Theoretical treatment of fluid flow for accelerating bodies

Abstract

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.<p>Funding agencies: DRDB [KT466921, KT528944, KT470887]</p

Modelling of Powder Removal for Additive Manufacture Postprocessing

“…This appears as a source term on the right hand side of the momentum equation for the particle phase [65]. It is assumed that the air phase is unaffected by centrifugal forces due to its relatively low density.…”

Modelling of Powder Removal for Additive Manufacture Postprocessing

“…This appears as a source term on the right hand side of the momentum equation for the particle phase [62]. It is assumed that the air phase is unaffected by centrifugal forces due to its relatively low density.…”

Eulerian derivation of the conservation equation for energy in a non-inertial frame of reference in arbitrary motion

“…Acceleration and deceleration are often encountered in a multitude of engineering applications including, helicopter rotors in hover and forward flight [1], missile aerodynamics [2], manoeuvring fighter planes during acceleration and deceleration [3], aerodynamics around a decelerating Formula 1 and various high performance cars [4] and aero-ballistic ordinance [5]. Accelerating/decelerating motion is considered here to combine unsteady translation and unsteady rotation of an object immersed in a compressible fluid [2,3,6,7,8,9]. This can also include combined oscillating translation and rotation [10,11,12].…”

“…In the above studies, the effects observed increased with an increase in the acceleration magnitude. Thus in applications where the acceleration/deceleration is significant, it becomes important to not only investigate the transient effects but also the acceleration effects that result from the acceleration of the objects centre of mass [3].…”

“…The conservation equation for mass remains unchanged when transformed from an inertial frame to a non-inertial frame of reference both for incompressible [6,21,22] and a compressible fluid [3,5,7,8,9,11,12]. The type of motion is insignificant when considering the conservation equation for mass as can be seen by the various studies that have looked at various cases, pure steady rotation [21,22], unsteady pure rotation [7] and arbitrary motion [3,5,6,8,9].…”