I solved the Navier-Stokes equation to determine the analytic solution. I used scaling to simplify the equation.
The boundary conditions were (refer to image in description): u(y=0)=0 & u(y=h(t))=0 where h(t)=H+delta*cos(omega*t)
To solve for the pressure differential (to substitute into the velocity equation) I equated an expression for the flow rate found by integrating the velocity and an equation for the flow rate found my knowing how much fluid was displaced.
Hi, could you provide the reference about the analytic solution? many thanks
jsliu54 2 years ago
I solved the Navier-Stokes equation to determine the analytic solution. I used scaling to simplify the equation.
The boundary conditions were (refer to image in description): u(y=0)=0 & u(y=h(t))=0 where h(t)=H+delta*cos(omega*t)
To solve for the pressure differential (to substitute into the velocity equation) I equated an expression for the flow rate found by integrating the velocity and an equation for the flow rate found my knowing how much fluid was displaced.
JaysonMartinez 2 years ago
Good task, could you interpret the symbols definition in the analytic solution, for example, "H, Delta".
jsliu54 2 years ago
I've added a link to a schematic in the description
JaysonMartinez 2 years ago
thanks for uploading~
minidickcn 2 years ago