Riemann solver with internal reconstruction (RSIR) for compressible single-phase and non-equilibrium two-phase flows

Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.

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Zuber-Type Parameter Distributions for Non-Equilibrium Two-Phase Flows: Generalization for Annular Channel and Rod Cluster Geometries

Volume 8C: Heat Transfer and Thermal Engineering ◽

10.1115/imece2013-64755 ◽

2013 ◽

Author(s):

Y. Kornienko

Keyword(s):

Current Method ◽

Annular Channel ◽

Elementary Functions ◽

Two Phase Flows ◽

Principle Of Superposition ◽

Two Phase ◽

Drift Flux Model ◽

Drift Flux ◽

Cross Section Profile ◽

Non Equilibrium

This study presents the main results of the analysis of the previously developed generalized hierarchical closed system of analytical closure relations for the distribution parameters (DPs) Cks (k = f - fluid or g - vapor; s = 0,1,2,3 - mass, energy, momentum) that are used in quasi-one-dimensional form of the conservation laws for mass, momentum and energy in non-equilibrium two-phase flows. The current method has been expanded to account for non-uniform in cross-section profile of void fraction. The main assumptions of the received quadrature relationships for DP are: (a) the use of the drift flux model, (b) the quasi-steady-state approximation, and (c) the power-mode approximations of the local distribution profiles of the variables. These DPs Cks quadrature are expressed in terms of elementary functions, they directly reflect the principle of superposition, generalize and unify not only the Zuber-Findlay method, but also Hancox-Nicoll and Hibiki-Ishii methods. The revealed complementarity properties are particularly useful for the purposes of testing, validating and verifying DPs.

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Friction Factor Equations Accuracy for Single and Two-Phase Flows

Volume 11: Petroleum Technology ◽

10.1115/omae2020-18682 ◽

2020 ◽

Author(s):

Germano Scarabeli Custódio Assunção ◽

Dykenlove Marcelin ◽

João Carlos Von Hohendorff Filho ◽

Denis José Schiozer ◽

Marcelo Souza De Castro

Keyword(s):

Pressure Drop ◽

Friction Factor ◽

Single Phase ◽

Computational Cost ◽

Two Phase Flows ◽

Two Phase ◽

Explicit Equation ◽

Implicit Equation ◽

Lower Accuracy ◽

Statistical Metrics

Abstract Estimate pressure drop throughout petroleum production and transport system has an important role to properly sizing the various parameters involved in those complex facilities. One of the most challenging variables used to calculate the pressure drop is the friction factor, also known as Darcy–Weisbach’s friction factor. In this context, Colebrook’ s equation is recognized by many engineers and scientists as the most accurate equation to estimate it. However, due to its computational cost, since it is an implicit equation, several explicit equations have been developed over the decades to accurately estimate friction factor in a straightforward way. This paper aims to investigate accuracy of 46 of those explicit equations and Colebrook implicit equation against 2397 experimental points from single-phase and two-phase flows, with Reynolds number between 3000 and 735000 and relative roughness between 0 and 1.40 × 10−3. Applying three different statistical metrics, we concluded that the best explicit equation, proposed by Achour et al. (2002), presented better accuracy to estimate friction factor than Colebrook’s equation. On the other hand, we also showed that equations developed by Wood (1966), Rao and Kumar (2007) and Brkić (2016) must be used in specifics conditions which were developed, otherwise can produce highly inaccurate results. The remaining equations presented good accuracy and can be applied, however, presented similar or lower accuracy than Colebrook’s equation.

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