A mechanistic non-equilibrium model for two-phase critical flow

Mechanistic Imonequilibrium Modeling of Critical Flashing Flow of Subcooled Liquids Containing Dissolved Noncondensables

“…The data of Sozzi and Sutherland were among the most qualified critical flow data selected by Elias and LeIlouche [6], and were utilized in Refs. [9] and [10] for validation of their mechanistic models. The experiments of Zaloudek [65], as utilized in [7] for model validation, were also performed in a test section including a 46-mm-Iong tapered conical section at the inlet, where the apex angle of the cone was 20°, connected to a 254-mm-long straight tube with 12.8 mm inner diameter.…”

“…(6) represents the force due to virtual mass and is represented in the following form, derived in Ref. [30] for an assembly of spherical bubbles, and [31,32]: (8) The energy conservation equation for the vapor-nonrecondensable mixture is (9) Equations (1)-(6) and (9), which are in conservative form, are expanded, and a system of seven quasi-linear hyperbolic first-order ordinary differential equations is derived: (10) where A is a 7 X 7 coefficient matrix, C represents a column vector with seven elements, and (11) For the above expansion, the following thermodynamic relations were used: where X represents the mole fraction. Assuming that vapor and the noncondensable are both perfect gases, the property partial derivatives can be shown to be [33] (14)…”

“…Nonequilibrium mechanistic models based on the numerical solution of the two-fluid conservation equations represent an advanced group of two-phase critical flow models and can account for the integral flow effects on local flow properties at the critical cross section [7][8][9][10][11][12][13][14][15]. In these models the one-dimensional (I-D) phasic conservation equations are numerically solved for flow through a channel and by iteratively varying the channel discharge rate, the flow rate leading to the critical conditions at the channel throat, i.e., an infinitely large pressure gradient [10,12,IS]; a vanishing determinant of the coefficient matrix for the system of I-D, quasi-linear first-order differential equations representing the phasic conservation equations [11,13,16]; or a flow rate independent of downstream pressure [8,14] is specified.…”

Critical flashing flow in convergent–divergent nozzles with initially subcooled liquid

“…Abuaf et al [5] suggested that the flashing inception is located at the minimal area plane (throat) of the convergent-divergent nozzle when the flow is stable. Although there are evidences that the bubbles are created in front of the nozzle throat [16][17][18][19], the result of Shin and Jones [19] shows that the computed maximum throat void fraction is less than 1%, which supports Abuaf's result [5]. On the basis of this fact, Schrock et al [6] suggested a two-step model to investigate the pressure profile in the convergentdivergent nozzles, and found that it only could give the pressure profile in the divergent section with trend and magnitudes similar to the tested data.…”

“…In order get the purpose, the models of bubble formation and growth are needed. On the basis of the mass, momentum, and energy conservation laws, Elias and Chambre [16], Richter [17], Ardron [18], Shin and Jones [19], and Blinkov et al [20] respectively established different two-phase fluid models to investigate the critical flow in nozzles or pipes. Pinhasi [21] gave a detailed review of the modeling of flashing two-phase flow.…”