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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This investigation focuses on the aerodynamic effects caused by acceleration and retardation. It shows that, when an object is accelerated in a compressible fluid, the aerodynamic forces and moments experienced by the object at any instantaneous Mach number are different to those, experienced at the same Mach number, when the object moves at constant velocity. A supersonic biconvex aerofoil was chosen, with Fluent as the computational fluid dynamic (CFD) software. Constant velocity (steady state) simulations were conducted at Mach numbers ranging from 0.1 to 1.6 for the aerofoil. The aerofoil was then accelerated at 1041 m/s 2 (106 g) and 86.77 m/s 2 (8.845 g), starting at Mach 0.1, and decelerated at −1041 and −86.77 m/s 2 , starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were shown between the steady and the unsteady cases with the greatest differences observed in the transonic region. In this region, for each specific Mach number, acceleration-dependant variations in the position of the shock wave on the upper surface of the aerofoil were also observed. This was used to explain the great differences in the aerodynamic forces and moments between the steady and the unsteady cases in the transonic region.