Thermal modelling and optimization of low-grade waste heat driven ejector refrigeration system incorporating a direct ejector model

Journal Pre-proofs Thermal modelling and optimization of low-grade waste heat driven ejector refrigeration system incorporating a direct ejector model Fahid Riaz, Poh Seng Lee, Siaw Kiang Chou PII: DOI: Reference:

S1359-4311(19)33196-5 https://doi.org/10.1016/j.applthermaleng.2019.114710 ATE 114710

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Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

10 May 2019 15 November 2019 20 November 2019

Please cite this article as: F. Riaz, P. Seng Lee, S. Kiang Chou, Thermal modelling and optimization of low-grade waste heat driven ejector refrigeration system incorporating a direct ejector model, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114710

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© 2019 Published by Elsevier Ltd.

Thermal modelling and optimization of low-grade waste heat driven ejector refrigeration system incorporating a direct ejector model Fahid Riaza,*, Poh Seng Leea, Siaw Kiang Choua a

Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive, Singapore 117575, Singapore

Abstract This paper presents the modeling and optimization of an ejector refrigeration system (ERS). Engineering Equation Solver (EES) has been used for modeling. These models have been validated against published experimental results. Refrigerant R245fa is used as a working fluid. A new analytical model for predicting the optimum (on-design) performance (entrainment ratio) of ejectors is presented. The analytical model of the ejector is validated against two sets of published experimental data and good agreement is established with an average error of 3.4%. The presented ERS model has also been validated with two sets of published experimental results and an average error of 2.9% is obtained. The ERS model is further compared with a model developed in EBSILON (a commercial tool). The results show that for the optimum design of an ERS, the generator pressure increases linearly with heat source temperature while the output (refrigeration effect) increases exponentially. For the case study, the designed ERS produces 1.8 MW of cooling with estimated annual savings of S$0.42 million while operating at 0.3 COP. The presented models can be used for designing ejector and ERS for various applications. Keywords: Ejector, refrigeration, low grade heat, modelling, thermodynamics * Corresponding author. Tel.: +65-83240830, -mail address: [email protected]

Nomenclature

Subscripts

0-D

Zero dimensional

1

Motive fluid inlet

1-D

One dimensional

2

Entrance of mixing chamber

2-D

Two dimensional

3

Section at which primary and secondary are fully mixed

CFD

Computational fluid dynamics

4

Location before shock wave

COP

Coefficient of performance

5

Location after the shock wave occurs

D

Diameter, mm

6

Secondary fluid inlet

EES

Engineering Equation Solver

7

Diffuser outlet

ER

Entrainment Ratio

c

Condenser

ERS

Ejector Refrigeration System

d

Diffuser

h

Enthalpy, kJ/kg

e

Evaporator

k

Isentropic exponent

g

Generator

m

Mass flow rate, kg/s

id

Ideal

NXP

Nozzle exit position, mm

is

Isentropic

P

Pressure, bar

m

Mixing chamber

T

Temperature, oC

mc

Constant area mixing chamber

V

Velocity, m/s

n

Nozzle

η

Efficiency

p

Primary fluid

T_hotwater,out

Temperature of exiting hot water (source stream)

s

Secondary fluid

HRVG

Heat recovery vapour generator

t

Throat of primary nozzle

1- Introduction The rise in global population, rapid urbanization and economic development contributes to increasing energy demand. The exploitation of fossil resources and their environmental impact demand a transition towards sustainable energy systems. At the 2015 conference of the parties (COP21) of the United Nations, both renewable energy and energy efficiency were recognized as essential means towards a low-carbon future. Building energy use (mainly heating and cooling) currently accounts for over 40% of the total primary energy consumption in the U.S. and the E.U. [1]. In the near future, the energy demand for cooling is expected to increase significantly due to increasing incomes in developing countries [2]. It is estimated that about 20-50% of industrial energy input is released to the atmosphere through stacks, vents and flares as waste heat [3]. In addition, low-grade thermal energy in the range from 60 to 100ºC is available from renewable sources such as geothermal and solar energy. Therefore, low-grade heat represents an energy potential and its recovery can lead to increasing energy efficiency and the share of renewable energy in the global energy mix. The ejector refrigeration system (ERS), being a heat-driven technology, offers a viable means to convert low-grade heat into useful cooling. The most important aspect to design an ERS is the performance prediction of ejectors. Ejectors have existed for long and have been used in a wide variety of chemical, nuclear, power and chiller industries [4]. Ejectors have been studied for use in various applications such as in ERS [5], [6], [7], [8], [9], ejector enhanced

organic Rankine cycles [10], and combined cooling and power systems [11], [12], [13]. Ejectors are inexpensive, robust and require minimal maintenance because there are no moving parts inside ejectors. The ERS generally has a lower COP compared to vapour compression systems [14] owing to the nature of ejector operation, which relies on fluid-fluid entrainment and mixing. The COP of an ERS can be improved by optimizing the design of the ejector as it is the component where a major part of the exergy is destroyed [15] in the system. In improving the design of the ejector, the two key parameters needing to be addressed are the area ratio and the primary nozzle exit position. The area ratio of an ejector is the ratio of the area of the mixing chamber to the area of the primary nozzle throat. Area ratio is considered to be the most sensitive [16] factor for improving the performance. As reported by researchers [9], [17]–[19], when operating conditions are changed, the area ratio needs to be changed to get the optimized geometry. Various studies [18], [20]–[23] demonstrated that the performance of the ejector is also highly sensitive to the nozzle exit position (NXP). The NXP can affect the entrainment ratio (the mass flow ratio of the secondary to primary fluid stream)by up to 40%. The detailed geometric design of an ejector can be studied by employing CFD modelling or experimental investigation. Scott et al. [14] used CFD simulations of a supersonic ejector for a refrigeration system. They studied the impact of varying the operating conditions on the critical condenser pressure. Zhang et al. [12] used CFD analysis to study the flow and transport processes in an ejector. Also, they performed a sensitivity analysis for selected design parameters. For performance prediction of the ejector, Keenan et al. [24] proposed an analytical model. Their 1-D constant pressure mixing model developed the foundation for the analytical models used by Huang et al. [25] and Chen et al. [19]. This constant pressure mixing theory is applicable when the converging and diverging nozzle exit plane is upstream of the constant area section of the mixing chamber. Huang et al. [25] improved the 1-D model by considering flow choking occurring in the mixing chamber . They assumed that the secondary fluid stream accelerates when being entrained and becomes choked somewhere upstream of the entrance of the constant area mixing chamber. Huang’s 1-D analytical ejector model is mainly derived from isentropic flow relations, assuming ideal gas conditions, and requires iterations to obtain the entrainment ratio of the ejector. Chen et al. [19] proposed a different improvement to the analytical model, which also considered the choking phenomenon. However, the model does not need any geometrical dimensions to obtain the ejector performance. This model needs double iteration for two parameters, that is, the pressure of the constant area mixing chamber and the entrainment ratio. Currently, in the literature, there is no analytical model which can directly calculate the entrainment ratio without the need of iterations. In this paper, a new analytical model is utilized which incorporates some of the assumptions from Huang’s and Chen’s analytical models and employs the Engineering Equation Solver (EES) for using real properties of working fluid. The proposed model can predict the performance without the need of iterations. The main advantage of the proposed model is that it can be integrated with the overall system model. Many researchers have studied various suitable working fluids for ERS application and many has recommended and used R245fa as a suitable working fluid [3], [26], [27], [28], [29]. In this paper, R245fa, a dry fluid, has been used as a working fluid because of its suitable critical temperature and pressure ranges. Also, it has zero ozone depletion potential and is not flammable. Some commercial companies are also using R245fa for low-grade heat driven systems [30]. In this paper, although R245fa has been used in the presented models, it is convenient to simulate the ERS performance with other working fluids as well. ERS system has been studied and reported by many researchers. Chen et al. [31] developed a real gas model and reported that it performs better than the ideal gas model of ejector. They used R141b and R11 for

system performance of ERS. However, they used condenser temperature of 30ºC and the lowest generator temperature of 85ºC. Shestopalov et al. [29] did experimental investigation of ERS operating with R245fa. They tested the system for both on-design and off-design conditions. The minimum generator temperature they used is 90ºC with maximum cooling capacity of 12kW. They found that for on-design conditions, their theoretical model gave 10% lower performance. F. Mazzelli, et al. [32] did experimental and theoretical investigation of ERS with R245fa which had a nominal cooling capacity of 40kW and the minimum heat source temperature of 90ºC. They recommended to account for surface roughness of ejector for off-design performance. Although, many researchers have studied heat driven ERSs, literature lacks data for harnessing very lowgrade heat with temperature as low as 60ºC with ERS in tropical climate. Tropical and hot climates is of interest because there is always a strong cooling demand for thermal comfort. Higher ambient (heat sink) temperatures makes the utilization of very-low grade very challenging for tropical climates. In this paper an ERS model is presented which is developed in Engineering Equation Solver (EES) which enables utilizing the built-in real data of working fluids. The model has been validated and then used to explore the application of ERS for very-low temperature heat sources. A case study is also presented where the presented model is used to design an ERS for a multiutility facility in the tropical climate of Singapore. The novelty of this work is signified by the following points 



 

A new analytical model is used for on-design ejector performance prediction which does not need iteration to get the performance of ejector. This model utilizes CFD analysis and is not dependent on experimental data An ERS model is presented where the heat exchangers are designed based on the pinch point temperature difference. This ERS model is integrated with the new ejector analytical model. The presented ERS model has been validated with experimental results as well as with another model built in EBSILON which is a commercial tool The application of ERS for very low-grade heat temperatures has been evaluated for tropical climate with higher heat sink temperatures A case study is presented which elaborates the utilization of the presented models for designing an ERS for various applications

2- Modelling In this section, first the analytical modeling of ejector is described and later the modeling of the whole ERS is discussed. The validation of these models is provided in the results section.

2.1 – Ejector Modelling The ejector model used in the system is a new analytical model which predicts the on-design and optimum entrainment ratio of ejector for available working conditions. The details of modelling and its validation is given below. An ejector is powered by a high pressure (primary or motive) fluid which expands to a supersonic jet through a convergent-divergent nozzle. Upon exiting the primary nozzle, the primary jet spreads towards the wall of the mixing chamber. In so doing, it meets and entrains the secondary fluid. Mixing of the two fluid streams continues through the mixing chamber and the back pressure for condensation of the mixed flow is achieved through the pressure gain from compression shock and pressure recovery in the diffuser at the expense of velocity. The performance of an ejector is described through the entrainment ratio (ER), which is the ratio of the mass flow rate of the secondary fluid to the mass flow rate of the primary fluid.

Figure 1 shows the structure of a supersonic ejector along with variation of pressure and velocity of the primary and secondary fluids at various sections of the ejector. As shown in Figure 1, the primary fluid (in red colour) enters at pressure Pg (P1) and expands in the primary nozzle. It should be noted that the primary fluid reaches sonic velocity at the throat of the choked primary nozzle. The secondary fluid (blue) enters at pressure Pe and expands until it reaches sonic velocity at section 2. The two fluid streams are totally mixed at section 3, and the mixed flow undergoes a compression shock at section 4. The diffuser further increases the pressure of the mixed fluid which is delivered at pressure Pc.

Figure 1: Ejector structure and variation of pressure and velocity at various positions (modified from [33]) Figure 2 shows the variation of enthalpy and entropy of the primary and secondary fluid streams at various sections of the ejector. As shown, the pressure inside the constant area mixing chamber is Pmc and is assumed to be constant until section 4 where the shock happens. The primary fluid keeps expanding after leaving the nozzle until section 2 where it starts mixing with the secondary fluid and pressure does not drop further. The losses in the primary nozzle are accounted for by the isentropic efficiency of primary nozzle (ηn). The mixing losses are estimated by the mixing efficiency (ηm) and the losses due to shock and compression in the diffuser are accounted for by a single diffuser efficiency (ηd).

Figure 2: h-s diagram of the modelled ejector (modified from [33]) A new analytical model is being proposed in this study. Referring to Figure 1 and Figure 2, a brief description and assumptions of the model are given below: 1. The proposed model is a simplified and simpler-to-use model to predict the optimum (on-design) performance (entrainment ratio) of an ejector without the need of any iterative process. This feature makes the model quick and facilitates its incorporation into an overall system model. 2. The model predicts the optimum performance of an ejector for a given set of operating conditions. This means that both primary and secondary fluids reach choking conditions with respect to the critical condenser pressure. 3. This is a zero-dimensional (0-D) model, meaning it predicts the entrainment ratio based on operating conditions (pressure, temperature, working fluid) irrespective of the size of the ejector and the mass flow rates. Hence, this model cannot predict off-design performance of an ejector of a given geometry. 4. There is no heat loss through the walls of the ejector, and it operates under steady state conditions 5. The primary and secondary flows are saturated, and their velocities are negligible before entering the ejector. The velocity of the mixed flow leaving the ejector is negligible. 6. The effects of frictional and mixing losses are considered by using isentropic efficiencies of the nozzle, mixing chamber and diffuser sections. The losses due to the shock inside the mixing chamber are accounted for by the diffuser efficiency. These efficiencies need to be determined experimentally for a given working fluid and range of operating conditions. 7. After exiting the supersonic nozzle, the primary flow keeps expanding until section 2 (the start of the constant area mixing section) without mixing. The two streams start to mix from section 2 under uniform pressure until the shock condition is reached. 8. It is assumed that the secondary fluid is chocked at section 2. This assumption allows us to calculate the pressure at section 2 by using the isentropic expansion relation. 9. The model primarily uses real fluid properties obtained from the built-in working fluid data in EES [34]. The ideal gas assumption has only been used to predict the choking pressure of the secondary fluid expansion and for that the isentropic exponent (k) value is assumed to be constant at the secondary flow inlet conditions.

2.2.1- CFD Modelling of Ejectors

CFD is a powerful tool to numerically solve and analyze problems that involve fluid flows. Many researchers have used CFD analysis to study the design of ejectors and to capture the physics in detail. In this study, a commercial CFD package ANSYS FLUENT is used to simulate the ejector performance. FLUENT model 19.1 commerical software package has been used. Pianthong et al. [35] did a comparison between axisymmetric 2-D and three dimensional (3-D) cases and concluded that results were almost the same. Also, other studies had shown that using 3-D flow will produce similar results to an 2-D axisymmetric solver [18], [36]. Therefore, in this paper, the ejector has been modelled using axisymmetric model. By choosing the axisymmetric solver, the center line of the ejector is taken as the axis of rotation with the assumption that there are no circumferential gradients. By selecting an axisymmetric solver, a 2-D axisymmetric form of the governing equations is solved instead of a 2-D Cartesian form. The 2-D axisymmetric flow dynamics equations for the ejector simulation consist of the standard mass, momentum and energy conservation equations as used by [37] and [38]. These governing equations are solved by FLUENT by using a control volume discretization technique. The second-order upwind scheme is applied to numerically solve the governing equations.

Entrainment Ratio

Meshing is an important part of any numerical study. Mesh quality plays an important part in the quality and reliability of results of any CFD analysis. The mesh should be refined enough so that the discretization error becomes very small and negligible. A mesh independence study is conducted to make sure the selected mesh quality is high enough to give reliable results. Figure 3 (a) shows the mesh independence study conducted on the ejector. The figure shows that with the reduction of element size (refinement of mesh), the entrainment ratio values are converging. When the element size is reduced further from 0.05 to 0.037, the increase in entrainment ratio is only 0.2%, therefore, 0.05 element size has been selected as it gives accurate enough results without causing very high computational cost (time). The validation of the CFD model and settings is presented in the section 3.1. Some more details of the presented mesh independence test have been provided in the Appendix (A). 0.25 0.2 0.15 0.1 0.05 0 0.02

0.03

0.04 0.05 0.06 Element Size [mm]

0.07

0.08

(a)

(b) Figure 3: (a) Mesh Independence study; variation of ejector performance with different mesh sizes, (b) Finalized structured mesh for AG1-model as mentioned in reference [25]

For validating the FLUENT model, the geometry of published experimental work [25] is used as shown in the figure below. A mesh sensitivity analysis is carried out on Model AG1. This is to ensure that the solution is independent from the spatial discretization. The mesh grid was built using ANSYS Meshing software. A structured mesh with 9940 elements was selected because increasing the mesh refinement beyond this value yielded insignificant changes in entrainment ratios of under 1% difference but increased computational cost significantly. A structured mesh is used it has lower requirements for computational memory and reduces computational cost. In addition, a structured mesh allows the better control over the number of cells, elements and skewness. The fluid domain is meshed with quadrilateral elements. For a high compression fluid flow density based solver is preferred but with the advancement in numercial model coding, pressure based solver is also able to handle the high compression fluid flow without divergence in solution. Hence, Pressure based, steady state axisymmetric solver is selected. Pressure inlet and pressure outlet boundary conditions are used. Reliable k-epsilon model which is a viscous turbulence model is selected as it is robust to handle shock and tubulence at high speed. As discussed in various references including [37], and [38], the k-ε realizable model is known to provide acceptable mass flow rates and entrainment ratios and has been employed by various researchers. As compared to other turbulence models, the k-ε realizable model better captures the adverse pressure gradients at boundary layers [39]–[41]. While some researchers have also used k-omega SST model for ejector simulations, most people have used k-epsilon model. Although, in this paper, k-epsilon model has been used in FLUENT to run all the CFD simulations, for the optimized ejector design, k-omega model was also run to see the comparison with k-epsilon. While the k-epsilon gives the entrainment ratio of 0.235, the k-omega gave the entrainment ratio value of 0.225 with a difference of the 4.2%. These comparison results are shown Appendix (B). Because k-epsilon model has shown very good agreement with experimental results as given in the validation section (3.1) and because k-omega is not able to capture shock at high speeds, in this paper k-epsilon model has been selected for axisymmetric ejector CFD. Scalable wall function with compressibility effect is opted to avoid any y+ effect in the flow field. Energy is switched on being a crucial paramter for thermal sensitive simulation as it is in our case. Table 1: Fluent Settings Meshing

Structured Mesh

Turbulence model

k-ε realizable model

Solver type

Pressure-Based

2D-Space

Axisymmetric

Energy equation

On

Compressibility effects

On

Fluid density

Ideal gas

Boundary condition for inlets

Pressure-inlet

Boundary condition for outlet

Pressure-outlet

Spatial discretization

Second order

Residuals

1e-06

Initialization method

Hybrid

The table summarizes the various settings used within the CFD FLUENT model. The convergence criteria were set for the residual to fall below 1e-06 which was achieved around 100,000 iterations. Mass flow rate of evaporator and generator is monitored to verify stable convergence. These numerical settings produced results which are in good agreement with experimental results as presented in Figure 10 and Figure 13. The optimum ejector design is not scalable geometrically. Therefore, for every new operating condition, a new ejector needs to be designed. And because there are many parameters in the ejector design, all the parameters are needed to be optimized for getting optimum performance. In the past it has been very challenging to design ejectors for various applications because of this issue as there was only one way to optimize the geometry, that is, the experimental investigation. But now, due to the advancements in numerical methods and tools, it is much easier to optimize the design of ejectors for different applications. It should be noted that even in a case where all the operating conditions remain the same and only the mass flow rate of motive fluid and hence the suction fluid is increased, the ejector design is still not scalable. This means that we cannot just simply calculate a new primary nozzle diameter and scale up all the other parameters accordingly. It is still required to go through the CFD optimization process and find a new optimum design of ejector for new mass flow rates. The starting point in designing of an ejector is the determination of primary nozzle throat diameter because it controls the primary fluid mass flow rate. The mass flow rate of primary fluid is known from the system requirements and operating conditions. Once the primary nozzle diameter is determined, the rest of the paraments of ejector design are studied and optimized one by one in an iterative process by using numerical CFD tools. The optimized design is the one which gives maximum entrainment ratio and by changing any geometric parameter the entrainment ratio drops from the maximum value.

2.2.2- Governing Equations for Analytical Modelling Engineering Equation Solver (EES) is used for modelling. All the governing equations are written in EES and solved simultaneously in a unique way to obtain the value of the entrainment ratio of the ejector for the given working conditions. With EES, the built-in properties of real working fluid can be utilized by calling the values at the desired state points. In the first step, the working conditions are entered as input parameters. These are type of the working fluid and the values of Pg, Pe, Pc, ηn, ηm, ηd. The primary and secondary fluids are assumed to be saturated vapour, if not, the temperature values should be entered as well. For programming we define

𝑃𝑔 = 𝑃1

(1)

𝑃𝑒 = 𝑃6

(2)

As the pressures P1 and P6 are known, the values of h1, s1, h6 and s6 for saturated vapor conditions can be obtained. The value of isentropic exponent (k) is taken at the state 6 (secondary fluid inlet conditions). As discussed before, it is assumed that the secondary flow is choked at section 2 which is at pressure Pmc. Therefore, the adiabatic expansion relation for secondary flow starting stagnation conditions at inlet can be used. The ratio of pressure is given by the equation 𝑃6 𝑃𝑚𝑐

( ) 𝑘

(

= 1+

)

𝑘―1 2

𝑘―1

(3)

After determining the pressure Pmc, as evident from Figure 2, the values of enthalpies after isentropic expansion h6,is and h1,is can be found. With assumption of stagnation conditions at both the inlets, the velocities of primary (Vp,2) and secondary (Vs,2) fluids at section 2 are calculated by using the conservation of energy principle as follows

𝑉𝑝,2 = 2 𝜂𝑛(ℎ1 ― ℎ1,𝑖𝑠) 𝑉𝑠,2 = 2 (ℎ6 ― ℎ6,𝑖𝑠)

(4) (5)

Due to a relatively smaller pressure difference between P6 and Pmc, the expansion losses are neglected in the above equation. As shown in Figure 1, the fluids are assumed to be totally mixed (same velocity) at section 3. At section 4, the flow experiences a compression shock. If ER is the entrainment ratio, then 𝑚𝑒

(6)

𝐸𝑅 = 𝑚𝑔

Here m denotes the rate of mass flow in kg/s. By applying momentum balance between section 2 and section 4, we can obtain another relation for V4. Figure 4 shows the conceptual diagram for application of conservation of momentum between section 2 and section 4.

Figure 4: Schematic of the constant area mixing chamber before compression shock for applying conservation of momentum principle The inlet velocities are previously calculated and the pressure and area for section 2 and 4 are the same. The mixing efficiency (ηm) is defined as the ratio of kinetic energy at the outlet for actual and ideal cases. That is

𝜂𝑚 =

𝐴𝑐𝑡𝑢𝑎𝑙 𝐾.𝐸. 𝑎𝑡 𝑒𝑥𝑖𝑡 𝐼𝑑𝑒𝑎𝑙 𝐾.𝐸. 𝑎𝑡 𝑒𝑥𝑖𝑡

= 𝑉2

𝑉24

4, 𝑖𝑑𝑒𝑎𝑙

(7)

Applying the conservation of momentum between section 2 and 4, we get

𝑉4 = 𝜂𝑚

𝑉𝑝,2 + (𝐸𝑅) 𝑉𝑠,2

(

1 + 𝐸𝑅

)

(8)

If the value of V4 is known, h4 can be calculated by energy conservation because both the inlet velocities are zero (stagnation conditions). Hence, an equation relating h4 and V4 can be obtained by applying conservation of energy principle from both inlets (primary and secondary) until the section 4 which is the outlet of constant area mixing chamber. This means that energy entering the section is equated to the energy leaving. This approach is similar to the method used by Zhao et al. [42]The resulting relation is

ℎ4 =

ℎ1 + (𝐸𝑅) ℎ6 1 + 𝐸𝑅

―

𝑉24 2

(9)

Referring to Figure 2 again, the diffuser efficiency (ηd) is the isentropic efficiency which accounts for compression by shock and by diffuser section. If h4 and diffuser efficiency are known along with condenser

pressure, another equation relating V4 and h4 can be derived by applying the energy conservation principle between section 4 and the exit of ejector. This means that the energy at section 4 is equated to the energy of fluid at the exit of ejector. That is

𝑉4 =

2 (ℎ4,𝑖𝑠 ― ℎ4)

(10)

𝜂𝑑

And eliminating the velocities and solving equations 4, 5, 8 and 10, the relation for ER in the form of enthalpies and efficiencies only can be obtained. The resulting relation is given below-

ER =

2ηn(h1 ― h1,is) ―

2(h4,is ― h4)/(ηmηd)

2(h4,is ― h4)/(ηmηd) ― 2(h6 ― h6,is)

(11)

2.1.3- Computational Procedure for Analytical Modelling The computational procedure is summarized in Figure 5. All the equations used are explained in the previous section. In the first step, the model takes the input parameters which define the working conditions and the working fluid and suitable efficiency values. Then the working fluid property data is used to find the enthalpies and entropies at both the inlets. Next, equation 3 is used to calculate the pressure of the constant area mixing chamber. Calculation of this pressure enables the determination of isentropic enthalpies h1,is and h6,is and by using equations 4 and 5, velocities at section 2 (Vp,2, Vs,2) can be found. This leaves three equations and three unknown variables hence equations 8, 9 and 11 can be solved simultaneously to get V4, h4, and finally ER. This all is a single step process to calculate ER.

Figure 5: Computational Procedure for the presented model for ejector performance

2.1.4 – Ejector Efficiencies Ejector efficiencies are employed in the analytical models to account of losses. The validity of the proposed model is highly dependent on the efficiency values used but little information is available in the literature

on a procedure to accurately calculate the ejector efficiencies. Lui et al. [43] studied efficiencies of two phase CO2 ejectors by using experimental and analytical modelling and concluded that ejector efficiencies vary with ejector geometry and significant change in operating conditions. Zhang et al. [38] used CFD to calculate the ejector efficiencies based on a friction co-efficient. They used a fixed design of ejector and employed CFD analysis with different friction co-efficient values and then matched the CFD results with experimental data to find out the most suitable values of friction coefficient. Thus, their methodology is dependent on the availability of experimental data. A study by Varga et al. [16] had shown that nozzle efficiency can be considered as a constant while the efficiencies for the mixing and diffuser sections may vary with the operating conditions. Huang et al. conducted both 1D analytical and experiments based on 11 different ejectors and 39 operating conditions to determine the ejector efficiencies [25]. Chen et al. also used a similar method to determine the ejector efficiencies from experimental data [33]. This work uses and proposes a systematic approach to find the ejector efficiencies using CFD analysis results. The efficiencies thus obtained are used in the analytical model. The results of the analytical model with these efficiency values have been validated with another set of CFD results data as well as with published results for R245fa working fluid reported by Zheng et al. [13], F. Mazzelli et al. [32] and Eames et al. [44]. To find the efficiencies, as a first step, an ejector has been designed and optimized by using CFD analysis in FLUENT. The CFD modelling and its validation has also been discussed earlier in this paper. The ejector has been designed for a small ejector refrigeration system (ERS) with 0.5 kW cooling capacity. The ERS is designed to harness low-grade heat at 90 ºC and below. The design of ERS supplies the motive (5.77 bar), suction (0.82 bar) and delivery (1.97 bar) pressures for the ejector. R245fa has been used as a working fluid. The motive mass flow rate is 0.0106 kg/s. For this application, the ejector designed and optimized with CFD analysis gives the entrainment ratio of 0.27. Determination of nozzle efficiency For the primary nozzle the inlet pressure is 5.77 bar and saturated vapour is entering as the motive fluid. The enthalpy of the motive flow inlet (h1) is 453.6 kJ/kg. From the CFD results it is noted that the velocity of the motive flow at the inlet and outlet of the primary nozzle is 38.9 m/s and 249 m/s respectively. The pressure at the exit of the nozzle is found to be 1 bar, see Figure 6, and therefore the ideal enthalpy for isentropic expansion is calculated to be 422 kJ/kg.

Figure 6: Variation of static pressure along the axis of the ejector (optimized geometry) Because the nozzle efficiency is the ratio of actual change in kinetic energy to the ideal change in kinetic energy, as discussed in governing equations’ section, the nozzle efficiency is found to be 96 %. Determination of diffuser efficiency The diffuser efficiency accounts for the losses due to compression shock and losses in the diffuser section. The section where the compression shock starts is shown in Figure 6. From the FLUENT results, the values of enthalpy at the section before the shock and at the delivery section are found to be 414.5 kJ/kg and 437.5 kJ/kg respectively. The values of velocity at the section before the shock and at the delivery section are found to be 235.1 m/s and 54.8 m/s respectively. As the diffuser efficiency is defined as the ratio of the actual increase in enthalpy and ideal increase in enthalpy, as discussed in the governing equations section, the diffuser efficiency is found to be 88 %. Determination of mixing efficiency From the results of optimized design in FLUENT, it is found that the velocity of the mixed fluid just before shock section is 235.1 m/s and the average velocity at the start of constant area mixing section is 252 m/s. Because the mixing efficiency of a constant pressure section is the ratio of kinetic energies at the start and end of the section, the mixing efficiency comes out to be 87 %.

2.2 – Modelling of ERS The ERS has been modelled in EES and it is integrated with the ejector’s analytical model. An EBSILON model of ERS is also developed which is used only to validate the EES model. The validated EES model is used to optimize the ERS for maximum output. R245fa has been used as a suitable working fluid for lowgrade heat utilization. The ERS models can be easily used to obtain system performance with various working fluids.

2.2.1- Modelling of ERS in EES The ERS has been modelled in EES by solving the governing equations for all the components of the system as shown in the Figure 7. The modeling of ejector is discussed in previous section. The heat recovery vapor

generator (HRVG), the evaporator and the condenser are heat exchanger which are modelled by applying mass and energy balance equations as well as by defining a suitable pitch point temperature difference (PPTD).

Figure 7: Schematic of ERS model (left), T-s diagram of modelled ERS (right) As shown in the T-s diagram, there are three pressure levels. The condenser pressure is the medium pressure and is dictated by the ambient (or heat sink) temperature. The pump increases the pressure of working fluid from condenser pressure to the HRSG pressure. The expansion valve reduces the pressure of working fluid from condenser pressure to the evaporator pressure. The evaporator pressure is dictated by the required temperature of cooling produced. The HRVG pressure needs to be calculated based on the heat source temperature, mass flor rate of working fluid and ejector entrainment ratio. The inputs required for the EES model are Tsource = Temperature of heat source

(12)

msource = Mass flow rate of heat source

(13)

Tsink = Temperature of heat sink

(14)

Tcooling = Required temperature for cooling or evaporator temperature

(15)

Working Fluid = Type of working fluid or refrigerant

(16)

The PPTD occurs at a point where the difference between the hot and cold fluids is minimum. For HRVG, the PPTD occurs at point 7 shown on T-s diagram in Figure 7. For a given pressure and PPTD for HRVG it is possible to calculate the mass flow rate of the working fluid through HRVG and hence throughout the system if the entrainment ration of ejector is known. For HRVG modeling, an initial value of saturation temperature is used which enables to find the properties of working fluid at point 3 (saturated vapour) and point 7 (saturated liquid). The PPTD value of 3ºC is used for HRVG. Applying the energy balance on the heating water (source) and the working fluid from point 3 to 7, we get msourceCp,w(Tsource ― Tw,7) = m3(h3 ― h7)

(17)

Here, Tw,7 is the temperature of heat water (source) at point 7 and can be found by Tw,7 = T3 + PPTDHRVG

(18)

Hence, m3 can be calculated and because we know the entrainment ratio from ejector model, we can calculate the m5 m5

(19)

ER = m3 Also, mass balance in ejector gives

(20)

m6 = m1 = m3 + m5

Please note that the notation m is for the flow rate of mass as indicated in nomenclature section. The condenser is modelled by assuming 5ºC approach temperature that the difference between the condensing temperature and cooling water (sink) inlet temperate. Because we know the sink temperature, we thus know the condensing temperature and pressure. Therefore, we know the state 1 and we know how much pressure difference the pump needs to provide. The specific pumping power (wpump) is calculate as wpump = v1(P2 ― P1) = h2 ― h1

(21)

Here, v1 is the specific volume of the liquid entering the pump at state 1. Because h1 is known, we can figure out the value of h2 and hence the pumping power can be calculated with the equation (22)

Wpump = m3(h2 ― h1)ηpump

The pump efficiency (ηpump) value of 0.8 is used although the pump power is very less as compared to heat supplied and therefore the losses in pump can also be assumed negligible without any significant changes to results. To find out the temperature of heating water leaving the system (Thotwate,out), energy conservation is applied on the pre-heating (state 2 to state 7) of working fluid in HRVG as follows msourceCp,w(Tw,7 ― Thotwater,out) = m3(h7 ― h2)

(23)

Thotwater,out is an important parameter to calculate for waste heat driven systems because many times this is constrained due to the overall system integration requirements. The total heat supplied is calculated as Heat Supplied = msourceCp,w(Tsource ― Thotwater,out) = m3(h3 ― h2)

(24)

The evaporator pressure and temperature are dictated by the temperature of cooling which is demanded by the system. For a required evaporator temperature, the pressure is the saturation pressure and the working fluid leaving the evaporator is saturated vapour as shown on the T-s diagram. Therefore, state 5 is known for a known evaporator temperature. The expansion process from state 1 to state 4 is isenthalpic and therefore state 4 is known as well. The refrigeration effect (cooling produced) and COP is calculated as Refrigeration Effect = m4 (h5 ― h4) Refrigeration Effect Wpump

COP = Heat Supplied +

(25) (26)

The state 6 is the ejector outlet and because the condensation pressure is known, the enthalpy at state 6 (h6) is found out by applying energy balance to the ejector as m3h3 + m5h5 = (m3 + m5)h6

(27)

Therefore, the heat rejected by the condenser is calculate as Heat Rejected = m1 (h6 ― h1)

(28)

For a given working fluid, the entrainment ratio (ER) of ejector depends on the inlets states of primary and secondary fluids and the delivery pressure, that is

ER = f (P3, T3,P5,T5,P1)

(29)

Because both the primary and secondary fluids are saturated vapour, for this case, the ER becomes a function of pressures only, that is ER = f (P3,P5,P1)

(30)

The variation of pressure of HRVG (P3) changes both the m3 and ER and therefore, there lies an optimum value at which the ERS will give maximum refrigeration effect. Therefore, the coupling of ejector model with ERS model is achieved in such a way that both the models are solved simultaneously to get the performance of ERS.

2.2.2- Modelling of ERS in EBSILON EBSILON Professional is a powerful tool for the design, analysis, optimization and monitoring of various thermal systems [45] and has been under development for more than two decades [46]. It is widely used by various researcher for simulating thermal system including low-grade heat driven systems [47]. An ERS model is developed in EBSILON so that the EES model can be validated and verified. The ejector is not a built-in component within EBSILON and hence a macro object has been created for simulating the performance of ejector in EBSILON. The macro object applied the energy balance to the primary and secondary streams while taking the entrainment ratio as an external input. This way the ejector component calculates the properties of the leaving fluid while the value of entrainment ratio needs to be fed to this macro object.

Figure 8: ERS model developed in EBSILON

The steady state ERS model developed in EBSILON is shown in Figure 8 which shows all the components of ERS. For the heat exchangers (generator, condenser and evaporator) the heating and cooling circuits are also shown. The system shown in the figure uses the operating conditions same as reported by the experimental work of Eames et al. [28] which are given in the table below Table 2: ERS operating conditions used in EBSILON model for validation with Eames et al. [28] T_gen

P_gen

T_eva

P_eva

T_con

P_con

Compression Ratio

Entrainment Ratio

COP

[C]

[bar]

[C]

[bar]

[C]

[bar]

-

-

-

110

15.74

15

1

33.5

2

2.000

0.94

0.67

To have a generator saturation temperature of 110ºC, the source (heating water) temperature of 125ºC is used as shown in Figure 8. Similarly, to have a condenser temperature of 33.5ºC, the sink (cooling water) temperature of 26ºC is used. The ER value of 0.94 is used in EBSILON as reported by Eames et al. As indicated in Figure 8, the COP obtained with EBSILON model is 0.684 and the COP reported by Eames et al. is 0.67 which means EBSILON model is quite accurately predicting the performance of system with error of 2%.

(a)

(b) Figure 9: (a) Heat transfer diagram of generator obtained EBSILON, (b) T-s diagram of ERS cycle obtained from EBSILON model Figure 9 (a) shows the heat transfer diagram of the generator. The pinch point temperature visible in the figure is approximately 3ºC which is also the value used in the EES model as explained in the previous section. Figure 6 (b) shows the T-s diagram of the ERS cycle which is automatically obtained from the developed EBSILON model. As explained earlier, the figure elaborates that the saturated vapour conditions exist at the outlet of both generator and evaporator. Similarly, the condenser outlet is saturated liquid as visible in the T-s diagram.

3- Results and Discussions To simulate the performance of ERS with EES model, first we need to solve the analytical model of ejector developed in EES and for this we need to first find out the suitable values of isentropic efficiencies used in the analytical model of ejector. Suitable values of isentropic efficiencies are obtained by matching the performance of ejector obtained with analytical model with the optimized performance obtained with CFD analysis. In this section, first the validation of CFD FLUENT model, EES ejector analytical model and EES ERS model is provided. Then the results for ERS performance obtained from validated EES model are presented. In the end, a case study is presented to show how the developed model can be used to design an ERS for an industrial application.

3.1- Validation of Ejector CFD Model For validation, a geometric model was selected for which Huang et al. [25] performed experiments. Figure 10 shows the Mach number contours of the CFD simulation of the model AB with the boundary conditions of same as reported by Huang el al., which are, 4 bar of motive or generator pressure, 0.4 bar of evaporator or suction pressure and a delivery or critical condenser pressure of 0.7 bar. As indicated in the figure, the

CFD results are in good agreement with experimental results [25] and other simulation result [14] with an error of 0.35% and 1.1 % respectively. As shown, the sonic (Mach number=1) condition exists at the throat of primary nozzle. The primary flow accelerates in the divergent part of the nozzle and keeps expanding even after leaving the nozzle which is in line with the assumption used in the analytical model. Due to mixing of primary and secondary fluids, the velocities average out along the length of the ejector. The compression shock brings the mixed flow from supersonic (Mach number >1) state to the subsonic (Mach number <1) state. The mixed subsonic fluid is gradually compressed in the diffuser section until the delivery pressure.

Figure 10: Mach number contour of validated ejector CFD model with R141b [14], [25] The large velocity gradient between the motive and entrained fluids at the exit of primary nozzle causes a shear layer between the motive and entrained fluids and thus the secondary fluid gets accelerated. This is seen in Figure 11 as the velocity vectors changes from dark blue to light blue to yellow. After coming out of the primary nozzle, the primary fluid starts slowing down from the outer boundary due to its interaction with secondary fluid and the secondary fluid in turn get accelerated. As the fluids move forward in the constant area mixing chamber, the velocity vectors become more uniform in colour (and length) indicating better mixing along the way.

Figure 11: Velocity vectors of fluids of validated ejector CFD model with R141b Figure 12 shows the pressure distribution along the center line of the ejector. The primary fluid experiences a sharp decline in pressure inside the primary nozzle. Inside the constant area mixing chamber the average pressure remains almost constant. The slight increase in pressure inside the constant area mixing chamber is due to the loss of velocity due to friction. When the mixed supersonic fluid enters the diffuser section, its pressure decreases due to the supersonic flow and then the shock increases the pressure almost instantaneously to bring the flow from supersonic to subsonic range.

Figure 12: Pressure distribution along the centerline of the ejector

Simulation Results (ER)

The ejector geometry and boundary conditions used for validation is based on the experimental configuration reported by Huang et al. [25]. For validation, we compare the entrainment ratios of the CFD model to other published papers. The summary of various CFD simulations is shown in Figure 13 which presents and compares the CFD FLUENT results with published data. The solid line (slope=1) represents a perfect match between the modelling and experimental results for the used geometry. Results closer to the solid line will indicate a closer match. The entrainment ratio of the proposed CFD model has an average difference of 3.3% from experimental data. 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000

1D (Huang) CFD (Scott) Experimental (Huang) CFD Simulation Perfect Correlation 0.2

0.3

0.4 0.5 Experimental Results (ER)

0.6

0.7

Figure 13: Comparison of ejector entrainment ratios for validation

3.2 – Validation of Ejector Analytical Model For validation of the proposed analytical model, three sets of data available in literature have been used which are all using R245fa as the working fluid. The first step in using the analytical model is the determination of three ejector efficiencies which are to be used in the model. The determination of ejector efficiency is generally done by either using experimental data or CFD data for on-design performance of ejector with R245fa. In this paper, a systematic and innovative approach of using CFD analysis for the determination of ejector efficiencies is presented. This method is scientific rather than hit-and trial base and this method applied for any working fluid and working condition in a quick manner. Because the proposed analytical model predicts on-design conditions, this model cannot predict off-design performance. As the proposed model predicts the optimum performance of ejector, the first step is to find out the optimum geometry of ejector to be used in FLUENT for the available conditions. This is done by varying the geometric parameters of ejector specially the area ratio and NXP (nozzle exit position) of the ejector to find the best performance. These two parameters have been reported to be the most critical for the geometric optimization of ejectors. The primary or motive nozzle diverging part length is an important geometric parameter as well. As we know that the primary flow is chocked and sonic velocity (Mach number 1) is achieved at the throat of primary nozzle, therefore, in the divergent part of the nozzle, the velocity increases further, and supersonic flow is achieved with Mach number greater than 1. For a fixed divergence angle , the length of the divergent part decides how much is the velocity of motive fluid when it comes out of the nozzle and this length dictates whether the motive flow is under expanded or over expanded. In supersonic ejectors, under expansion is desired because we want the motive fluid to keep expanding even after coming out of the nozzle. This helps with the mixing process and accelerates the suction fluid in a better way. Too little length gives highly under expanded nozzle which results in strong pulsating flow in the mixing chamber which causes losses and reduces the entrainment ratio of ejector.

Therefore, the divergence length (or the exit diameter) of the primary nozzle needs to be carefully optimized as well. Because a 2-D axisymmetric model has been employed, the suction chamber shape used in the ejector simulation is annular form around the primary nozzle. For the optimization of ejector geometry, all the ejector parameters need to optimize such that an optimum value of the all the parameters is achieved. While optimizing the geometry, it was found that the inlet area of the suction chamber (for secondary fluid) has little effect on the performance of the ejector unless the area is too small that it offers a restriction. Because the secondary fluid becomes chocked after mixing with primary fluid, its inlet area becomes irrelevant for defining the mass flow rate and hence the entrainment ratio. Because of chocking of secondary fluid in the ‘constant area mixing chamber’, its diameter and hence the area ratio becomes a very important parameter to be optimized because the entrainment ratio is very sensitive to area ratio. The area ratio is one of the most important shape parameters for ejector optimization and maximization of its entrainment ratio. It is defined as the ratio of the area of the mixing chamber and the area of the primary nozzle throat. Thereby, a greater area ratio will represent a greater mixing chamber diameter. The area ratio is deemed as the most sensitive parameter [16] for optimization of ejector. As shown in previous studies [17]–[19], when operating conditions are changed, area ratio needs to be changed to determine the optimized geometry. Another sensitive geometric parameter is the nozzle exit-position. Previous studies [18], [20]–[23] demonstrated that the performance of the ejector is highly sensitive to the nozzle exit position where the entrainment ratio can be affected by up to 40% by varying the nozzle exit position. The inlet and outlet diameters of ejector had been shown to have little impact on overall ejector performance because the chocking diameters control the mass flow rate in supersonic flows [48]. To find the optimum on-design performance of the ejector for the available working fluid and operating conditions, the geometry optimization is shown in Figure 14 which shows the results are for R245fa working fluid with fixed operating conditions. The pressures of 5.5 bar, 0.8 bar and 2 bar are used for primary, secondary and discharge pressures respectively. The mass flow rate of 0.1492 kg/s has been used for primary fluid.

Figure 14: Geometric optimization with CFD FLUENT: Area ratio (left), NXP (right) Because the primary nozzle throat area defines the primary flow rate due to chocked flow in the supersonic nozzle, and because the primary flow rate is fixed, the area ratio is changed and optimized by changing the mixing chamber diameter. The figure (left) shows the effect of changing the area ratio by varying the constant area mixing chamber radius. The graph shows that for the available working conditions, there is

unique Area Ratio for which the ejector gives maximum performance. When the value of the Area Ratio is varying increased or decreased from this optimum point the performance of ejector drops significantly. The diagram on the right shows the effect of varying the NXP. First, the optimum area ratio value as obtained and fixed and later the NXP value was optimized which give the best value of entrainment ratio of 0.235. If the value of area ratio of NXP is increased or decreased from these optimum values the entrainment ratio value dropped below 0.235 which means it the optimum value for this design. This is because for lower values of NXP, the secondary fluid does not get enough ejector length (and hence time) to accelerate by coming in contact with primary fluid and for too-high values of NXP, the frictional losses become prominent and reduce the entrainment ratio. For validation of the analytical model, its performance has been compared with the results obtained (for the optimized geometry) from CFD FLUENT. As discussed in the previous section, the used values of efficiencies are 0.96, 0.87 and 0.88 for nozzle for mixing and diffuser efficiencies respectively in the analytical model. Figure 15 shows the comparison and a good agreement of FLUENT results with the proposed analytical model with a difference of 6 % has been obtained.

Figure 15: Validation of analytical model with FLUENT results To further validate the performance of the proposed analytical model, its results are compared with published experimental results. Figure 16 shows very good agreement of the results with the experimental data (for on-design case) published by F. Mazzelli et al. [32] with an average error of 3 %.

Figure 16: Comparison of the proposed analytical model with experimental results of F. Mazzelli et al. To further check and validate, another published set of data for R245fa based ejector’s analytical results from Zheng et al. [13] is used. Again, a good agreement with an error of 5.7% is obtained as shown in Figure 17.

Figure 17: Validation of the proposed analytical model with published results of Zheng et al. Having validated the proposed analytical model with 2 separate sets of data, it can be deduced that the proposed analytical model is a reliable tool to predict the ejector performance. The third data set used for validation is taken from experimental results reported by Eames et al. [44]. The comparison is shown in Figure 18. The error of 3.75% shows good agreement.

Validation of ejector analytical model, Error=3.75% Entrainment Ratio

1.1 1 0.9 0.8 0.7

Experiment

0.6

Simulation

0.5 0.4 1.900

2.000

2.100 2.200 Compression Ratio

2.300

2.400

Figure 18: Validation of ejector analytical model with experimental results of Eames et al. Hence, after validating the analytical model, it can be used for ejector performance prediction for various applications with confidence.

3.3- Validation EES Model of ERS To validate the EES model of ERS, two methods are used. Firstly, the results from EES model are compared with the developed EBSILON model. Secondly, the results from EES model are compared with the published results.

3.3.1 – Validation with EBSILON To compare the EBSILON and EES model of ERS, the EES model is run with the same operating conditions as used for EBSILON model shown in Figure 8. The results from both models are summarized in Table 3. Table 3: Comparison of EES and EBSILON models of ERS Calculated values Heat input Refrigeration effect Condenser load T_hotwater,out

Unit EES Model EBSILON Model Error (%) kW 132.15 132.09 0.045424 kW 90.83 90.8 0.033 kW 223.56 223.6 0.017889 ºC 102.2 102.55 0.341297

Pump power COP

kW -

0.735 0.6835

0.733 0.6837

0.272851 0.029253

As shown in the table, the results of EES model and EBSILON model are in very good agreement with each other with the difference of less than 1%. This means both EES model and EBSILON model validate each other and hence can be used to design and optimize ejector refrigeration systems of various sizes and under various working conditions. Both EES and EBSILON are powerful tools which their respective advantages and they can be used simultaneously to complement each other for detailed designing of systems.

3.3.2 – Validation with Published ERS Performance Data

The EES model of ERS has been validated with the published experimental performance of ERS. The Figure 19 below shows the comparison of simulated COP with experimental COP reported by Eames et al. [28]. The average difference of 3.4% indicates a good agreement and authenticates the EES model. ERS performance, T_evap=12ºC, R245fa, Error=3.4%

COP

0.6 0.5 0.4 Experiment

0.3

Simulation (EES)

0.2 2.100

2.200

2.300 2.400 2.500 Compression Ratio

2.600

2.700

Figure 19: Validation of EES model of ERS with experimental results reported by Eames et al. To further check the accuracy of the EES model, another set of experimental data reported by Shestopalov et al. [26] is used. Figure 20 shows the results with an error average error 2.4 % which indicates strong agreement. Validation of ERS model, R245fa, T_gen=95ºC, Error=2.4% 0.6 COP

0.5 0.4 0.3 0.2 0.1 1.700

Experiment Simulation 1.900

2.100 2.300 2.500 Compression Ratio

2.700

2.900

Figure 20: Validation of EES model of ERS with experimental results reported by Shestopalov et al.

3.4 – Design and Optimization of ERS with Validated EES Model The developed analytical model of ejector can now be used to find out the performance of ejector for various operating conditions. Figure 21 shows the on-design optimum performance curves of an ejector operating with R24fa as the working fluid. As shown, the ejector performance (entrainment ratio) increases rapidly for very low values of compression ratios and for higher values of compression ratios, the entrainment ratio does not vary much for different expansion ratios.

Ejector Entainment Ratio with R245fa

Entrainment Ratio (me/mg)

3.5 3

Pg/Pe= 6.25

2.5

Pg/Pe= 3.75

2

Pg/Pe= 12.5 Pg/Pe= 18.75

1.5 1 0.5 0 1.2

1.4

1.6 1.8 2 2.2 Compressoin Ratio (Pc/Pe)

2.4

2.6

Figure 21: Ejector performance curves for R245fa obtained from the validated analytical model The validated EES models of ejector and ERS can be used simultaneously to design and optimization of ERS for conversion of low-grade heat into cooling for various applications and locations. The quality (temperature) of available heat is a very important factor along with the ambient temperature as it defines the heat rejection (condenser) temperature. An ERS can be designed for various applications including refrigeration, air-conditioning, process cooling etc. The application dictates the evaporator temperature of ERS. Figure 22 shows the performance of an ERS with heating water (source) available at a temperature of 70ºC. The ambient (sink) temperature of 30ºC is used which corresponds to a tropical climate like Singapore where cooling demand for thermal comfort exists throughout the year. The ERS has been designed to have its evaporator at 15ºC. As shown, the generator pressure has a strong effect on output (refrigeration effect) and COP of the system.

9 8 7 6 5 4 3 2 1 0

0.5 0.4 0.3

Refrigeration Effect COP m_generator

0.2 0.1 0

3.5

4

4.5 5 Generator Pressure [bar]

5.5

COP / m_generator [kg/s]

Refrigeration Effect [kW]

ERS performace, Source=70ºC, Sink=30ºC, T_evap=15ºC

Figure 22: Variation of ERS performance for different generator pressures With the increase in generator pressure the mass flow rate of working fluid through the generator decreases. This is because for higher generator pressure, less heat is extracted from heating (source) stream and hence only smaller mass flow of working fluid can be heated to reach saturated vapour state. Less mass flow rate of working fluid from generator means less motive fluid for ejector, hence less entrained flow and refrigeration effect. On the other hand, the increase in generator pressure increases the inlet pressure of motive fluid of ejector which increases its entrainment ratio. More entrainment ratio means more mass flow rate of working fluid through the evaporator hence more refrigeration effect. Because of these two contradicting effects, there exists an optimum generator pressure where the refrigeration effect is maximum. For a generator pressure lower than the optimum pressure, the entrainment ratio too low and for a generator pressure higher than the optimum pressure, the mass flow through generator is too low. The COP of the cycle keeps increasing with generator pressure because of higher temperature heat addition to the cycle. It should be noted that the COP is not an important factor for most low-grade heat driven system and mostly for waste heat driven systems. As clear form Figure 22, for a higher generator pressure a higher COP can obtained but the system produces less output because of less heat extraction from heating stream. Hence for higher COP the system becomes more efficient but less effective. Figure 23 shows the ERS output for various heat source temperatures. For higher temperature of heat source, the optimum generator pressure shifts to the right of the graph. If the ERS is operating with a generator pressure somewhere near the optimum pressure, the performance of ERS does not vary a lot but as the generator pressure moves far away (on either side) from the optimum point, the performance decreases sharply.

Refrigeration Effect [kW]

ERS performace, Sink=30ºC, T_evap=15ºC, R245fa 60

source=60ºC source=70ºC source=80ºC source=90ºC source=100ºC

50 40 30 20 10 0 3

4

5 6 Generator Pressure [bar]

7

8

Figure 23: ERS output variation for different generator pressures for various heat source temperatures Figure 24 summarizes the optimum configurations of systems shown in Figure 23 with heat source temperature on the horizontal axis. It shows that with the increasing heat source temperature, while the optimum generator pressure increases almost linearly, the refrigeration effect increases exponentially.

7

70

Optimum Generator Pressure Refrigeratoin Effect

6

60

5

50

4

40

3

30

2

20

1

10

0

Refrigeration Effect [kW]

Optimum Generator Pressure [bar]

ERS optimum performance, Sink=30ºC, T_evap=15ºC, R245fa

0 55

65

75 85 95 Heat Source Temperature [ºC]

105

115

Figure 24: Optimum pressure and output of ERS for various heat source temperatures These values of optimum generator pressure for various heat source temperatures can be used as a quick reference while designing low-grade heat driven ERS. It can also be referred as a starting point for any experimental investigation.

3.4.1 – Effect of Evaporator and Sink Temperature The developed EES model has been used to study the effect of evaporator and sink temperate on the performance of ERS. The evaporator temperature is dictated by the requirement for which the ERS is designed. Figure 26 shows the effect of varying the evaporator temperature on the optimum generator pressure of ERS for various heat source temperatures and corresponding change in refrigeration effect is shown in Figure 26. Lower evaporator temperate requires higher generator pressure. With the increase in evaporator temperature, the ejector’s compression ratio decreases, and expansion ratio increases. The ejector entrainment ratio is more sensitive to the compression ratio as compared to expansion ratio as shown in Figure 21. Therefore, increasing the evaporator pressure, increases the entrainment ratio of ejector hence shifting the ERS optimum generator pressure to lower value and thereby increasing the refrigeration effect.

Optimum Generator Pressure [bar]

ERS performance, effect of T_evap, Sink=30ºC, R245fa 7.00 T_evaporator=20ºC

6.50

T_evaporator=15ºC

6.00

T_evaporator=10ºC

5.50 5.00 4.50 4.00 3.50 55

65

75 85 Heat Source Temperature [ºC]

95

105

Figure 25: Effect of evaporator temperature on the optimum generator pressure of ERS

Optimum Refrigeration Effect [kW]

As shown in Figure 26, the refrigeration effect increases significantly for higher evaporator temperature specially for higher source temperatures. Because of the lower optimum generator pressure, more heat is extracted form source stream thereby increasing the output of ERS. ERS performance, effect of T_evap, Sink=30ºC, R245fa 100 T_evaporator=20ºC 80

T_evaporator=15ºC

60

T_evaporator=10ºC

40 20 0 60

70 80 90 Heat Source Temperature [ºC]

100

Figure 26: Effect of evaporator temperature on the cooling produced by ERS for fixed sink temperature This is an important aspect for ERS applications. Because ERS output is a strong function of evaporator temperature, every effort should be made to design the system for higher evaporator temperature. For example, for air-conditioning, the latent and sensible loads should be segregated so that higher evaporator temperature could be exploited. Also, the system should be designed for higher temperature cooling technologies for example radiant cooling for thermal comfort. The effect of varying the sink temperature on the optimum generator pressure is shown in Figure 27 and its effect on the maximum refrigeration effect is shown in Figure 28.

Optimum Generator Pressure [bar]

ERS performance, effect of sink temp., T_evap=15ºC, R245fa 8.00 7.00 6.00 5.00 4.00 3.00

Sink=35ºC Sink=30ºC Sink=25ºC

2.00 1.00 0.00 50

60

70 80 90 Heat Source Temperature [ºC]

100

110

Figure 27: Effect of sink temperature on the optimum generator pressure of ERS

Optimum Refrigeration Effect [kW]

Increasing the sink temperature, increases the condensation temperate and pressure which increases the compression ratio for the ejector while the expansion ratio remains the same because of same evaporator temperature. Increasing the compression ratio decreases the entrainment ratio hence the ERS optimum generator pressure shifts to higher values. ERS performance, effect of sink temp., T_evap=15ºC, R245fa 120 Sink=35ºC

100

Sink=30ºC

80

Sink=25ºC

60 40 20 0 60

70 80 90 Heat Source Temperature [ºC]

100

Figure 28: Effect of sink temperature on cooling produced by ERS for fixed evaporator temperature As shown in Figure 28, decreasing the sink temperature increases the refrigeration effect significantly specially for higher source temperatures due to lower values of optimum generator pressure. It is clear from the figure that for 10ºC change in sink (or condenser) temperature, the change in output is about 250% which is much more than that for 10ºC change in evaporator temperature which is about 115%. Therefore, the output of ERS is much more sensitive for condenser temperature than evaporator temperature. The reason is that the condenser temperature change alters the compression ration without any effect on expansion ratio as discussed earlier.

The sink temperature is defined by ambient conditions and for most of cases cannot be manipulated. However, if there is possibility to use a nearby river or sea water as heat sink with lower temperature, it must be considered. Ground source heat sinks can also be explored for some applications. These results also suggest preferring the use of water-cooled condensers rather than air-cooled ones.

3.5 - Case Study: Utilizing ERS in a Multi-Utility Facility To utilize the developed model for designing an ERS, a case study has been considered. This case study evaluates the applicability of ERS for harnessing low-grade heat from a multiutility facility (Sembcorp) situated in tropical climate (Singapore). The schematic of the available waste heat stream and the currently employed system is given in Figure 29.

Figure 29: Schematic and working condition of the case study (Sembcorp utilities facility) [49] [50] The facility runs a demineralized (DM) water plant which receives steam condensate returning at a temperature range of 105-110C. The DM water is supplied to User 1 and User 2 as shown in the figure. In the present situation, the heat of steam condensate being utilized to heat the demineralized (DM) water from 35-40C to 70-75C for User 1. There is no need to heat DM water for user 2. The flow rates of condensate and DM water users vary for different cases as shown in the figure. Mainly, there are two cases with different requirements for user 1 and 2. As indicated in the diagram, the temperature of the hot steam condensate to the DM plant should not exceed the design temperature of 40C and the temperature of the hot DM water supply to User 1 should be maintained between 70-75C. To meet the requirements of demineralization plant, the facility needs to use sea water to cool down the condensate. If the heat of condensate is utilized in a low-grade heat driven ERS, dual benefit may be obtained. Firstly, free cooling is produced by ERS and secondly, the cooling water requirement is reduced. To always meet the requirements of user 1 and 2, an ERS system is being proposed and designed for case 2 which has more stringent requirement due to higher flow rate of higher temperature stream (user 1). The schematic of the proposed modification in the system is shown in Figure 30. As shown, more stringent

requirements of the temperature ranges are considered so that the normal operation of system is always uninterrupted with the proposed modification. Because the user 2 requires the temperature of 75C, it is proposed to exploit the temperature range of 75-105C by using an ERS.

Figure 30: Schematic of the proposed modification in the facility to utilize heat driven ERS Considering the heat exchanger shown in Figure 30, an approach temperature of 5C allows 40C temperature for condensate outlet. By applying the energy balance on the heat exchanger, the minimum value of temperature of condensate inlet to heat exchanger (x) can be found as mDMW Cp (75 ― 35) = mcondensate Cp (x ― 40) => 320 (40) = 275 (x ― 40) => x = 86.5 ℃ Therefore, the generator of ERS can be designed to allow minimum 86.5C temperature for condensate exiting from it. Figure 31 shows the performance of ERS obtained from the presented EES model for the available working conditions of the case study.

Figure 31: ERS performance variation with generator pressure for working conditions of case study, The figure (a) shows the variation of refrigeration effect, COP and the temperature of heating water exiting the ERS system (T_hotwater,out) with the variation of generator pressure. As clear for the figure, the ERS system produces maximum refrigeration (2.36 MW) at the generator pressure of 7.52 bar. At 7.52 bar generator pressure, T_hotwater,out is 71.9C which is lower than 86.5C needed to fulfil the requirements of user1. Therefore, for this case, the ERS system should not be designed for maximum refrigeration output. To design the ERS which fulfills the system constraint of minimum value of 86.5C for the condensate exiting the generator of ERS, shown in the figure by red dotted lines, the system operates at the generator pressure of 10.1 bar to give T_hotwater,out value of 86.5 C. Hence, the system operates at 0.3 COP and generates 1.8 MW of cooling as indicated in the figure.

Figure 32: P-h diagram of final operating condition of the designed ERS for the case study. Figure 32 shows the P-h diagram of ERS system designed for the case study. The system states are mentioned are with same notation as described in Figure 7. The ejector is compressing vapour of R245fa from evaporator pressure (P5) of 0.82 bar to condenser pressure (P6) of 2.18 bar by consuming the motive or generator pressure (P3) of 10.1 bar. The 1.8 MW of refrigeration means that the ERS can provide 512 RT of free cooling throughout the year without disturbing the overall operation of the utility facility. If a water-cooled electrical chiller is used to provide 512 RT of cooling, it would need 300 kWe of electricity assuming it has a COP of 6 [51] [52]. Therefore, assuming a price of 0.16 S$/kWh for electricity in Singapore for industrial consumers [53] [54], the designed ERS provides annual savings of 0.42 million S$/year. The presented model can be used for designing ERS for various industries, locations and working conditions. Due to the robust nature and relatively low-cost of ERS technology, it is a strong candidate for adoption by industries in near future for moving towards efficiency and sustainability.

4- Conclusion This paper presents theoretical modelling of ERS which can be used for designing and optimization of ERS for various working conditions and applications. Thermodynamic models of ejector and ERS has been developed in Engineering Equation Solver (EES) which enables utilizing the built-in real data of working fluids. The models have been validated against published experimental results. A systematic approach is

presented to find the optimum operating conditions of ERS for available heat source with any temperature and flow rate. A case study is also presented where an ERS is designed for a multiutility facility in a tropical climate. A new analytical model for predicting the optimum (on-design) performance (entrainment ratio) of ejectors is presented and has been used in ERS system simulations. This ejector model does not employ any iterative process and directly calculates the entrainment ratio of ejector for available working conditions. This model uses real thermodynamic properties of working fluid in combination with supersonic gas flow equations for calculations. The proposed analytical model uses CFD results to find ejector efficiencies rather than employing hit and trial method to match experimental results. Hereby, CFD modelling has been employed to optimize the geometry of ejector which gives the optimum performance (ER) of ejector and this optimized CFD result is used to find suitable values of ejector efficiencies for analytical model. Once the suitable values of ejector efficiencies are known, the analytical model does not need to use CFD anymore and it can quickly simulate the on-design ejector performance for any operating conditions. The presented analytical model of ejector is validated against published experimental and analytical data and a good agreement is established. The presented ERS model is validated against published experimental data and with another model developed in EBSILON which is a commercial tool. Two sets of published experimental results are used for validation and a good agreement is found with an average error of 2.9%. The validated model is used to design and optimize ERS for very low-grade heat (60-100ºC) utilization for various sink and cooling temperatures. The ERS has been optimized to give maximum output rather than COP by selecting the unique generator pressure which gives the maximum refrigeration effect. It is found that the ERS output is much more sensitive to condenser temperature as compared to evaporator temperature. For a 10ºC decrease in condenser temperature, the output of ERS increased by 250% while for a 10ºC increase in evaporator temperature the output of ERS increased by 115%. In the presented case study for the designing of an ERS, it is shown that designed ERS produces 1.8 MW of cooling by converting the available waste heat with estimated annual savings of 0.42 million S$.

5- Appendix (A) Figure 33 Shows the meshing for different element sizes used in the mesh independence study. With the refinement of element size, the number of elements increases significantly which increases the computational time. Aa rule of thumb from many ejector CFD simulations, for ejectors operating with motive pressure of 4-10 bars, and in the range of cooling capacity of 0.5-10 kW, a suitable mesh element size lies in the range of 0.05-0.15 while running on axisymmetric model. A good agreement presented in the validation section of 3.1, indicates that the mesh element size and other CFD settings have been correctly selected.

Figure 33: Mesh element sizes for the mesh independence study

(B) Figure 34 shows the comparison of k-epsilon and k-omega models in FLUENT for optimized ejector design. As discussed in section 2.2.1, the k-epsilon model gives 4.2% higher values of entrainment ratio. Because the k-epsilon model is in very good agreement with the experimental results as discussed in section 3.1, in this paper, k-epsilon method has been adopted. 0.25

0.235

0.225

Entrainment Ratio

0.2 0.15 0.1 0.05 0 Realizable k-epsilon

SST k-omega

Figure 34: Comparison of k-epsilon and k-omega models in FLUENT for optimized ejector design Figure 35 shows the comparison of k-epsilon and k-omega models in terms of pressure variation at the axis of the ejector. The k-omega model is not able to capture the compression shock in a realistic way which the k-epsilon model is able to capture the shock wave in a conventional way as reported in many other researchers as well. Also, k-epsilon model profile is in line with the assumptions of the analytical model

where it is assumed that the compression shock happens instantaneously, and the pressure is suddenly increased when the velocity of the mixed fluid dips from supersonic speed to subsonic speed.

Figure 35: Pressure variation at the centerline (axis) of the ejector

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Available:

author statement

Fahid Riaz: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing-Original Draft, Writing-Review and Editing, Project Administration, Funding Acquisition

Poh Seng Lee: Supervision, Reviewing, Funding Acquisition, Resources

Siaw Kiang Chou: Supervision, Reviewing, Funding Acquisition, Resources

Highlights  An analytical model for on-design optimum performance of ejector is presented  Using CFD, this direct analytical model employs a scientific approach to find ejector efficiencies  The ejector and ERS models have been developed in EES and validated with experimental data  Validated models are used to optimize ERS performance based on operating conditions  Detailed parametric analysis and a case study has been presented