Detailed numerical study of flow and vortex dynamics in staggered pin-fin arrays within a channel

Pin-fin arrays are known to enhance heat transfer from heated surfaces and provide important industrial applications such as increasing internal heat transfer to a turbine blade or solar receiver. Several studies on heat transfer characteristics of various pin-fin arrangements and effects of geometrical parameters on heat transfer have been performed in the past. The present paper aims to address main aspects of fluid flow and heat transfer interactions through a pin-fin array with the help of high-fidelity numerical simulations and focuses on three issues. The first one is to evaluate the effect of three dimensional flow physics such as horseshoe vortices and periodic unsteadiness from vortex shedding on the spatial variation of heat transfer. The second target is to analyze the effect of free end clearance in the case of finite height pin-fin arrays with added flow complexity relative to wall-bounded pin-fin arrays, to provide a comprehensive picture of the flow physics introduced by free ends. The third one is to provide a general guideline for the numerical simulation of flows through pin-fin arrays by comparing simulations on reduced span-wise domains with the full multi-row pin configuration, to elucidate the significance of wall effects. In addition, comparison of the flow characteristics in different stream-wise row locations, is performed to establish the domain length where self-similarity might occur with inflow/outflow conditions. All simulations are conducted for low Mach number incompressible ⇤Correspondence author: K. Kannan flow with temperature as a passive scalar. The current formulation assumes that variations in temperature have no effect on the fluid motion by choosing appropriate thermal boundary conditions that are still within the realistic parameter range for turbine cooling. In this paper, we perform flow simulations using the Large Eddy Simulation methodology. Two numerical codes, one based on a Finite Volume method and the other based on a Spectral Element approach, are benchmarked with each other and validated versus experiments available in the literature (Ostanek and Thole, 2012). NOMENCLATURE Cs Smagorinsky constant D Pin Diameter DH Hydraulic Diameter e Relative error compared to the experiment f Frequency of vortex shedding FV M Finite Volume Method H Channel height, Pin-fin height Lr D Wake closure position, location of zero mean streamwise velocity along the wake axis PrSGS Sub-grid scale Prandtl number q 00 Heat flux ReD Pin-fin Reynolds number, ReD =UmaxDn 1 ReDH Pin-fin hydraulic Reynolds number, ReDH =UmDHn 1 1 Copyright c 2016 by ASME ReH Channel Reynolds number, ReH =UmHn 1 St Strouhal number, St = f D Umax SEM Spectral Element Method T Temperature Um Bulk velocity Umax Average velocity through minimum flow area U,V,W Instantaneous stream-wise, transverse and span-wise velocity components x Stream-wise distance y Transverse distance y+ Dimensionless transverse distance from wall, y+ = Ut yn 1 z Span-wise distance Greek Letters n Molecular kinematic viscosity nt Turbulent kinematic viscosity l2 Lambda vortex Dt Non-dimensional time step, Dt = tUm D INTRODUCTION Flow over pin-fin arrays mounted on a wall is of considerable practical interest in fluid mechanics. It has numerous applications such as heat exchangers in gas turbine airfoils, nuclear power plants, boilers and directly irradiated volumetric receivers. The operating principle is based on air being forced through the array and energy transport takes place to the working fluid flowing within and over the array via heat convection. Because of the wide range of applications, prediction of the energy transport capability along each pin and effects of their interaction, rate of convective heat transfer between the pin surface and the working fluid, and temperature distribution through the array are of great importance for designing more efficient and reliable pinfin configurations. The considerable fundamental interest in flow through pin-fin arrays is due to a highly unsteady and three dimensional nature of the flow and various interacting vortex systems. One of these interacting vortex systems is the horseshoe vortex (HV) which is present at the pin-fin and end-wall junction. There is also another vortex system known as Von-Karman vortex (KV). Earlier studies on the dynamics of horseshoe vortex systems have shown that they include a primary horseshoe vortex (HV), a secondary vortex upstream of the horseshoe vortex (SV), a tertiary vortex upstream of the secondary vortex (TV), and a small vortex in the corner region of the junction (CV) (Hunt et al. [1] Praisner et al. [2]). There have been a wide range of studies on the time mean and instantaneous flow, and on the mechanisms that give rise to an increase in the end-wall heat transfer of a body end-wall junction. Ames et al. [3] performed a detailed study of the end-wall heat transfer distributions in a staggered pin-fin array using an infrared camera at Reynolds numbers of 3000, 10000, 30000. Their detailed heat transfer distributions highlighted the influence of the horseshoe vortex system in the entrance region on the end-wall heat transfer and the wake generated turbulence throughout the pin-fin array. Ostanek [4] made more detailed flow field and heat transfer measurements for an array of staggered pin-fins. He showed that, for low Reynolds numbers, average heat transfer was dominated by the horseshoe vortex in the initial row. In the downstream rows, however, the horseshoe was not as distinguished as in the first row. In another work, Ostanek and Thole [5] performed a detailed isothermal experimental study on the effect of stream-wise spacing on the near wake. The stream-wise spacing was varied between 3.46D and 1.73D and experiments were conducted at Reynolds numbers of 3000 and 20000. Their results showed that the vortex shedding frequency increases for decreasing stream-wise spacing. Moreover, in the third pin-fin row, the wake closure position was reduced to a greater extent than in the first row wake due to the generated turbulence in the upstream rows. The level of turbulent kinetic energy also decreased for decreasing stream-wise spacing. Ames and Dvorak [6] investigated the pin-fin midline heat transfer. They used hot wire anemometry to acquire turbulence measurements and velocity distributions at three Reynolds numbers of 3000, 10000, 30000. Their results showed that heat transfer augmentation due to turbulence is highest in row 4 and beyond. Delibra et al. [7] used large eddy simulation coupled with a URANS treatment to compute the flow and heat transfer in a matrix of staggered, cylindrical, thermally passive pins bounded by heated end-walls at two Reynolds numbers of 10000 and 30000. According to their results, large scale coherent vortical structures are the general mechanisms for heat removal from the end-walls. They showed that large vortex systems are the dominant heat transfer modes away from the end-wall. These results are consistent with what has been previously reported in [6]. If free ends are present, the free ends also add to these flow complexities and the vortices being shed from the free end interact with the vortex shedding from the cylinder surface [8]. Sparrow and Ramsey [9] performed mass transfer experiment on a staggered array of circular cylinders situated in a cross-flow of air in a flat rectangular duct. According to their experiments, tip clearance gives rise to a transverse flow component superposed on the main flow that passes around the circumference and as a result, the wake flow is strongly three dimensional. The fully developed heat transfer coefficients were quite insensitive to a cylinder height (or extent of tip clearance). The effect of tip clearance on the performance of the heat transfer and pressure drop at low Reynolds number was investigated through numerical and experimental studies by Deqing et al. [10]. According to their results, the heat transfer and pressure drop performance in the case of low Reynolds number is quite sensitive to the tip clearance, and the introduced tip clearance can enhance the heat transfer and reduce the pressure drop effectively. Moores and Joshi [11] experimentally evaluated the effect of tip clearance 2 Copyright c 2016 by ASME on a liquid cooled array of shrouded pin-fins. Three arrays of height to diameter ratios ranging from 0.5 to 1.1 and tip clearance of 0 to 25% of pin height were evaluated. Increased mean heat transfer and lower overall pressure drop were realized for clearances of less than 10%. The increase in heat transfer was attributed to the additional surface area when clearance was introduced. However, they showed that the heat transfer efficiency of the fin at the tip is lower compared to the array as a whole. According to other studies [12][13], tip clearance results in two competing effects. The first is the promotion of the heat transfer rate due to the increase in the heat transfer coefficient at the tip surface. The second is the restraint of the heat transfer rate due to the effect of flow bypass. In the present study two different numerical approaches are employed to perform large eddy simulation of flow over staggered arrays of cylindrical, thermally active pins bounded by heated end-walls. Considered is a Reynolds number of 3000, based on the pin diameter and velocity through the minimum flow area. In the first part of the present study, the two numerical methods are validated against the isothermal experiments of Ostanek and Thole [5]. In the second part, a second geometry based on the geometry in [5] is defined with a free space of 1D above the pins. A detailed study of the flow field, the complex flow structures, and a comparison of the flow topology with the full height case provides a comprehensive picture of the complex flow behavior. The data at different locations are analyzed and compared between the two geometries which may allow for further op