Numerical Domain and Boundary Conditions

The computational domain is limited to a single vane passage by two sur­faces as shown in Figure 1. There are three types of boundary conditions to be imposed. At the hub and tip radii, and vane surfaces we have solid sur­faces, along which we apply the impermeability conditions, u ■ n = 0. Along
the free surfaces (upstream and downstream of vane section), we impose the quasi-periodicity conditions for the pressure and the normal velocity compo­nent, {p u • n} (x, r, §) = {pf, u • n} (x, r, 0)elcr. Here § = y – is the an­gular vane spacing, V is the number of stator vanes, and a = 2py" is the inter-blade phase angle. At inflow and outflow non-refecting boundary condi­

tions are implemented. We seek a relationship between the values of p’ at an outgoing section, жі, to those inside the numerical domain, x2, of the form, p'(x1,r, 6) = Mp'(x2,r, 6). Here M is a mapping function. This mapping function has been developed and tested by Elhadidi, 2002.