A multicomponent real-fluid fully compressible four-equation model for two-phase flow with phase change

Abstract

A fully compressible four-equation model for multicomponent two-phase flow coupled with a realfluid phase equilibrium-solver is suggested. It is composed of two mass, one momentum, and one energy balance equations under the mechanical and thermal equilibrium assumptions. The multicomponent characteristics in both liquid and gas phases are considered. The thermodynamic properties are computed using a composite equation of state (EoS), in which each phase follows its own Peng-Robinson (PR) EoS in its range of convexity, and the two-phase mixtures are connected with a set of algebraic equilibrium constraints. The drawback of complex speed of sound region for the two-phase mixture is avoided using this composite EoS. The phase change is computed using a phase equilibrium-solver, in which the phase stability is examined by the Tangent Plane Distance (TPD) approach; an isoenergetic-isochoric (UVn) flash including an isothermal-isobaric (TPn) flash is applied to determine the phase change. This four-equation model has been implemented into an inhouse IFP-C3D software. Extensive comparisons between the four-equation model predictions, experimental measurements in flash boiling cases, as well as available numerical results were carried out, and good agreements have been obtained. The results demonstrated that this four-equation model can simulate the phase change and capture most real-fluid behaviors for multicomponent two-phase flows. Finally, this validated model was applied to investigate the behaviors of n-dodecane/nitrogen mixtures in one-dimensional shock and double-expansion tubes. The complex wave patterns were unraveled, and the effects of dissolved nitrogen and the volume translation in PR EoS on the wave evolutions were revealed. A three-dimensional transcritical fuel injection is finally simulated to highlight the performance of the proposed four-equation model for multidimensional flows.

Real-fluid phase transition in cavitation modeling considering dissolved non-condensable gas

“…On the other hand, the current model avoids the cumbersome process of prescribing the empirical coefficients for the calculation of cavitation and collapse terms. The validations of the current model applied to flash boiling cases and high temperature, high pressure (HTHP) diesel injection process can be found in our recent studies [30], [38]. One noting point about the employment of cubic EoSs series in the multiphase flow equation is the risks of losing hyperbolicity when entering the spinodal region as discussed by many researchers [27], [32], [39], [40].…”

“…This paper has been organized as followings: first, the mathematics descriptions about the two-phase flow model and thermodynamics solver are briefly recalled. More detailed descriptions can be found in our previous work [38] [53]. Next, the numerical results of the three-dimensional (3D) simulations of a real size cavitating nozzle are reported along with a detailed analysis.…”

“…One noting point about the employment of cubic EoSs series in the multiphase flow equation is the risks of losing hyperbolicity when entering the spinodal region as discussed by many researchers [27], [32], [39], [40]. However, this risk can be prevented through adopting the composite EoS in which liquid flow and gas flow are described with its independent EoS instead of a mixture EoS [38]. Thus, the validity of the speed of sound in the two phase region is sustained by the mixing of each individual positive speed of sound in the liquid phase and vapor phase through the Wood formula [41].…”

Machine Learning and transcritical sprays: A demonstration study of their potential in ECN Spray-A

“…18,19 Such effects require accurate thermodynamic closures and have been progressively described with more advanced models. Most notable works are the pioneering work of Knudsen et al 20 utilising cubic Equations of State (EoS) to model fuel properties, followed chronologically by Matheis and Hickel 21 and Yi et al, 22 both introducing Vapor-Liquid Equilibrium (VLE) calculations for the fuel/gas mixture, and Koukouvinis et al 23,24 examining higher order thermodynamic models, such as NIST REFPROP 25 and Perturbed Chain Statistical Associating Theory (PC-SAFT). 26 All the aforementioned works, represent rather detailed examples, involving a high computational cost and requiring large computing resources, which are not always readily available on the industrial level.…”

A one-dimensional full-range two-phase model to efficiently compute bifurcation diagrams in sub-cooled boiling flows in vertical heated tube

“…The three conservation equations can be derived for each phase (liquid and vapor), leading to six conservation equations. These can be combined to end up in three conservation equations for the two-phase mixture, depending on the ability to model interaction terms linking liquid and vapor phases across their interfaces and at solid walls [58]. These are the two main issues to overcome when dealing with one-dimensional boiling channel models.…”