Multibody flows

Vorticity annihilation and inviscid blocking in multibody flows... 

It would seem natural to ask how both drag forces and inviscid blocking may be included in current incompressible computational models of multibody flows. To demonstrate this for the case of an isolated body, we first note that that the inertial terms in the momentum equation may be expressed as... 

For a concentrated system this represents the ratio of the diffusive timescale of the quiescent microstructure to the convection under an applied deforming field. Note again that we are defining this in terms of the stress which is, of course, the product of the shear rate and the apparent viscosity (i.e. this includes the multibody interactions in the concentrated system). As the Peclet number exceeds unity the convection is dominating. This is achieved by increasing our stress or strain. This is the region in which our systems behave as non-linear materials, where simple combinations of Newtonian or Hookean models will never satisfactorily describe the behaviour. Part of the reason for this is that the flow field appreciably alters the microstructure and results in many-body interactions. The coupling between all these interactions becomes both philosophically and computationally very difficult. 

The flow generated by an isolated planar body in an unbounded uniform stream may be surprisingly, far more complicated than the multibody counterpart. Vorticity of opposite signs is continuously shed from the surface of a rigid body (see Fig. 7.2a). 

The first is determined by the drag on the body, the second by viscosity and distance while the last one is determined by the shape of the body. For an isolated body, the first two lengthscales characterise the far field flow which makes the problem more difficult than the multibody counterpart, where only one lengthscale is required. 

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