The aim of this study is to investigate CO 2 two-phase nozzle flow in terms of both experimental and analytical aspects for the optimum design of two-phase flow nozzle of CO 2 two-phase flow ejector. In the experiment, it is measured that the temperature profile in the stream-wise direction of a divergent-convergent nozzle through which CO 2 in the supercritical pressure condition is blown down into the atmosphere. In the analysis, a one-dimensional model which assumes steady, adiabatic, frictionless, and equilibrium is proposed. In the convergent part of the nozzle the flow is treated as single-phase flow of liquid, whereas in the divergent part the flow is treated as separated two-phase flow with saturated condition. The analytical results indicate that the temperature and the pressure decrease rapidly in the divergent part, and the void fraction increases immediately near the throat. Although this analysis is quite simple, the analytical results can follow the experimental results well within this study.
In recent years, natural refrigerants are regarded as refrigerants of refrigeration cycles. Because of the highly safety and the small global warming coefficient, carbon dioxide (CO2) is especially focused. However, wasted available energy which is discarded in a pressure reduction process at an expansion valve in the cycle of using CO2 is three times as much as that of using R-134a. Therefore, it is important to recover the available energy, and a gas-liquid two-phase flow ejector (two-phase flow ejector) is used to recover the energy [
A two-phase flow ejector consists of a driving flow nozzle, a suction chamber, a mixing section and a diffuser, respectively. Many researches for single-phase flow ejectors have been carried out. However for two-phase flow ejectors, the mechanisms of the internal flow with phase change have not been sufficiently made clear yet because of the complexly of the flow. This study is carried out on a gas-liquid two-phase flow nozzle (two-phase flow nozzle) of a driving nozzle flow section which is the most important section.
A divergent-convergent nozzle is generally used as a two-phase flow nozzle [
For the two-phase nozzle flow there are studies conducted by Nakagawa et al. [
The purpose of this study is to conduct experimental and analytical investigations of the flow in the two-phase flow nozzle. In the experiment, in the similar way used by Nakagawa et al. [
The pressure in the high pressure tank is set four stages from 7.2 MPa to 10.3 MPa, and the CO2 gas is left until the tank temperature is the same temperature of the room of 300.15 K. At the time of starting the experiment, valve 3 and valve 4 in
In the CO2 nozzle flow, the temperature and the pressure distributions change rapidly, and the phase condition changes from supercritical to saturated two-phase condition. To get the most important aspect of the complex flow, in this study, a one-dimensional analytical model is used. For this analysis, the flow is assumed to be steady, adiabatic, no friction and equilibrium.
The flow in the convergent part of the nozzle is treated as a single-phase flow.
where
The flow in the divergent section is treated as a saturated separated two-phase flow. A model of the separated gas-liquid two-phase flow is shown in
where
In
Simple and typical models of a gas-liquid two-phase flow are a separated flow model neglecting friction between the phases and a homogeneous flow model neglecting velocity difference between the phases. In the divergent section of the two-phase flow nozzle, since it is expected that the distribution of the void fraction changes significantly from 0 to 1, appropriate application of the two models is desirable. However, in this study, the whole flow in the divergent section of the two-phase flow nozzle is simply treated as a separated flow.
The analysis is carried out on the flow in the convergent-divergent nozzle [
is 84 mm is divided into 8400 cells (each section interval is 0.01 mm), and the flow is numerically analyzed by using fundamental equations which is appropriate for each section. There are not much difference between the results of the cases of 8400, 4200 and 16800 cells. Needed CO2 properties for the calculation process are obtained by PROPATH.
In the convergent section of the nozzle in which flow is treated as the single-phase flow, a flow which reached saturated condition is addressed as saturated liquid. Therefore, excluding
The experimental conditions at the nozzle inlet are listed in
The comparison of the experimental and the analytical results of the temperature distribution (a) or the pressure distribution (b) in the cases that the tank pressure is set to 7.2, 8.0, 9.2 and 10.3 MPa are shown in Figures 7-10.
In the case of the tank pressure of 7.2 MPa, as shown in
In the case of the tank pressure of 8.0 MPa, as shown in
Regarding
Tank pressure (MPa) | Inlet temperature (K) | Inlet pressure (MPa) | Inlet velocity (m/s) | Mass flow rate (kg/m3) |
---|---|---|---|---|
7.2 | 300.0 | 6.7 | 2.92 | 0.06 |
8.0 | 300.6 | 7.6 | 3.65 | 0.08 |
9.2 | 300.0 | 8.5 | 4.34 | 0.10 |
10.3 | 302.2 | 9.7 | 5.59 | 0.13 |
experimental results around the throat. However, in area excepting the near throat, the analytical and the experimental results are approximately the same.
For the pressure in the divergent section and the temperature distribution in the case of the tank pressure of 10.3 MPa shown in
Figures 11-14 show the analytical flow property distributions of the cases that the tank pressure set to 7.2, 8.0, 9.2 and 10.3 MPa, respectively. In Figures 11-14, the analytical results are marked with dotted line for cross sectional area,
where
In the case of the tank pressure of 7.2 MPa, as shown in
Compared with the sonic velocity defined in this paper, the gas-phase and the liquid-phase velocity is larger. From perspective of the sonic velocity defined in this paper, the flow in the divergent section can be considered as the supersonic flow.
In the case that the tank pressure is set to 8.0 MPa, as shown in
The flow field of the carbon dioxide high-speed two-phase nozzle flow has been investigated by the experiment and the one-dimensional analysis. Obtained results are as follows.
1) For the nozzle form used in this research and the experimental condition, the CO2 temperature and the pressure have been significantly and monotonously decreased in the nozzle, and satisfactory accelerating performance has been presumed.
2) For the nozzle flow, the one-dimensional analytical model which assumes to be steady, adiabatic, no friction and equilibrium is proposed. In this analytical model, the nozzle convergent section is assumed to be single- phase flow, and the nozzle divergent section is assumed to be separated gas-liquid two-phase flow.
3) The proposed analytical model is simple, and the assumption that the flow is the separated saturated gas- liquid two-phase flow does not necessarily satisfy the actual flow. However, in this experimental condition, these analytical results satisfactorily predicted these experimental results.
4) By the one-dimensional analysis, the velocity distribution in the mainstream direction in the nozzle is obtained, and the satisfactory accelerating performance has been indicated. Further, it is made clear that from the perspective of the sonic velocity defined in this analysis the flow in the divergent section can be considered as the supersonic flow.