Onset Of Vortex Shedding Research Articles

A comparison of immersed boundary and body-fitted methods: Transient vortex shedding in elaborate bio-mimetic cylinders

In this study, two contrasting computational fluid dynamics (CFD) methods are used to simulate flow around bio-mimetic cylinders. Cylindrical shapes are proposed to represent a cross-sectional view of complex geometries, such as cylinders with biofouling or cylinders with helical strakes. The non-conformal Cartesian immersed boundary method (IBM) and conformal curvilinear body-fitted method (BFM) are applied to solve the governing equations. A critical assessment of the accuracy and efficiency of IBM is presented by employing an open-source solver with similar discretization, algorithms, and properties. It has been found that IBM can reduce computation time by up to 49% for protrusions with different numbers of sides. Results show that IBM can reduce required computation time up to an outstanding 71% for protrusions with different heights. Results also indicate that transient duration doesn't significantly change the reduction trend in required computation time. For this reason, the onset of vortex shedding and eventually fully-developed flow takes place substantially sooner in IBM simulation than in BFM. It is also found that the height and shape of protrusions affect BFM performance but have no effect on IBM performance. This study proves that non-conformal IBM is a robust numerical approach when simulating vortex shedding in complex geometries.

Rectangular Cylinder Orientation and Aspect Ratio Impact on the Onset of Vortex Shedding

Rectangular cylinders have the potential to provide valuable insights into the behavior of fluids in a variety of real-world applications. Keeping this in mind, the current study compares the behavior of fluid flow around rectangular cylinders with an aspect ratio (AR) of 1:2 or 2:1 under the effect of the Reynolds number (Re). The incompressible lattice Boltzmann method is used for numerical computations. It is found that the flow characteristics are highly influenced by changes in the aspect ratio compared to the Reynolds number. The flow exhibits three different regimes: Regime I (steady flow), Regime II (initial steady flow that becomes unsteady afterward), and Regime III (completely unsteady flow). In the case of the cylinder with an aspect ratio of 2:1, vortex generation, variation in drag, and the lift coefficient occur much earlier at very low Reynolds numbers compared to the cylinder with an aspect ratio of 1:2. For the cylinder with an aspect ratio of 1:2, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 120, 121 ≤ Re ≤ 144, and 145 ≤ Re ≤ 200, respectively. For the cylinder with an aspect ratio of 2:1, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 24, 25 ≤ Re ≤ 39, and 40 ≤ Re ≤ 200, respectively. The cylinder with an aspect ratio of 1:2 is found to have the ability to stabilize the incoming flow due to its extended after-body flatness. Generally, it has been found that a cylinder with an AR of 2:1 is subjected to higher pressures, higher drag forces, higher curvatures of cross-flow rotations, and higher amplitudes of flow-induced drag, as well as higher lift coefficients and lower shedding frequencies, compared to cylinders with an AR of 1:2. In Regime III, elliptic and vertically mounted airfoil-like flow structures are also observed in the wake of the cylinders.

Square cylinder in the interface of two different velocity streams

We investigate the incompressible flow past a square cylinder immersed in the wake of an upstream nearby splitter plate separating two streams of different velocity. The bottom stream Reynolds number, based on the square side, $Re_B=56$ is kept constant while the top-to-bottom Reynolds numbers ratio $R\equiv Re_T/Re_B$ is increased in the range $R\in [1,6.5]$ , corresponding to a coupled variation of the bulk Reynolds number $Re\equiv (Re_T+Re_B)/2\in [56,210]$ and an equivalent non-dimensional shear parameter $K\equiv 2(R-1)/(R+1)\in [0,1.4667]$ . The onset of vortex shedding is pushed to higher $Re$ as compared with the square cylinder in the classic configuration. The advent of three dimensionality is triggered by a mode-C-type instability, much as reported for open circular rings and square cylinders placed at an incidence. The domain of minimal spanwise-periodic extension that is capable of sustaining spatiotemporally chaotic dynamics, namely one accommodating about twice the wavelength of the dominant eigenmode, has been chosen for the analysis of the wake transition regime. The path towards spatiotemporal chaos is, in this minimal domain, initiated with a modulational period-doubling tertiary bifurcation that also doubles the spanwise periodicity. At slightly higher values of $R$ , the flow has become spatiotemporally chaotic, but the main features of mode C are still clearly distinguishable. Although some of the nonlinear solutions found along the wake transition regime employing the minimal domain might indeed be unstable to long wavelength disturbances, they still are solutions of the infinite cylinder problem and are apt to play a relevant role in the inception of spatiotemporally chaotic dynamics.

Micro-particle image velocimetry study on hydrodynamic characteristics of in-line and staggered micro pin fin arrays

Detailed hydrodynamics in microchannels with in-line and staggered circular micro pin fin structures over Reynolds number ranging from 50 to 700 are experimentally studied with micro-particle image velocimetry. The velocity field, vortex structure and vorticity distribution is obtained and analyzed, and differences in flow behavior in the two arrangements are examined. The result indicates a delay in the onset of vortex shedding in micro pin fin arrays as compared to their macro scale counterpart due to the confinement effect of channel walls. Flow pattern in the in-line arrangement is featured by the microchannel-like main stream between the pin rows and the double vortex wake flow behind the pins, while flow in the staggered arrangement is characterized by the wavy main stream and a pair of accelerated flow streams on two sides of the pins. Vorticity bands along the sides of the wake region intensify with the Reynolds number, diffuse further downstream, but narrow in width. Visualization and data extraction results reveal that flow behavior in the staggered arrangement differs from that in the in-line arrangement in terms of a smaller area occupied by the low-velocity wake region and a more sufficient mixing of fluid.

Effects of viscoelasticity on the onset of vortex shedding and forces applied on a cylinder in unsteady flow regime

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number (Recr), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The Recr is also calculated at every retardation ratio (β) and elongational viscosity. The results revealed a significant impact of viscoelasticity on Recr so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, Recr decreases linearly with β according to Recr=−34.5β+46.525 and increases with extensional viscosity. It is also found that β plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient (CD¯) and the amplitude of lift coefficient (CLmax) do not have similar behaviors for low and high β. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of CLmax with El are also similar to CD¯, but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.

Onset of vortex shedding around a short cylinder

This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$ , cylinder length over diameter) and Reynolds numbers ( $Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$ , one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short- ${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

Onset of vortex shedding from a bluff body modified from square cylinder to normal flat plate

This study numerically investigates the time-resolved laminar flow over rectangular cylinders with cross-sectional aspect ratio Ar varying from square cylinder (Ar = 1) to normal flat plate (Ar = 0.1) for Reynolds number Re = 40–100. The focus is given on how Ar influences the wake structure, fluid force, St, and critical Reynolds number Rec associated with the onset of vortex shedding. The Stuart-Landau equation is employed to determine Rec. With increasing Re, time-mean drag coefficient C‾D increases and decreases for Ar < 0.5 and Ar > 0.5, respectively. The Re effect on C‾D is strongest for Ar = 0.1 and weakest for Ar = 0.5. On the other hand, St monotonically increases with Re for all Ar values examined. Both C‾D and St at a given Re diminish with increasing Ar. A decrease in Ar from 1.0 to 0.1 destabilizes the flow, reducing the Rec from 47.8 to 29.8. The dependence of Rec on the flow attack angle α = (0° - 45°) for the square cylinder shows Rec declining from Rec = 47.8 at α = 0° to Rec = 40.2 at α = 45°. A comparison of Ar effects on Rec is made between rectangular (present study) and elliptical cylinders, both changing toward the normal flat plate. The rectangular cylinders have a smaller Rec than the elliptical cylinders for Ar < 1 while the opposite is the case for Ar = 1.

Perturbation of Wall Boundary Condition to Trigger Vortex Shedding Over a Circular Cylinder

A circular cylinder placed in a uniform flow with its axis perpendicular to the flow direction can result in an unsteady flow caused by vortex shedding. Numerical simulations attempting to capture this phenomenon may lack a trigger to cause the appropriate vortex shedding, consequently, asymmetric vortex shedding can be delayed or may not occur. Therefore, an artificial disturbance can be introduced into the flow field to initiate an earlier onset of vortex shedding. Here, the wall boundary condition is used to perturb the local shear layer. It is tested for a circular cylinder at Reynolds numbers of 40, 60 and 150. Application of wall perturbation technique triggers the onset of asymmetrical vortex shedding and in the absence of a perturbation, asymmetrical vortex shedding does not occur. The effect of the patch size and duration of application of initial perturbation on the onset of vortex shedding for Re = 150 is reported.

Flow around a diamond-section cylinder at low Reynolds numbers

The steady separated flow past a diamond cylinder at low Reynolds numbers, Re, is associated with diverse separation topologies not resolved for a circular or square cylinder. The present study, conducted for Re≤150, also uncovers three unique separation topologies for the time-averaged flow. In this regard, the most striking observation is the formation of a small sub-wake around the base of the cylinder at certain Re between 80 and 90. While two of these structures were previously captured by some recent studies, these studies did not investigate their origin or kinematics. In the present study, conducted via stabilized finite-element computations in two-dimensions, these wake topologies are analyzed in detail. For secondary separation, the pressure at the reattachment point on the cylinder rear surface exceeds the pressure at the corresponding separation point located upstream. In a similar manner, for primary separation, the pressure at the wake stagnation point(s) surpasses the one at the separation points. Via direct steady and unsteady computations, the value of the critical Re indicating the onset of vortex-shedding is found to be 41, approximately. At this Re, the flow quantities, such as wake length, drag, and pressure coefficients, obtained from the steady and unsteady computations are found to diverge. The presentation of wake length and drag as a function of base suction establishes that the drag and wake length share an inverse relationship.

Flow over rectangular cylinder: Effects of cylinder aspect ratio and Reynolds number

Numerical simulations of two- and three-dimensional unconfined flows over rectangular cylinders are conducted at Reynolds number Re = 30 – 200. The cylinder cross-sectional aspect ratio AR (length-to-width) is varied as 0.25, 0.5, 1.0, 2.0, 3.0 and 4.0. The focus is given on how AR and Re influence the flow structure and associated aerodynamic parameters. The first critical Reynolds number (Recr1) associated with the transition from the steady flow to the two-dimensional unsteady flow is determined for each AR and found to linearly increase with increasing AR. The same observation is made for the second critical Reynolds number (Recr2) where the two-dimensional unsteady flow metamorphoses into the three-dimensional unsteady flow. A larger Re is required for a larger AR to have the onset of vortex shedding or the transition from two-dimensional flow to the three-dimensional. Three distinct scenarios of the flow separation and reattachment are identified in the ranges of Re and AR examined. The physical insight into the flow dependence on AR and Re is provided. Both AR and Re play a role in the formation of separation bubbles on the cylinder side surfaces. Two distinct mechanisms of the separation bubble formation are imparted. The detailed flow structures are linked to the mean and fluctuating forces and Strouhal numbers. The vortex strength beefs up with increasing Re but diminishes with AR, as do the normal and shear stresses and fluctuating forces.

Effect of superhydrophobicity on the flow past a circular cylinder in various flow regimes

The flow over a superhydrophobic and a smooth circular cylinder is investigated using particle image velocimetry-based experiments. The objective is to understand the effect of surface modification on the ensuing flow. The experiments are conducted over a wide range of Reynolds numbers, , thereby uncovering the effect of superhydrophobicity in various flow regimes of a cylinder wake. Superhydrophobicity is found to substantially affect the flow. An increased recirculation length is observed for the superhydrophobic cylinder in the steady regime. The onset of vortex shedding is delayed for the superhydrophobic cylinder. The superhydrophobic cylinder helps in an early rolling-up of vortices; therefore, the recirculation length reduces in unsteady regimes. The velocity deficit experienced by the superhydrophobic cylinder wake is comparatively less and the effect is more profound in the range 300–860. A maximum drag reduction of 15 % is observed at . The Reynolds shear stress and turbulent kinetic energy values are higher for the superhydrophobic cylinder in the unsteady regime. Also, the peaks of the turbulent wake parameters lie closer to the superhydrophobic cylinder compared to the smooth cylinder. The effect of superhydrophobicity on coherent structures is examined using proper orthogonal decomposition, and a considerable difference in the wake structure is noticed at . A larger number of coherent structures and change in vortex shedding pattern to are observed in the near wake of the superhydrophobic cylinder. The results of this study show that surface modification can reduce the drag coefficient and have a profound effect on the near wake.

On the transition behavior of laminar flow through and around a multi-cylinder array

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with ϕ and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with ϕ. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.

A switching ILU(0)-SGS preconditioner for matrix systems of incompressible flow and heat transfer using condition number estimates

Preconditioning of matrix systems obtained from an unstructured finite volume discretisation of the incompressible NS equations are studied. The condition number is first estimated by providing Gershgorin-type theoretical bounds. The linear algebraic equations are solved using the preconditioned-BiCGSTAB algorithm. Condition numbers of velocity and temperature matrices show these to be well-conditioned compared to pressure. As a result, the symmetric Gauss Seidel (SGS) preconditioner performs well for velocity matrices on single and multiple processors when compared to ILU(0) that requires LU factorisation. The present study proposes a preconditioning algorithm that switches from ILU(0) to the SGS preconditioner for velocity and temperature. The composite algorithm shows a reduction in the overall simulation time. For a power law fluid, the upper bound of the condition number correlates with the power law index. For flow past a circular cylinder, the temporal oscillation of the largest singular value relates to the onset of vortex shedding.

Condition number analysis of flow fields arising from CFD simulations

Condition numbers of pressure and velocity matrices obtained from an unstructured finite volume discretization of the three dimensional Navier–Stokes equations are studied for two distinct flow configurations. The exact condition number is calculated based on singular values. The continuous estimation of condition number of the velocity matrices with respect to the time varying velocity field is achieved through the Gershgorin theoretical bounds for the eigenvalues. The focus of the present study is on the analysis of flow dynamics with respect to the degree of ill-conditioning of the linear systems. For the two benchmark problems, condition numbers of pressure and velocity matrices are presented. The pressure matrix is shown to be more ill-conditioned than velocity and requires strong preconditioning. For a 3D lid-driven cavity, the appearance and disappearance of corner vortices at higher Reynolds number is clearly reflected in the condition number variation with time. In a second application of flow past a circular cylinder, condition number variation with time during the initial phase clearly reveals the onset of vortex shedding. The condition number based on Gershgorin bounds is also used to switch the SGS and ILU preconditioners for velocity matrices when they are well conditioned. Consequently, an overall reduction in the simulation time is demonstrated.

Stability analysis of the onset of vortex shedding for wakes behind flat plates

Above a critical Reynolds number, wake flows behind flat plates become globally unstable, the leading modal instability in this case is known as Kelvin–Helmholtz mechanism. In this article, both local and BiGlobal linear instability analyses are performed numerically to study the onset of the shedding process. Flat plates with different base shapes are considered to assess geometry effects, and the relation between the critical shedding Reynolds number, $$Re_\mathrm{cr}$$ , and the boundary layer thickness is studied. Three types of base shapes are used: square, triangular and elliptic. It is found that the base shape has a great impact on the growth rate of least stable disturbance mode, thus would influence $$Re_\mathrm{cr}$$ greatly, but it has little effect on the vortex shedding frequency. The shedding frequency is determined mainly by boundary layer thickness and has little dependence on the Reynolds number and base shape. We find that for a fixed Reynolds number, increasing boundary layer thickness acted in two ways to modify the global stability characteristics: It increases the length of the absolute unstable region and it makes the flow less locally absolutely unstable in the near-wake region, and these two effects work against each other to destabilize or stabilize the flow.

Transitions in the flow patterns and aerodynamic characteristics of the flow around staggered rows of cylinders

A two-dimensional numerical study of flow across rows of identical square cylinders arranged in staggered fashion is carried out. This study will unreveal complex flow physics depending upon the Reynolds number (Re) and gap spacing (g) between the cylinders. The combined effect of Reynolds number and gap spacing on the flow physics around staggered rows of cylinders are numerically studied for 20 ≤ Re ≤ 140 and 1 ≤ g ≤ 6. We use the lattice Boltzmann method for numerical computations. It is found that with increase in gap spacing between the cylinders the critical Reynolds number for the onset of vortex shedding also increases. We observed a strong effect of Reynolds number at g = 2 and 4. Secondary cylinder interaction frequency disappears for large Reynolds number at g = 6 and 5 and the flow around cylinders are fully dominated by the primary vortex shedding frequency. This ensures that at large gap spacing with an increase in the Reynolds number the wakes interaction between and behind the cylinders is weaken. Furthermore, it also ensures that the wake interaction behind the cylinders is strongly influenced by the jets in the gap spacing between the cylinders. We also found that g = 2 is the critical gap spacing for flow across rows of staggered square cylinders for the considered range of Reynolds number. Depending on the Reynolds number we observed; synchronous, quasi-periodic-I, quasi-periodic-II, and chaotic flow patterns. In synchronous flow pattern, an in-phase and anti-phase characteristics of consecutive cylinders has been observed. The important physical parameters are also analyzed and discussed in detail.

On the onset of vortex shedding from 2D confined rectangular cylinders having different aspect ratios: Application to promote mixing fluids

This work deals with a numerical study to characterize the onset of vortex shedding from a rectangular cylinder with different length-to-width aspect ratios (AR) and confined in a channel under the consideration of constant blockage ratio (BR=1/5). For AR ranging from 1/8 to 4, it has found that the onset of vortex shedding can be promoted and can take place at lower Reynolds numbers by reducing the aspect ratio of the cylinder, decreasing the critical Reynolds number almost linearly with AR for AR≤2, being the lowest critical Reynolds number around 30 for an aspect ratio of 1/8. The drag coefficient, Strouhal number and pumping power needed to run the channel have been also characterized and correlations proposed to fit both the drag coefficient and pumping power as function of AR and critical Reynolds number. The gained knowledge has been later applied to mix two fluids in the channel at constant Reynolds number. The mixing has been characterized in terms of the mixing efficiency and mixing energy cost. It has been observed that configurations with vortex shedding can intensify mixing with efficiencies between 50% and 100% higher and two order of magnitude cheaper than those without vortex shedding.

Numerical Simulation of Steady Flow and Forced Convection Heat Transfer from Two Offset Square Cylinders Placed in a Channel

Flow over two isothermal offset square cylinders in a channel is simulated for various offset distance (OD) and Reynolds number (Re). The distance between the cylinders in normal direction and the blockage ratio are fixed. Simulation is carried out for Re that varies from 1 to 40, and OD that varies from 1 to 10 for a fixed Prandtl number equals to 0.71. The hydrodynamic results and forced convection heat transfer are more pronounced for variation in Re and OD. Flow separation begins when Re is >5 from the rear wall of the cylinders. The onset of vortex shedding is found when Re is greater than 45 for OD upto 10. The average skin friction coefficient is reported to reveal the role of Re and OD. The top wall Nusselt number shows higher than remaining walls. The downstream offset cylinder is more pronounced for Re and OD, and it shows a nonlinear trend for average Nusselt number.

Fluid flow and heat transfer around a confined semi-circular cylinder: Onset of vortex shedding and effects of Reynolds and Prandtl numbers

Flow and heat transfer characteristics around a semi-circular cylinder placed in a confined channel are investigated in the unsteady regime. The two-dimensional simulations are carried out for varying values of control parameters: Reynolds number (Re)=50–200 and Prandtl number (Pr)=0.7, 10 and 100 at a fixed blockage ratio of 25% for Newtonian constant-property fluid. Continuity, Navier–Stokes and energy equations with appropriate boundary conditions are solved using the commercial computational fluid dynamics solver Ansys Fluent. The transition from steady to time-periodic flow occurs between Re=69 and 70. The effect of Prandtl number on Nusselt number is pronounced; the ratio of Nusselt number values belonging to Pr=100 and those belonging to Pr=0.7 ranges from 6.3 to 6.5 over the Reynolds number domain investigated. Finally, the present numerical results are used to develop drag coefficient, Strouhal number and Nusselt number correlations.