Force and moment in incompressible flows

On an attempt to simplify the Quartapelle–Napolitano approach to computation of hydrodynamic forces in open flows

“…We will investigate this possibility as a generalization of the standard approach introduced by Quartapelle and Napolitano (1983). First we show that the different approaches to calculation of forces mentioned in Section 1 and the approach we are about to investigate can in fact be derived using the following general procedure: …”

“…In this investigation we analyze the possibility of extending the approach to calculation of forces proposed by Quartapelle and Napolitano (1983). We will be concerned with incompressible flows in unbounded exterior domains ( Figure 1a).…”

“…A different approach was proposed by Quartapelle and Napolitano (1983) where, before integrating over the domain, the momentum equation (1a) is multiplied by the gradient ∇ ∇ ∇η a of a harmonic function η a which satisfies a Neumann-type boundary condition n ·∇ ∇ ∇η a = −n · a on Γ 0 and whose gradient decays to zero at the outer boundary. As a result, the hydrodynamic force in the direction of the vector a ∈ R D is given by the expression…”

Load-estimation techniques for unsteady incompressible flows

“…Let us consider the simple fact that, as described by Protas (2007), this above approach rapidly breaks down as vorticity advects away from the body of interest and across the control surface (field of view). To combat this limitation, Quartapelle and Napolitano (1983) developed a clever approach weighting vorticity closest to the body instead. Despite attempts to reformulate this approach by Protas (2007), complete information regarding the wall-bounded vorticity around the body of interest is required, thus making the approach impractical for most physical experiments.…”

On the Force Decompositions of Lighthill and Morison

“…Comprehensive data on C B and C K have been presented by Sarpkaya (1976Sarpkaya ( , 1986Sarpkaya ( , 1999a The generalized formulations of the force exerted on a rigid body in translational motion in an incompressible viscous #uid require either the velocity or the vorticity "eld to be known throughout the whole #uid space [see e.g. Wu (1981), Quartapelle & Napolitano (1983), Lighthill (1986a), and Howe (1989)]. Wu (1981) and Lighthill (1986a) expressed the force F in terms of the moment of the vorticity distribution over the entire space, as…”