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Outputs
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\dot m = \dot m_1 + \dot m_2
| body | --uriencoded--\%7B s_\alpha \%7D_%7B\alpha=1..n%7D |
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| phase holdup |
| LaTeX Math Inline |
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| body | --uriencoded--\%7B q_\alpha \%7D_%7B\alpha=1..n%7D |
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| phase volumetric flowrate |
Inputs
| pipe cross-sectional area |
| LaTeX Math Inline |
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| body | --uriencoded--\%7B \dot m_\alpha \%7D_%7B\alpha = 1..n%7D |
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| phase mass flowrates |
| LaTeX Math Inline |
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| body | --uriencoded--\%7B \rho_\alpha \%7D_%7B\alpha = 1..n%7D |
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| phase densities |
Solver
| LaTeX Math Block |
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A = A_1 + A_2 |
| LaTeX Math Block |
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s_1 = A_1/A |
| LaTeX Math Block |
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s_2 = A_2/A |
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\frac{\dot m_\alpha}{\rho_\alpha \, u_\alpha} \cdot \ |
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\beta \frac{\dot m_\beta}{\rho_\beta \, u_\beta} \right)^{-1} |
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| LaTeX Math Block |
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| q_1\alpha = \dot m_1 / \rho_1 = A_1 s_\alpha \, u_1 \Rightarrowalpha \dot, m_1 = \rho_1 \, A_1 \, u_1 A |
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Derivation
Given the multiphase flow of
phases: and mass flowrates ...
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| LaTeX Math Block |
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\sum_\alpha s_\alpha = 1 |
| LaTeX Math Block |
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u_m = \sum_\alpha s_\alpha \cdot \dot u_\alpha |
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dot m_\alpha / \rho_\alpha = A_\alpha \, u_\ |
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For homogeneous 2-phase pipe flow:
| LaTeX Math Inline |
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| body | u_1 = u_2 \alpha = u_m, \, \forall \alpha \in [1..n] |
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and volumetric shares are going to be:
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left( \sum_\beta \frac{\dot m_ |
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See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Pipe Flow / Pipe Flow Dynamics / Pipe Flow Simulation
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