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Torque term coming from added mass effects

I’m studying a quasi-steady force model (for a 2D problem) published in a fluids journal, and one of the torque terms is a bit perplexing: the term is a product of a difference of added mass coefficients and translational velocities in the x and y variables, e.g.

$$(m_1 – m_2)dot x(t) times dot y(t).$$

The other torque terms in the model are from fluid forces and dissipative drag. How can the term above describe a torque in the system?

MathOverflow Asked by user114331 on January 24, 2021

2 Answers

2 Answers

maybe a necro, but for posterity i think this is the "Munk Moment"

notice that it only applies to non symmetric bodies (m1=/= m2). it should even apply in the absence of any viscocity.

imagine a long thin object inclined into a flow ( an ellipse or a plane, or just a line segment in 2d)

as an example a line segment in 2d with flow coming from left to right, with the line segment at 45 degrees.

imagine a line of flow, it hits the line segment and gets diverted upwards roughly parallel to the surface.

that change in direction to divert it means a force has to be applied to it by the plane, and consequently the fluid applies a force to the plane.

on the trailing edge the situation is reversed. in ideal conditions these will be equal, and opposite in direction, so the net force on the plane will be zero, however those forces are being applied at different locations, so the net torque need not be. ideal means no viscosity and the plane/ellipse has to be prevented from rotating, or the flow will end up doing work on it. the torque ends up causing the plane to rotate so its flat edge is facing the flow.

it ends up coming up with things like arrows, where it's considered destabilising- in the absence of fletching/ an arrowhead, it would be naturally unstable and want to rotate till it was perpendicular to its direction of motion, obviously something that is undesirable.

that's my layman's understanding anyway.

Answered by Dylan Davies on January 24, 2021

This looks like a momentum or impulse-momentum type of term. You can check from here why it gives rise to a torque in the system.

Answered by Igor on January 24, 2021

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