Added masses and volumes of stationary bodies in non-uniform streams 2019-01-0661
The added mass is an abstract concept that found its usefulness in the determination of the forces and moments on bodies accelerating in an otherwise still fluid. It is based on the observation that a body accelerating relative to the surrounding fluid changes the kinetic energy of the fluid. In manner analogous to Newton’s second law of motion, the force that the body must exert to accelerate the surrounding fluid is identified as the product of the acceleration and the mass of the fluid, “added” to that of the body. Equivalent results can be obtained for a stationary body in unsteady flow, with the exception of fluid rotations.
The connection between the added masses and the forces on stationary bodies in steady, non-uniform streams can be established using the long wave analogy. Similarly to the “volume times pressure gradient” formula in hydrostatics, of interest is rather the added volume than the mass of the fluid added to that of the body. Since the added volume is a tensor, the direction of the pressure gradient may not coincide with the direction of the force induced. For example, an axial pressure gradient in a wind tunnel does not just influence the measured drag force, but also the lift or side force.
Apart from some simple bodies such as the sphere or ellipsoid, where the added masses (or volumes) can be obtained analytically, numerical solutions have to be sought. Based on Lagally’s theorem, a new formula for the evaluation of the added volume is proposed. Computed examples are given for the MIRA notch-back car and the SAE car models, for which a collection of experimental data is also available.