functiondp_tau_const_isentrop

Information

This is a model of isentropic expansion or compression of an ideal gas with a fixed isentropic efficiency.

The isentropic exponent (kappa) by default is retrieved from the media model at the inlet. It can be set to a fixed value to allow compressor operation in two-phase region.

The computation is as follows:

1. with the scaling factors omega_ref, m_flow_ref and the scewness factor skew, the pressure ratio pr=p_outlet/p_inlet is computed as quadratic function of omega/omega_ref, m_flow/m_flow_ref:
pr  := abs(omega)*omega/(omega_ref^2)  - skew*omega*m_flow/(omega_ref*m_flow_ref)  - abs(m_flow)*m_flow/(m_flow_ref^2)  + 1;
2. if the pressure ratio is smaller then 1 (expansion of gas), to limit it to 0 compute:
   pr := k^(pr-1);
3. compute specific technical work w_t from pr using a isenthalpic process
4. apply constant isentropic efficiency
5. compute static moment by the following law:
   • if m_dot and omega both > 0 (nominal operation): W_t = w_t*m_flow = tau*omega
   • else (not nominal operation; with area of fluid A and radius of pump r) tau = F*r = dp*A*r = dp*V_ref
   both are scaled so they are smooth at the border to nominal operation. Additionally for small omega, a small tau is added, so the standing pump can be pushed by the fluid.

omega_ref and m_flow_ref are supposed to be scaling factors for omega and m_flow respectiveley. omega_ref is the angular velocity that produces a pressure ratio of 2 at m_flow=0. m_flow_ref is the massflow, that produces a negative pressure ratio of 1 at omega=omega_ref. The skewness factor can be used to shape the characteristic curve inbetween (see fig. 1).

When pr < 1, the reciprocal pressure ratio 1/pr = p_inlet/p_outlet is more interesting. It can be seen for different values of skew in fig. 2.

Fig. 1: different skewness factors for omega/omega_ref=1. pressure ratio pr over m_dot/m_dot_ref

Fig. 2: different skewness factors for omega/omega_ref=1. Reciprocal pressure ratio 1/pr over m_dot/m_dot_ref

Inputs