Arun K. Saha

Three-dimensional study of flow past a square cylinder at low Reynolds numbers

Abstract The spatial evolution of vortices and transition to three-dimensionality in the wake of a square cylinder have been numerically studied. A Reynolds number range between 150 and 500 has been considered. Starting from the two-dimensional Karman vortex street, the transition to three-dimensionality is found to take place at a Reynolds number between 150 and 175. The three-dimensional wake of the square cylinder has been characterized using indicators appropriate for the wake of a bluff body as described by the earlier workers. In these terms, the secondary vortices of Mode-A are seen to persist over the Reynolds number range of 175–240. At about a Reynolds number of 250, Mode-B secondary vortices are present, these having predominantly small-scale structures. The transitional flow around a square cylinder exhibits an intermittent low frequency modulation due to the formation of a large-scale irregularity in the near-wake, called vortex dislocation. The superposition of vortex dislocation and the Mode-A vortices leads to a new pattern, labelled as Mode-A with dislocations. The results for the square cylinder are in good accordance with the three-dimensional modes of transition that are well-known in the circular cylinder wake. In the case of a circular cylinder, the transition from periodic vortex shedding to Mode-A is characterized by a discontinuity in the Strouhal number–Reynolds number relationship at about a Reynolds of 190. The transition from Mode-A to Mode-B is characterized by a second discontinuity in the frequency law at a Reynolds number of ≈250. The numerical computations of the present study with a square cylinder show that the values of the Strouhal number and the time-averaged drag-coefficient are closely associated with each other over the range of Reynolds numbers of interest and reflect the spatial structure of the wake.

Parametric study of unsteady flow and heat transfer in a pin-fin heat exchanger

Abstract A numerical study has been carried out to analyze the unsteady three-dimensional flow and heat transfer in a parallel-plate channel heat exchanger with in-line arrays of periodically mounted rectangular cylinders (pins) at various Reynolds number and geometrical configurations. The three-dimensional unsteady Navier–Stokes and energy equations are solved using higher order temporal and spatial discretizations. The simulations have been carried out for a range of Reynolds number based on cylinder width (180–600) and a Prandtl number of 6.99 (corresponding to water). Conjugate heat transfer calculations have been employed to account for the conduction in the solid cylinder and convection in the fluid. The thermal performance factor (TPF) increases significantly when the flow becomes unsteady. The choice of aspect ratio of the cylinders is judged by their relative increase in friction factor and heat transfer at transitional Reynolds number. The TPF is found to increase with the increase in pitch of the cylinders. The increase in channel height enhances the TPF though the heat transfer decreases at higher channel height.

Far-wake characteristics of two-dimensional flow past a normal flat plate

Direct numerical simulation of flow past a normal flat plate having an aspect ratio of 0.125 has been carried out at Reynolds number range of 30–175. The unsteady far-wake observed at low Reynolds number becomes steady for 75⩽Re⩽140. The steady far-wake undergoes a transition at Re=145 with large scale unsteadiness observed in the far-wake. The frequency of the large scale vortex structures, also called secondary vortex structures, is lower than that of the near-wake. At Re=150, the low frequency far-wake vortex street undulates at another frequency, which increases with increasing Reynolds number, resulting in a tertiary vortex pattern. The transitions are found to have no significant effect on the mean integral parameters such as the drag coefficient and the Strouhal number.

UNSTEADY SIMULATION OF TURBULENT FLOW AND HEAT TRANSFER IN A CHANNEL WITH PERIODIC ARRAY OF CUBIC PIN‐FINS

An unsteady three-dimensional numerical study is performed to explore flow and heat transfer in a periodic array of cubic pin‐fins housed inside a channel. The pin‐fins are arranged in an in-line pattern with both streamwise and transverse periodicity set to 2.5 times the pin-fin dimension. Calculations are done in the turbulent flow regime for Reynolds numbers in the range of 7,090–13,280. The unsteady Reynolds-averaged Navier–Stokes (URANS) and energy equations are solved using higher-order temporal and spatial discretization schemes. An unsteady k – ϵ turbulence model is employed to model the unresolved turbulence fluctuations. Large eddy simulations (LES) are also performed for a Reynolds number of 7,090 for validation purposes. The URANS results are able to resolve the discrete large-scale spatial and temporal fluctuations in the flow, and the time-averaged predictions with URANS match the LES results very well. The large-scale fluctuations in the flow appear primarily in the region between the cubic fins, but are linked to low-amplitude oscillations in the outer flow.Three thermal boundary conditions are studied: (1) only channel wall heated (2) only pin‐fins heated, and (3) both channel wall and pin‐fins heated. The overall heat transfer enhancement is about 1.8–2.0 times the heat transfer from a smooth duct flow. The heat transfer from pin‐fins is found to be 5–9% higher than that from the top wall at low Reynolds numbers (7,090 and 8,900), while it is of comparable magnitude at higher Reynolds number (13,280).

Blade Tip Leakage Flow and Heat Transfer with Pressure-Side Winglet

A numerical study has been conducted to explore the effect of a pressure-side winglet on the flow and heat transfer over a blade tip. Calculations are performed for both a flat tip and a squealer tip. The winglet is in the form of a flat extension, and is shaped in the axial chord direction to have the maximum thickness at the chord location, where the pressure difference is the largest between the pressure and suction sides. For the flat tip, the pressure-side winglet exhibits a significant reduction in the leakage flow strength. The low heat transfer coefficient “sweet-spot” region is larger with the pressure-side winglet, and lower heat transfer coefficients are also observed along the pressure side of the blade. For the flat tip, the winglet reduces the heat transfer coefficient locally by as much as 30%, while the average heat transfer coefficient is reduced by about 7%. In the presence of a squealer, the role of the winglet decreases significantly, and a 5% reduction in the pressure loss coefficient is achieved with the winglet with virtually no reduction in the average heat transfer coefficient. On the other hand, the suction-side squealer with constant width winglet shows lower heat transfer (reduction of 5.5%) and pressure loss coefficient (reduction of 26%) than its baseline counterpart.

Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder

Abstract Direct Numerical Simulation of unsteady, two-dimensional flow past a square cylinder placed centrally in a channel has been carried out using a higher order finite difference scheme. A Reynolds number of 100 has been considered in the computation. The flow in the wake is found to be unsteady with a strong periodic component. The instantaneous vorticity field at this Reynolds number is seen to be spatially coherent. Maps of stress components formed from the oscillatory components of the velocity field ũ and ṽ show double peaks in u u and u v but a single peak in v v . The maps are seen to be symmetric about the centreline of the flowspace. The results obtained in the present work are qualitatively similar to the phase-averaged plots from the experiments reported at high Reynolds numbers. Hence, the primary conclusion of the present study is that the unsteady flows with one or a few dominating frequencies (periodic or quasi-periodic) are statistically similar to a fully turbulent flow. To assess the similarity further, the energy transfer mechanism between the mean motion and the fluctuations has been studied through different terms associated with kinetic energy budget of the fluctuating velocities. The total pressure, the advection of the time-mean flow and production terms are found to be primarily responsible for the energy cascade. In contrast, diffusion and dissipation do not appear to have a significant influence on the energy transfer mechanism.

Turbulent Heat Transfer in Ribbed Coolant Passages of Different Aspect Ratios: Parametric Effects

Turbulent flow and heat transfer in rotating ribbed ducts of different aspect ratios (AR) are studied numerically using an unsteady Reynolds averaged Navier-Stokes procedure. Results for three ARs (1:1, 1:4, and 4:1) and staggered ribs with constant pitch (Ple = 10) in the periodically developed region are presented and compared. To achieve periodic flow behavior in successive inter-rib modules calculations are performed in a computational domain that extends to two or three inter-rib modules. The computations are carried out for an extended parameter set with a Reynolds number range of 25,000-150,000, density ratio range of 0-0.5, and rotation number range of 0-0.50. Under rotational conditions, the highest heat transfer along the leading and side walls are obtained with the 4:1 AR, while the 1:4 AR has the highest trailing wall Nu ratio and the lowest leading wall Nu ratio. The 1:4 AR duct shows flow reversal near the leading wall (leading to low Nu) at high rotation numbers and density ratios. For certain critical parameter values (low Re, high Ro, and/or DR), the leading wall flow is expected to become nearly stagnant, due to the action of centrifugal buoyancy, leading to conduction-limited heat transfer The 4:1 AR duct shows evidence of multiple rolls in the secondary flow that direct the core flow to both the leading and trailing surfaces which reduces the difference between the leading and trailing wall heat transfer relative to the other two AR ducts.

Two-Dimensional Study of the Turbulent Wake Behind a Square Cylinder Subject to Uniform Shear

The flow past a square cylinder at a Reynolds number of 20,000 has been simulated through direct calculations and through the calculations using turbulence model. The present investigation highlights significant differences between the two approaches in terms of time-averaged flow, Strouhal number, and aerodynamic forces. The timeaveraged drag coefficient and the rms fluctuations due to the direct calculations are higher than those due to the turbulence model. However, Strouhal number is underpredicted in the direct calculations. The effect of shear on the flow has also been determined using the turbulence model. The time-averaged drag coefficient is found to decrease with the increase in shear parameter up to a certain value. Then it increases with the further increase in the shear parameter. On the other hand, lift coefficient increases with the increase in shear parameter. Strouhal number shows a decreasing trend with the increase in shear parameter whereas the rms values of drag and lift coefficients increase with the

Three-dimensional numerical simulations of the transition of flow past a cube

The wake of a cube placed in a uniform flow is numerically studied. The present study concentrates on the first two transitions, one spatial and the other a temporal one. Computations are carried out for a Reynolds number range of 20–300. Starting from a steady symmetric flow, the transition to asymmetric steady flow occurs at a Reynolds number between 216 and 218. The loss of symmetry increases with increasing Reynolds number. The asymmetric steady flow experiences a Hopf bifurcation at a Reynolds number between 265 and 270 and becomes unsteady but maintains the planar symmetry. The transitions of the present study are compared to the transitions of flow past a square cylinder and a sphere. The transition sequence and flow structures match closely to that of a sphere. The drag and side force coefficients are calculated and it is observed that they are in accordance with the spatial structures of the wake. The drag coefficient is found to decrease with Reynolds number in the steady flow regime. Similarly,...

Computations of Turbulent Flow and Heat Transfer Through a Three-Dimensional Nonaxisymmetric Blade Passage

The design of a three-dimensional nonaxisymmetric end wall is carried out using three-dimensional numerical simulations. The computations have been conducted both for the flat and contoured end walls. The performance of the end wall is evaluated by comparing the heat transfer and total pressure loss reduction. The contouring is done in such a way to have convex curvature in the pressure side and concave surface in the suction side. The convex surface increases the velocity by reducing the local static pressure, while the concave surface decreases the velocity by increasing the local pressure. The profiling of the end wall is done by combining two curves, one that varies in the streamwise direction, while the other varies in the pitchwise direction. Several contoured end walls are created by varying the streamwise variation while keeping the pitchwise curve constant. The flow near the contoured end wall is seen to be significantly different from that near the flat end wall. The contoured end wall is found to reduce the secondary flow by decreasing radial pressure gradient. The total pressure loss is also lower and the average heat transfer reduces by about 8% compared to the flat end wall. Local reductions in heat transfer are significant (factor of 3). This study demonstrates the potential of three-dimensional endwall contouring for reducing the thermal loading on the end wall.