ARTICLE Year : 2011  Volume : 1  Issue : 2  Page : 6569 Flow Structure and Heat Transfer Analysis in a Laminar Channel Flow with Builtin SidebySide Dual Triangular Prism Munish Gupta^{1}, Rajesh Dudi^{2}, Satish Kumar^{3}, ^{1} Department of Mechanical Engineering, University Institute of Engineering and Technology, Kurukshetra University, Kurukshetra, India ^{2} Department of Mechanical Engineering, JCD Engineering College, Sirsa, Haryana, India ^{3} Department of Mechanical Engineering, Thapar University, Patiala, Punjab, India Correspondence Address: This paper presents the numerical analysis of fluid flow in a parallel plate channel having dual triangular prisms in sidebyside arrangement. The computational domain is considered two dimensional. The fluid flow is assumed to be incompressible, steady and laminar with constant thermophysical properties. The computations are performed for a Reynolds number of 100 and blockage ratio (b) of 0.25, where the blockage ratio (b) is the ratio of prism base to the channel height (b = B/H). The unstructured triangular grid is used for the computational domain. The results are compared with the channel having single triangular prism and plane channel. The channel walls are subjected to a constant wall temperature. Unsteady twodimensional Navier Stokes and energy equations are solved numerically using a control volume method. The SIMPLE discretization algorithm is used for the convective terms in the solution equations. CFD software FLUENT 6.2 is used to simulate the fluid flow and temperature field. A preprocessor GAMBIT is used to generate the required mesh for the solver. Results illustrate that the Nusselt numbers on the channel walls are strongly modified by the vortices induced by the presence of triangular prisms. In the presence of triangular prisms, the average Nusselt number is 8.5% more as compared to plane channel and 4.5% as compared to channel having single prism at the same Reynolds number and blockage ratio.
1. Introduction Compact heat exchangers are of great importance in the automotive industry, airconditioning and refrigerant applications, internal cooling for gas turbine blades, electrical circuits in electronic chipsets, etc. In compact heat exchangers, thermal resistance is generally dominant on the air side and it may account for 80% or more of the total thermal resistance. The airside heat transfer surface area has to be about 810 times larger than that of the water side. The heat transfer coefficient of the water side is 4050 times higher than that of the air side. Any improvement in the heat transfer on air side therefore improves the overall performance of the heat exchanger. Achieving higher heat transfer rates through various heat transfer enhancement techniques can result in considerable energy savings, more compact and less expensive apparatus with higher thermal efficiency. Different mechanisms such as creating electric or magnetic fields, jets, forced oscillations, fluid additives and special surface geometries may be used for heat transfer enhancement [1],[2] . Methods such as electric or acoustic fields, surface vibration and mechanical devices are called active because they require external power, whereas passive methods use special surface geometries or fluid additive, and do not require any external power. One of the passive methods is the use of vortex generators which produces longitudinal vortices. These vortices generate secondary flow by swirl and destabilize the flow. Different types of vortex generators such as rectangular and triangular wings, winglets [3],[4] and different types of bluff bodies have been considered by different researchers. Among these bodies, triangular prisms have very basic shape and their effect on flow have not been studied in detail. Abbassi et al. [5] numerically studied the consequence of using triangular prism in the flow structure and heat transfer. It was observed that the heat transfer enhancement took place with the use of triangular prism. Chattopadhyay [6] numerically studied the heat transfer in a channel in the presence of triangular prism. The numerical simulation was performed in a turbulent flow regime up to the Reynolds number of 40,000.The aspect ratio of the channel to the prism element was taken as 4. The heat transfer enhancement was found to be 15%. However, there was an increase in skin friction also. Further, Manay et al. [7] numerically studied the effect of dual triangular bluff bodies in a channel on heat transfer and flow characteristics. The flow was taken 2D and Reynolds number was varied from 10,000 to 40,000 under steadystate condition. It was found that at Re = 40,000, the best Nusselt number was obtained as 463. Oztop et al. [8] numerically analyzed the heat transfer and fluid flow in an isothermally heated block located in a channel having laminar flow and 2D domain. The channel had three blocks attached on its bottom wall. A triangular crosssectional bar was used as a control element. Both the top wall of the channel and the bar were isothermal. The bar was located in two different points in the ydirection and these parameters were tested at three different Reynolds numbers ranging between (400 ≤ Re ≤ 1300). Results were also compared for no triangle case. It was observed that insertion of a triangular crosssectional bar enhanced the heat transfer for all Reynolds numbers and the best heat transfer was observed for the position of the bar with y = 3.5. In the most recent studies, Henze et al. [9] experimentally obtained data set at Re = 300,000 for validation of numerical models in a channel with tetrahedral, full body vortex generator. Henze further [10] experimentally studied the effect of the same vortex generator in a channel flow. The height of the vortex generator; Reynolds number and the effect of turbulence intensity were measured. The heat transfer was found to increase with the Reynolds number and the height of the vortex generator. For regions which were affected by vortices, the effect of turbulence was less prominent. On the contrary, the base level of heat transfer for the smooth channel clearly depended on turbulence intensity. The heat transfer was obtained with transient method using thermochromatic liquid crystals for surface temperature measurements. The flow measurements were performed by particle image velocimetery (PIV) system. The literature review shows that the triangular prism has a great potential to enhance the heat transfer. The heat transfer coefficient on the air side is low and hence the use of these bluff bodies on air side is of great importance. The present investigation is performed to study the fluid flow and heat transfer characteristics of a channel with dual builtin triangular prisms with sidebyside arrangement. The simultaneous developing flow in laminar regime is taken. 2. Numerical Modeling The numerical simulation is performed in a 2D laminar flow channel. Two neighboring plates form a channel of height H and length 8.4 H. The triangular prisms placed sidebyside are used as vortex generator as shown in [Figure 1]. The height of the channel is taken as unity, i.e. H = 1.0. The prism base is perpendicular to the direction of flow. The blockage ratio, B/H, is taken as 0.25, where B is the base of the prism. The sides of the prism form an equilateral triangle. Air has been taken as working fluid for which the Prandtl number is 0.71. The flow is taken incompressible with constant properties. The governing flow equations, i.e. continuity, momentum and energy equations, are used to simulate the incompressible steady flow in the given computational domain.{Figure 1} The continuity equation in two dimensions for an incompressible flow is: [INLINE:1] A uniform onedimensional velocity is applied at the inlet of the computational domain. The pressure at the outlet of the computational domain is taken equal to zero gauge. The inlet temperature of air is considered to be uniform at 300 K. On the walls, no slip boundary conditions are applied for the momentum equations. A constant surface temperature of 400 K is applied to the top and bottom walls of the channel. The CFD software FLUENT 6.2 is used to simulate the fluid flow and temperature field. A preprocessor GAMBIT is used to generate the required mesh for the solver. The governing equations are discretized using the finite volume method. The SIMPLE discretization algorithm is used for the convective terms in the solution equations. The secondorder upwinding scheme is used to calculate the flow variables. The under relaxation factor is varied between 0.3 and 1.0. The residuals for continuity, velocity and energy equations are taken as 104, 104 and 106, respectively. The solver iterates the equations till the convergence is obtained for the set residuals. The grid independence test was investigated by conducting simulations in the plane duct by using different unstructured grids with the number of triangular cells ranging from 47,000 to 84,000 cells. The average Nusselt numbers for 96,060, 84,328, 61,800 and 47,086 cells are 1.831162, 1.826417, 1.817059 and 1.806722, respectively. The variation in Nusselt number decreases as the number of cells is increased. The variation in Nusselt number is 0.2% when the triangular cells are increased from 84,328 to 96,060. Hence, to save computation cost and time, the number of cells is taken as 84,328. 3. Results and Discussion The computations are performed for a Reynolds number of 100 and blockage ratio (b) of 0.25, where the blockage ratio (b) is the ratio of prism base to the channel height (b = B/H). 3.1 Flow Characteristics [Figure 2] shows the velocity vector plot for Re = 100 and dual prism in sidebyside arrangement. By inserting dual prisms, two vortex regions are obtained. The vortices are parallel to each other. The flow is divided into four streams and combines the main stream after the prism's location. Hence, in case of dual prism, the overall strength of the vortices increases and there is more mixing of the flowing fluid.{Figure 2} 3.2 Temperature Contours and Heat Transfer Characteristics [Figure 3] shows the temperature contours of the computation domain with dual prism in sidebyside arrangement at Re = 100 and blockage ratio = 0 . 25. Due to the presence of dual prism, the overall strength of the vortices increases and there is additional mixing of fluid in the core region and wall boundaries. Due to this mixing, the temperature gradient at the walls is increased. The higher temperature gradient at the walls leads to higher heat transfer rates. [Figure 4] shows the variation of Nusselt number for the three cases. The fluid entering the duct is cold and the surface of the plates is hot. At the entrance of the duct, the Nusselt number is high. The higher values of Nusselt number at the entrance can be attributed to large temperature gradient and thin boundary layer. The actual effect of the triangular prisms is revealed at the portion of the duct along and downstream of the obstacle.{Figure 3}{Figure 4} The values of Nusselt number decrease moving away from the inlet. In the case of a duct with an obstacle, the Nusselt number curve shows separation from the leading edge of the obstacle showing a peak. Behind the obstacle, the strength of the vortices decreases gradually, causing the decrease in the values of Nusselt number. The value of Nusselt number at any location from the leading edge of the obstacle is higher than the plane duct. Further, the rise in case of dual triangular prisms is higher than single triangular prism as well as plane duct. 3.3 Pressure Characteristics [Figure 5] shows the pressure variation along the channel length with prisms in sidebyside arrangement and blockage ratio of 0.25 at Reynolds Number = 100. There is a rise in the pressure drop when the obstacle is attached. The flow blockage due to the triangular prism is the main factor to cause a rise in the pressure drop.{Figure 5} 4. Conclusions In the present study, the numerical simulation of laminar flow in a parallel plate channel with builtin dual triangular prisms has been performed. Heat transfer enhancement for dual triangular prisms is additional as compared to the single triangular prism for the same blockage ratio. The percentage increase in the average Nusselt number is 8.5% as compared to plane channel and 4.5% as compared to channel having single prism at same Reynolds number and blockage ratio. But the increase in heat transfer is associated with enlarged pressure drop. 5. Nomenclature [INLINE:2] 6. Greek Symbols [INLINE:3] [11] References


