement of fuel and control rods in nuclear reactor core, pin-fin arrangement, LED backlit module and heat exchanger. Such arrangements can be tuned to receive required flow and thermal characteristics. This exemplifies the reason for trending of the research on porous media and associated modeling theory. The modeling of different thermal systems using porous media towards optimal heat transfer requires the knowledge on various influencing parameters such as momentum, buoyancy, magnetic field, alignment and size of the porous body. Also, the combined effects of aforementioned parameters are expected to produce a notable impact on the designing of permeable bluff bodies. Thus, understanding the impression of these factors is one of the main driving forces for research in flow and heat transfer from porous bluff bodies. Moreover, the recent literature surveyindicates the paucity of education in this field. Key observations from the available literature are (i) the unsteady flow and heat transfer characteristics of a porous bluff body with different fore-body and aft-body are not studied, (ii) the influence of aiding buoyancy condition on hydrothermal behaviour of porous bluff body is not probed, (iii) the buoyancy and permeability interactions along with fore-body effects on hydrodynamic and thermal dissipation of porous bluff body have not yet been estimated, (iv) natural convection characteristics of porous bluff body have not been reported and (v) the influence of magnetic field and nanofluid on natural convection characteristics of porous bluff body are also not available. Apart from these observations, the lattice Boltzmann method, which has a significant advantage over conventional numerical methods (especially while dealing with complex flows such as porous media) [8], has not been employed to study the flow and heat transfer traits of porous bluff bodies. In the first analysis, the unsteady flow and heat transfer around a diamond shaped porous cylinder placed in an infinite stream of fluid have been numerically analysed using lattice Boltzmann method. The variations in hydrothermal behaviour of the porous cylinder have been studied for different values of Darcy number (10􀀀6 Da 10􀀀2) and Reynolds number (50 Re 150). A substantial reduction in vortex shedding strength is witnessed for the same momentum of the fluid with higher permeability. A finite amount of fluid which enters into the permeable cylinder reduces the resultant pressure and shear force acting in the direction normal to the flow. Hence, the amplitude of oscillation is observed to be greater under lower permeable condition with relatively lower frequency of oscillation. Moreover, the permeable square-shaped body produces flow instabilities which is found to be absent in porous diamond-shaped cylinder. Reduction in drag and heat transfer augmentation in overall heat transfer are seen while enhancing permeability of the cylinder. At Da = 10􀀀4, due to large deviation in fluid path and less fluid velocity in porous region, the heat transfer rate is less significant than other higher values of non-dimensional permeability values. The low values of temperature gradient on frontal surfaces of the cylinder at rich permeable values (i.e.Da = 10􀀀2), dominates over low heat dissipation rate of rear surfaces. As a result of this, the heat transfer enrichment is drastic for this permeability range. Correlation for time-averaged mean Nusselt number, valid for the range of parameters considered is also provided, and this indicates the strong influence of momentum on heat transfer increment than permeability. Furthermore, a comparative study on thermal dissipation from the permeable square and diamond shaped cylinders is carried out at Re = 50, 100 & 150 at different values of Da. Due to the dominance of thick thermal boundary layer formation at rear surfaces of diamond-shaped cylinder, the percentage increment in mean Nusselt number of the diamond-shaped cylinder with reference to square decreases monotonously with the increase of non-dimensional permeability. For example, at Re = 100, the percentage enhancement of diamondshaped cylinder at Da = 10􀀀6, 10􀀀4, 10􀀀3 and 10􀀀2 is 15.87%, 15.37%, 12.95% and 21.84%, respectively with reference to permeable square cylinder. At Da = 10􀀀2, the influence of frontal surfaces is more than rear surfaces and thus, at this condition the percentage enhancement of diamond-shaped cylinder is high. Broadly, from this study, it is seen that the increment in permeability reduces flow instabilities as well as an increment in thermal performance in comparison to square shape is obtained. Thus, while modeling porous bodies or a group of bodies for pragmatic applications the alignment and permeability level have to be considered. From literature, it is evident that the mixed convection characteristics can greatlyalter the flow and thermal behaviour in the vicinity of heated cylinder. In particular, the aiding buoyancy condition intensifies the thermal performance and also it suppresses the flow instabilities [9]. In this regard, numerical experiments have been conducted to study the hydrodynamic and thermal behaviour of permeable square cylinder under aiding buoyancy condition. Reynolds number and Darcy number considered in this study vary from 2 to 40 and 10􀀀6 to 10􀀀2, respectively. The flow and heat transfer traits at Prandtl number (Pr) value of 0.71 is compared for three different values of Richardson number (Ri) i.e. 0, 0.5 and 1. In general, the flow and heat transfer characteristics are found to be a function of non-dimensional permeability (Da), buoyancy condition and Reynolds number. It is observed that amonotonous reduction in wake length and drag coefficient values occur at higher permeability levels. On the other hand, aiding buoyancy depicts a pronounced reduction in wake length and an increment in drag coefficient values. The increment in permeability causes dominance of inertial force over the viscous force of porous medium, and hence, fluid flows through it with different deviation levels. Besides, the Richardson number increment reduces the pressure over the cylinder and more amount of fluid is noticed to be attached over it. Conversely, the buoyancy increment reduces the flow path deviation in the cylinder. A significant augmentation in heat dissipation is reported for increasing values of Ri and/or Da. The permeability increment stretches the isotherms and also reduces the temperature gradient at side surfaces. Whereas, Richardson number significantly enhances the temperature gradient which is evident from the narrow isotherms. Moreover, the increment in buoyancy level enhances the impact of permeability on heat transfer enhancement. For instance, the percentage increase in mean Nusselt number at Re = 40, Da = 10􀀀4 at Ri = 0, 0.5 and 1 is 2.04%, 2.2% and 3.03%, respectively, in comparison to Da = 10􀀀6 case. Furthermore, the heat transfer intensification is prominent while Ri shifts from 0 to 0.5 and it is less sensitive while it varies from 0.5 to 1.In the next investigation, the influence of fore-body and aft-body shapes on hydrothermal behaviour of porous bluff body under aiding buoyancy condition have been concentrated. The combination of flat and slant edges of the triangular cylinder, has shown impressive heat transfer characteristics than square shape [10]. On this subject, shape of the permeable body is chosen triangular, which is aligned at two different orientations (i.e. apex-facing flow and side-facing flow). Objective of this study is to investigate the effects of Darcy number and fore-body shape on flow and heat transfer characteristics, under forced convection (i.e. Ri = 0) and aiding buoyancy conditions (i.e. Ri = 0.5 & 1) for Pr = 0.71. The ranges of Reynolds number and Darcy number considered in this study are 1 Re 40 and 10􀀀6 Da 10􀀀2, respectively. The flow deviation produced by apex-facing triangular cylinder is lesser than that of side-facing flow. Also, at higher Richardson number (i.e. Ri = 1) the flow is completely attached over the side-facing configurations for all values of Re and Da. However, apex-facing triangular cylinder has produced flow separation and it is due to the enhancement in fluid momentum at slant surfaces and sharp corners. The excess viscous force offered by buoyancy causes a substantial increment and decrement of drag coefficient and recirculation length, respectively. On the contrary, a more permeable triangular cylinder experiences less drag value with short eddies. Also, drag coefficient values of solid square cylinder with triangular cylinders at different values of Re and Ri have been compared. For all values of Re and/or Ri, the drag coefficient of square cylinder is higher than that of triangular configurations. In the absence of buoyancy, the drag coefficient values of side-facing triangular cylinder lie between the square and apex-facing cylinders. Under aiding buoyancy condition, the side-facing triangular cylinder experiences less drag than apex-facing for all values of Da. The mean Nusselt number of apexfacing triangular cylinder is seen to be higher than that of side-facing configuration irrespective to the variation in Re, Da and Ri.The next analysis is focused on the natural convection between a hot porous body and a square enclosure in which the body is placed. The effects of aspect ratio (A), non-dimensional permeability (Da), Rayleigh number (Ra) and orientation of porous square body on flow and heat transfer characteristics have been extensively analysed. The ranges of Ra and Da considered in this study are 103 Ra 106 and 10􀀀6 Da 10􀀀2, respectively, for Pr = 0.71. The porous body is aligned at two different alignments (i.e. stand-on-side (SOS) and stand-on-edge (SOE)) for the fixed aspect ratio (porous body width/enclosure height) values of 0.5, 0.25 and 0.125. In addition, the SOES configuration, which is 45o inclination of SOS configuration is investigated. Also, the entropy generation variations with the aforementioned parameters have been performed. It is seen that the flow field dependence on Ra and Da is less at low values of aspect ratio for both configurations of porous body. It is inferred that the increment in permeability value enhances the kinetic energy of the fluid in and around the porous zone. Besides, the flow path deviation in the porous zone is seen to be more at A = 0.5 of SOS configuration and the same is observed to be minor while reducing the size of the porous body. On theother hand, the increment in Da level causes thinning and thickening of thermal boundary layer at bottom and top surfaces of the porous body, respectively. Also, the thermal gradient of side surfaces of SOS cylinder is dependent on the aspect ratio. The Nusselt number values of SOE configuration are found to be relatively higher than that of SOS configuration. The enclosure mean Nusselt number of SOS configuration is higher than SOE configuration. Thus, it indicates that the enclosure with SOE permeable body will contain higher amount of denser or cold fluid. The entropy generation is seen to be less in SOE configuration and also at lower aspect ratio. In the final investigation, natural convection heat transfer, between a hot permeable triangular-shaped cylinder and a cold square enclosure, is examined under the influence of magnetic field. Al2O3-water nanofluid with 5% volume fraction is considered as a working fluid. The ranges of Rayleigh number and Darcy number considered in this study are 104 Ra 106 and 10􀀀6 Da 10􀀀2, respectively. The flow and thermal characteristics of triangular body for two different alignments (i.e. apex-facing up and apex-facing down) are critically investigated for the aforementioned parameters at different values of Hartmann number (i.e. Ha = 0, 25 & 50). It is seen that the permeability increment enhances the fluid momentum, whereas the presence of magnetic field reduces the kinetic energy of the fluid. Also, the Ha has shown a strong impact on vertical velocity field at annular, whereas this effect is found to be trivial in porous zone. The increment in Ha suppresses the intensity of permeability on heat transfer enhancement. Further, the overall heat transfer of apex-facing up triangular configuration are reported to be higher than that of apex-facing down configuration for all values of Ra, Da and Ha considered in this study. Also, the impact of permeability on thermal enhancement is higher in apex-facing up permeable triangular body than apex-facing down case irrespective to the intensity of magnetic field. On contrary, the heat transfer reduction due to Ha increment is seen to be less in apex-facing down configuration at Ra 105.