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Journal ArticleDOI

Multidimensional Modeling of Condensing Two-Phase Ejector Flow

TL;DR: In this paper, the authors describe the construction of a multidimensional simulation capability built around an Eulerian pseudo-fluid approach, where the fluid is treated as being in a non-thermodynamic equilibrium state, and a modified form of the homogenous relaxation model (HRM) is employed.
Abstract: Condensing ejectors utilize the beneficial thermodynamics of condensation to produce an exiting static pressure that can be in excess of either entering static pressure. The phase change process is driven by both turbulent mixing and interphase heat transfer. Semi-empirical models can be used in conjunction with computational fluid dynamics (CFD) to gain some understanding of how condensing ejectors should be designed and operated. The current work describes the construction of a multidimensional simulation capability built around an Eulerian pseudo-fluid approach. The fluid is treated as being in a non-thermodynamic equilibrium state, and a modified form of the homogenous relaxation model (HRM) is employed. The CFD code is constructed using the open-source OpenFOAM library. Using carbon dioxide as the working fluid, the results of the simulations show a pressure rise that is comparable to experimental data. It is also observed that the flow is near thermodynamic equilibrium in the diffuser, suggesting that turbulence effects present the greatest challenge in modeling these ejectors.

Summary (4 min read)

1.1 Description of Condensing Ejector

  • The condensing ejector is a two-phase jet device in which a fluid in a liquid state or in the two-phase region is mixed with its vapor phase, producing a mixed stream with a pressure that is higher than the pressure of either of the two inlet streams [1].
  • Figure 1.1 presents the predicted behavior of a condensing ejector.
  • As can be seen from the picture, liquid and vapor enter the nozzle and mix in the converging section.
  • The high relative velocity between the suction and motive streams produces a high heat transfer value and vapor phase condensation rate.
  • The simulations will be used to predict the flow for various boundary conditions and different fluids (in these cases, water and carbon dioxide).

1.2 Application of Condensing Ejector

  • The two-phase condensing ejector that is being modeled in this work could potentially be put into a refrigeration cycle.
  • This superheated vapor moves through the condenser and is cooled to a saturated liquid state.
  • Earlier work using a single-phase ejector resulted in a theoretical improvement of 16 percent and an experimental improvement of 4 percent [4].
  • This will be discussed later in the chapter.

1.3 Early Experimental Work on Condensing Ejectors

  • The condensing ejector has a long history going back to the early 1900’s [5], but there are still questions of how to correctly model the flow and to determine the best nozzle shape.
  • Analytical models have been made to better describe the experimental results.
  • In the past few decades, CFD has been used to describe two-phase flow through nozzles, with some work particularly looking at the condensing ejector [8- 14].
  • Even when a mixture has a high percentage of one of the phases, the speed of sound is still significantly lower.

1.4 Modeling of Two-Phase Flow

  • Previous works have looked at modeling turbulent flow for two-phase mixtures, having mixed results overall [8] [20] [21].
  • The authors noticed that the standard k-epsilon model can incorrectly predict the disappearance of a steady condensation shock for a nozzle with a low level of inlet turbulence [21].
  • It was concluded that the moment-based method was efficient and would be most practical for two-dimensional and three-dimensional calculations.
  • The 7 Eulerian-Lagrangian method had accurate results, at a cost of longer computational time [22]; this method has also been used for modeling flow through de Laval nozzles and turbine blades [23].
  • The authors suggest that the HRM model is a better model than the HEM.

1.5.2 Ejector Flow Studies Using CFD

  • There has been some work done with CFD that directly deals with the condensing ejector cycle, and more specifically just the ejector.
  • More sophisticated turbulence models have been used to better predict the flow and compressibility effects have been added too.
  • 13 The CFD simulation package Fluent was used to simulate the flow through the ejector [12].
  • In Sriveerakul et al. [13], when the primary nozzle area is increased, there is a lower entrainment ratio since less secondary fluid can enter the mixing section.
  • When the downstream pressure is increased, this will move the second series of oblique shocks further upstream, closer to the first series [13].

1.6 Use of Carbon Dioxide in a Refrigeration Cycle with an Ejector

  • The working fluid for most of the results presented in this thesis is carbon dioxide.
  • Several authors have experimentally studied the condensing ejector refrigeration cycle with carbon dioxide as the working refrigerant where the fluid is above the critical point before entering the motive nozzle [40 – 45].
  • When the flow from the motive nozzle and suction nozzle meet in the mixing section, both streams are in the two-phase region.
  • 19 Most studies have looked at the overall cycle, but there has been some experimental work that analyzes the flow within the ejector nozzle [42].
  • Thermocouples were placed inside the mixing section and diffuser, and the pressure values were calculated at each point.

MODELING APPROACH

  • Overall, from the previous works, numerous authors have looked at how an ejector can be utilized in a refrigeration cycle.
  • The model was originally used for flash with some modifications the same idea can be applied for condensing flow.
  • The first term on the right-hand side of Eqn. 8 represents the density change due to compressibility.
  • An adjusted form of the PISO (Pressure Implicit with Splitting of Operators) algorithm [56] is used to calculate the pressure and velocity implicitly.

4.2.1 Water as Working Fluid

  • The velocity at the gas inlet is set to Mach 1 and the velocity at the liquid inlet is set to 30 m/s, which are values used by Levy and Brown [16].
  • One way to make the simulations more stable is to treat the fluid flow as incompressible.
  • The outlet pressure is only greater than the liquid inlet pressure.
  • 32 noticeable mixing between the vapor and liquid treams , while The turbulent viscosity is shown in Figure 4.5. 33 tures, vapor mass fraction, x, is shown in the top half, and x̄, is shown in the bottom half.

4.2.2 CO2 as Working Fluid

  • Since using water can lead to numerical instability, the working fluid used for the cases in this sub-section is carbon dioxide.
  • Stated earlier in Chapter 1, CO2 has become a more commonly studied refrigerant [40 - 45].
  • Fig. 4.6 shows the mixing between the vapor and liquid streams.
  • As expected, the greatest the midpoint of the This corresponds Changing the operating pressure at the outlet was also investigated.
  • In Fig. increased, the point of rapid deceleration of the flow is more upstream.

5.1 Nakagawa et al. Two-Phase CO2 Ejector Cycle

  • The ejector being modeled is described in Nakagawa et al. [42].
  • A diagram of the ejector refrigeration cycle used in the work by Nakagawa et al. [42], along with a corresponding p-h diagram, is shown in Figure 1.7.
  • The full nozzle dimensions can be found in Nakagawa et al. [42], and the dimensions of the parts modeled in the CFD mesh are stated here.
  • The use of an IHX lowers the temperature of the super-critical fluid exiting the gas cooler.

5.2.1 Model Validation

  • Using the exit pressure value, the pressure at the inlets is predicted.
  • The pressure rise in the nozzle with the 5 mm mixing section length is significantly lower than the other two ejector types (for when the IHX is used and also when not used), and this is especially noticed when the gas cooler pressure is higher.
  • From Table 5.1 a-c, it is noticed that the CFD results under-predict pressure recovery for the cases that do not use the IHX, and over-predict recovery for the cases with the IHX with the exception of the 15 mm and 25 mm types when the gas cooler pressure is set to 9.5 MPa.
  • Other Reynolds-averaged Navier-Stokes (RANS) turbulence models, such as the realizable k-epsilon model, and the RNG model and the k-omega SST model will be examined in section 5.4.

5.2.2 CFD Results

  • The CFD results show the distribution of the pressure rise.
  • Figure 5.3 shows the pressure throughout the nozzle (the nozzle is reflected about the horizontal axis for clarity).
  • It can be seen that most of the pressure recovery occurs in the mixing section and the beginning of the diffuser section.
  • It can be seen that the mixing of the two streams and the occurring pressure rise cause the velocity to gradually decrease in the mixing section.
  • At the very beginning of the mixing section, the turbulent viscosity is lower (compared to the rest of the mixing section) because the motive and suctio 50 er horizontal axis).

5.3 Mesh Quality

  • A mesh quality study was done to test the accuracy of the meshes used in the previous sections of this chapter.
  • The two cases that had a greater difference were the ejector with the 25 mm mixing section and the gas cooler pressure set to 10.5 MPa, both for the without the IHX, the difference was 3 kPa (0.75% difference for the case with the IHX, the difference was 6 kPa (1.12% difference).
  • Since the finer meshes resulted in a very small change in pressure recovery, it can be concluded that the coarser meshes used in the previous sections of this chapter are acceptable.
  • The local differences in pressure with the finer mesh can be attributed to the fluctuations in turbulent viscosity in this area.

5.4 Comparison of Different Turbulence Models

  • From the results in the previous sections of this chapter, it is noticed that the choice of turbulence model has an important role is predicting the pressure recovery.
  • Along with the standard k-epsilon model that was used in the previous sections, three other RANS models were tested: realizable k-epsilon, RNG k-epsilon, and k-omega SST.
  • All 18 cases were tested again with each of the other three turbulence models.
  • This can be attributed to the change in the suction stream density at the inlet of the mixing section caused by the choice of turbulence model.
  • In the first 10 - 15 mm of the ejector, the highest rate of pressure recovery is seen with the k-omega SST model, and the lowest rate of pressure recovery is seen with the realizable k-epsilon model.

CONCLUSIONS

  • The goal of this project was to use CFD to model fluid flow inside a two-phase ejector.
  • A minor drawback of using CO2 is that the relaxation model constants are potentially mis-matched to the fluid.
  • The ∑-Y model has a dominant effect on the mixing of the streams and the overall pressure recovery in the nozzle.
  • Because most of the mixing occurs in this section, the choice of RANS turbulence model has an important effect on pressure recovery since the pressure at the outlet is already specified and the inlet pressures are being predicted.
  • The attempt to validate the HRM—∑-Y model to the experimental work of Nakagawa et al. [42] was a partial success.

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University of Massachusetts Amherst University of Massachusetts Amherst
ScholarWorks@UMass Amherst ScholarWorks@UMass Amherst
Masters Theses 1911 - February 2014
2011
Multidimensional Modeling of Condensing Two-Phase Ejector Multidimensional Modeling of Condensing Two-Phase Ejector
Flow Flow
Michael F. Colarossi
University of Massachusetts Amherst
Follow this and additional works at: https://scholarworks.umass.edu/theses
Part of the Heat Transfer, Combustion Commons
Colarossi, Michael F., "Multidimensional Modeling of Condensing Two-Phase Ejector Flow" (2011).
Masters Theses 1911 - February 2014
. 672.
Retrieved from https://scholarworks.umass.edu/theses/672
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MULTIDIMENSIONAL MODELING OF CONDENSING TWO-PHASE EJECTOR
FLOW
A Thesis Presented
by
MICHAEL COLAROSSI
Submitted to the Graduate School of the
University of Massachusetts Amherst in partial fulfillment
of the requirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
September 2011
Mechanical and Industrial Engineering

© Copyright by Michael Colarossi 2011
All Rights Reserved

MULTIDIMENSIONAL MODELING OF CONDENSING TWO-PHASE EJECTOR
FLOW
A Thesis Presented
by
MICHAEL COLAROSSI
Approved as to style and content by:
_______________________________________
David Schmidt, Chair
_______________________________________
Stephen de Bruyn Kops, Member
_______________________________________
Ashwin Ramasubramaniam, Member
________________________________________
Donald Fisher, Department Head
Mechanical and Industrial Engineering

iv
ACKNOWLEDGMENTS
I would like to thank my advisor, Professor David Schmidt, for all of his support
throughout my entire time as a graduate student. His helpful insight and advice kept me
motivated to complete my thesis. I would also like to thank the other members of my
committee, Profs. de Bruyn Kops and Ramasubramaniam, for their input on my thesis
project. Also, thanks to Dr. Bergander for the collaboration on my research.
Thanks go to the National Science Foundation, STTR Phase II Project No.
0822525 and the Department of Energy, under Award Number DE-FG36-06GO16049
for sponsoring this research and providing financial support.
Thank you to everyone I worked with in the CFD lab, for helping me whenever I
needed advice and for making the lab an enjoyable place to work.

Citations
More filters
Journal ArticleDOI
TL;DR: In this paper, a comprehensive literature review on ejector refrigeration systems and working fluids is presented, which deeply analyzes ejector technology and behavior, refrigerant properties and their influence over ejector performance.
Abstract: The increasing need for thermal comfort has led to a rapid increase in the use of cooling systems and, consequently, electricity demand for air-conditioning systems in buildings. Heat-driven ejector refrigeration systems appear to be a promising alternative to the traditional compressor-based refrigeration technologies for energy consumption reduction. This paper presents a comprehensive literature review on ejector refrigeration systems and working fluids. It deeply analyzes ejector technology and behavior, refrigerant properties and their influence over ejector performance and all of the ejector refrigeration technologies, with a focus on past, present and future trends. The review is structured in four parts. In the first part, ejector technology is described. In the second part, a detailed description of the refrigerant properties and their influence over ejector performance is presented. In the third part, a review focused on the main jet refrigeration cycles is proposed, and the ejector refrigeration systems are reported and categorized. Finally, an overview over all ejector technologies, the relationship among the working fluids and the ejector performance, with a focus on past, present and future trends, is presented.

359 citations


Cites background from "Multidimensional Modeling of Conden..."

  • ...The rapid condensation process causes shock waves resulting in a completely liquid state downstream of the shock [85,89,90]....

    [...]

Journal ArticleDOI
TL;DR: A review of developments in the use of ejectors for expansion work recovery in vapor-compression systems focusing on the past several years is presented.
Abstract: Previous reviews on ejectors for expansion work recovery have provided detailed discussions of operating characteristics and control of ejector cycles, zero-dimensional ejector modeling, ejector geometry effects, and alternate ejector cycles. However, important advances in the field of ejector technology have occurred since previous reviews were written. Several focuses of recent ejector research are the development of multi-dimensional CFD ejector models, investigation of alternate ejector cycles and uses of the work recovered by the ejector, implementation of effective control strategies for ejector cycles, and application of ejectors in real systems. The objective of this paper is to present a review of developments in the use of ejectors for expansion work recovery in vapor-compression systems focusing on the past several years. Although the first commercial applications are being introduced to the market, it is suggested that future works continue in these areas in order to make ejectors more suitable for additional applications.

212 citations

Journal ArticleDOI
TL;DR: In this paper, a mathematical model of the compressible transonic single and two-phase flow of a real fluid is discussed, in which the specific enthalpy, instead of the temperature, is an independent variable.

111 citations

Journal ArticleDOI
TL;DR: In this paper, the geometry of a CO2 ejector mixing section was optimized using genetic algorithm (GA) and an evolutionary algorithm (EA) with a validated CFD model based on the homogeneous equilibrium model (HEM).

77 citations

Journal ArticleDOI
TL;DR: In this article, a validated CFD tool was used to investigate three cases that were differentiated by the mass flow rate per unit area (mass flux) that passed through the mixer, which represented three dissimilar flow patterns.
Abstract: A CFD-based numerical analysis of the flow irreversibility in R744 ejectors is presented. A validated CFD tool was used to investigate three cases that were differentiated by the mass flow rate per unit area (mass flux) that passed through the mixer, which represented three dissimilar flow patterns. The mixer mass flux was found to significantly affect the ejector performance both locally and globally. An original approach was introduced to assess the contribution of the local irreversibilities to the overall entropy increase. A new factor was proposed to evaluate the ejector performance based on the reference entropy increase in a classic expansion valve. In addition, the influence of the mixer diameter and length on the ejector performance was numerically analysed, which showed that the effects of both geometric parameters may be significant. Namely, in the conditions considered, both enlargement of the mixer cross section area by 17.4% as well as shortening the mixer length by 33.3% resulted in the increase of the overall entropy growth rate by 8.9% and 5.4%, respectively.

75 citations

References
More filters
Journal ArticleDOI
TL;DR: In this article, a non-iterative method for handling the coupling of the implicitly discretised time-dependent fluid flow equations is described, based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations.

4,019 citations

Journal ArticleDOI
TL;DR: The implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented.
Abstract: In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.

3,987 citations


"Multidimensional Modeling of Conden..." refers methods in this paper

  • ...The structure for solving these equations is provided by OpenFOAM, which allows rapid construction of CFD codes in an object-oriented framework [58]....

    [...]

02 Apr 2007

3,356 citations


"Multidimensional Modeling of Conden..." refers methods in this paper

  • ...Fluid properties are obtained using REFPROP (Reference Fluid Thermodynamic and Transport Properties Database) from the NIST (National Institute of Standards and Technology) database [57]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a 1D analysis for the prediction of ejector performance at critical-mode operation is carried out, where constant pressure mixing is assumed to occur inside the constant-area section of the ejector and the entrained flow at choking condition is analyzed.
Abstract: A 1-D analysis for the prediction of ejector performance at critical-mode operation is carried out in the present study. Constant-pressure mixing is assumed to occur inside the constant-area section of the ejector and the entrained flow at choking condition is analyzed. We also carried out an experiment using 11 ejectors and R141b as the working fluid to verify the analytical results. The test results are used to determine the coefficients, h p, h s, f p and f m defined in the 1-D model by matching the test data with the analytical results. It is shown that the1-D analysis using the empirical coefficients can accurately predict the performance of the ejectors. q 1999 Elsevier Science Ltd and IIR. All rights reserved.

854 citations


"Multidimensional Modeling of Conden..." refers result in this paper

  • ...Using CFD to specifically look at the ejector flow, the entrainment ratio was calculated for the simulations and compared to previous experimental work [37], with reasonable agreement seen between the results....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a review of previous research related to the application of optimum values of Sct for engineering flowfields relevant to atmospheric dispersion is reviewed and it is recommended that Sct should be determined by considering the dominant flow structure in each case.

428 citations


"Multidimensional Modeling of Conden..." refers background in this paper

  • ...Different turbulent Schmidt numbers within the acceptable range determined in Koeltzsch [59] and Tominaga [60] were investigated....

    [...]

Frequently Asked Questions (13)
Q1. What is the key reason of using an ejector in a refrigeration cycle?

Adjusting the constants that determine the timescale does not have an effect on the pressure recovery, the key reason of using an ejector in a refrigeration cycle, but it has the ability to adequately show the nonthermodynamic equilibrium state of the fluid. 

CFD has been used to simulate two-phase flow, with some work being done forflow through a condensing ejector (mostly one-dimensional modeling for condensing ejector simulations). 

The diameter of the constant area section was thought to be the most influential parameter on ejector performance due to its direct proportion with the secondary flow area. 

Within the diverging part of the nozzle there is an expectation of a shock wave that leads to increased mixing and circulation of the two streams, according to Levy and Brown [16]. 

A finite volume method based on an approximate Riemann solver is used to solve the conservation equations for two-phase compressible flow [32]. 

Sriveerakul et al. [13] concludes that changing the length of the mixing section of the ejector has little effect on the entrainment ratio, but it does change the shape of the oblique shocks. 

Because most of the mixingoccurs in this section, the choice of RANS turbulence model has an important effect on pressure recovery since the pressure at the outlet is already specified and the inlet pressures are being predicted. 

CFD is used to model the flow inside the ejector because many different operating conditions and geometries can be tested at a minimal cost. 

This approach assumes that at high Reynolds and Weber numbers, the scales at which turbulent mixing occurs are separate from those of the bulk fluid motion, allowing the turbulent mixing and generation of interfacial surface area to be resolved through classical turbulence closures. 

It is seen that the ideal gas model underestimates the nozzle exit pressure by about 35 percent when compared to the metastable model. 

It is also noted that the constant area diameter can be increased to improve ejector performance, but at a certain diameter the shock disappears [10]. 

In the results of Rusly et al. [10], moving the nozzle exit distance 1.5 times further away from the constant area duct (compared to the base model) resulted in a better ejector performance. 

Because of this, and that the density gradient where the two streams meet near the splitter was lower for cases with CO2 as the working fluid, the CFD results were better when using CO2.