What does “delta_vel_pos_AI” in Pipe (G) means?

% Change in flow velocity
delta_vel_AI = (1/rho_I - 1/rho_AI)*mdot_A/area;
delta_vel_BI = (1/rho_I - 1/rho_BI)*mdot_B/area;
delta_vel_pos_AI = sqrt(delta_vel_AI^2 + (0.001*a_AI)^2);
delta_vel_pos_BI = sqrt(delta_vel_BI^2 + (0.001*a_BI)^2);

and line 326–328

% Momentum balance
p_A - p_I == delta_vel_pos_AI*mdot_A/area + pressure_loss_AI;
p_B - p_I == delta_vel_pos_BI*mdot_B/area + pressure_loss_BI;

What do delta_vel_pos_AI and delta_vel_pos_BI mean?

According to the documentation Rigid conduit for gas flow — MATLAB — MathWorks Deutschland, the momentum balance does not consider anything related to the speed of sound for unchoked flow. What is the meaning of the term “(0.001*a_AI)²”? I tried to find it in the two references of the documentaion but could not find anything related.

Should it not simply be

p_A - p_I == delta_vel_AI*mdot_A/area + pressure_loss_AI;

so that it matches the momentum balance equation stated in the documentation?

ANSWER

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Hi ,

The term is using a trick to avoid using the abs() function, which may otherwise trigger frequent zero-crossing when mdot is small. Using the sqrt() formulation and having a value that’s always > 0, no zero-crossing would be triggered when solving the equations.

Later the momentum balance equation needs to compute abs(delta_vel_AI)*mdot_A/area. Here delta_vel_pos_AI is approximately abs(delta_vel_AI) when delta_vel_AI is not very small. If delta_vel_AI is small or close to 0.001*speed_of_sound, the mdot_A term would also be small, and the impact on the total momentum balance should also be neglible.

I’m curious what you found after modifying the block. Would you be able to share the .ssc file and a test model?

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