Equations for Simscape component Pipe (2P)

Currently, I'm using the Simscape component Pipe (2P) as part of a larger system, and I want to understand the equations governing the behaviour of the pipe. There are however a few equations that confuse me, for example the calculation of the Nusselt number. The documentation says

But after studying the code, I can't see any so called "blending" of the Nusselt numbers in laminar and turbulent flow. Instead, it seems as if the Nusselt number in subcooled or superheated fluid is calculated as

, where is the Nusselt number in turbulent flow, and is the Nusselt number in laminar flow. Likewise, in the two-phase region, with a mixture of gas and liquid, the Nusselt number is given by

, where is the Nusselt number in the two phase region in the turbulent flow regime. As far as I can see when looking through the code, there is no blending here. Am I missing something, or is there a discrepancy between the documentation and the actual code?

Answer 1

[Yifeng Tang]

The blending happens in lines 324-327 (R2022a):

    % Smooth transition for heat transfer coefficient between liquid, mixture, and vapor
    heat_transfer_coeff = simscape.function.blend( ...
        simscape.function.blend(Nu_I*k_I/Dh, Nu_mix_I*k_sat_liq_I/Dh, 0, A.transition_range, alpha_I), ...
        Nu_I*k_I/Dh, (1 - A.transition_range), 1, unorm_I);
    

The simscape.function.blend applies a 3rd order polynomial inside. You can select it and right click to open its code (or Ctrl+D).

    function y = blend(y1,y2,x1,x2,x)
% y = blend(y1,y2,x1,x2,x)
% Blend between two values y1 and y2 as x varies between x1 and x2. The
% blending function ensures y is continuous and differentiable in the
% range x1 <= x <= x2.

% Copyright 2017-2018 The MathWorks, Inc.

definitions
    u = (x-x1)/(x2-x1);
    transition = 3*u^2 - 2*u^3;
    y = if le(x,x1)
        y1;
    elseif ge(x,x2)
        y2
    else
        (1-transition)*y1 + transition*y2;
    end
end

end

[Lukas Mårtensson]

First of all, thanks for the answer! However, I'm not quite sure this answers my question. What I'm confused about is the calculation of the variables Nu_I and Nu_mix_I, as it is stated in the documentation that these are calculated via interpolation (with blend) in the transitional region between laminar and turbulent flow. I could not find where this interpolation/blending is performed in the code, however. Lines 324-327 that you are referring to seem to only blend the Nusselt number in the region between subcooled, mixed and superheated fluid, not turbulent vs laminar flow.