ID: 347

CFD ANALYSIS OF AN EJECTOR FOR COOLING APPLICATIONS

SCOTT, D.A.(*), AIDOUN, Z. (*) Natural Resources Canada – CanmetENERGY, 1615 boul. Lionel Boulet, P.O. Box 4800,

Varennes, Québec, J3X 1S6, Canada david.scott@nrcan.gc.ca

ABSTRACT

Vapour-jet ejectors have been used in cooling/refrigeration applications since the early 1900s. Recent efforts to reduce energy consumption by harnessing energy from low grade industrial waste heat or renewable energy sources have resulted in a renewed interest in this technology. This paper presents the results of computational fluid dynamics (CFD) simulations of a vapour-jet ejector operating with R245fa as the working fluid. The impact of varying operating conditions on ejector performance is presented. Also considered in this study is the impact of varying three geometrical parameters on ejector performance: the mixing section length and radius, and the primary nozzle exit radius (representative of the velocity of the motive stream). The results of this study show that CFD is a useful tool in the design and optimization of ejectors for refrigeration devices.

1. INTRODUCTION

Ejectors are a simple type of jet-pump that are often used for vacuum generation or for vapour compression. They provide an alternative to conventional mechanical vapour compressors in that they can be primarily powered by relatively low grade thermal energy instead of by electricity. Ejectors have been used in different applications since the 1850’s. As noted by Elbel (2008), two-phase ejectors were used in a condensing configuration by Giffard as early as 1858. Also noted is that the first vapour-jet ejector applications appeared in the 1900’s, notably by Parsons in 1901 and by Leblanc in 1910. In Parsons and Leblanc’s applications, vapour-jet ejectors used steam as both the driving and suction fluids in the ejectors. The use of vapour-jet ejectors operating with steam continues today, however the applications are limited to evaporator temperatures above zero degrees Celsius. One of the principle advantages of operating ejector-based cooling systems is their ability to operate using relatively low grade thermal energy. Sources of low grade thermal energy, typically at temperatures below 120 oC, are found in the reject streams from many different industrial applications such as in the rejected steam and exhaust gasses from boilers, turbines and engines, as well as from renewable sources such as solar energy or geothermal wells. As much of the world’s electricity is generated from fossil-fuels, any reduction in electricity consumption will result in a reduction in the emission of carbon dioxide and other combustion by-products from the energy conversion processes. An additional benefit of ejector-based cooling systems is that the ejector has no moving parts, thus requiring very little maintenance and providing highly reliable cooling over very long periods of time. With advances in refrigerants over the past fifty years, it has become feasible to operate vapour-jet ejectors with fluids other than steam. The use of refrigerants other than water provides two principal benefits; the potential elimination of the zero degree Celsius limit on evaporators, and a possible improvement of the performance of a vapour-jet ejector cooling system. Some notable studies of vapour-jet ejectors operating with steam include the works of Eames et al. (1995), Sun (1997), and Riffat and Everitt (1999). Some studies focussed on the use of synthetic or natural refrigerants in ejector-based cooling systems are described in the works of Eames and Ablwaifa (2004), Chen and Sun (1997), Bartosiewicz and Aidoun (2006) and Selvaraju and Mani (2004).

Studies on vapour-jet ejectors may be generalized into two categories, experimental or numerical studies. While the literature contains relatively few experimental results, numerical studies are much more plentiful, especially descriptions of one-dimensional models. Detailed numerical descriptions of the fluid flow and heat transfer inside ejectors, such as those that may be found in Computational Fluid Dynamics (CFD) models of ejectors, are of great value as they provide a more complete simulation of the physics inside the ejectors than is possible with 1D models, although this comes with an increased computational cost. Once a CFD model of an ejector has been validated with experimental results, it becomes possible to have high confidence in the results of numerical “experiments” of ejectors that are performed with these CFD models. The costs associated with designing, fabricating and assembling experimental test benches can be reduced by maximizing the use of CFD models to perform much of the screening of ejector design prior to the assembly of prototypes. In addition, CFD models, using only “virtual” refrigerants, have no potential for environmental damage due to leakage from the test bench. Also, numerous refrigerants can be investigated without concern of the flammability or toxicity issues associated with some refrigerants. The goal of the present study is to present some details of a CFD study of a vapour-jet ejector operating with R245fa. The CFD model was used to screen a number of different ejector geometries in order to determine which geometrical factors have the greatest impact on ejector performance, as well as to determine the dependency on operating temperatures of the optimal values found. Geometric parameters investigated include the mixing section diameter and length, the primary nozzle throat diameter, converging section geometrical variations. The results presented are based on two simple ejector geometries.

2. EJECTOR REFRIGERATION CYCLE

In the simplest form of the vapour-jet ejector refrigeration cycle, the compressor of a standard refrigeration cycle is replaced by a pump, a vapour generator and the ejector. Instead of driving the compressor with electrical energy, the ejector is driven by vapour from the vapour generator, vapour provided by harnessing low-grade thermal energy. As seen in Fig. 1, the simplest vapour-jet ejector cycle consists of two loops that interact in the ejector. In the primary loop, liquid from the condenser is pumped into the generator where it is boiled using an external heat source. The resulting high-pressure, high-temperature vapour then flows through a converging-diverging nozzle where its energy is converted to kinetic energy in the form of a supersonic velocity flow of gas. The secondary stream is entrained into the ejector by both the low pressure generated by the expansion of the primary stream and the momentum transfer from the primary stream to the secondary stream along the surface of contact between these two. The two streams mix and the resulting flow exits the ejector through a diffuser. Pressure recovery occurs in the mixing process, in the flow of the mixed stream through a series of shocks and as the mixed streams flow through the diffuser. The mixed stream then flows through the condenser and the liquid is then divided and either pumped to the vapour generator or expanded before flowing into the evaporator.

Condenser

Evaporator

Pump

Expansion Valve

Generator

Thermal Energy

Figure 1: Schematic illustration of the simplest vapour-jet ejector cycle.

The ejector cycle is best characterized by the entrainment ratio and the critical condenser pressure. The entrainment ratio (ω) is defined as the ratio of the primary mass flow rate that comes from the generator to

the secondary mass flow rate that comes through the evaporator. In a feature unique to supersonic vapour-jet ejectors, the entrainment ratio of the ejector is constant over a wide range of condenser pressures. Munday and Bagster (1977) suggested that choking of the secondary flow explains the independence of the entrainment ratio on condenser pressure; when the condenser pressure is high enough that the secondary flow is no longer choked, the entrainment ratio will rapidly decrease with further increases of the condenser pressure. The condenser pressure at which the entrainment ratio begins to depend on the condenser pressure is known as the critical condenser pressure (pc*). A typical vapour-jet ejector performance curve showing the constant entrainment ratio and critical condenser pressure is presented in Fig. 2. For condenser pressures below pc*, the ejector is referred to as operating in “critical mode” and both primary and secondary flows are choked. In “subcritical” operation, the ejector condenser pressure is greater than pc*, however a secondary flow continues to be entrained. “Malfunction” occurs when the ejector ceases to entrain any secondary flow.

pc* pcond

ω Critical mode Malfunction

Subcritical mode

Figure 2: Illustration showing the dependence of the vapour-jet ejector entrainment ratio (ω) on condenser

pressure (pcond) showing the critical condenser pressure (pc*). The performance curve shown in Fig. 2 can be generated by either 1D numerical modelling or detailed CFD models of ejectors. Both 1D and CFD models solve the equations of conservation of mass, momentum and energy to predict the performance of the ejector, however the 1D model requires the use of a series of efficiencies and coefficients that account for losses in the converging/diverging nozzle, the converging section of the ejector, mixing of the two fluid streams, shock waves, and expansion of the mixed stream through the diffuser. Unless previous knowledge of a particular ejector design is available, these coefficients must be assigned based on best guesses for a particular geometry. The results of the 1D model are thus highly dependent on the values used for these coefficients. Also, 1D models generally only provide global performance data for the ejector and simply describe the conditions at the inlets and outlet. In a CFD model, the conservation equations are solved in a series of interconnected volumes that fill the ejector geometry. Models are used that account for turbulence, however no correlations for expansion, contraction or mixing are required. The CFD model thus provides not only a more complete picture of the fluid flow and heat transfer inside an ejector, but also eliminates the need for multiple coefficients, increasing the accuracy of the predicted ejector performance. One of the first CFD studies of vapour-jet ejectors in refrigeration applications was presented by Riffat et al. (1996). This study assumed that all three working fluids considered (ammonia, R134a and propane) were incompressible. Eames and Ablwaifa (2004) performed CFD simulations of steam ejectors using the ideal gas model to describe the variation of the density in the ejector and used constant values for the remaining fluid properties. In further work, Ablwaifa (2006) performed complementary experimental and detailed CFD analyses of several different ejectors operating with either R245fa or R236fa. Rusly et al. (2005) performed a CFD analysis of an ejector operating with R141b. He compared his results to the experimental data from Huang et al. (1999) and to a corresponding 1D model of Huang’s ejectors. The study showed that the results of the CFD model were in better agreement with the experimental results than were those from the 1D model, demonstrating one of the benefits of detailed CFD models of ejectors. Bartosiewicz et al. (2005) investigated the impact of different turbulence models on an ejector operating with air. In further work, Bartosiewicz et al. (2006) used the real gas properties of R142b in a CFD model of an ejector instead of

using an ideal gas model to describe the thermodynamic properties of the refrigerant. Scott et al. (2008) used CFD to investigate the impact of several different geometrical factors on ejector performance; however this work was restricted to a single set of operating conditions. The goal of the present study is to expand on this work and show the impact of ejector geometry on performance at several different operating conditions (different generator and evaporator saturation temperatures).

3. MODELING OF THE PROBLEM

A schematic drawing of a vapour-jet ejector that shows the characteristic dimensions used in this study is shown in Fig. 3. It has been assumed that the ejector is axi-symmetric along the z-axis, thus only a thin slice of an ejector is modelled. Essentially, the ejector consists of two annular converging-diverging nozzles. In the outer nozzle, gas from the evaporator enters axially into the space outside the primary nozzle. Along l2, the secondary flow is accelerated until it mixes with the primary flow in l3. Along l4, the mixed flow is expanded through the diffuser until it exits the ejector. The primary flow from the generator enters and is compressed along l5 until it reaches the throat, at which point the flow is choked. Along l6, the primary flow is expanded to supersonic speeds.

Figure 3: Typical ejector geometry used in CFD model.

3.1. Governing Equations The flows in the presented vapour-jet ejectors model are considered to be compressible, steady-stated, two-dimensional and axi-symmetric. The model was written using the commercial CFD code PHOENICS V3.5.1. Under steady-state conditions, the general form of the governing equations, neglecting time-derivatives, can be expressed as:

Sxx kk

U (1)

Specific definitions of the variables φ, Γφ and Sφ for the cases of the continuity, momentum and energy equations are provided in Table 1.

Table 1: Values of φ, Γφ and Sφ in Eq. 1. Equation φ Γφ Sφ Continuity 1 0 0

z-momentum w ρ(νt+νL) ...frictiongravityzp

r-momentum v ρ(νt+νL) ...frictiongravityrp

energy h

LL

t

tPrPr

... sourcesheatDtDp

Turbulence effects in the CFD model were accounted for through the use of the standard k-epsilon turbulence model of Launder and Spalding (1972). While CHAM (2003) notes that this model is not always recommended for simulations of compressible flows or of jet flows, Ablwaifa (2006) found that simulations using this turbulence model yielded good results for the simulation of fluid flow in ejectors using R141b as the working fluid.

3.2. Calculation Procedure The CFD model was built using a body-fitted-coordinates (BFC) grid. The base grid used in the calculations consisted of 10 volumes in the r- and 113 volumes in the z-direction. Further refining of the grid was accomplished by multiplying the base grid by a grid-refinement factor, δ, which was varied from 1 (base grid) to 4 (most refined grid). Results from CFD runs with increasingly refined grids were compared both qualitatively and quantitatively in order to determine the dependence of the results on the grid. This showed that the results were essentially independent of the grid for δ = 4. A sample of the base grid used in the calculations is shown in Fig. 4.

Figure 4: Sample of the base grid used in the domain discretization (not to scale).

In the staggered grid formulation used in the solution, scalar quantities (pressure, temperature, thermophysical properties) are stored at nodes at the centre of each control-volume. Vector quantities (velocities) are stored at points in the centre of the control-volume faces. The solution of the coupled, non-linear sets of discretized equations for v, w, P and H was performed using the SIMPLEST procedure of Spalding (1980). Discretization of the transport terms related to the convection and diffusion fluxes have been treated using the hybrid scheme of Patankar (1980).

3.3. Thermophysical Properties, Geometry and Boundary Conditions The thermophysical properties of the refrigerants used in the ejectors were initially calculated using the NIST REFPROP v7.0 database (2002). To reduce calculation time, curves that describe the variation of the superheated gas density, viscosity, thermal conductivity and specific heats were fitted to the data from REFPROP to generate curve-fits describing the properties as functions of enthalpy and pressure. The geometry of the ejectors used in the CFD model varied in the different cases considered. In all cases, the walls were considered to be adiabatic, no-slip boundaries. The fluids at the primary and secondary inlets were considered to be gasses with very little superheat. A constant pressure was applied at the ejector outlet. The dimensions used in the basic ejector used for this study are summarized in Table 2.

Table 2: Description of the geometry of the base ejector used in the present study (all dimensions in mm). L1 L2 L3 L4 L5 L6 L7

27.0 36.0 37.36 85.78 17.0 10.0 L2 R1 R2 R3 R4 R5 R6 3.0 1.48 2.35 15.0 4.5 12.14

Only a brief description of the procedure used to validate the CFD model used in this study is presented here. A thorough description of the methods used is included in Scott et al. (2008). The ejector geometry and thermophysical properties were initially set to mimic those of Huang et al. (1999) using R141b. Additional validation was performed by comparing results of the current model to that from Ablwaifa’s 2006 Ph.D. thesis. It should be noted that two different geometries were used for each validation. Three of the geometries can be described by the general configuration described in Fig. 3. The final geometry, the so-called “optimized” geometry of Ablwaifa, used a two-part converging section. The “optimized” converging section was not linear but had a radius of curvature in the first part followed by a linear cone that joined the end of the curved section to the constant area section in the middle of the ejector. It was found that the CFD model used in this study matched the corresponding data of Huang et al. and Ablwaifa very well.

4. RESULTS AND DISCUSSION

The CFD model was initially used to verify the performance of a single ejector geometry, operating with R245fa, over a wide range of operating temperatures. The generator temperature ranged from 60 oC to 120 oC in 20 oC increments, the evaporator temperature ranged from -10 oC to 20 oC in increments of 5 oC. A summary of these results showing only the critical point is presented in Fig. 5. The critical point for the ejector is shows the value of the entrainment ratio at the critical condenser pressure where, for the purposes of this study, the critical condenser pressure was defined as the condenser pressure at which the entrainment ratio was reduced to 95 % of the critical operation value.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Critical Condenser Pressure (MPa)

Entr

ainm

ent R

atio

Tg=60Tg=80Tg=100Tg=120

Te=20oC

Te=15oC

Te=10oC

Te=5oC

Te=0oC

Te=-5oC

Te=-10oC Te=20oC

Te=20oC

Te=20oC

Figure 5: Summary of performance predictions for the base ejector used in the present study.

The trends seen in Fig. 5 reflect those expected for a vapour-jet ejector. An increase in the generator temperature results in an increase in pc* and a decrease in ω. An increase in the evaporator temperature results in an increase in both pc* and in ω. Using these results as a baseline, the CFD model was adapted to simulate ejectors with different geometries at three different operating conditions. The results of modifications to three variables were studied and their results are presented in this paper. These variables are: the dimensionless mixing section length (=L3/(2r2)); the dimensionless mixing section radius (=r5/r2); and the dimensionless primary nozzle exit diameter (=r3/r2). The results of these studies are presented in Figs. 6, 7, and 8, respectively. The dimensionless primary nozzle exit diameter is a measure of the motive velocity of the primary flow. In all cases, results were obtained for four different operating conditions. The evaporator temperature was maintained constant at 10 oC and generator temperatures of 60 oC, 80 oC, 100 oC and 120 oC were used. The results are presented as the ratios over the average value: the average value for a given Tgen is the average value of pc* or ω over the range of variables considered. The graphs indicate the magnitude of change in performance that can be expected for a particular change in geometrical variable values. As can be seen in Fig. 6, the impact of varying the mixing section length is quite small. The total range of variation of pc* is only 10% over the entire range of values used. The variation of ω is even less when the results for Tgen=120 oC are ignored: the entrainment ratio in this case was very small and little absolute difference in value was necessary to cause a significant relative difference. The impact of changes to the mixing section diameter is significantly greater. As seen in Fig. 7, the performance of the ejector is greatly impacted by the dimensionless mixing section radius. Over the range of values considered, the impact on pc* was greater than 45% of the average values. The impact on ω was even greater, with variations of nearly 160%. Changes to the motive velocity result in small differences in both pc* and ω (<10% variation for most cases). The greater impact seen for Tgen = 120 oC is again a reflection of the small absolute value of ω.

0.85

0.9

0.95

1

1.05

0 10 20 30 40 50L3/(2R2)

P c*/P

c*av

g

0

0.5

1

1.5

2

2.5

3

ω/ω

avg

Pc*(60C)Pc*(80C)Pc*(100C)w*(60C)w*(80C)w*(100C)w*(120C)

Figure 6: Variation of the ejector performance with changes in the dimensionless mixing section length.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2 3 4 5 6r5/r2

P c*/P

c*av

g

0

0.5

1

1.5

2

2.5

3

ω/ω

avg

Pc* (60C)Pc* (80C)Pc* (100C)Pc* (120C)w* (60C)w* (80C)w* (100C)w* (120C)

Figure 7: Variation of the predicted ejector performance with changes in the dimensionless mixing section

radius.

0.6

0.7

0.8

0.9

1

1.1

1 1.5 2 2.5r3/r2

P c*/P

c*av

g

0

0.5

1

1.5

2

2.5

ω/ω

avg

Pc* (60C)Pc* (80C)Pc* (100C)Pc* (120C)w* (60C)w* (80C)w* (100C)w* (120C)

Figure 8: Variation of the predicted ejector performance with changes in the dimensionless primary nozzle

exit radius (motive velocity).

5. CONCLUSIONS

The present study has used a CFD model of ejectors operating with R245fa to investigate the impact of varying different geometric parameters on the performance of the ejector at different operating conditions. Three parameters were investigated; the mixing section length, the mixing section radius and the primary nozzle exit radius (indicative of the primary flow velocity). The study clearly demonstrates that changes to these parameters do impact the performance; however the parameter that has the greatest impact on ejector performance is the ratio of the mixing section radius to the primary nozzle throat radius. The study also demonstrates the usefulness of CFD models in studies of ejectors; once a model is validated, extensive simulations can be run in a relatively short period of time.

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CHAM Ltd., 2003, PHOENICS V3.5.1, Wimbledon, UK. Eames, I.W. and Ablwaifa, A.E., 2004, “Use of CFD in the Prediction of Jet-Pump Performance,” Proc. HPC

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Patankar, S.V., 1980, “Numerical heat Transfer and Fluid Flow,” Hemisphere Publishing Corp.., Washington, D.C.

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Riffat, S.B. and Everitt, P., 1999, “Experimental and CFD Modelling of an Ejector System for Vehicle Air Conditioning,” J. Inst. of Energy, 72, pp. 41-47.

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Scott, D., Aidoun, Z., Bellache, O. and Ouzzane, M., 2008, “CFD Simulations of a Supersonic Ejector for Use in Refrigeration Applications,” Proc. Int. Refr. Air Cond. Conf. at Purdue, July 14-17, West Lafayette, IN.

Selvaraju, A. and Mani, A., 2004, “Analysis of an ejector with environment friendly refrigerants,” Applied Thermal Engineering, Vol. 24, pp. 827-838.

Spalding, D.B., 1980, “Mathematical Modelling of Fluid Mechanics, Heat Transfer and Mass Transfer Processes,” Mechanical Engineering Report HTS/80/1, Imperial College of Science, Technology and Medicine, London, UK.

Sun, D-W., 1997, “Experimental investigation of the performance characteristics of a steam jet refrigeration system,” Energy Sources, Vol. 19, pp. 349-367.