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Technical Briefs

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

[+] Author and Article Information
Miad Yazdani

e-mail: yazdanm@utrc.utc.com

Thomas D. Radcliff

Thermal and Fluid Sciences Department,
United Technologies Research Center,
East Hartford, CT 06108

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 29, 2012; final manuscript received September 3, 2013; published online November 6, 2013. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 136(1), 014503 (Nov 06, 2013) (6 pages) Paper No: FE-12-1657; doi: 10.1115/1.4025647 History: Received December 29, 2012; Revised September 03, 2013

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.

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References

Figures

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Fig. 1

Transcritical CO2 cycle with ejector work recovery

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Fig. 2

Dimensional parameters of converging-diverging nozzle adopted from Nakagawa et al [6]

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Fig. 3

The model's prediction along the diverging section of nozzle 1 with supercritical inlet conditions: (a) pressure profile and comparison against the Nakagawa et al. measurements [6], (b) vapor volume fraction, (c) Mach number clipped at M ≤ 1, and (d) dimensionless velocity magnitude. Both axes are normalized with respect to the throat hydraulic diameter Dh.

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Fig. 4

The model's prediction along the diverging section of nozzle 2 with supercritical inlet conditions: (a) pressure profile and comparison against the Nakagawa et al. measurements [6], (b) vapor volume fraction, (c) Mach number clipped at M ≤ 1, and (d) dimensionless velocity magnitude. Both axes are normalized with respect to the throat hydraulic diameter Dh.

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Fig. 5

The model's prediction along the diverging section of nozzle 1 with subcritical inlet conditions: (a) pressure profile and comparison against the Nakagawa et al. measurements [6], (b) vapor volume fraction, (c) Mach number clipped at M ≤ 1, and (d) dimensionless velocity magnitude. Both axes are normalized with respect to the throat hydraulic diameter Dh.

Grahic Jump Location
Fig. 6

The model's prediction along the diverging section of nozzle 2 with subcritical inlet conditions: (a) pressure profile and comparison against the Nakagawa et al. measurements [6], (b) vapor volume fraction, (c) Mach number clipped at M ≤ 1, and (d) dimensionless velocity magnitude. Both axes are normalized with respect to the throat hydraulic diameter Dh.

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