Investigation of acceleration effects on missile aerodynamics using computational fluid dynamics

Theoretical treatment of fluid flow for accelerating bodies

“…The first is that a number of effects in a non-inertial frame are familiar, such as the Coriolis effect, and should be shown in the context of flow around accelerating bodies; the second is that terms for linear acceleration and angular acceleration in rotation and revolution should be identifiable; and the third is to illustrate the use of dimensionless parameters in this field. In a previous paper, the derivation of the conservation equations for mass and momentum was presented by Gledhill et al [1]. In the following paragraphs, the mass and momentum equations are summarised, and the energy equation is derived.…”

“…Transformation of the continuity and momentum equations [1] is extended here to the energy equation. Part of the motivation for developing this theory is to develop guidance about what constitutes "significant" acceleration, and how the regimes of flow about accelerating objects can be distinguished and quantified.…”

“…Inoue et al [37] used an early simulation in the inertial frame to simulate a constant speed diamond aerofoil describing a parabolic path, for the purpose of investigating shock focussing within the arc. Forsberg et al [30] and Gledhill et al [1] provided the basis of the theory for the continuity and momentum equations as given here, validated an implementation in the inertial frame within the finite-volume code EURANUS using the oscillating aerofoil data of Landon [38], and then used a model of the NACA0012 aerofoil on constant pitch trajectories [39] to illustrate the necessity for inclusion of acceleration effects in the calculation of pitch damping. It was then demonstrated that drag on an axisymmetric flare missile dropped by 20% in comparison with steady values if the flare geometry was accelerated through the transonic range at 4 500 ms -1 .…”

“…Gledhill et al [1] published the continuity and momentum equations and demonstrated an implementation in the code EURANUS [31], by performing the computations in the inertial frame. This approach has the considerable advantages of (1) a very simple development path from an existing moving-mesh model with spatial conservation [31], in which boundary conditions are the main modifications required, and (2) the fact that the source terms appearing in the relative frame model (below) do not need to be discretised, implemented, verified or validated.…”

“…The equations should include both viscous and gravitational terms as well as linear or turning acceleration. In this paper the energy equation for arbitrary acceleration in general non-inertial frames of reference is presented, based on the work of Löfgren (unpublished reports FFAP-A-1040 and FFAP-B-066, The Aeronautical Research Institute of Sweden, 1995 and 1998 respectively) and Forsberg (unpublished report, The Aeronautical Research Institute of Sweden, 1998) and following the continuity and momentum conservation equations previously formulated by Gledhill et al [1]. From the accelerating frame formulation, a set of dimensionless constants is derived, which, under specified circumstances, can be used to determine whether acceleration effects are likely to be significant in a specified regime of interest in terms of the relative importance of linear terms.…”