Physical explanation: Smooth absolute value of mass flow rate for energy flow rate calculations (Simscape 2P domain)

Can anybody suggest a documentation or literature about the theory of the implemented solution for mass flow zero-crossing in the new two phase domain (2P)? I'd like to understand the derivation of the formula.

Look at the sections:

% Thermal conductance coefficient for each half of the component 
% Approximate conduction using specific internal energy differential 
% instead of temperature differential'

and

    % Smooth absolute value of mass flow rate for energy flow rate calculations
    % There can be non-zero energy flow even at zero mass flow due to conduction

of the component file 'port_two_dynamic.ssc' in the 'MATLAB_path\R2015b\toolbox\physmod\simscape\library\m\+foundation\+two_phase_fluid'

Answer 1

[Sebastian Castro]

For the first question, the closest thing I found was in the "Full Flux Scheme" section of the Thermal Liquid Modeling Framework documentation page. In this technology, just like the two-phase domain, thermal conduction is modeled by splitting the volume into halves and determining conduction from port A to the center, and from the center to port B.

For the second question on the smoothing term under flow reversal, refer to the "Mass Balance" section in the documentation for the Pipe (2P) block.

- Sebastian