Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Miad Yazdani ◽  
Abbas A. Alahyari ◽  
Thomas D. Radcliff
Keyword(s):  
Phase Change ◽  
Velocity Model ◽  
Attractive Alternative ◽  
Sonic Velocity ◽  
Shock Train ◽  
Alternative Refrigerants ◽  
Two Phase ◽  
Expansion Waves ◽  
Fluid Properties ◽  
Layer Flow

Carbon dioxide is an attractive alternative to conventional refrigerants due to its low direct global warming effects. Unfortunately, CO2 and many alternative refrigerants have lower thermodynamic performance resulting in larger indirect emissions. The effective use of ejectors to recover part of the lost expansion work, which occurs in throttling devices, can close this performance gap and enable the use of CO2. In an ejector, the pressure of the motive fluid is converted into momentum through a choked converging-diverging nozzle, which then entrains and raises the energy of a lower-momentum suction flow. In a two-phase ejector, the motive nozzle flow is complicated by the nonequilibrium phase change affecting local sonic velocity and leading to various types of shockwaves, pseudo shocks, and expansion waves inside or outside the exit of the nozzle. Since the characteristics of the jet leaving the motive nozzle greatly affect the performance of the ejector, this paper focuses on the details of flow development and shockwave interaction within and just outside the nozzle. The analysis is based on a high-fidelity model that incorporates real-fluid properties of CO2, local mass and energy transfer between phases, and a two-phase sonic velocity model in the presence of finite-rate phase change. The model has been validated against the literature data for two-phase supersonic nozzles and overall ejector performance data. The results show that due to nonequilibrium effects and delayed phase change, the flow can choke well downstream of the minimum-area throat. In addition, Mach number profiles show that, although phase change is at a maximum near the boundaries, the flow first becomes supersonic in the interior of the flow where sound speed is lowest. Shock waves occurring within the nozzle can interact with the boundary layer flow and result in a ‘shock train’ and a sequence of subsonic and supersonic flow previously observed in single-phase nozzles. In cases with lower nozzle back pressure, the flow continues to accelerate through the nozzle and the exit pressure adjusts in a series of supersonic expansion waves.

Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles

2011 ◽  
Author(s):  
Miad Yazdani ◽  
Thomas D. Radcliff ◽  
Abbas A. Alahyari ◽  
Mohsen Farzad
Keyword(s):  
Phase Change ◽  
Equilibrium Phase ◽  
Velocity Model ◽  
Attractive Alternative ◽  
Sonic Velocity ◽  
Shock Train ◽  
Alternative Refrigerants ◽  
Two Phase ◽  
Expansion Waves ◽  
Non Equilibrium

CO2 is an attractive alternative to conventional refrigerants due to its low direct global warming effects. Unfortunately, CO2 and many alternative refrigerants have lower thermodynamic performance resulting in larger indirect emissions. Effective use of ejectors to recover part of the lost expansion work, which occurs in throttling devices can close this performance gap and enable the use of CO2. In an ejector, the pressure of the motive fluid is converted into momentum through a choked converging-diverging nozzle, which then entrains and raises the energy of a lower-momentum suction flow. In a two-phase ejector, the motive nozzle flow is complicated by non-equilibrium phase change affecting local sonic velocity and leading to various types of shockwaves, pseudo shocks, and expansion waves inside or outside the exit of the nozzle. Since the characteristics of the jet leaving the motive nozzle greatly affect the performance of the ejector, this paper focuses on the details of flow development and shockwave interaction within and just outside the nozzle. The analysis is based on a high-fidelity model that incorporates real-fluid properties of CO2, local mass and energy transfer between phases, and a two-phase sonic velocity model in the presence of finite-rate phase change. The model has been validated against literature data for two-phase supersonic nozzles as well as overall ejector performance data. The results show that due to non-equilibrium effects and delayed phase change, the flow can choke well downstream of the minimum-area throat. Also, Mach number profiles show that, although phase change is at a maximum near the boundaries, the flow first becomes supersonic in the interior of the flow where sound speed is lowest. Shock waves occurring within the nozzle can interact with the boundary layer flow and result in a ‘shock train’ and a sequence of subsonic and supersonic flow observed previously in single-phase nozzles. In cases with lower nozzle back pressure, the flow continues to accelerate through the nozzle and the exit pressure adjusts in a series of supersonic expansion waves.

On the Application of the Method of Landau and Lifshitz to Sonic Velocities in Homogeneous Two-Phase Mixtures

1996 ◽  
Vol 118 (1) ◽  
pp. 186-188 ◽  
Author(s):  
Joseph C. Leung
Keyword(s):  
Thermal Equilibrium ◽  
Mass Fraction ◽  
Sonic Velocity ◽  
Simple Correlation ◽  
Velocity Correlation ◽  
Two Phase ◽  
Fluid Properties ◽  
Vapor Mass

A theoretical sonic velocity correlation for homogeneous two-phase mixtures under thermal equilibrium is proposed. By application of the method of Landau and Lifshitz, a dimensionless correlating parameter ω is found whereby different fluid properties and vapor mass fraction (quality) can be adequately accounted for by the simple correlation.

A Pressure Pulse Model for Two-Phase Critical Flow and Sonic Velocity

1969 ◽  
Vol 91 (3) ◽  
pp. 371-381 ◽  
Author(s):  
F. J. Moody
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Present Model ◽  
Pressure Pulse ◽  
Critical Flow ◽  
Sonic Velocity ◽  
Phase Pattern ◽  
Two Phase ◽  
Theoretical Formulation ◽  
Pulse Transmission

Pressure pulse transmission in a flowing mixture provides the basis for a theoretical formulation of two-phase critical flow and sonic velocity. Homogeneous and separated phases are considered, showing that phase pattern plays an important role in pulse transmission. Graphs are presented for critical flow and sonic velocity of steam-water mixtures, based on no phase change or heat transfer across the pulse. The present model predicts most available data with homogeneous and separated phase patterns and suggests quality ranges for which each pattern applies.

Computation of two-phase shear-layer flow using an Eulerian-Lagrangian analysis

1988 ◽  
Author(s):  
JAYANT SABNIS ◽  
SANG-KEUN CHOI ◽  
RICHARD BUGGELN ◽  
HOWARD GIBELING
Keyword(s):  
Shear Layer ◽  
Lagrangian Analysis ◽  
Two Phase ◽  
Layer Flow

scholarly journals Numerical Study of a Cooling System Using Phase Change of a Refrigerant in a Thermosyphon

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3634
Author(s):  
Grzegorz Czerwiński ◽  
Jerzy Wołoszyn
Keyword(s):  
Mass Transfer ◽  
Phase Change ◽  
Heat Dissipation ◽  
Cooling System ◽  
Numerical Study ◽  
Relaxation Parameter ◽  
Phase Changes ◽  
Transfer Time ◽  
Two Phase ◽  
Time Relaxation

With the increasing trend toward the miniaturization of electronic devices, the issue of heat dissipation becomes essential. The use of phase changes in a two-phase closed thermosyphon (TPCT) enables a significant reduction in the heat generated even at high temperatures. In this paper, we propose a modification of the evaporation–condensation model implemented in ANSYS Fluent. The modification was to manipulate the value of the mass transfer time relaxation parameter for evaporation and condensation. The developed model in the form of a UDF script allowed the introduction of additional source equations, and the obtained solution is compared with the results available in the literature. The variable value of the mass transfer time relaxation parameter during condensation rc depending on the density of the liquid and vapour phase was taken into account in the calculations. However, compared to previous numerical studies, more accurate modelling of the phase change phenomenon of the medium in the thermosyphon was possible by adopting a mass transfer time relaxation parameter during evaporation re = 1. The assumption of ten-fold higher values resulted in overestimated temperature values in all sections of the thermosyphon. Hence, the coefficient re should be selected individually depending on the case under study. A too large value may cause difficulties in obtaining the convergence of solutions, which, in the case of numerical grids with many elements (especially three-dimensional), significantly increases the computation time.

Shock–like structure of phase-change flow in porous media

1981 ◽  
Vol 104 ◽  
pp. 467-482 ◽  
Author(s):  
L. A. Romero ◽  
R. H. Nilson
Keyword(s):  
Porous Media ◽  
Phase Change ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Flows In Porous Media ◽  
Dissipative Effects ◽  
Condensing Flows ◽  
Self Similar ◽  
Phase Change Flows

Shock-like features of phase-change flows in porous media are explained, based on the generalized Darcy model. The flow field consists of two-phase zones of parabolic/hyperbolic type as well as adjacent or imbedded single-phase zones of either parabolic (superheated, compressible vapour) or elliptic (subcooled, incompressible liquid) type. Within the two-phase zones or at the two-phase/single-phase interfaces, there may be steep gradients in saturation and temperature approaching shock-like behaviour when the dissipative effects of capillarity and heat-conduction are negligible. Illustrative of these shocked, multizone flow-structures are the transient condensing flows in porous media, for which a self-similar, shock-preserving (Rankine–Hugoniot) analysis is presented.

Effect of back pressure and freestream dynamic pressure on a typical Ramjet engine duct under realistic supersonic inlet condition

2017 ◽  
Vol 122 (1247) ◽  
pp. 83-103 ◽  
Author(s):  
R. Saravanan ◽  
S.L.N. Desikan ◽  
T.M. Muruganandam
Keyword(s):  
Dynamic Pressure ◽  
Back Pressure ◽  
Flow Visualisation ◽  
Pressure Measurements ◽  
Shock Train ◽  
Unsteady Pressure ◽  
Expansion Waves ◽  
Ramjet Engine ◽  
Flap Deflection ◽  
Unsteady Pressure Measurements

ABSTRACTThe present study investigates the behaviour of the shock train in a typical Ramjet engine under the influence of shock and expansion waves at the entry of a low aspect ratio (1:0.75) rectangular duct/isolator at supersonic Mach number (M = 1.7). The start/unstart characteristics are investigated through steady/unsteady pressure measurements under different back and dynamic pressures while the shock train dynamics are captured through instantaneous Schlieren flow visualisation. Two parameters, namely pressure recovery and the pressure gradient, is derived to assess the duct/isolator performance. For a given back pressure, with maximum blockage (9% above nominal), the duct/isolator flow is established when the dynamic pressure is increased by 23.5%. The unsteady pressure measurements indicate different scales of eddies above 80 Hz (with and without flap deflection). Under the no flap deflection (no back pressure) condition, the maximum fluctuating pressure component is 0.01% and 0.1% of the stagnation pressure at X/L = 0.03 (close to the entry of the duct) and X/L = 0.53 (middle of the duct), respectively. Once the flap is deflected (δ = 8°), decay in eddies by one order is noticed. Further increase in back pressure (δ ≥ 11°) leads the flow to unstart where eddies are observed to be disappeared.

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