Taylor Couette Bernoullis

Has anyone studied a Taylor-Couette flow in the presence of a varying diameter pipe. Is there any research that i can be pointed to to understand how the pressure differences develop in a purely momentum flow (in the absence of a streamwise pressure gradient) ?

• These are the results of numerical simulation shown in the pictures? What software did you use? – Alex Trounev Feb 14 at 16:39
• Hi @AlexTrounev these are from a simulation in Autodesk CFD ? – Tom Chester Feb 15 at 10:53
• Do you need to calculate the distribution of $\nabla p$ in this flow? – Alex Trounev Feb 15 at 12:57
• Hi @AlexTrounev Yes that would be good, At present if we took out the radial acceleration pressure variance across the streamline (and the outer wall velocity being equal to flow speed) then it looks to be plain old Bernoullis. That's what i am trying to confirm so an explanation of why the pressure gradients develop would be great . – Tom Chester Feb 17 at 8:03
• Obviously, a viscous flow model is used. The Reynolds number is not specified, apparently this is a laminar flow. We can calculate the Bernoulli integral for this flow. – Alex Trounev Feb 17 at 13:56

I calculated a similar flow in the numerical model using Mathematica 11.3. The model uses the Navier-Stokes equations for a flat laminar non-compressible flow, finite element method and the method of the false transient. The outer cylinder rotates, the inner one is fixed, Reynolds number $$Re=100$$. In fig. shows the distribution of the square of velocity $$u^2+v^2$$, pressure and analogue of the Bernoulli integral $$\frac {1}{2}\rho (u^2+v^2)+p$$. The pressure difference arises in the process of establishing the solution of a system of equations. The physical reason for the pressure difference is obvious - this is a change in the cross section of the gap.