Theoretical treatment of fluid flow for accelerating bodies

Irvy M.A. Gledhill, Hamed Roohani, Karl Forsberg, Peter Eliasson, Beric W. Skews, Jan Nordström

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)449-467
Number of pages19
JournalTheoretical and Computational Fluid Dynamics
Issue number5
Publication statusPublished - 1 Oct 2016
Externally publishedYes


  • Arbitrary acceleration
  • Computational fluid dynamics
  • Fluid physics
  • Manoeuvre
  • Navier–Stokes equations
  • Non-inertial frame

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes


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