A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme
TL;DR: In this article, the initial development of viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically.
Abstract: The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in αm on the timing of the formation of the vortices, the closed wake length, and the thickness of the boundary layer is investigated.
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TL;DR: In this paper, the duality of solutions and the flow and heat transfer of the hybrid nanofluid past a shrinking cylinder in the appearance of Joule heating were observed.
Abstract: The objectives of the present study are (i) to observe the duality of solutions, and (ii) to investigate the flow and heat transfer of the hybrid nanofluid past a shrinking cylinder in the appearance of Joule heating. The single phase nanofluid model with modified thermophysical properties are used for the mathematical model. The similarity transformation simplifies the model (PDEs) into similarity (ordinary) differential equations. bvp4c solver is used to compute the reduced equations. For the validation part, the analytical solution is developed using an exact analytical method and compared with the numerical values for several cases. First and second solutions are observable for the shrinking cylinder case only if suction parameter is applied. Meanwhile, only the first solution is found to be stable from the stability analysis. The application of high suction strength make the reduced heat transfer rate is lower for hybrid nanofluid (Cu-Al2O3/water) than alumina-water nanofluid but, opposite result is found for the skin friction coefficient. The addition of curvature parameter (flat plate to cylinder) can quicken the separation process of boundary layer. This results are conclusive to the pair of alumina and copper only.
88 citations
TL;DR: In this article, a case study on an examination of hydrodynamic forces experienced by partially heated circular obstacles in a grooved channel is devoted to report case study, where two partially heated rectangular ribs are placed in between channel as obstacles.
38 citations
TL;DR: In this paper, a heated rotationally oscillating circular cylinder placed in a uniform cross flow of constant properties fluid is investigated and the two-dimensional governing equations of flow motion and energy are solved numerically on non-uniform polar grids using a higher order compact (HOC) formulation.
25 citations
TL;DR: Sengupta et al. as discussed by the authors explored the effect of compressibility by solving two-dimensional Navier-Stokes equations and reported the sensitive dependence of the temporal instability on the accuracy of the simulation for the growth of the disturbance field during the transient monotonic variations of lift and drag.
Abstract: In the present research, the instability suffered by flow past a rotating cylinder with very high rotation rates is studied. Special emphasis is given on exploring the effects of compressibility by solving two-dimensional Navier–Stokes equations. The first account of this instability has been provided in “T. K. Sengupta, K. Gupta, and M. T. Nair, “Lift generation and limiting mechanism via unsteady flow development for Magnus-Robins effect,” Proceedings of the 8th Asian Congress of Fluid Mechanics, Shenzhen, China (1999).” Subsequently, there have been other efforts on the same with different numerical models based on incompressible and compressible flow formulation. Apart from the efforts reported by the present group, other reported results did not identify this as a phenomenon of flow instability. The perceived temporal variations of lift and drag by both the incompressible and compressible flow formulation have been correlated with each other, without highlighting the role of compressibility in triggering the flow instability. Here, we report the sensitive dependence of the temporal instability on the accuracy of the simulation for the growth of the disturbance field during the transient monotonic variations of lift and drag. Of specific interest is the role of compressibility in promoting the disturbance growth and limiting the maximum lift that is generated. The compressibility effects have been incorporated by considering lower Mach numbers for the oncoming uniform flow, so that nowhere in the flow field there is the formation of a supersonic pocket.
14 citations
TL;DR: In this article, the authors numerically investigated the time-resolved laminar flow, fluid forces, Strouhal number, and convective heat transfer over two isothermal co-rotating and counterrotating circular cylinders in tandem arrangements for scaled cylinder center-to-center spacing S* and Re.
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TL;DR: In this article, a large increase or decrease in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation.
Abstract: Exploratory experiments have been performed on circular cylinders executing forced rotary oscillations in a steady uniform flow. Flow visualization and wake profile measurements at moderate Reynolds numbers have shown that a considerable amount of control can be exerted over the structure of the wake by such means. In particular, a large increase, or decrease, in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation.
394 citations
TL;DR: In this article, the Navier-Stokes equations were integrated numerically for the time-dependent flow past an impulsively started circular cylinder, based on the diameter of the cylinder, from 5 to ∞.
Abstract: An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated for R = 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder for R = 500 is also found to be in reasonable agreement with experimental measurements for the case R = 560.For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. For R > 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the case R = 500, but for higher Reynolds numbers, including the case R = ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.
252 citations
TL;DR: In this paper, a numerical study of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with a constant speed is made.
Abstract: A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Karman vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.
173 citations
TL;DR: Early stages of viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analyzed numerically by direct integration of the Navier-Stokes equations as discussed by the authors.
Abstract: Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.
151 citations
TL;DR: In this paper, the early phase of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs.
Abstract: The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers (Re [les ] 1000). The rotating-to-translating-speed ratio α increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E1 Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies Ei (i = 2,3,…) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter.
145 citations