Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow

Parmar, M.; Haselbacher, Andreas; Balachandar, S.

doi:10.1103/physrevlett.106.084501

Cited by 105 publications

(33 citation statements)

References 8 publications

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“…Several early authors performed analytical studies of Stokes flow over bodies accelerating in incompressible viscous flow at low Reynolds numbers, deriving the force on a sphere and an expression for the boundary layer. This led to the formulation of the Basset-Bousinessq-Oseen equation for the motion of a particle in the limit of low Mach and Reynolds numbers and its subsequent extension to compressible flow [11]. The terms Bousinessq-Basset force, Basset force [12] or history force refer to the fact that the development of a boundary layer over an accelerating particle in a fluid depends on the temporal history of the fluid near the particle surface.…”

Section: Earlier Workmentioning

confidence: 99%

Theoretical treatment of fluid flow for accelerating bodies

Gledhill¹,

Roohani

Forsberg

et al. 2016

Theor. Comput. Fluid Dyn.

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Most computational fluid dynamics simulations are, at present, performed in a body-fixed frame, for aeronautical purposes. With the advent of sharp manoeuvre, which may lead to transient effects originating in the acceleration of the centre of mass, there is a need to have a consistent formulation of the Navier–Stokes equations in an arbitrarily moving frame. These expressions should be in a form that allows terms to be transformed between non-inertial and inertial frames and includes gravity, viscous terms, and linear and angular acceleration. Since no effects of body acceleration appear in the inertial frame Navier–Stokes equations themselves, but only in their boundary conditions, it is useful to investigate acceleration source terms in the non-inertial frame. In this paper, a derivation of the energy equation is provided in addition to the continuity and momentum equations previously published. Relevant dimensionless constants are derived which can be used to obtain an indication of the relative significance of acceleration effects. The necessity for using computational fluid dynamics to capture nonlinear effects remains, and various implementation schemes for accelerating bodies are discussed. This theoretical treatment is intended to provide a foundation for interpretation of aerodynamic effects observed in manoeuvre, particularly for accelerating missiles.

Funding agencies: DRDB [KT466921, KT528944, KT470887]

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Section: Earlier Workmentioning

confidence: 99%

Theoretical treatment of fluid flow for accelerating bodies

Gledhill¹,

Roohani

Forsberg

et al. 2016

Theor. Comput. Fluid Dyn.

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Funding agencies: DRDB [KT466921, KT528944, KT470887]

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“…[19,20]. For a compressible now, the dependence of the added-mass force on the instantaneous relative acceleration is no longer valid [21][22][23]. Due to the finite speed of the propagation of sound, the added-mass force depends on the history of the particle relative acceleration and is expressed in an integral form.…”

Section: Introductionmentioning

confidence: 98%

Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

Jaiman

Parmar

Gurugubelli

2013

Journal of Applied Mechanics

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This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler-Bemoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

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“…27,28 The detailed model for particles in a compressible flow has been developed recently. [29][30][31] It has also been shown that for certain particle parameters, the point-particle model can still be used to study the particle-shock interaction. 32 In this study, we will investigate inertial particles with different density advected in a compressible homogeneous isotropic turbulence by using numerical simulations.…”

mentioning

confidence: 99%

“…For finite size sphere interacting with a shock, the force experienced by the sphere has been discussed in detail. 29,30 Here, we shall assume point particle and employ a simple model to explain the behavior of v n . Starting from Eq.…”

mentioning

confidence: 99%

Interactions between inertial particles and shocklets in compressible turbulent flow

et al. 2014

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Numerical simulations are conducted to investigate the dynamics of inertial particles being passively convected in a compressible homogeneous turbulence. Heavy and light particles exhibit very different types of non-uniform distributions due to their different behaviors near shocklets. Because of the relaxation nature of the Stokes drag, the heavy particles are decelerated mainly at downstream adjacent to the shocklets and form high-number-density clouds. The light particles are strongly decelerated by the added-mass effect and stay in the compression region for a relatively long time period. They cluster into thin filament structures near shocklets.

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Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow

Cited by 105 publications

References 8 publications

Theoretical treatment of fluid flow for accelerating bodies

Theoretical treatment of fluid flow for accelerating bodies

Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

Interactions between inertial particles and shocklets in compressible turbulent flow

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