Equation-oriented formulation

[RoberAgro]

Develop an equation-oriented model formulation for centrifugal compressors.

Key elements to include:

• Conservation of mass at each station

• Conservation of rothalpy in each component

• Velocity triangle calculations

• Calculation of fluid properties with CoolProp:

  • Should we use enthalpy-entropy function calls as for the axial-turbine model?
  • Should we use pressure-enthalpy function calls only to be able to use look-up-tables easily?

• Boundary conditions:

• Stagnation pressure/temperature at inlet

• Inlet mass flow rate (subsonic flow without choking)

• Exit pressure or "throttle valve" boundary conditions for cases with choking in the future

Hi,

I would like to discuss some approaches for modeling the vaneless diffuser space. If I remember correctly from our meeting we planned to use the conservation of angular momentum with a loss term:
$$r_{in}c_{\theta, in} = r_{out}c_{\theta, out} + \Delta AM $$

Is this used in combination with a correlation for the pressure or enthalpy loss? I see Meroni presented an equation for calculating the exit static pressure:
$$p_{out} = p_{in} + CP(p_{0,in} - p_{in})$$
while in the Oh and Chaowei paper use a correlation for the enthalpy loss:
$$\Delta h = C_pT_{0,in} \left[\frac{p_{out}}{p_{0, out}}^{\frac{\gamma - 1}{\gamma}} - \frac{p_{out}}{p_{0, in}}^{\frac{\gamma - 1}{\gamma}}\right]$$

If I am not mistaken, both approaches can be used mathematically, but is one approach more appropriate than the other?

[RoberAgro]

See dev_projects/centrifugal_compressor/model_development.md

I think that it makes sense to use the conservation of angular momentum with a loss term. This term can be calculated as a function of the friction factor.

For the losses, I suggest to use the enthalpy loss coefficient and calculate its value based also on the friction factor. I think that using the loss coefficient would is better ("closer to the physics") than the approaches using the diffuser effectiveness ($C_p$)

[lasseband]

The framework for the Equation-Oriented approach is implemented. Equations for the following components are implemented:

• Impeller
• Vaneless diffuser
• Vaned diffuser
• Volute

The boundary conditions include the total inlet state, mass flow rate, rotational speed and inlet absolute flow angle. The model evaluates the equations for each component given these boundary condition, and accumulates the residual equations.

The independent variables and residuals for each component:

• Impeller
  • Independents: $[v_\mathrm{in}, w_\mathrm{out}, s_\mathrm{out}, \beta_\mathrm{out}]$
  • Residuals: $[ \Delta m_\mathrm{in}, \Delta m_\mathrm{out}, \Delta Y_\mathrm{out}, \Delta v_{\theta ,s}]$
• Vaneless diffuser:
  • Independents: $[w_\mathrm{out}, s_\mathrm{out}, \alpha_\mathrm{out}]$
  • Residuals: $[\Delta m_\mathrm{out}, \Delta Y_\mathrm{out}, \Delta AM]$
• Vaned diffuser:
  • Independents: $[w_\mathrm{out}, s_\mathrm{out}]$
  • Residuals: $[\Delta m_\mathrm{out}, \Delta Y_\mathrm{out}]$
• Volute:
  • Independents: $[w_\mathrm{out}, s_\mathrm{out}]$
  • Residuals: $[\Delta m_\mathrm{out}, \Delta Y_\mathrm{out}]$

For now, the calculations are done using enthalpy-entropy function calls.

Choking calculations will further add independent/residuals. See own task.

Nomenclature

• $\Delta v_{\theta ,s}$: slip velocity residual, difference between slip velocity calculated by the given relative flow angle, and the slip velocity calculated by the slip model.
• $\Delta AM$: Difference in angular momentum due to losses.