We have seen there are two basic approaches to water turbine calculations.

With in the momentum equation

physical setting

model setting

Without explicit in the momentum equation

Following table shows possible boundary conditions for the pressure variable

Table: Boundary conditions

pressure

setting

inlet

outlet

, physical

hTP

=

fMV

=

, model

hTP

=

fMV

=

hTP

=

fMV

=

We note that hTP stands for hydrostaticTotalPressure boundary condition and values listed in the Table for this type represent values of hydrostatic pressure in the centre of mass of the inlet surface. Whereas fMV stands for fixedMeanValue boundary condition and values listed in the Table for this type represent values of static pressure in the centre of mass of the outlet surface.
We add that pressureInletVelocity boundary condition is prescribed for the inlet velocity field for all of the above settings, where the velocity magnitude is computed from the difference between total and static pressure and its direction is taken as a local normal to the inlet surface (usually planar). Also zeroGradient boundary condition is prescribed for the outlet surface for all of the above settings.

The computational model solves following system of equations:

Mass conservation

Momentum conservation

Energy conservation and , two options

where: Einstein summation is used, is partial derivative, is i-th Cartesian coordinate, is density, is i-th velocity vector component, is time, is static pressure, shear stress tensor, is Kronecker delta, is total specific energy, is dynamic viscosity, is rate-of-deformation tensor, is static temperature, is Prandtl number, specific gas constant, specific heat capacity (at constant pressure), specific heat capacity (at constant volume), i-th heat flux component (Fourier law), heat conductivity coefficient.

The whole system is closed with boundary conditions.