Triggering Vortex Shedding by Superimposed Thermal Buoyancy Around Bluff Obstacles in Cross-Flow at Low Reynolds Numbers

Influences of superimposed thermal buoyancy on the initiation of vortex shedding process behind bluff obstacles (such as circular and square cylinders in 2-D) in cross-flow at low Reynolds numbers (10 ≤ Re ≤ 40) are discussed. The flow which is steady and separated at this Reynolds number range eventually becomes unsteady periodic with the introduction of thermal buoyancy. The aim here is to numerically predict the critical value of the buoyancy parameter (Richardson number, Ri) for the onset of vortex shedding. The critical Ri is found to have a decreasing tendency for both types of cylinder geometries with increasing Re.     

Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.     

Steady Mixed Convection in Power-Law Fluids from a Heated Triangular Cylinder

The steady mixed convective transport from a heated triangular cylinder immersed in power-law fluids in an unconfined vertical domain is investigated numerically. Two different configurations of the cylinder are chosen; one when the base of the cylinder is facing the flow and the other when the apex of the triangle is facing the flow. The simulation is performed for: Reynolds number (1 to 35), Richardson number (0 to 2), power law index (0.4 to 1.8) and Prandtl number, 50. The flow and thermal fields are visualized through the streamlines and isotherm contours at the close proximity of the heated object for various Reynolds numbers, Richardson numbers and power law indices. The distributions of the surface pressure coefficient and local Nusselt number provide further insight of the hydrodynamic and thermal characteristics. Finally, the total drag coefficient and average Nusselt numbers on the surface of the cylinder are computed to explore the overall macroscopic behavior of the involved thermo-hydrodynamics. The flow separation is observed to be more when the apex of the cylinder is facing the flow. The average heat transfer, measured in terms of the Nusselt number, and the total drag on the cylinder are also found higher for that configuration.     

Mixed Convection Heat Transfer From an Equilateral Triangular Cylinder in Cross Flow at Low Reynolds Numbers

A two-dimensional numerical study is undertaken to investigate the influences of cross buoyancy on the vortex shedding phenomena behind a long heated equilateral triangular cylinder for the low-Reynolds-number laminar regime. The flow is considered in an unbounded medium; however, fictitious confining boundaries are chosen on the lateral sides to make the problem computationally feasible. Numerical calculations are performed by using a finite-volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid system. The range of Reynolds number is chosen to be 10–100 with a fixed Prandtl number, 0.71. The mixed convection effect is studied for the Richardson number range of 0–1. The effects of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as the overall drag and lift coefficients, local and surface average Nusselt numbers, and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and discussed. The critical Richardson and average Nusselt numbers are plotted against the Reynolds and Richardson numbers, respectively, to elucidate the role of thermal buoyancy on flow and heat transfer characteristics. It is observed that the vortex shedding frequency (Strouhal number) increases with increased heating and suddenly reduces to zero at the critical Richardson number. The critical Richardson number is again found to increase with Reynolds number for a particular blockage ratio, and the higher the blockage ratio, the less is the critical Richardson number. The results obtained from the commercial solver are extensively validated with the available numerical results in the literature and an excellent agreement is observed.     

The Effect of Aiding/Opposing Buoyancy on Two-Dimensional Laminar Flow Across a Circular Cylinder

The effect of thermal buoyancy on the upward flow and heat transfer characteristics around a heated/cooled circular cylinder is studied. A two-dimensional finite-volume model is deployed for the analysis. The influence of aiding/opposing buoyancy is studied for the range of parameters ?0.5 ≤ Ri ≤ 0.5, 50 ≤ Re ≤ 150, and the blockage ratios of B = 0.02 and 0.25. The flow shows unsteady periodic nature in the chosen range of Reynolds numbers for the forced convective cases (Ri = 0), and the vortex shedding stops completely at some critical values of Richardson numbers.     

HEAT AND FLUID FLOW ACROSS A SQUARE CYLINDER IN THE TWO-DIMENSIONAL LAMINAR FLOW REGIME

The flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7. The effect of vortex shedding on the isotherm patterns and heat transfer from the cylinder is discussed. Heat transfer correlations between Nusselt number and Reynolds number are presented for uniform heat flux and constant cylinder temperature boundary conditions.     

Dual role of thermal buoyancy in controlling boundary layer separation around bluff obstacles

We establish through numerical simulation a dual role played by the superimposed thermal buoyancy in controlling the boundary layer separation around bluff obstacles. The work essentially demonstrates the influence of superimposed thermal buoyancy on flow around bluff obstacles of circular and square cross sections in aiding/opposing and cross buoyancy configurations. For the aiding/opposing configuration we show two phenomena such as the suppression of flow separation which occurs at relatively low Reynolds numbers (10–40) and the suppression of vortex shedding at a moderate range of Reynolds numbers (50–150). In the cross buoyancy configuration, the initiation of vortex shedding by the introduction of thermal buoyancy is shown at relatively low Reynolds numbers (10–40). Hence, depending on the direction of interaction with the free stream flow, the buoyancy sometimes stabilizes the flow and sometimes destabilizes the flow. Accordingly, there is a dual role of superimposed thermal buoyancy in controlling the boundary layer separation around bluff obstacles. Such duality cannot be observed in case of other agents such as rotation, magnetic force which also control the boundary layer separation around bluff obstacles.     

Steady mixed convective flow and heat transfer from tandem square cylinders in a horizontal channel

The two-dimensional laminar steady mixed convective flow and heat transfer around two identical tandem square cylinders confined in a horizontal channel are simulated by the high-accuracy multidomain pseudo-spectral method. The blockage ratio of the channel is chosen as 0.1, whereas the spacing between the cylinders is fixed with four widths of the cylinder. The Prandtl number is fixed at 0.7, the Reynolds number (Re) is studied in the range 5?≤?Re?≤?60, and the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1. Numerical results reveal that, with the thermal buoyancy effect, the mixed convective flow remains steady. The variations of the overall drag and lift coefficients and the Nusselt numbers, are presented and discussed. Furthermore, the influence of thermal buoyancy on fluid flow and heat transfer is discussed and analyzed.     

Influence of Aiding Buoyancy on the Suppression of Flow Separation for Power-Law Fluids Around a Circular Object

Numerical computations are performed to analyze the influence of aiding thermal buoyancy on the phenomenon of suppression of flow separation in power-law fluids around a circular object. The idea has been borrowed from some recent similar works in Newtonian fluids. Owing to the contradictory behavior of shear-thinning and shear-thickening fluids in regard to the separation mechanism, we intend to understand the role of superimposed thermal buoyancy on the suppression phenomena in non-Newtonian power-law fluids, for which a range of power-law indices (0.4 to 1.8) is considered. The Reynolds numbers are kept intentionally low, within 10 to 40, such that the isothermal flow remains steady and separated without imposition of thermal buoyancy. The buoyancy causes a delay in the separation, thereby affecting the suppression phenomena. We determine the critical heating parameter (Richardson number) for the complete suppression of the flow separation and from there we construct a bifurcation diagram to show the typical flow regime evolved due to the complex interplay between the aiding thermal buoyancy and fluid rheology. The Richardson number in the simulation lies in the range 0 to 0.35, keeping the Prandtl number fixed at 50. The heat transfer rates from the object are also obtained and important inferences are drawn in regard to the inhibition/augmentation of heat transfer due to fluid rheology.     

Numerical Investigation of Convective Heat Transfer in Unsteady Laminar Flow Over a Square Cylinder in a Channel

Unsteady laminar flow past a heated square cylinder mounted inside a plane channel was investigated numerically. The blockage ratio was chosen as 1/8 and the Reynolds number based on the mean flow velocity and chord length of the square cylinder was selected as less than 200, for which the two-dimensional behavior of the flow is assured. The time-averaged Nusselt number as well as some integral parameters such as drag coefficient, recirculation length, and Strouhal number were obtained and compared with literature. Results show a nearly linear increase in recirculation length and decrease in drag coefficient with increasing Reynolds number for the steady flow regime. There is an increase in the total Nusselt number and drag coefficient with a Reynolds number for unsteady flow regime, where vortex shedding is observed from the cylinder. A correlation was obtained for the variation of the total Nusselt number with the Reynolds number.     

Characteristics for flow and heat transfer around a circular cylinder near a moving wall in wide range of low Reynolds number

The present study numerically investigates two-dimensional laminar fluid flow and heat transfer past a circular cylinder near a moving wall. Numerical simulations to calculate the fluid flow and heat transfer past a circular cylinder are performed for different Reynolds numbers varying in the range of 60–200 and a fixed Prandtl numbers of 0.7 (air) in the range of 0.1 ? G/D ? 4, where G/D is the ratio of the gap between the cylinder and a moving wall, G and the cylinder diameter, D. The flow and thermal fields become the steady state below the critical gap ratios of 0.8, 0.4 and 0.2 for the Reynolds numbers of 60, 80 and 100, respectively. As the gap ratio decreases, the magnitude of lift coefficient for all Reynolds numbers increased significantly with diminishing G/D due to the ground effect. The cases of Reynolds numbers of 60, 80 and 100 revealed the sharp slope of drag coefficient in the range of the gap ratio where the flow transfers from the unsteady state to the steady state. As the Reynolds number decreases, the variation of Nusselt is much significant and increases considerably with decreasing G/D.     

Effect of Prandtl number and rotation on vortex shedding behind a circular cylinder subjected to cross buoyancy at subcritical Reynolds number

We perform a two-dimensional numerical simulation following a finite volume approach to understand the vortex shedding (VS) phenomena around a circular cylinder subjected to cross thermal buoyancy at a subcritical Reynolds number, Re = 40. The flow is considered in an unbounded medium. The cylinder may either be stationary or rotating about its centroidal axis. At the subcritical Reynolds number, the flow and thermal fields are steady without the superimposed thermal buoyancy (i.e. for pure forced flow). However, as the buoyancy parameter (Richardson number, Ri) increases, flow becomes unstable, and eventually, at some critical value of Ri, periodic VS is observed to characterize the flow and thermal fields. An extended Stuart–Landau model is used in this work for the accurate quantitative estimation of the critical Richardson number for the onset of VS. The above phenomena of VS with imposed buoyancy is strongly dependent on the type of the fluid being used. We quantify here the minimum heating requirement for the initiation of VS by choosing three different types of fluids having Prandtl numbers, Pr = 0.71, 7, and 100. The dimensionless rotational speed (Ω) ranges between 0 and 4. It is revealed that as Pr increases, heating requirement also increases for the initiation of VS. A possible explanation for the observation is provided.     

Combined convection heat transfer in a channel with two ribs attached to one wall

Two-dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisted flow and buoyancy-opposing flow. The effect of Reynolds number, Re_L, and modified Richardson number, Ri^*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri^* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy-assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999     

Correlation for laminar mixed convection from a rotating cylinder

The problem of laminar mixed convection from a rotating isothermal cylinder was solved numerically. A correlation for the average Nusselt number as a function of Reynolds number and buoyancy parameter is proposed. The correlation gives an accurate estimate of the Nusselt number over the range of Reynolds numbers and buoyancy parameter values studied.     

Synthetic and Continuous Jets Impinging on a Circular Cylinder

Synthetic and continuous water jets impinging onto an electrically heated circular cylinder were experimentally investigated. The slot nozzle width was 0.36 mm, the cylinder diameter was 1.2 mm, and the cylinder-to-nozzle spacing related to the slot width was 5–21. Two optical methods were used: qualitative laser-induced fluorescence (LIF) visualization and laser Doppler vibrometry (LDV) measurements. Simultaneously with the optical experiments, the overall convective heat transfer from the circular cylinder was evaluated. The LDV quantified the velocity of the oscillating piezo-driven diaphragm at frequencies from 30 to 68 Hz. A majority of the study was performed at the near-resonant frequencies from 46 to 49 Hz. For all investigated jets, the Reynolds numbers based on the nozzle width ranged from 36 to 171. The LIF visualization revealed a dominant flow separation occurring on the windward cylinder side. This result is attributed to the effect of the miniscales, a relatively small ratio of the nozzle width to the cylinder diameter, and low Reynolds numbers. An increase in the Reynolds number changes the flow pattern from a steady jet-flow separation to a vortex shedding wake-flow regime. The heat transfer experiments were validated in a natural convection regime. An enhancement of the average Nusselt numbers by 4.2–6.2 times by means of the synthetic jets was quantified by comparison with the natural convection regime. A correlation for the average Nusselt number was proposed for both the continuous and synthetic jets.     

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.     

A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights

The numerical solution is obtained for unsteady two-dimensional fluid flow and heat transfer in a confined impinging slot jet using the finite volume method. In order to consider the effect of Reynolds number and height ratio on the flow and temperature fields in the channel, the numerical simulations were performed for different Reynolds numbers of 50–500 and different height ratios of 2–5. The critical Reynolds number, beyond which the flow and thermal fields change their state from steady to unsteady, depends on the Reynolds number and height ratio. The unsteadiness gives a big impact on the flow and temperature fields and as a result the pressure coefficient, skin friction coefficient and Nusselt number in the unsteady region show different characteristics from those in the steady region.     

Mixed Convection from a Cylinder with Highly Conductive Fins in Cross Flow

The problem of laminar mixed convection from an isothermal cylinder with highly conductive fins in cross flow was solved numerically. The average Nusselt number was calculated at different combinations of number of fins (0–17), fin height (0–2), Reynolds number (10–200), and buoyancy parameter (0–5). The fins were most effective at low Reynolds numbers and low buoyancy. The addition of short fins at high values of the Reynolds number and buoyancy parameter resulted in a slight reduction in the Nusselt number. There was an optimal number of fins beyond which additional fins did not increase or even reduce the average Nusselt number. This number was Reynolds number- and buoyancy parameter-dependent. When using a small number of long fins at low buoyancy, an even number of fins was better than an odd number of fins.     

Heat transfer enhancement in a channel with a built-in square cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in square cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two square cylinder sizes. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study shows that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.