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Two-dimensional flow around semi-circular cylinder at zero angle of attack and at Re = 50000 during the self-oscillatory regime has been extensively studied within the URANS method with the use of different-structure grids (multiblock, structured overlapping, unstructured composite), the SST turbulence model and its versions (1993) and (2003) considering the streamline curvature influence modified within the Rodi–Leschziner–Isaev approach and numerical different-approximation methods realized in two codes (VP2/3, Fluent). Experiments have been made on flow around a semi-circular cylinder in the wind tunnel of the Lomonosov Moscow State University, Institute of Mechanics to obtain data for verification of numerical predictions. The double-mode character of a periodic time history of a drag force caused by a periodically forming and disappearing jet flap and acting upon a body is explained. With increasing compressibility at a Mach number ranging from 0 to 0.5, it is observed that periodic flow around the semi-circular cylinder is restructured, and the time history of the drag force acting upon it is described by a dependence close to a sinusoidal one. It is found that, as the Mach number is increased, pressure field distortions in the form of concentric cylindrical waves propagating from the semi-circular cylinder and the vortex street behind it grow over the infrasonic range.

The flow and heat transfer characteristics in slip flow regime at low pressure state are numerically investigated by using CFD solver. The complete boundary conditions of first-order velocity slip are considered by User Defined Functions (UDFs), which include effects of thermal creep and wall curvature, as well as temperature jump. Based on the dimensionless continuity, momentum and energy equations along with these boundary conditions, the numerical simulation for flow and heat transfer behaviors over a circular cylinder is conducted in a wide range of Re = 0.001 to 20 and Kn = 0.01 to 0.1. It is found that the prediction results without considering the slip boundary conditions obviously deviate from the experimental values with the increase of Knudsen number, while the one by the developed model is in good agreement with the experimental results. Meanwhile, the variation of physical fields under different Reynolds and Knudsen numbers is discussed in detail. The empirical correlations in the slip flow regime for predicting average drag coefficient and average Nusselt number are proposed on the basis of simulation data, which makes the traditional method used for continuous flow regime be successfully applied into the prediction of flow and heat transfer performances in the slip flow regime.

Large Eddy Simulations (LES) with Smagorinsky subgrid scale model have been performed for the flow past two circular cylinders in tandem placed in the vicinity of a horizontal plane wall at very small gap ratios, namely G ∕ D = 0 . 1 , 0 . 3 and 0.5, in three-dimension (3D). The ratio of cylinder center-to-center distance to cylinder diameter, or the pitch ratio, L ∕ D , considered in the simulations is L ∕ D = 2 and 5. This work serves as an extension of Abrahamsen Prsic et al. (2015). In essence, six sets of simulations have been performed in the subcritical Reynolds number regime at R e = 1 . 31 × 1 0 4 . Our major findings can be summarized as follows. (1) At both pitch ratios, the wall proximity has a decreasing effect on the mean drag coefficient of the upstream cylinder. At L ∕ D = 2 , the mean drag coefficient of the downstream cylinder is negative since it is located within the drag inversion separation distance. (2) At L ∕ D = 2 , a squarish cavity-like flow exists between the cylinders and the flow circulates within the cavity. A long lee-wake recirculation zone is found behind the downstream cylinder at G ∕ D = 0 . 1 . However, a much smaller lee-wake recirculation zone is noticed at L ∕ D = 5 with G ∕ D = 0 . 1 . (3) At L ∕ D = 2 , the reattachment is biased to the bottom shear layer due to the deflection from the plane wall, which leads to the formation of the slanted squarish cavity-like flow. At both pitch ratios, as G ∕ D becomes smaller, stronger vortices are found between the two cylinders. Less intense vortices are observed in the near wake of the downstream cylinder due to the vortex shedding suppression of the neighboring wall.

In simulations of flow around a concave curved cylinder, i.e. free-stream aligned with the plane of curvature and directed towards the inner face of the curvature, one cannot avoid interactions between the cylinder and the inlet boundary. To get rid of the effects brought about by this interaction, we consider different lengths of upstream straight extensions at the lower end of the curved cylinder (0D, 5D and 10D, where D is the cylinder diameter), referred to as horizontal extensions. In this study, we directly solve the time-dependent three-dimensional Navier–Stokes equations. Results reveal that the appended horizontal extension allows the boundary layer to develop, so that the velocity profile at the curved cylinder inception is significantly different from the case where no horizontal extension is considered. The laminar boundary layer is thinner than that in the flat plate flow, which is given by Blasius’ solution. The results from 5D and 10D extensions show a clear convergent tendency. We therefore suggest that a horizontal extension is essential for concave curved cylinder flow simulation, and 10D would be a preferred choice. © 2018. This is the authors’ accepted and refereed manuscript to the article. Locked until 14.8.2019 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

The selection of interface boundary conditions between porous-medium and clear-fluid regions is vital for the extensive range of applications in engineering. As such, present paper reports an analytically investigating Stokes flow over Reiner–Rivlin liquid sphere embedded in a porous medium filled with micropolar fluid using Brinkman’s model and assuming uniform flow away from the obstacle. The stream function solution of Brinkman equation is obtained for the flow in porous region, while for the inner flow field the solution is obtained by expanding the stream function in a power series of S . The flow fields are determined explicitly by matching the boundary conditions at the interface of porous region and the liquid sphere. Relevant quantities such as velocity and pressure on the surface of the liquid sphere are determined and exhibited graphically. The mathematical expression of separation parameter SEP is also calculated which shows that no flow separation occurs for the considered flow configuration and also validated by its pictorial presentation. The drag coefficient experienced by a liquid sphere embedded in a porous medium is evaluated. The useful features of the Stokes flow for numerous values of parameters are analyzed and discussed. The dependence of the drag force and stream line pattern on permeability parameter( η 2 ), viscosity ratio( λ ), micropolar parameter( m ), coupling number( N ), and dimensionless parameter S is presented graphically and discussed. The analysis also aims at the explanation of velocity overshoot behavior. Some previous noted results are then also obtained from the ongoing analysis.

Supersonic flow past a wavy cylinder has been investigated numerically using scale-adaptive simulation technique. The free-stream Reynolds number and Mach number for this supersonic flow are chosen as 2 × 105 and 1.7, respectively. For the sake of comparison and discussion, a corresponding circular cylinder for the same computational parameters also has been calculated. Unlike the subsonic operating condition, drag reduction and fluctuating lift suppression of wavy cylinder in supersonic flow are less dramatic. Results indicate that wavy surface as a flow control technique is invalid for supersonic flow over a circular cylinder. This is because the existence of bow shock-wave and no large-scale vortex shedding in the flow field of circular cylinder. Further, two different flow states have been found in the near wake of wavy cylinder. One is a quasi-steady flow state behind the nodal position with converged wake, and the other is an unsteady flow state behind the saddle position with obvious vortex street. Based on the analyses of flow patterns, pressure power spectral densities, and proper orthogonal decomposition of pressure fields, some novel characteristics of wavy cylinder in supersonic flow are systematically investigated.

The flow around a twisted elliptic cylinder is numerically calculated using large eddy simulation (LES) at the Reynolds number of 2 × 104, along with a circular cylinder for comparison. The mean drag coefficient and the fluctuating lift coefficient of the twisted cylinder are 27.99% and 94.01% lower, respectively, than that of the circular cylinder. The twisted surface leads to more stable wake, longer vortex formation length, higher base pressure and three-dimensional separation. In addition, cluster-based reduced-order modelling (CROM) is performed to analyze phase-dependent variations of the wake flow and evaluate the relationship between derived characteristic flow structures and their impact on forces. It captures the oscillatory behavior of Karman vortex shedding in the wake of the circular cylinder. Meanwhile, two flow regimes, anti-phased and in-phase-dominated vortex shedding, generated by the twisted cylinder are extracted and distinguished. The two regimes prevail alternately with changing probability of occurrence along the spanwise of the twisted cylinder, which can be attributed to the different separation angles. The in-phase-dominated vortex shedding inhibits the effect of Karman vortex shedding and is subjected to a lower force compared with the anti-phased vortex shedding.

A numerical analysis is carried out to investigate the wake flow control behind a circular cylinder with corona discharge. The electrohydrodynamic flow is utilized to suppress the boundary layer separation and modify the vortical structures of the flow past a circular cylinder. Numerical simulations consist of the interaction between the electric and flow fields. In this article, the finite volume approach is employed to simulate the flow affected by EHD actuator. The effects of applied voltage, shape of the grounded electrode, location and radius of the discharge electrodes on the swirling flow patterns and drag reduction have been studied. The Reynolds numbers are considered from 4000 to 16000. The results shown that, the modification in EHD actuator design can be used to enhance the flow control effects. The present achievements indicate that, EHD-induced flow can significantly reduce the wake flow behind a circular cylinder. Moreover, the study suggested that this actuator can be applied to practical separation suppression and drag reduction. Furthermore, the predicted numerical results are in excellent agreement with the experimental data.

The flow dynamics over a vibrissa-shaped cylinder at the sub-critical Reynolds number of 1.8 × 104 are comparatively investigated using the large eddy simulation (LES) approach, with particular emphasis on the wake structure and self-induced force. Three reference configurations with the same hydrodynamic diameters, i.e., a circular cylinder, an elliptical cylinder and a wavy cylinder, are compared with the vibrissa-shaped cylinder configuration. The results demonstrate that the fluctuation of lift force for the vibrissa-shaped cylinder is reduced by approximately 79.2% compared with that for the circular cylinder, and the predicted RMS magnitudes for the four configurations agree reasonably well with the experimental data. For the vibrissa-shaped cylinder, only one sharp peak with relatively low magnitude is observed at the characteristic frequency f D / U 0 = 0.20 , and the wake shedding does not dominate the dynamics, while the vortex structures show significantly three-dimensional features. Meanwhile, the separation line of the recirculation zone shows a remarkable wavy structure that corresponds to the trailing geometrical surface with a spanwise shift of approximately a half-period of undulation. A proper orthogonal decomposition (POD) analysis is performed to explore the three-dimensional structures in the wake behind the vibrissa-shaped cylinder. The POD modes reveal a completely three-dimensional and periodically staggered arrangement along both the spanwise and streamwise directions. The spectra of the first two time coefficients reveal that the wake shedding processes on the nodal and saddle planes are not synchronous. Finally, the phase-averaging results show sequential processes of vortex shedding in the wake behind the vibrissa-shaped cylinder, and demonstrate marked differences between this and the other cylinders. Two symmetrical vortices are attached closely to the backward side of the vibrissa-shaped cylinder, resulting in smaller fluctuations of velocity and wall pressure, which in turn contribute to reducing the vortex-induced force and suppressing its vibrations.

The three-dimensional unsteady problem of impulsive stagnation-point flow on a rotating vertical circular cylinder along with mixed convection heat transfer has been solved, numerically for the first time. This is because similarity solution techniques are not always possible to be accomplished. Initially, the fluid is considered to be at rest and with a uniform temperature T∞ and at t = 0 it starts flowing toward a vertical cylinder at the strength rate of k ¯ and the cylinder surface's temperature rises to Tw, simultaneously. The cylinder possesses a rotational movement, with a constant angular velocity ω. The Navier-Stokes and energy equations in cylindrical coordinate system have been descritized and solved in a 2-D domain by using a SIMPLE based algorithm. The buoyancy effects are also included in the computations, so the problem is investigated as mixed convection heat transfer. Considering a sample case of incompressible flow with Re = 1,5,10,15,20 and Pr = 0.7 , the results of Nusselt number, wall shear-stress and dimensionless velocity and temperature have been obtained at different states of cylinder's wall temperature and for some selected values of Grashof numbers.

Laminar flow past a rotating cylinder near a plane wall is studied numerically using a second-order accurate immersed boundary method. The wake-wall interactions are investigated in detail, for different wall heights and varying rotational rates. Flow patterns are classified based on the wake structure and the effect of rotation on critical wall heights is discussed for both clockwise and counterclockwise rotation. For the configuration studied i.e. rotating cylinder above a bottom plane wall, counterclockwise rotation of cylinder favors the wake-wall interactions, while clockwise rotation influences in an adverse manner. In addition to conventional analysis, the evolution of the vortical structures in the wake region are examined using Lagrangian analysis of individual vortical structures. The diffusion of the positive vortex shed from the wall facing side of the cylinder is accelerated due to the influence of boundary layer with net negative vorticity. The wall augmented diffusion of positive cylinder vortices is compensated by the creation of secondary wall vortices from the bottom wall boundary layer. Counterclockwise rotation of cylinder increases the shear inside boundary layer resulting in more pronounced diffusion.

A numerical simulation of transverse flow-induced vibrations of a rotating circular cylinder is presented. Rotation rate and direction is imposed to be proportional either to the cylinder’s position or cylinder’s velocity. A 2D Lattice Boltzmann method is used to solve the flow dynamics and the cylinder is spring-mounted and free to undergo transverse vibrations. In all cases, non-dimensional mass is 12.7, Reynolds number 100, and zero damping is considered, so the analysis is focused on the role of the rotation law and the reduced velocity. Results are presented in terms of steady-state oscillations characterization (say amplitude and frequency), fluid forces on the cylinder, and wake-pattern topology. It is shown how the imposed rotation changes the cylinder’s response significantly, fluid forces on it and the flow field in the wake. Depending on the rotation law imposed flow-induced vibrations can be increased or diminished. The former can be of interest for energy harvesting purposes; whereas the later can be useful to avoid unwanted oscillations. When rotatory law is proportional to the cylinder’s position, a galloping-type response has been found. In this case, the cylinder’s amplitude can be reasonably well predicted with a quasi-steady theoretical model. For rotation proportional to the cylinder’s velocity only vortex-induced-type responses have been found.

In this study a new two degrees-of-freedom wake oscillator model is proposed to describe vortex-induced vibrations of elastically supported cylinders capable of moving in cross-flow and in-line directions. The total hydrodynamic force acting on the cylinder is obtained here as a sum of lift and drag forces, which are defined as being proportional to the square of the magnitude of the relative flow velocity around the cylinder. The two van der Pol type oscillators are then used to model fluctuating drag and lift coefficients. As the relative velocity around the cylinder depends both on the fluid flow velocity and the velocity of the cylinder, the equations of motions of the cylinder in cross-flow and in-line directions become coupled through the fluid forces. It is shown that such approximation of the fluid forces allows to obtain the well known low dimensional models in the limit case, and the model proposed by Facchinetti et al. [1] to describe the cross-flow vibrations is used as an example. Existing experimental data and Computational Fluid Dynamics (CFD) results are used to calibrate the proposed model and to verify the obtained predictions of complex fluid-structure interactions for different mass ratios. The "super upper" branch phenomenon, exclusive for a two degrees-of-freedom motion at low mass ratios, has been observed. The influence of the empirical parameters of the wake oscillators and fluid forces coefficients on the dynamic responses is also discussed.

International audience; Flow-induced vibration in square cylinder arrangement under viscous fluid incompressible cross-flow is investigated in the present work. The purpose is to contribute to better mod-eling and understanding external fluid loads exerted on long thin cylinders inducing flow perturbations. Due to high flow confinement, thin cylinders may be subjected to strong vibrations, which may lead to dynamic instability development. A theoretical approach is developed to determine a stability criterion of the dynamical system. The influence of geometric, mechanical and flow parameters such as reduced velocity and pitch ratio is investigated. The proposed model is derived from the potential flow theory and enhanced through an algebraic phase lag model in order to predict the critical limit of the reduced velocity for a square cylinder arrangement submitted to an external in-line cross flow. A theoretical formulation of the total damping, including added damping in still fluid, the damping due to fluid flow and the damping derived from the phase shift between the fluid load and the tube displacement, is expressed. A function depending on fluid and structure parameters, such as reduced velocity, pitch ratio and Scruton number is thus obtained. It is shown that this function provides a prediction of the dynamic stability limit of the system for several ranges of the major parameters to be considered. The results are compared to experimental reference solutions and to those provided by other theoretical models. This work proposes a consistent original model based on a potential flow theory enriched by using an algebraic formulation based on standard physical assumptions from literature. The major advantage of this model is due to the fact that it is in the same time robust and very user-friendly from a computational point of view thanks to the potential framework. In order to describe fluid and solid dynamics in the domain, terms coming from the potential flow theory are estimated by using a finite element method and complementary terms acting on damping are obtained through an algebraic formulation. Therefore this is a convenient way to propose a hybrid numerical / algebraic model for predicting dynamic instability limit in cylinder arrangements.

A large-eddy simulation method of calculating the flow past an elastically-supported body, has been constructed based on the finite difference method formulated in the coordinates fixed on the moving body. The boundary conditions on the body can be applied in the same way as on a fixed body. Reconstruction of computational mesh or interpolation of the computational points is not needed as the body moves. The coding of the method is simple and the computation is efficient, but the equations of motion must be written in the non-inertial coordinates and the boundary conditions on the outer boundaries of the flow domain that also move must be adjusted as the orientation of the body changes. The method has been tested in the computation of the flow past a rectangular cylinder supported by a spring and dashpot and the motion of the cylinder for which experimental data are available. Comparison with experimental data in the case of a rectangular cylinder of depth to breadth ratio of D/B=2 indicates that the characteristics of the translational oscillation corresponding to the heaving of long beams and the rotational oscillation corresponding to the torsional deformation are reproduced well.

Vortex shedding and heat transfer around a cylinder in pulsating cross-flow have been studied experimentally. Analysis of flow visualization results enabled to classify flow patterns around the cylinder into four groups. New dimensionless number has been submitted, which is a ratio of the inertial force due to the oncoming flow acceleration in its global unsteady motion to the centrifugal inertial force due to curved streamlines around the cylinder. A map of flow patterns around the cylinder has been plotted in terms of the newly submitted dimensionless number and the relative amplitude of oncoming flow pulsations. Distributions of the local heat transfer coefficient over the cylinder surface depending on the flow pattern and the amplitude of forced flow pulsations have been obtained. It has been shown that forced pulsations of oncoming flow can enhance average heat transfer from the cylinder in the cross-flow.

The present work analyzed the hydromagnetic effect on three-dimensional Couette flow of viscous incompressible, electrically conducting and Newtonian fluid through a porous medium bounded by two horizontal parallel porous flat plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by periodic suction through the plate in uniform motion. The flow becomes three dimensional due to this injection/suction velocity. Approximate solutions are obtained for the flow field, the pressure, the skin-friction, the temperature field, and the rate of heat transfer. It is found that the cross velocity w is reduced considerably with a rise in the magnetic body parameter ( M ), permeability parameter ( K ) and injection/suction ( λ ) in the forward flow, while a reverse effect is observed in the backward flow. An increase in K or λ is found to escalate the main flow velocity whereas an increase in the magnetic body parameter ( M ) is shown to exert the opposite effect. Similarly, the shear stress due to main flow is considerably increased with an increase in M and K . The results show that both methods, perturbation and electrical network schemes provides excellent approximations to the solution of this nonlinear system with high accuracy. The acquired knowledge in our study can be used by designers to control Magnetohydrodynamic (MHD) flow as suitable for a certain application. Other possible applications include materials processing, MHD propulsion thermo-fluid dynamics, boundary layer in aerodynamics, chemical engineering etc.

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u / U o and transverse, v / U o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u rms and transverse, v rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f k .

The effect of a cylindrical bluff body on the interface characteristics of stratified two-phase, oil-water, pipe flows is experimentally investigated with high speed Particle Image Velocimetry (PIV). The motivation was to study the feasibility of flow pattern map actuation by using a transverse cylinder immersed in water in the stratified pattern, and particularly the transition from separated to dispersed flows. The cylinder has a diameter of 5 mm and is located at 6.75 mm from the bottom of the pipe in a 37 mm ID acrylic test section. Velocity profiles were obtained in the middle plane of the pipe. For reference, single phase flows were also investigated for Reynolds numbers from 1550 to 3488. It was found that the flow behind the cylinder was similar to the two dimensional cases, while the presence of the lower pipe wall diverted the vorticity layers towards the top. In two-phase flows, the Froude number (from 1.4 to 1.8) and the depth of the cylinder submergence below the interface affected the generation of waves. For high Froude numbers and low depths of submergence the counter rotating von Karman vortices generated by the cylinder interacted with the interface. In this case, the vorticity clusters from the top of the cylinder were seen to attach at the wave crests. At high depths of submergence, a jet like flow appeared between the top of the cylinder and the interface. High speed imaging revealed that the presence of the cylinder reduced to lower mixture velocities the transition from separated to dual continuous flows where drops of one phase appear into the other.

Computer simulations of steady plus low-amplitude oscillatory flow about a circular cylinder are reported at a fixed Reynolds number of 150 based on the steady component. The conventional Keleugan–Carpenter number based on the oscillatory component is fixed at π/5. The oscillation frequency is varied so as to study a wide spectrum of flows where inertial forces dominate at one end and viscous drag forces at the other as a function of the modified Keleugan–Carpenter number. The hydrodynamic force on the cylinder in-line with the flow direction is represented by Morison's equation and an extended version with three terms. The drag and inertia coefficients in Morison's equation are determined by least-squares fits to data directly computed from integration of skin friction and pressure distributions around the periphery of the cylinder. The root-mean-square value of the residue of reconstructed minus directly-computed forces varies between 2 and 41% depending on the flow parameters. Comparable results can be obtained with a semi-theoretical approach using inviscid inertia and quasi-steady viscous drag terms. Physical explanations for the variation of the force coefficients are provided and implications for pertinent flow–structure interactions are discussed.

The coupled evolution of an eroding cylinder immersed in a fluid within the subcritical Reynolds range is explored with scale resolving simulations. Erosion of the cylinder is driven by fluid shear stress. Karman vortex shedding features in the wake and these oscillations occur on a significantly smaller time scale compared to the slowly eroding cylinder boundary. Temporal and spatial averaging across the cylinder span allows mean wall statistics such as wall shear to be evaluated; with geometry evolving in 2-D and the flow field simulated in 3-D. The cylinder develops into a rounded triangular body with uniform wall shear stress which is in agreement with existing theory and experiments. We introduce a node shuffle algorithm to reposition nodes around the cylinder boundary with a uniform distribution such that the mesh quality is preserved under high boundary deformation. A cylinder is then modelled within an infinite array of other cylinders by simulating a repeating unit cell and their profile evolution is studied. A similar terminal form is discovered for large cylinder spacings with consistent flow conditions and an intermediate profile was found with a closely packed lattice before reaching the common terminal form.

In the present study, a traveling wave wall (TWW) was employed to manipulate the vortex shedding behind a fixed circular cylinder based on a 2-D CFD numerical simulation method at a low Reynolds number of 200. The study mainly focused on four types of TWW propagation directions combined with nine different wave velocities to eliminate vortex shedding, and the lift and drag coefficients and vortex shedding modes at different propagation directions or velocities were analyzed in detail to access the effectiveness of the TWW flow control method. The control mechanism of eliminating wake stemming from the flow around a TWW-controlled circular cylinder was revealed by the boundary vorticity flux (BVF) and relative flow fields. The results show that the type of downstream propagating TWW can effectively eliminate the alternating wake. When the ratio of the wave velocity to the oncoming velocity is 2.0, the fluctuations of the lift coefficients descended to the lowest point. The averages of the drag coefficients decreased with increasing wave velocity and descended to the lowest point when the ratio of the wave velocity to the oncoming velocity was 5.0. Owing to the capture of small-scale vortices, there was a relatively larger level of vorticity in the wave valley of the TWW cylinder. The relative flow fields showed that the vortex shedding from the cylinder was completely eliminated and that the goal of eliminating the oscillating wake and suppressing the potential vortex-induced vibration (VIV) of flow around a cylinder was achieved.

A coupled viscous-inviscid interaction scheme combining the continuity equation for potential flow with the three-dimensional integral boundary layer equations is presented. The inviscid problem is ...

A velocity decomposition method is developed for the solution of three-dimensional, unsteady flows. The velocity vector is decomposed into an irrotational component (viscous-potential velocity) and a vortical component (vortical velocity). The vortical velocity is selected so that it is zero outside of the rotational region of the flow field and the flow in the irrotational region can thus be solely described by the viscous-potential velocity. The formulation is devised to employ both the velocity potential and the Navier–Stokes-based numerical methods such that the field discretization required by the Navier–Stokes solver can be reduced to only encompass the rotational region of the flow field and the number of unknowns that are to be solved by the Navier–Stokes solver is greatly reduced. A higher-order boundary-element method is used to solve for the viscous potential by applying a viscous boundary condition to the body surface. The finite-volume method is used to solve for the total velocity on a reduced domain, using the viscous-potential velocity as the boundary condition on the extent of the domain. The two solution procedures are tightly coupled in time. The viscous-potential velocity and the total velocity are time dependent due to the unsteadiness in the boundary layer and the wake. The solver is applied to solve three-dimensional, laminar and turbulent unsteady flows. For turbulent flows, the solver is applied for both Unsteady-Reynolds-Averaging-Navier–Stokes and Large-Eddy-Simulation computations.

Secondary flows and corresponding endwall heat transfer around a fully permeable (porous) short circular cylinder differ from those around an impermeable (solid) cylinder. There exists a through flow which is portion of the mainstream entering the front of the cylinder and exiting at the rear of the cylinder, and the alteration of an adverse pressure gradient along the plane of symmetry that causes three-dimensional boundary layer separation (or forms horseshoe vortices). This study experimentally demonstrates how these distinctive features vary horseshoe vortices, wake patterns, and endwall heat transfer around the porous short circular cylinder. Furthermore, the fluidic effect of the extent of the through-flow that is determined by the permeability of the porous cylinder on downstream heat transfer is discussed.

The present paper deals with the numerical simulation of unsteady, two-dimensional laminar fluid flow past a circular cylinder. An unstructured grid finite volume method has been used, and the commercial CFD code ANSYS Fluent was employed to perform the simulations. Effects of injection of a second dissimilar fluid from two diametrically opposite peripheral slots on the cylinder are of prime interest in the study. Two distinct injection arrangements have been investigated–a co-counter flow arrangement, in which the injected fluid is aligned with the free stream flow, and a cross flow arrangement, in which the second fluid is injected perpendicular to the free stream flow direction. A parametric variation of the velocity of the injected stream in the downstream wake region of the cylinder have been studied qualitatively by observing the velocity, vorticity, and mass fraction contours. Effects of injection on the vortex shedding have also been studied by observing the variations of the Strouhal number. The two injection arrangements affected the vortex shedding in distinctly different manners. Effect of lateral walls on the flow dynamics were also investigated. The presence of lateral walls was found to delay the onset of aperiodic wake structures and to promote better mixing in the downstream wake of the cylinder. Proper orthogonal decomposition of the vorticity field was also performed in order to identify the dominant modes and their respective enstrophy contents. Significant differences in the modal structures were observed with increase in the value of the control parameter. At lower values, large scale POD modes dominate, while at higher values, the wake comprised of small scale structures, for both the flow arrangements. A gradual dominance of the injected stream on the free stream was also observed.

Flow past a circular cylinder in a uniform flow is investigated for 1 × 10 4 ≤ Re ≤ 4 × 10 5 . A stabilized finite element method is used to solve the incompressible flow equations in primitive variables in three dimensions. The computations capture the phenomenon of drag crisis: a significant reduction in drag with increase in Re in the critical regime. The mechanism for this decrease in drag during the drag crisis is explored. It is found that the transition of the boundary layer from a laminar to turbulent state, as well as the formation of the laminar separation bubble (LSB), is intermittent. The LSB does not exist in the sub-critical regime while it appears at all times beyond the critical regime. The frequency of its appearance as well as the duration of its stay, in the critical Re regime, increases with increase in Re . This is established by studying the rms of the high pass filtered fluctuations in the surface pressure and flow close to the cylinder. A procedure to capture these fluctuations due to the shear layer activity responsible for the formation of LSB is proposed and implemented. It is utilized to estimate the intermittency factor of the LSB at various Re . It is found that the intermittency can be utilized to explain the variation of mean drag with Re . Weakening of vortex shedding is observed in critical regime and beyond.

Within the framework of two-dimensional Euler equations, the stability is investigated of a system consisting of an inner unfastened round cylinder, an incompressible fluid flow around this cylinder with circular streamlines, and an outer fastened cylinder (vessel). An equation is obtained for the natural frequencies with different mean flows between the cylinders. Accurate solutions of this equation are derived and an analysis of these solutions is given. An energetic investigation of the loss of stability in the system is carried out.

In this paper, complicated hydrodynamics of a horizontal circular cylinder entering water is investigated numerically for low Froude numbers. A numerical approach is used to model the solid-liquid interactions in presence of a free-surface. The governing equations for the 3D incompressible fluid flow are continuity and Navier-Stokes equations along with an equation for the free surface advection. To track the free-surface motion, the fast-fictitious-domain method is integrated into the volume-of-fluid (VOF) technique. The governing equations are solved everywhere in the computational domain including the horizontal cylinder. A rigid body motion is applied to the region occupied by the circular cylinder. The no-slip boundary condition on the solid-liquid interface is exerted implicitly via increasing the viscosity of the region occupied by the solid. To validate the numerical scheme, the results are compared with those of the experiments available in the literature. The effects of cylinder diameter, length, impact velocity, and cylinder-water density ratio on the non-dimensional depth are also investigated.

Vortex-induced vibration (VIV) has been studied extensively and much attention has been devoted to the “lock-in” phenomenon, which is primarily responsible for fatigue damage to structures. Nevertheless, the behavior of the surrounding flow can also be important. This paper investigates the flow characteristics of the wake in the initial branch for a vibrating cylinder using a new PIV technique capable of a high sampling rate of 200 Hz. The experiments were carried out over a wide range of reduced velocities to better understand the important trends. The mean velocities and turbulence characteristics were obtained by ensemble averaging repeated velocity measurements. This study reveals new insights on the flow characteristics of the wake in the initial branch. In particular, the cylinder vibration is found to lead to the formation of oblique jets, which have a profound influence on the mean flow velocity, turbulence intensity, formation and convection of the vortices, and variations to the stagnation and separation points of the cylinder during vibration. Accepted version

Numerical solutions are presented for fluid flow past a rotating elliptic cylinder for different non-dimensional rotational rates (0.5, 1.0 and 1.5) and various axis ratios (0.1, 0.3, 0.5, 0.7 and 1.0). The two-dimensional, incompressible Navier–Stokes equations are solved using Immersed Boundary method on a non-body conforming Cartesian grid. Reynolds number based on the perimeter of the elliptic cylinder is 100. Periodic flow after an impulsive start of the elliptic cylinder is studied. Flow patterns and variation of aerodynamic force coefficients are reported for different set of parameters and it is observed to be very different from that of rotating circular cylinder. As the cylinder rotates, the trailing edge of the cylinder aids the flow while the leading edge deters the flow. This has significant effect on the wake region and vortex shedding pattern. Complex interactions between cylinder and shed vortices result in many interesting phenomenon, such as formation of hovering vortex. Parameters affecting the formation of hovering vortex and its underlying mechanism are analyzed. Aerodynamic force coefficients and vortex shedding frequencies are presented and it is observed that force coefficients have multiple amplitudes and frequencies.

This note studies the accuracy of Isogeometric Analysis (IGA) applied in the simulation of incompressible flows around a cylinder in two and three dimensions. Quantities of interest, like the drag coefficient, the lift coefficient, and the difference of the pressure between the front and the back of the cylinder are monitored. Results computed with standard finite element methods are used for comparison.

The steady axi-symmetric laminar boundary-layer slip flow of a viscous incompressible fluid and heat transfer towards a vertical stretching cylinder in the presence of a uniform magnetic field is investigated. It is assumed that the left surface of the cylinder is heated by a hot convective flow. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of coupled non-linear ordinary differential equations. The resulting intricate non-linear boundary value problem is solved numerically by the fourth-order Runge Kutta method with shooting iteration technique. The analytical solutions are presented for a special case. The effects of various physical parameters on velocity and temperature profiles are discussed through graphs. The values of skin friction coefficient and the Nusselt number are tabulated and examined. It is found that the thermal boundary layer thickness increases with the increase of velocity slip, magnetic field, surface convection parameter and curvature parameter and decreases with Prandtl number.

In this work, the characteristics of flow over a circular cylinder with two filaments are numerically investigated. The circular cylinder is fixed, and the filaments with the same properties are symmetrically attached to the rear surface of the cylinder. Moreover, the leading ends of the filaments are fixed, and their trailing ends are free to flap in the wake of the cylinder. To implement numerical simulations, an improved immersed boundary-lattice Boltzmann, which is efficient for moving boundary problems, is employed. By fixing the length of two filaments, their influences on the flow control of the cylinder are examined systematically through varying the filament mass ( M r ) , the filament flexibility ( w r ) , and the attachment angle between two filaments (α). Moreover, the effect of flow viscosity is also examined. Based on the numerical results established, it is found that the fluctuation of lift force together with the mean drag force can be suppressed effectively. In the meanwhile, the flow control of two filaments is independent of Reynolds number. Particularly, the filaments with relatively low flexibility and large attachment angle can achieve high performance, which is caused by the vortex interaction between the cylinder and the filaments as well as the pressure redistribution along the surface of the cylinder.

Laminar flow over a twisted cylinder is numerically simulated at a Reynolds number of 100. The flow past a smooth cylinder is calculated for comparison. Jung and Yoon (J. Fluid Mech., 759, 2014) showed the considerable suppression of force coefficients at the subcritical Reynolds number of 3000. The present results verify that the twisted shape of the cylinder can be used to reduce the force coefficients at a low Reynolds number containing the laminar flow. This suppression of the force coefficients is supported by a longer vortex formation length produced by the twisted cylinder. We investigated the characteristics of the local force coefficients for a twisted cylinder. The simple periodic oscillation of the time histories of total and local lift coefficients for the twisted cylinder exhibits the same pattern as that of a smooth cylinder. However, the time history of drag for the twisted cylinder reveals the presence of multi-frequency oscillations, resulting in harmonic behavior of the power spectra. This is confirmed by a time sequence of the instantaneous flow fields during the half-period of the time histories of force coefficients. The nature of the three-dimensional (3-D) twisted shape forms the 3-D vortical structures along the spanwise direction, which leads to the harmonic behavior of the drag time trace power spectra.

Direct numerical simulation is performed for flow past an isolated cylinder at R e = 1 , 000 . The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R + = R / D = 0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of time-averaged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R + = 0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R + further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticeable in the shear layer for the square and R + = 0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy ( ω z 2 ) for the rounded cylinders.

In this work, the flow past surface-piercing cylinders with free lower ends is studied numerically with computational fluid dynamics (CFD) at varying aspect ratios (AR = H/D) from around 1 to 19, and compared against experimental measurement across the same range. Numerical and experimental work is carried out at Re = 2900 and Fr = 0.65. The aspect ratio of the cylinder is varied by raising and lowering the cylinder into the water. The resulting flow field and loads on the cylinder as a result of changing the cylinder’s depth of submergence are investigated in terms of drag, lift and frequency content. First, the effects of changing the aspect ratio are examined. CFD simulations demonstrate a reduced drag coefficient, consistent with the experimental measurements, as compared to a fully-submerged, infinite cylinder at the same Reynolds number. A significant reduction in the drag coefficient is observed at an aspect ratio of 2. For aspect ratios 3 and below, Karman vortex shedding is completely suppressed due to the dominance of free surface effects. With increasing aspect ratio the Strouhal number is found to approach 0.2. Second, the flow regime is investigated as a function of cylinder length for a cylinder with aspect ratio of 12. Different regions of vortex shedding are observed along the length of the cylinder, as demonstrated by lift forces, Strouhal numbers and CFD flow visualizations. Strouhal numbers below 0.2 were observed for regions near the free surface. Additionally, the drag coefficient was found to decrease near the free surface. This study over a wide range of aspect ratios exhibits the effects of a free surface, free end and also the length of the cylinder on both the flow regime and loading.

This work proposes a numerical investigation of the main flow field characteristics and pressure field analysis around a freely oscillating rigid circular cylinder immersed in a high Reynolds number flow in the subcritical range. The cylinder is characterized by high value of mass ratio and mass damping, while the damping itself is quite low. Here the numerical results are compared with experimental data obtained in the Politecnico di Milano wind tunnel under the same fluid dynamic and mechanical conditions. The preliminary check of this numerical setup was provided by considering the case of a fixed cylinder in the subcritical region. Based on this benchmark, the full setup was checked by considering fluid dynamic conditions outside the lock-in region. Finally, a number of points were investigated on the cylinder's steady state response curve in the lock-in region. The numerical model yielded good results in terms of cylinder amplitude response, aerodynamic forces and pressure field analysis, in agreement with the results of the experiment. Analysis of the numerical reconstruction of the flow field evolution is therefore considered to yield further information on the vortex shedding mode, especially in the transition region between 2S and 2P mode.

This article presents the steady drag flow problems. The incompressible Oldroyd eight constant fluid flow is considered between two infinite parallel plates. Three flow problems including the Couette flow, Poiseuille flow and Couette–Poiseuille flow are modeled. The source term appearing in the nonlinear differential equation for each case is simplified with the application of modified homotopy perturbation method, and thus the general solution is obtained. The validity of second order approximate analytic solutions is tested with the aid of a numerical technique. The order of accuracy has been obtained in tabular form and the graphs are presented to demonstrate the difference between the three flow regimes.

Computational methods based on Cartesian mesh are popular in simulating fluid flow with moving boundaries of complex geometry. In this paper, a sharp-interface Cartesian grid method is proposed for simulating viscoelastic fluid flow. We implement a finite volume numerical scheme with an improved Rhie-Chow interpolation on the open-source toolbox OpenFOAM. In the benchmark test of flow past a stationary cylinder, the velocity for Newtonian fluid flow is found to be second-order accurate with linear/bi-linear fitting functions for local reconstruction and third-order accurate with quadratic fitting functions. Only first-order accuracy is achieved with current solver for the Oldroyd-B fluid flows due to the difficulty in handling the extra stress near the boundary. However, our sharp-interface Cartesian grid method has been verified to correctly predict the extra stress on the surface of the cylinder. Simulation results of confined Oldroyd-B fluid flow past a pair of cylinders are also reported. A comparison between the proposed sharp-interface Cartesian grid method and a smoothed-interface immersed boundary method is carried out with respect to accuracy and efficiency.

Although vortex-induced vibration (VIV) has been extensively studied, much of existing literature deals with uniform flow in the absence of a boundary. The VIV flow field of a structure close to a boundary generally remains unexplored, but it can have important engineering implications, such as pipeline scour if the boundary is an erodible seabed. In this paper, laboratory experiments are performed to investigate the flow characteristics of an elastically mounted circular cylinder undergoing VIV, and a rigid plane boundary is considered to simplify the problem. The initial gap-to-diameter ratio is fixed at 0.8, and six different reduced velocities are considered. The velocity field is measured using a high resolution particle image velocimetry (PIV) system, which has several advantages over traditional PIV systems, including high sampling rate and the ability to mitigate scatter of laser light near the boundary, allowing accurate measurements at the viscous sublayer. This paper presents the vibration amplitude and oscillation frequency for different Vr; in addition, the mean velocity field, turbulence characteristics, vortex behavior, gap flow velocity, and normal/shear stresses on the boundary were measured/calculated, leading to new insights on the flow field behavior.

A series of experiments was conducted in a re-circulating water tunnel with a uniform flow profile, in which a flexible tension-dominated cylinder was held fixed at both ends and placed perpendicular to the incoming flow direction. The circular cylinder had an aspect ratio of L / D =67 and a low mass ratio of m *=0.43. Dynamic response of the system was studied in the reduced velocity range of U *=2.9–14.5 and Reynolds numbers of Re =315–1580. The oscillations of the cylinder in the inline (IL) and crossflow (CF) directions were captured using two synchronized high speed cameras. Continuous response of the cylinder was reconstructed from limited number of measurement points based on modal expansion theorem modified using Modal Assurance Criterion (MAC). The MAC enhanced the response reconstruction by adjusting the contributions from each structural mode. A distinct advantage of implementing the MAC in this method compared with the previously used methods was reconstructing the VIV response accurately when the experimental measurement points were clustered in a small region along the length of the cylinder. Mono- and multi-frequency excitation responses as well as transition from a low mode number to a higher one were observed. Flow forces acting on the cylinder were calculated and a consistent relation between the regions where the cylinder was being excited by the flow and the counterclockwise figure-eight trajectories of oscillations was observed.

A pressure-based finite volume method on unstructured grids is developed for incompressible viscoelastic fluid flow simulations. To avoid the need for information about the stresses at any singular point within the computational domain, an edge (or face for 3D cases) based formulation with all variables located at the cell centroid is used. To avoid possible decoupling between the stress and velocity fields, and ensure consistencies in discretization under the collocated variable arrangement, the deformation rates and stress tensors at the midpoint of an interface straddled by two adjacent cells are linearly interpolated with the variable gradients expressed in terms of the values at all neighboring cell centroids using a least-squares method. An innovative solution strategy that removes the need for explicitly specifying the flow boundary conditions at an open boundary, originally developed for incompressible Newtonian flow simulations, has been extended for viscoelastic cases. With this method, the traditional requirement for flow conditions at an outflow boundary, i.e. fully developed flow, is removed. The outflow channel can thus be truncated so that the flow outlet can be located arbitrarily as long as there is no inflow (e.g. due to recirculation) across this boundary. This not only greatly reduces computational costs, but avoids numerical instabilities due to inconsistencies between the imposed flow behavior and that calculated at the outflow boundary for cases where the outflow channel is not long enough to realize the flow condition imposed. The proposed methodology is demonstrated/validated by simulating, • developing flow of an Oldroyd-B fluid between two parallel plates, and • slip-stick flow of an upper convected Maxwell fluid; with successively truncated flow domains. These results clearly demonstrate that the predicted flow behavior is unaffected by using even a highly truncated domain, whilst this methodology allows a higher critical Weissenberg number to be reached than previously reported in the literature.

The problem of viscous incompressible flow past a periodic array of porous cylinders (a model of flow in an aerosol filter) is solved. The approximate periodic cell model of Kuwabara is used to formulate the fluid flow problem. The Stokes flow model is then adopted to model the flow outside the cylinder and the Darcy law of drag is applied to find the filtration velocity field inside the porous cylinder. The boundary value problems for biharmonic and Laplace equations for stream functions outside and inside the porous cylinder are solved using a boundary elements method. A good agreement of numerical and analytical models is shown. The analytical formulas for the integrals in the expressions for the stream function, vorticity and Cartesian velocity components are obtained. It is shown that the use of analytical integration gives considerable advantage in computing time.

The principle of velocity decomposition is used to efficiently and accurately solve the Navier–Stokes boundary-value problem for lifting flows. The velocity vector is decomposed as the sum of irrotational and vortical components. The irrotational component is represented using a velocity potential which satisfies the Laplace equation with a modified boundary condition that is written in terms of the Navier–Stokes solution. A viscous potential can be found which satisfies the Navier–Stokes problem directly outside of the rotational regions of the fluid such that the fluid domain over which the Navier–Stokes equations must be solved numerically can be greatly reduced. The viscous potential is used as a Dirichlet boundary condition for the total velocity on the boundaries of the reduced fluid domain. The velocity decomposition approach is used to solve for the flow over a 2D NACA0012 foil in both laminar and turbulent regimes.

The flow characteristics and drag force of a square cylinder with a front jet injection were experimentally investigated in a wind tunnel. The evolution process of the characteristic flow patterns was recorded by the laser-assisted smoke flow visualization method. The time-averaged velocity fields measured by particle image velocimetry (PIV) were applied to analyze the velocity vectors, streamline patterns, vorticity contours, velocity distributions, and time histories of instantaneous velocities around the upstream region of the square cylinder. The drag force experienced by the square cylinder was obtained by measuring the surface pressures on the front and rear faces. The results show that the jet emitted from the upstream surface of the square cylinder periodically swings left-and-right in the experimental range of injection ratio ⩽0.9. In the time-averaged velocity field, the jet flow impinges the freestream at a four-way saddle and subsequently bifurcates into two streams; one stream goes toward the left edge of the upstream surface, while the other stream directs toward the right edge of the upstream surface. Two recirculation regions formed above the upstream surface of the square cylinder are enclosed by those two streams. The vorticity contours around the upstream surface of the square cylinder are characterized by two adjacent vorticity-concentrated areas of opposite signs. The time histories of the instantaneous velocities around the four-way saddle, jet exit, and shear layer of the swinging jet represent periodic oscillation. This characteristic oscillation frequency is dominated by the wake instability. The recirculation regions formed above the cylinder’s upstream surface prevent impingement from the freestream. Consequently, the surface pressure coefficients on the upstream surface of the square cylinder are reduced. This reduction in the surface pressure coefficient decreases the drag force acting on the square cylinder.

A novel two dimensional pure-Lagrangian vortex method based on instantaneous vorticity conserved boundary conditions (IVCBC) has been applied to investigate the hydrodynamic coefficients and patterns flow around two circular cylinders in side-by-side arrangements with pitch ratios T / D =1.1–7 at a high Reynolds number Re =6×10 4 . The benchmark case of viscous flow around a circular cylinder was first carried out to validate the novel vortex method. Then simulations of the flow around two side by side circular cylinders were performed. A new scheme was proposed to distinguish the wide wake (WW) and narrow wake (NW) by judging the velocity direction of a specific point in the gap flow. The hydrodynamic coefficients and Strouhal numbers were thoroughly studied as a function of the pitch ratios. A total of five kinds of flow patterns were identified. During the investigation of biased flow, an intermediate frequency between frequencies of NW and WW was found and approached to that of a single cylinder. The results show good agreement with the previously published experimental and numerical data.

The heat transfer and flow characteristics of a rectangular channel with a small scale slit-vent circular cylinder are numerically investigated by Large Eddy Simulation (LES). The small scale circular cylinder is used as vortex generator and located in the boundary layer. The gap ratio G/D (the distance between the lower of the cylinder and the bottom of the channel G to the cylinder diameter D) varies from 0.5 to 6.0. The Reynolds number based on the bulk velocity and half height of the channel is 3745. The influence of gap ratio on cylinder wake and flow structure near the bottom of the channel is probed. Then, the effect of the cylinder wake on the flow and heat transfer features of the channel is revealed. Compared with the result of the rectangular channel without cylinder, it can be found that the interaction between the wake of cylinder and the boundary layer can significantly improve the heat transfer performance of the channel. Compared with the result of the rectangular channel with a reference cylinder whose diameter is the same as the slit-vent cylinder and without slit-vent, it can be found that the impinging jet derived from the slit-vent can further strengthen the interaction between the wake from the lower cylinder and the boundary layer when the gap ratio is less than 2.0. When the gap ratio is more than 2.0, the overall thermal performance of rectangular channel with the slit-vent cylinder is improved, and the constraint of the channel bottom on the wake of the cylinder is gradually weakened. Meantime, the disturbance caused by the wake of the slit-vent cylinder wears off, which leads the synthesis thermal coefficient η lower. The impinging jet has obvious influence on the stability of cylinder wake which related to the features of flow and heat transfer of the channel.

In the present study heat transfer and entropy generation analysis of boundary layer flow of an incompressible viscous fluid over hyperbolic stretching cylinder are taken into account. The governing nonlinear partial differential equations are normalized by using suitable transformations. The numerical results are obtained for the partial differential equations by a finite difference scheme known as Keller box method. The influence of emerging parameters namely curvature parameter and Prandtl number on velocity and temperature profiles, skin friction coefficient and the Nusselt number is presented through graphs. A comparison for the flat plate case is given and developed code is validated. It is seen that curvature parameter has dominant effect on the flow and heat transfer characteristics. The increment in the curvature of the hyperbolic stretching cylinder increases both the momentum and thermal boundary layers. Also skin friction coefficient at the surface of cylinder decreases but Nusselt number shows opposite results. Temperature distribution is decreasing by increasing Prandtl number. Moreover, the effects of different physical parameters on entropy generation number and Bejan number are shown graphically.

In order to offer a detailed explanation for heat transfer enhancement caused by the instability, a computational model for offset cylinder arrays was established by using a compound grid system. The fully implicit forms of continuous equation, unsteady Navier–Stokes equations and energy equation were finite-differenced. The numerical results demonstrate that cylinder row pitch plays an important role on the flow effects, which enhance or deteriorate the heat transfer on cylinder surfaces. Among these flow effects, the acceleration effect and the instability effect are the main factors for enhancing the downstream cylinders. Moreover, heat transfer enhancement caused by the flow instability is an effective way to reach the aim of reducing flow resistance and promoting heat transfer.