A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme

Mittal, H. V. R.; Ray, Rajendra K.; Al‐Mdallal, Qasem M.

doi:10.1063/1.5001731

Cited by 31 publications

(26 citation statements)

References 37 publications

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“…The initial stage of the circular cylinder impulsively started, rotating and translating from rest is also obtained by Badr & Dennis (1985). Also, Al-Mdallal (2012) and Mittal, Ray & Al-Mdallal (2017) treated the initial stage of a circular cylinder impulsively started with streamwise and transverse oscillations and further rotational oscillation.…”

Section: Introductionmentioning

confidence: 94%

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Ueda

Kida

2021

J. Fluid Mech.

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The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of $1/\sqrt {\lambda }$ and $1/\lambda$ , respectively, within the second approximation of the present asymptotic analysis, where $\lambda$ is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453–1480). Based on the asymptotic solution, the influence of the penalization parameter $\lambda$ is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$ .

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Section: Introductionmentioning

confidence: 94%

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Ueda

Kida

2021

J. Fluid Mech.

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“…The technique used to discretize the governing equations is the higher order compact (HOC) finite difference scheme 36–39 which is second order accurate in time and at least third order accurate in space. The discretized equations can be written as: 19,40,41

([], A 1_{i j} δ_{r}^{2} + A 2_{i j} δ_{θ}^{2} + A 3_{i j} δ_{r} + A 4_{i j} δ_{r} δ_{θ} + A 5_{i j} δ_{r} δ_{θ}^{2} + A 6_{i j} δ_{r}^{2} δ_{θ} + A 7_{i j} δ_{r}^{2} δ_{θ}^{2}) Ψ_{i j} = G_{i j},

\begin{matrix} false \\ right & center & left [B 1 1_{i j} δ_{r}^{2} + B 1 2_{i j} δ_{θ}^{2} + B 1 3_{i j} δ_{r} + B 1 4_{i j} δ_{θ} + B 1 5_{i j} δ_{r} δ_{θ} \\ right & center & left + B 1 6_{i j} δ_{r} δ_{θ}^{2} + B 1 7_{i j} δ_{r}^{2} δ_{θ} + B 1 8_{i j} δ_{r}^{2} δ_{θ}^{2}] {normalΩ}_{i j}^{n + 1} \\ right & center & left = [B 2 1_{i j} δ_{r}^{2} + B 2 2_{i j} δ_{θ}^{2} + B 2 3_{i j} δ_{r} + B 2 4_{i j} δ_{θ} \end{matrix}

…”

Section: Numerical Schemementioning

confidence: 99%

Heat transfer past rotationally oscillating circular cylinder heated with time‐periodic pulsating temperature in a uniform flow

2021

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“…Otherwise, they are categorized as regular. Our numerical algorithm is based upon enforcing a nine point HOC scheme (Mittal et al, 2016(Mittal et al, , 2017a(Mittal et al, , 2017bMittal and Al-Mdallal, 2018) for discretization at regular points and a higher order accurate immersed interface method at the irregular points. However, as we contemplate on using a nine point HOC scheme on the regular points, if all the eight neighbours of a regular point cannot be found on the same side across Γ , there is a need for redefining such regular points.…”

Section: Immersed Interface Treatmentmentioning

confidence: 99%

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

Mittal

Ray

Gadêlha

et al. 2020

Exp. Comput. Multiph. Flow

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This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.

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A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme

Cited by 31 publications

References 37 publications

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Heat transfer past rotationally oscillating circular cylinder heated with time‐periodic pulsating temperature in a uniform flow

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

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