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Modelling of scroll expander for different working fluids for low capacity power generation
Applied Thermal Engineering 159 (2019) 113932
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Modelling of scroll expander for different working fluids for low capacity power generation
T
⁎
J. Muyea, G. Praveen Kumarb, J.C. Brunoa, R. Saravananb, , A. Coronasa a b
Universitat Rovira i Virgili, Department of Mechanical Engineering, CREVER, Avda Països Catalans 26, 43007 Tarragona, Spain Anna University, College of Engineering, Department of Mechanical Engineering, Guindy, Chennai, Tamil Nadu 600 025, India
H I GH L IG H T S
characterization of a scroll expander using R-134a and Ammonia. • Experimental of a general semi empirical model of a scroll expander for several fluids. • Development of the model generalization procedure performed with experimental data. • Validation model accurately predicts mass flow rate, shaft power and exhaust temperature. • The • This model can save time and material resources in experimental procedures.
A R T I C LE I N FO
A B S T R A C T
Keywords: Scroll expander Working fluid Modelling Leakage loss Mechanical loss
This paper presents the experimental investigation and development of a general semi empirical scroll expander model for different working fluids. Initially, the characterization and modelling of a scroll expander with R134a working fluid is performed. The influence of key operating variables on the main performance indicators such as isentropic efficiency, filling factor and specific power are investigated. The proposed semi empirical model for the scroll expander predicts mass flow rate, mechanical shaft power and exhaust temperature at accuracies of 3%, 9% and 2 K respectively. The developed semi empirical model is then modified to accommodate different working fluids; validation of the generalization procedure is performed with experimental data using ammonia/ water mixture and ammonia as working fluids. The generalized semi-empirical model predicts mass flow rate, mechanical shaft power and exhaust temperature to be less than 5%, 7% and 4 K error margin for both ammonia/water and pure ammonia working fluids. Therefore, the simulation model presented in this study can save the time and material resources for the selected scroll expander solely as a consequence of a change in the working fluid to predict the main performance indicators.
1. Introduction The world today is mostly dependent on fossil fuel for power generation. This dependency on fossil fuel is leading the world into a multifaceted crisis comprising the insecurity of supplies, environment impact and also the fluctuation of fuel price. In order to tackle this crisis, scientists are shifting their interest on new energy sources like biomass resources, solar, tidal and geothermal energies. Cost efficient power generation from low temperature heat sources requires an optimal usage of the available heat achieved through employing economical technologies [1–2]. The overall cost and thermodynamic performance of any low grade heat transforming system strongly correlates with that of its unitary
⁎
components, especially the expander. The selection of the expander is usually related to the size and the design of the system. Two main types of expanders can be distinguished: the dynamic (velocity/kinetic/ turbo) type, such as axial turbine expander, and positive displacement (volume) type, such as screw expander and scroll expanders [3–4]. Various reviews on expanders [5–6] have highlighted that the volumetric expanders are preferred for small capacity (up to 50 kW) low grade heat conversion applications. Since the scroll machine technology has become more and more matured in the residential and commercial markets (for air conditioning and refrigeration) it is therefore not surprising that currently, the majority of scroll expanders integrated into the low-grade energy utilization systems are mostly modified from refrigerant scroll compressors. This practice ensures that the expander
Corresponding author. E-mail address: [email protected] (R. Saravanan).
https://doi.org/10.1016/j.applthermaleng.2019.113932 Received 19 December 2018; Received in revised form 3 April 2019; Accepted 6 June 2019 Available online 06 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 159 (2019) 113932
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π ρ τ φ
Nomenclature Variables
A AU Cp D h K L ṁ N Nu P Pr Q̇ R Re T u U v̇ V V̇ w Ẇ X
area, m2 heat transfer coefficient, W K−1 specific heat at constant pressure, J kg−1 K−1 hydraulic diameter, m specific enthalpy, J kg−1 friction coefficient length, m mass flow rate, kg s−1 rotational speed, Hz Nusselt number pressure, Pa Prandtl number heat transfer rate, W ratio Reynolds number temperature, K velocity, m s−1 thermal transmittance, W m−2 K−1 specific volume, m3 kg−1 volume, m3 volumetric flow rate, m3/s specific power, J kg−1 power, W Concentration of ammonia in the ammonia/water mixture
Subscripts
amb calc com coul esp ex exp global hydro in int is leak loss max meas min nom p shaft shell su sw total v visc
Greek symbols
u Δ Σ η λ μ
3.1416 density, kg m−3 torque, N m filling factor
velocity, m s−1 change of value Summation Efficiency thermal conductivity, W m−1 K−1 dynamic viscosity, Pa s
ambient calculated compressor couloumb specific exhaust expander Overall hydrodynamic into internal isentropic leakage power loss maximum measured minimum nominal isobaric, pressure prime mover cover, wall supply swept summed up volumetric viscous
Acronym ORC
Organic Rankine Cycle
small capacity low-grade energy utilization systems. Lemort et al. [11] proposes an eight parameter semi-empirical simulation model of a scroll expander using R123 as working fluid. The losses considered by the model include: supply pressure drop loss, exhaust and ambient heat transfer losses, internal leakage loss, friction and expansion losses. The model, with its parameters identified, can predict the mass flow rate, the shaft power and the exhaust temperature with an accuracy of 2%, 5% and 3 K respectively. Because of its accuracy, low computational time, robustness and ease of integration into a thermodynamic cycle simulation, several researchers have studied the eight parameter semiempirical model for different working fluids (Water [12], Air [12], R245fa [3,13,14,15], R134a [14] and Solkatherm SES36 [15]). In the theoretical study of the performance of an Organic Rankine Cycle (ORC) at part load operation with R245fa and Solkatherm SES36 working fluids, Ibarra et al. [16] adopted a simplified four parameter semi empirical model. The simplification is a result of neglecting the supply pressure drop loss and the three thermal losses. Since the study is theoretical, the prediction accuracy of the models is not provided. Later, Mendoza et al. [17] also implements the simplified four parameter semi-empirical model for their experimental study of an open drive scroll expander with ammonia working fluid. Using this semiempirical model, the deviations in the calculated mechanical power, exhaust temperature and supply mass flow rate are ± 9%, ± 4 K and ± 5% respectively. The non-deterministic nature of the semi-empirical model ensures that the model is intrinsic to the particular expander and the working fluid that was used for calibrating and testing.
costs are kept low and thus contributing favourably to the overall cost effectiveness of the low grade energy conversion system. Many researchers have extensively reported experimental and numerical results on the scroll expander performance for various organic working fluids. In 1988, Yanagisawa et al. [7] carried out a performance test on a scroll expander that modified from off-the-shelf automotive scroll compressor. The adiabatic efficiency of the scroll expander reached up to 60–75% for the corresponding shaft speed of 1000–4000 rpm. Zanelli and Favrat [8] carried out an experimental study on hermetic scroll expander-generator modified from standard hermetic compressor fed with refrigerant R134a. The peak overall isentropic efficiencies are reported in the range of 63% to 65% for varying shaft rotation between 2400 and 3600 rpm. Eric et al. [9] proposed a simplified four-parameter model is proposed to predict the scroll compressor discharge temperature and mass flow rate of working fluid. In addition, driven electric power of compressor the predicted by using three-parameter model such as built in volume ratio, constant power loss and a power coefficient. Giuffrida [10] reports that up until recently, technical papers dealing with small-size power production systems did not always consider a specific modelling for the expander. In such theoretical works, the expander efficiency was taken constant in spite of variable operating conditions, such as fluid pressure and temperature at the inlet of the machine, expansion pressure ratio, type of working fluid and speed of rotation. Recent literature reports on scroll expanders nonetheless suggests that scientists have been developing and using thermodynamic models to simulate expander performance in 2
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To address the working fluid constraint resulting from rigidity of the model, Giuffrida [10] starts from the original eight parameter R123 scroll expander model [11] developed by Lemort et al. and outlines a thermodynamically realistic procedure to generalize the model to simulate the expander performance with fluids other than R123. Because of the theoretical nature of the study and a lack of experimental data, Giuffrida [10] was only able to perform a preliminarily verification of the generalization procedure against the results of previous experimental studies from the literature with the expander efficiency as the single mean of comparison. Clearly, this verification technique could not offer a qualitative validation of the proposed model generalization approach. The current investigation is performed with the aim of: (1) to study the influence of four independent input parameters on the behavior of an open drive scroll expander with R134a working fluid; (2) to propose a six parameter semi empirical model for the scroll expander operating with R134a; (3) present an improved expander model generalization approach for the six parameter model to facilitate adaptability to any working fluid and (4) to use experimental data obtained presently in this research work and also from the literature ([17;18]) to validate the generalised six parameter model with ammonia and ammonia/water working fluids. Eventually, the findings from this investigation will be very helpful in the study and design of low grade energy utilization systems such as ORCs and combined absorption power and cooling cycles [19] where researchers will not be forced to develop new semi empirical models for every time a switch in working fluid is required. The logic behind the selection of the working fluids employed in this study (R134a, ammonia and ammonia/water) is to ensure that the developed model captures a broad assortment of working fluids classifications: natural vs organic, dry vs wet etc. Furthermore, the selected working fluids cover a wide range of application systems especially when the absorption technology is also extended to R134a [20]. Engineering Equation Solver [21] software is used to simulate the behavior of the working fluids. Thermodynamic properties for R134a and ammonia are retrieved from the internal thermo-physical data base of the software while those for the ammonia/water mixture are sourced from the external routines database. The paper is structured as follows. In Section 1 (current section) the background and justification of the work performed with their objectives was explained. In Section 2 the characteristics of the experimental setup are described. This setup is used to measure the performance of an expander using R-134a (Section 3). A modified 6-parameter
empirical model is presented in Section 4 to model this expander with R-134a. In Section 5 a methodology is proposed to extend the model to other working fluids that is validated in Section 6 for ammonia and ammonia/water working fluids. The main findings are summarized as conclusions.
2. Experimental methods 2.1. Test bench description For this study, the expander test bench developed by Mendoza et al. [17], has been utilized with slight modifications in instrumentation and complete removal of the lubrication network as shown in Fig. 1. The test rig comprises of a diaphragm pump (Wanner Hydra-Cell), three plate heat exchangers (Alfa Laval), two 17 L steel vessels, the scroll device (Sanden, TRSA05) and an electrical brake. Working fluid from the expander (stream 7) is condensed by the chiller (stream 1) then fed to a liquid reservoir (stream 2) before being sub-cooled by the glycol based chiller (stream 3) and eventually pumped (stream 4) to the evaporator. From the evaporator (stream 5), the working fluid goes through a vapor tank (stream 6) and then straight to the scroll expander for power generation. The temperature of the working fluid at the inlet of the expander is controlled by the external boiler. Pressure at the expander inlet is provided by the pump whereas the condenser temperature sets the pressure at the exit of the expander. The electrical brake connected to the expander is used to control its rotational speed. A pulley and belt mechanism provides coupling of the electrical brake to the expander at a ratio of 1:3.08. It is true that this is transmission could provide a lower efficiency than a direct shaft connection but is a solution implemented in many open-drive automotive A/C compressors adapted as expanders [5]. Both the pump and the electrical brake are manually controlled by frequency drives. The vapor tank is fitted with a pressure relief valve which is activated at 2500 kPa and the hot water from the boiler is limited to temperatures below 403 K. Ambient temperature limits the water based chiller (condenser temperature) whereas the glycol based chiller (sub-cooler temperature) is limited to temperatures above 277 K as per pump specifications [22]. Steel piping was used to ensure compatibility with both ammonia/water and R134a working fluids.
Fig. 1. Schematic diagram of the scroll expander test bench. 3
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2.2. Measuring devices
3.2. Influence of supply temperature and pressure
Temperatures and pressures in the test rig are measured by resistance thermometers (in 4 wire configuration) and piezo-resistive (silicon) transducers, respectively. A Coriolis flow meter provides the density and mass flow rate of the working fluid while the rotational frequency and torque are measured by an integrated torque and speed transducer fitted on the shaft of the electrical brake. A data acquisition unit from Agilent technologies (34970A) is used for logging all the measured data. Table 1 shows the main characteristics of transducers in the test rig.
Dincer et al. [27] highlight that friction and leakage losses contribute the highest portion of irreversibilities in a scroll expander. The effect of these two losses is especially predominant when pressure ratio remains constant. The filling factor (Eq. (4)) can be redefined as:
φexp = 1 +
ṁ leak ṁ in
(5)
Therefore, a filling factor closer to unity implies low leakage losses and consequently suggests a desirable volumetric performance. However, the isentropic efficiency provides a measure for all the losses. Isentropic efficiency and filling factor exhibit no sensitivity to the supply temperature, they remain constant at 0.4 and 1.7 respectively. This suggests that both frictional and leakage irreversibilities remain constant when the supply temperature is varied. Conversely, a 19 K increase in the supply temperature leads to a 0.7 kJ/kg increase in specific power as a result of the increased enthalpy. The effect of supply pressure on the expander performance was found to be negligible. According to Lemort and Legros [28], leakages are due to the pressure gradients that are applied across leakage paths resulting from clearances between moving elements and friction losses result from the axial force that tends to separate the two scrolls. Therefore, a constant pressure ratio ensures that the proportion of these two losses remain virtually unchanged even under varying supply temperature and pressure conditions.
2.3. Scroll expander The Sanden, model TRSA05 open-drive scroll compressor (normally used in automotive refrigeration systems) was modified and operated in expander mode. According to the manufacturer, the volumetric displacement per revolution of the scroll device in compressor mode is 53.9 cm3, and it can withstand a maximum of 3500 kPa and 166 Hz of pressure and rotational speed respectively [23]. The built-in volume ratio is 1.9, calculated by measuring the cross section area at the suction and exhaust chambers [17]. This is a low pressure expander device according to the classification based on built-in volume ratio: low (< 2), medium (2-3) and high built-in volume ratio expanders (> 3) [24]. 3. Characterisation of the scroll expander with R134a
3.3. Influence of pressure ratio and rotational speed
Since the expander was adopted from a scroll compressor, performance and eventual characterization of such an expander can only be determined experimentally. Four independent input variables (supply pressure and temperature, pressure ratio and rotational speed) were identified and the effect they have on the expander performance (mechanical shaft power, global isentropic efficiency and filling factor) was investigated to facilitate an in-depth understanding of the expander behavior at different operating conditions with R134a working fluid. The experiments were carried out at: Tsu = 355–378 K; Psu = 850–1450 kPa; Rp = 1.3–1.8 and Nexp = 13–32 Hz.
Fig. 2 highlights the influence of varying pressure ratios on the scroll expander performance. An increase in both isentropic efficiency and filling factor is observed with an increase in pressure ratio. It is an indication that the volumetric performance of the device declines with increasing pressure ratio because as predicted by Lemort et al. [26] increasing the pressure gradient also increases leakage. As expected a clear improvement in specific power is observed with increasing pressure ratio. Therefore, the increasing isentropic efficiency suggests that when increasing the pressure ratio, the specific power increases at a faster rate than leakage and friction losses. On the contrary, a decrease in both the isentropic efficiency and filling factor is observed with an increase in the expander rotational speed as illustrated in Fig. 3. Similarly, increasing the expander rotational speed reduces the specific power. At lower rotational speeds, the filling factor is high, consequently the working chamber is overfilled by the working fluid and leakage occurs, thus the rotational speed improves the volumetric performance of the scroll expander [15]. However, increasing the rotational speed leads to increasing frictional losses on account of the increasing axial force which translates to the gradual reductions in isentropic efficiency and specific power. Fig. 4 shows the influence of pressure ratio and rotational speed on mechanical power loss and leakage loss of the TRSA05 scroll expander. It reveals that performance of scroll expander strongly depends on pressure ratio and rotational speed, since friction and leakage losses contribute highest portion of irreversibility.
3.1. Performance indices The three performance parameters of interest in the characterisation of the scroll device are the specific power, isentropic efficiency and filling factor. Specific power is the measured output power divided by the measured mass flow rate:
wesp =
Ẇshaft , meas ṁ su, meas
(1)
where
Ẇshaft , meas = 2π × τexp, meas × Nexp, meas
(2)
The global isentropic efficiency of the scroll expander can be defined as the ratio of the measured output power divided by the isentropic expansion power [25]:
ηis, global =
Table 1 Measuring ranges and uncertainties of the transducers in the test rig.
Ẇshaft , meas ṁ su, meas (hsu − hex , is )
(3)
The filling factor can be used to express the volumetric performance of the scroll machinery, it is the ratio of the measured mass flowrate and the mass flowrate theoretically displaced by the expander [26]:
φexp = ṁ su, meas
̇ Vsu ̇ , exp Vsw
(4) 4
Variable
Range
Uncertainty
Pressure Temperature Mass flow Density Torque Rotational speed
0 … 2500 kPa −33 … 573 K Max. 330 kg/h Max. 5000 kg/m3 0.1 … 50 N m 1 … 166 Hz
± 5 kPa ± 0.5 K ± 0.10% ± 0.2 kg/m3 < ± 0.075 N m ± 0.017 Hz
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Fig. 3. Effect of varying rotational speed on the (a) filling factor, (b) global isentropic efficiency and (c) specific power of the scroll expander.
Fig. 2. Effect of varying pressure ratio on the (a) filling factor, (b) global isentropic efficiency and (c) specific power of the scroll expander.
exhaust temperature, but do not significantly alter the calculation of mass flow rate and mechanical power [28]. The scroll device being studied in this investigation is not insulated, therefore the expander shell exchanges heat with the environment and should not be assumed as adiabatic. Therefore, in addition to including exhaust heat transfer, the proposed six-parameter semi empirical model shown in Fig. 5 also acknowledges ambient heat transfer. The flow of working fluid from the expander supply to exhaust can be theoretically simplified by the following processes:
4. Scroll expander semi empirical model for R134a working fluid 4.1. Model description The semi-empirical scroll expander simulation model proposed by Lemort et al. [11] required eight parameters to predict three outputs. To reduce the computational time and improve the robustness of the model some authors [15,16] have suggested a four parameter model which neglects irreversibilities caused by supply pressure drop and thermal losses. Thermal losses mostly influence prediction the fluid
• Isobaric heat exchange between the imaginary shell and the inlet 5
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Fig. 4. Influence of (a) Pressure ratio and (b) rotational speed on leakage area and mechanical power loss.
fluid stream and an imagined expander shell (su to su1)
fluid stream (su → su1)
• Isentropic internal leakage of the working fluid (su1 → leak) • Isentropic expansion of the working fluid to the device internal pressure (in → int) • Isochoric adaptation of the working fluid to the external pressure (int → ex ) • Isobaric adiabatic mixing of the leaked and the expanded working fluid streams (ex → ex ) • Isobaric heat exchange between the imaginary shell and the exhaust
̇ = ṁ su (hsu − h su1) = {1 − exp−AUsu / ṁ su Cp } ṁ su Cp (Tsu − Tshell ) Qex
The working fluid stream supplied to expander (ṁ su1) is split into two: a work producing stream (ṁ in ) and a non-work producing stream (ṁ leak ) which leaks between the scrolls.
2
2
(6)
ṁ in + ṁ leak = ṁ su1
1
(7)
The leaked mass flow is directly proportional to a theoretical leakage area (Aleak) as shown in Eq. (8) [17]. The leakage area comprises of all leakage routes aggregated into one imaginary leakage path linking the expander inlet and outlet ports.
fluid stream (ex1 → ex)
Detailed thermodynamic description of the processes can be found in refs. [3], [10], [11], [12], [15] and [17]. The process descriptions provided here will only highlight the salient expressions. To begin, a constant pressure heat exchange takes place between the
ṁ leak = ρleak Aleak 2(hsu − hleak )
(8)
The work producing stream is then expanded in a two stage process: the 6
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Fig. 5. Process diagram for the proposed semi-empirical scroll expander model.
first being isentropic (from in to int) then followed by an isochoric process (int to ex2 ). Internal pressure (Pint) is a limitation of the built in volume ratio (Rv).
̇ = ṁ in {(hin − hint ) + vint (Pint − Pex2)} Wexp
The four empirical parameters are determined using 45 steady state points. As hinted by Figs. 2 and 3 in Section 3.3, the leakage area and mechanical power loss are found to have strong correlations with pressure ratio and rotational speed. Correlations proposed to simulate leakage area and mechanical work loss are shown in Table 2. These correlations are fitted with experimental data to a linear model and achieve coefficients of determination of 90% and 93% respectively.
(9)
Reducing the total expander power produced (Eq. (9)) by all the mechanical power losses yields the shaft power available for use. Sources of mechanical power loss include friction in scrolls, bearings, transmission pulley and hydrodynamic effects.
̇ − Ẇloss, total Ẇshaft = Wexp
(10)
After the two stage expansion and eventually a power reduction processes, adiabatic mixing of the two streams (ṁ leak andṁ in ) occurs atex1.
ṁ leak hleak + ṁ in h ex2 = ṁ su h ex1
(11)
(12)
The overall exhaust heat conductance AUex is a function of mass flow based on the Reynolds analogy of turbulent pipe flow [10,11]:
AUex = AUex , nom (ṁ su / ṁ su, nom )0.8
(13)
where the nominal exhaust heat conductance AUex , nom is an empirical parameter and ṁ su, nom is a fixed nominal mass flow. Since the expander is not insulated, it is important to simulate the heat exchange between the fictitious expander shell and ambient.
̇ Qamb = AUamb (Tshell − Tamb)
(16)
Ẇloss, total = −3.19 × 10−1 + 8.83 × 10−3 (Nexp) + 1.38 × 10−1 (Rp)
(17)
At higher filling factors (meaning lower rotational speeds, Fig. 3(a)), the leakages become predominant because the working chamber is overfilled and the working fluid has the time to leak [11]; thus the leakage area decreased with increase in speed. A slight increase of the filling factor with supply pressure or pressure ratio increases internal leakages [29]. The effect of the pressure in leakage area is also taken into account in the calculation of the leakage area by other authors [30]. According to Lemort and Legros [28], leakages are due to the pressure gradients that are applied across leakage paths resulting from clearances between moving elements and friction losses result from the axial force that tends to separate the two scrolls. Therefore, a constant pressure ratio ensures that the proportion of these two losses remain virtually unchanged even under varying supply temperature and pressure conditions. The two heat conductance parameters are evaluated by minimizing a global deviation function that accounts for deviations between the
Finally, a constant pressure heat exchange takes place between the fluid stream and an imagined expander shell (ex1 to ex) [11].
̇ = ṁ su (hex − h ex1) = {1 − exp−AUex / ṁ su Cp } ṁ su Cp (Tshell − Tex1) Qex
Aleak = 5.36 × 10−6 − 7.18 × 10−8 (Nexp) + 2.48 × 10−7 (Rp)
(14)
The mechanical power loss is assumed to be completely dissipated in the expander shell, thus performing a steady state energy balance across the shell results to:
̇ ̇ − Qsu ̇ Ẇloss, total = Qamb + Qex
(15)
4.2. Parameter identification A block schematic of the six parameter semi-empirical model is illustrated in Fig. 6. It shows that the model requires six parameters and four independent variables (Psu, Tsu, Pex , Nexp ) to predict three output variables (Ẇshaft , ṁ su , Tex ). The six semi-empirical model parameters can be obtained in three ways: (1) from manufacture’s data (Vsw, com ); (2) from geometrical measurements (Rv ) and (3) experimental tests ( AUex , nom , AUamb , Aleak , Ẇloss, total ).
Fig. 6. Six parameter semi-empirical model block schematic. 7
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Table 2 The six model parameters for the scroll expander with R134a. Parameter
Value
Nominal exhaust heat conductance, UAex , nom (kW/K) Overall ambient heat conductance, UAamb (kW/K) Swept volume in compressor mode, Vsw, com (cm3) Built-in volume ratio, Rv (-) Leakage area, Aleak (m2)
0.06482 0.00469 53.9 1.9
5.36 × 10−6 − 7.18 × 10−8 (Nexp) + 2.48 × 10−7 (Rp)
Power loss, Ẇ loss, total (kW)
− 3.19 × 10−1 + 8.83 × 10−3 (Nexp) + 1.38 × 10−1 (Rp)
measured and calculated values of the three output variables (mass flow rate, mechanical shaft power and discharge temperature) [9,26,29 ]. To determine exhaust heat conductance, a nominal mass flow rate value of 0.07 kg/s was used. Equal weights are assigned to all the variables as shown in Eq. (18):
employing a different approach in the simulation of internal leakage and friction irreversibilities to accommodate the fluid alteration. Furthermore, this study presents a comprehensive validation of the generalized semi-empirical model with ammonia and ammonia/water working fluids. The assumptions used to extend the six-parameter semi-empirical scroll expander model to different fluids are the following: Parameters Vsw,com and Rv define the built in volumes of the suction and discharge chambers of the scroll machinery; they are fixed and are not altered when the working fluid is changed. On the other hand, the leakage area parameter is solely dependent of the operating conditions (Rp and Nexp) imposed on the scroll device as shown in correlation given in Table 2. Thus a fluid switch is not expected to modify Aleak. The overall ambient heat conductance (AUamb) is also independent of the working fluid since it simulates heat exchange between the scroll expander shell and the ambient. The same is not true for nominal exhaust heat conductance (AUex,nom) because it predicts heat transfer between the working fluid and expander casing. Finally, the friction losses which are represented by the work loss function (Table 2) are reliant on both the operating conditions (Rp and Nexp) and working fluid imposed on the scroll expander as discussed in Section 5.3.
Deviation = 1/3
/3
/3
⎧ ⎨ ⎩
⎧ ⎨ ⎩ ⎧ ⎨ ⎩
n
ṁ su − ṁ su, meas ⎞2 ⎫ +1 ṁ su ⎝ ⎠ ⎬ ⎭
∑⎛ ⎜
1 n
⎟
2 Ẇshaft − Ẇshaft , meas ⎞ ⎫ +1 ⎟ Ẇshaft ⎝ ⎠ ⎬ ⎭
∑ ⎛⎜ 1 n
2
Tex − Tex , meas ⎞⎟ ⎫ − T ex , meas _ max ex . meas _ min ⎝ ⎠ ⎬ ⎭
∑ ⎛T ⎜
1
(18)
Table 2 summarizes the six parameters of the semi-empirical model for Sanden TRSA05 scroll expander with R134a working fluid. 4.3. Semi-empirical scroll expander model validation A total of 100 steady state points are used to check the validity of the semi-empirical model, this includes the 45 points which were used to tune the model. The 55 extra states guarantee the model for noncalibrated points. Fig. 7 displays a graphical collation of the measured and calculated values of the three output variables: displaced mass flow, mechanical shaft power and exhaust temperature. Absolute disparities of 3%, 9% and 2 K are found between measured and calculated values of mass flow, mechanical shaft power and exhaust temperature respectively. The instrumentation availability and limited power values makes the absolute disparities of 9% in mechanical shaft power prediction. However, the achieved accuracies compare well with those reported in other studies using semi-empirical models as shown in Table 3.
5.1. Leakage area The Sanden TRSA05 scroll device is designed to be operated with lubrication. Introducing a substantial amount of lubrication oil into a scroll device enhances the internal sealing and improves its volumetric performance [34–35]. The main drawback of most volumetric expanders is the need for lubrication even though it has been demonstrated that oil free expanders are technically feasible [36] with marginally low performance. The oil effect in scroll expander modelling aspects is quite complex [37]. Due to some technical difficulties experienced with R134a (oil foaming and obsolete oil separator) and ammonia/water (water retention in oil separator and melting of oil pump discharge valve) working fluids, the authors were compelled to operate the expander oil-free. The data compiled by Mendoza et al. [17] for pure ammonia characterizes the same scroll expander at a lubrication rate of 2%. Therefore it is critical to quantify the influence of the 2% lubrication on the leakage area of the expander in order to include the data compiled by ref. [18] in the model validation campaign. The authors define the oil seal factor as the fraction of the leakage area that is unavailable (sealed off) to facilitate leakage as a result of lubrication oil. Thus, during oil-free operation the oil seal factor is nonexistent. Fig. 8 shows that the oil seal factor is approximately 30% when a 2% lubrication is applied. To estimate the leakage area for ammonia with 2% lubrication using the leakage area calculated for R134a (oilless operation) requires consideration of the 30% oil sealing:
5. Generalization of the six parameter semi empirical model for any working fluid The non-deterministic nature of the semi-empirical model ensures that the model is intrinsic to the particular expander and the working fluid that was used for calibrating and testing. In the past researchers have been forced to calibrate the semi-empirical models for every time a switch in working fluid is required. Consequently, the calibration process can be labor intensive, time consuming and financially costly since it requires experimental data. The six-parameter semi-empirical scroll expander model generalization procedure presented here is inspired by work performed by Byrne et al. [32] and Duprez et al. [33] on scroll compressors and later adopted for the scroll expander by Giuffrida [10]. Because of the theoretical nature of the study and a lack of experimental data, Giuffrida [10] was only able to perform a preliminarily verification of the generalization procedure against the results of previous experimental studies from the literature with the expander efficiency as the single mean of comparison. The current paper introduces novel features to the models available in the literature by
Aleak, NH3 = 0.7(Aleak, R134a )
(19)
In the case of ammonia/water, since the operation of the scroll expander was oil-free (same as with R134a), the leakage areas are equivalent:
Aleak, NH3/ H2 0 = Aleak, R134a 8
(20)
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Table 3 Estimation of accuracies for semi-empirical models from various authors. Parameters in model
Prediction accuracies
Literature source
[–]
ṁ su [±%]
Ẇ loss, total [±%]
Tex [±°C]
8 8 8 8 8 4 6
2 4 2 4 5 5 3
6 10 5 20 10 9 9
2 – 3 5 5 4 2
[26] [3] [30] [31] [15] [18] This study
Oil seal factor [-]
0.4
0.35
0.3
0.25
0.2 0
1
2
3
4
5
6
7
8
9
Rate of Lubrication [%] Tsu=352 K; Psu=1000 kPa; R p=1.46; Nexp =33 Hz Tsu=350 K; Psu=1000 kPa; R p=1.45; Nexp =25 Hz Fig. 8. The influence of lubrication on leakage gap sealing [18].
by a fluid through a surface. It can be used to evaluate the overall heat transfer coefficient of a fluid: (21)
U = Nu. λ / l
In 1930, Dittus and Boelter proposed a convective heat transfer correlation for turbulent flows in smooth tubes (10,000 < Re < 12,000 and 0.7 < Pr (1 2 0). This correlation is recommended only for rather small differences between tube wall (shell) and fluid temperatures [38].
n = 0.3(Tshell < Tfluid ) Nu = Re 0.8 Pr n ⎧ ⎨ n = 0.4(Tshell > Tfluid ) ⎩
(22)
Re = ρ . u. D / μ
(23)
Pr = Cp. μ/ λ
(24)
The characteristic length (L), hydraulic diameter (D) and fluid velocity (u) are all functions of the scroll expander physical make-up and will not be altered by fluid swapping. By combining Eq. (20)–(24), the heat conductance of the new fluid can be evaluated:
ρfluid ⎞0.8 ⎛ μR134a ⎞ AUfluid = AUR134a ⎜⎛ ⎟ ⎜ ⎟ ⎝ ρR134a ⎠ ⎝ μfluid ⎠ Fig. 7. Experimental and predicted magnitudes of (a) mass flow rate, (b) mechanical shaft power and (c) discharge temperature.
0.8 − n
n 1−n ⎛⎜ Cpfluid ⎞⎟ ⎛ λ fluid ⎞ ⎝ CpR134a ⎠ ⎝ λR134a ⎠ ⎜
⎟
(25)
Reflecting from Reynolds analogy, a nominal mass flow is required to evaluate heat conductance. To determine the overall exhaust heat conductance for ammonia/water and ammonia working fluids, nominal mass flow rate values of 0.0135 kg/s (ammonia) and 0.0162 kg/s (ammonia/water) are used.
It should be noted that for simplicity, the influence of the 2% lubrication on thermodynamic and transport properties of ammonia has been neglected.
5.3. Mechanical power loss 5.2. Heat conductance The mechanical power losses of the expander are dependent on torque losses and the rotational speed as shown:
Nusselt number compares convective and conductive heat transfers 9
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Ẇloss = 2. π . Nexp. τloss
mixing when determining the dynamic viscosity and thermal conductivity of ammonia/water. The improved prediction in shaft power however only implies that the model becomes more accurate when simulating power production in excess of 0.5 kW and should not be interpreted as a merit of the generalization procedure.
(26)
Schlösser [39] proposed a physical model to simulate the torque losses in a positive displacement machine by addressing the three main sources of frictional losses: viscous friction, coulomb friction and hydrodynamic friction. 5/3 τloss = Kvisc μωVsw, com + K coul ΔPVsw, com + Khydro ρω2Vsw . com
(27)
6.2. Ammonia
The first term in the torque loss equation (Eq. (24)) represents viscous friction arising from viscous forces between moving parts due to the presence of a film of fluid and the second term (coulomb friction) describes a pressure dependent dry friction. Lastly, the third term predicts the effects of fluid density on the machine performance. For this research, the viscous and coulomb friction terms are neglected because they simulate torque losses in laminar flow [40–41]. The mechanical power losses model could be improved considering the additional viscous and coulomb parameters but in this case the extension of the model to other working fluids could be more complicated [10]. Therefore, the density dependent turbulent loss term (hydrodynamic friction) is sufficient to relate torque losses and their respective working fluids:
τloss, hydro _fluid/ τloss, hyro_R134a = ρfluid / ρR134a
To test the accuracy of the generalized model for pure ammonia, the data utilized is from literature [18] for experiments performed on the same scroll device with 2% lubrication. This exercise employed 36 steady state points at: Tsu = 330–357 K; Psu = 1000–1400 kPa; Rp = 1.3–2.0 and Nexp = 25–50 Hz. As shown in Fig. 10, the accuracy
(28)
Mendoza et al. [17] established the mechanical losses exclusively generated by friction in the moving parts of the uncharged experimental system (scroll expander with coupling pulley and belt) shown in Fig. 1 to be:
Ẇloss, mech = 1.27 × 10−1 + 5.18 × 10−3 (Nexp)
(29)
Hydrodynamic friction losses can be estimated by subtracting the component of power loss that is generated exclusively by friction in the moving parts (Eq. (29)) from the total mechanical power loss:
Ẇloss, hydro = Ẇloss, total − Ẇloss, mech
(30)
From Eq. (28) it is clear that for a given scroll expander at a set pressure ratio and speed of rotation, the effect of hydrodynamic friction resulting from a change in the working fluid can be accounted for by a constant equivalent to the density ratio of the concerned fluids.
Ẇloss, hydro _fluid = Ẇloss, hydro_R134a ρfluid / ρR134a
(31)
The resulting expression for total mechanical losses adjusted to accommodate a fluid change can be denoted as:
Ẇloss, total _fluid = Ẇloss, hydro_fluid + Ẇloss . mech
(32)
6. Validating the generalized six parameter semi empirical model Proving the legitimacy of the proposed generalized six parameter semi empirical model involves comparing predicted and measured values for mass flow, mechanical shaft power and exhaust temperature for different working fluids and using the same expander. 6.1. Ammonia/water A total of 50 steady state points are collected at the following ranges: Tsu = 357–385 K; Psu = 1100–2000 kPa; X = 0.95–0.99; Rp = 1.3–2.0 and Nexp = 25–45 Hz. Fig. 9 illustrates that the accuracy of the generalized model to predict mass displacement, mechanical shaft power and discharge temperature for ammonia/water working fluid is 5%, 7% and 3 K respectively. Prediction of shaft power by the generalized model is improved by 2% (Fig. 9b) whereas exhaust temperature (Fig. 9) and mass displacement (Fig. 9a) simulation deteriorates by 1 K and 2% respectively when compared to the original R134a model. A decrease in the accuracy of simulating discharge temperature could be the effect of assuming ideal
Fig. 9. Accuracy of the generalized model to predict (a) mass displacement, (b) mechanical shaft power and (c) discharge temperature for ammonia/water working fluid. 10
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This error threshold is well within the range recorded by other researchers applying the original “non-generalized” semi empirical model [3,12,13,14,17,15,42]. Therefore, the generalization procedure presented in this study is thermodynamically sound and it should hold true for any working fluid. 7. Conclusion The development and experimental investigation of a general semi empirical scroll expander model for any working fluid has been presented. This paper can be organized in three sections. The first section deals with the characterization, modelling and eventual testing of a sixparameter semi-empirical model for R134a working fluid. The resulting model reports absolute disparities of 2 K, 3% and 9% between measured and calculated values of exhaust temperature, displaced mass flow and mechanical shaft power respectively. The second section presents a procedure for adopting the R134a semi-empirical model to operate with any working fluid. Of the six parameters employed in the model, only the nominal exhaust heat conductance and mechanical power loss are found to be fluid dependent. Finally, the last part involves testing the proposed generalized six parameter semi empirical model with different working fluids (ammonia/water and pure ammonia) to prove its validity (it reports the simulation errors for mass flow rate, mechanical shaft power and exhaust temperature to be less than 5%, 7% and 4 K respectively for both working fluids). In conclusion, the generalized semi-empirical model presented in this paper is simple, with a reduced computational time and a level of accuracy comparable with the original “non-generalized” semi-empirical models. Therefore, this simulation tool can save the time and material resources that are committed in the experimental and analytical procedures involved each time a semi empirical model has to be developed for a particular scroll expander solely as a consequence of change in the working fluid. Acknowledgements This work was supported by FEDER, Spanish Ministry of Economy and Competiveness (grant DPI2015-71306-R), Spain and Government of India-Department of Science and Technology (grant DST/TM/SERI/ 2K12/74(G)), India. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.113932. References [1] S. Shafie, A review on paddy residue based power generation: energy, environment and economic perspective, Renew. Sustain. Energy Rev. 59 (2016) 1089–1100, https://doi.org/10.1016/j.rser.2016.01.038. [2] H. Mergner, T. Weimer, Performance of ammonia–water based cycles for power generation from low enthalpy heat sources, Energy 88 (2015) 93–100, https://doi. org/10.1016/j.energy.2015.04.084. [3] F. Ayachi, E.B. Ksayer, P. Neveu, A. Zoughaib, Experimental investigation and modeling of a hermetic scroll expander, Appl. Energy 181 (2016) 256–267, https:// doi.org/10.1016/j.apenergy.2016.08.030. [4] G. Qiu, H. Liu, S. Riffat, Expanders for micro-CHP systems with organic Rankine cycle, Appl. Therm. Eng. 31 (2011) 3301–3307, https://doi.org/10.1016/j. applthermaleng.2011.06.008. [5] P. Song, M. Wei, L. Shi, S.N. Danish, C. Ma, A review of scroll expanders for organic Rankine cycle systems, Appl. Therm. Eng. 75 (2015) 54–64, https://doi.org/10. 1016/j.applthermaleng.2014.05.094. [6] M. Imran, M. Usman, B.-S. Park, D.-H. Lee, Volumetric expanders for low grade heat and waste heat recovery applications, Renew. Sustain. Energy Rev. 57 (2016) 1090–1109, https://doi.org/10.1016/j.rser.2015.12.139. [7] T. Yanagisawa, T. Shimizu, M. Fukuta, T. Handa, Study on fundamental performance of scroll expander, Trans. Jpn. Soc. Mech. Eng. Ser. B 54 (1988) 2798–2803. [8] R. Zanelli, D. Favrat, Experimental investigation of a hermetic scroll expandergenerator, in: Proceedings of the International Compressor Engineering Conference at Purdue, 1994, pp. 459–464.
Fig. 10. Accuracy of the generalized model to predict (a) mass displacement, (b) mechanical shaft power and (c) discharge temperature for pure ammonia working fluid.
of the generalized model to predict mass displacement, mechanical shaft power and exhaust temperature for ammonia is 5%, 7% and 4 K respectively. The prediction accuracy for exhaust temperature decreases by 2 K when compared to the original R134a model (Fig. 10c) possibly because of assuming the influence of lubricating oil on the thermodynamic and transport properties of ammonia to be negligible. The results from testing the generalized six parameter semi-empirical model with ammonia/water and pure ammonia working fluids report the simulation errors for mass flow rate, mechanical shaft power and exhaust temperature to be less than 5%, 7% and 4 K respectively. 11
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(2013) 168–186, https://doi.org/10.1016/j.rser.2013.01.028. [26] V. Lemort, S. Declaye, S. Quoilin, Experimental characterization of a hermetic scroll expander for use in a micro-scale Rankine cycle, Proc Inst Mech Eng. Part A: J. Power Energy 226 (2011) 126–136, https://doi.org/10.1177/0957650911413840. [27] I. Dincer, A. Midilli, H. Kucuk, Progress in exergy, energy, and the environment, Springer, Cham, 2014. [28] V. Lemort, A. Legros, Positive displacement expanders for Organic Rankine Cycle systems, in: E. Macchi, M. Astolfi (Eds.), Organic Rankine Cycle (ORC) Power Systems: Technologies and Applications, Woodhead Publishing, Cambridge, 2017, pp. 361–396, , https://doi.org/10.1016/B978-0-08-100510-1.00012-0 ISBN. 9780081005101. [29] A. Giuffrida, Improving the semi-empirical modelling of a single-screw expander for small organic Rankine cycles, Appl. Energy. 193 (2017) 356–368, https://doi.org/ 10.1016/j.apenergy.2017.02.015. [30] Lemort V. Contribution to the characterization of scroll machines in compressor and expander modes, Doctoral Thesis, Universite de Liege, Belgique, 2008. [31] D. Ziviani, A. Desideri, V. Lemort, M.D. Paepe, M.V.D. Broek, Low-order models of a single-screw expander for organic Rankine cycle applications, IOP Conf. Series: Mater. Sci. Eng. 90 (2015) 012061. [32] P. Byrne, R. Ghoubali, J. Miriel, Scroll compressor modelling for heat pumps using hydrocarbons as refrigerants, Int. J. Refrig 41 (2014) 1–13, https://doi.org/10. 1016/j.ijrefrig.2013.06.003. [33] M.-E. Duprez, E. Dumont, M. Frère, Modeling of scroll compressors – Improvements, Int. J. Refrig 33 (2010) 721–728, https://doi.org/10.1016/j.ijrefrig.2009.12.025. [34] I.H. Bell, E.A. Groll, J.E. Braun, Performance of vapor compression systems with compressor oil flooding and regeneration, Int. J. Refrig 34 (2011) 225–233, https:// doi.org/10.1016/j.ijrefrig.2010.09.004. [35] S. Ramaraj, B. Yang, J.E. Braun, E.A. Groll, W.T. Horton, Experimental analysis of oil flooded R410A scroll compressor, Int. J. Refrig 46 (2014) 185–195, https://doi. org/10.1016/j.ijrefrig.2014.08.006. [36] B. Aoun, D. Clodic, Theoretical and experimental study of an oil-free scroll type vapor expander, Proceedings of the Compressor Engineering Conference at Purdue, (2008) Paper 1188. [37] L.E. Olmedo, V. Mounier, L.C. Mendoza, J. Schiffmann, Dimensionless correlations and performance maps of scroll expanders for micro-scale Organic Rankine Cycles, Energy 156 (2018) 520–533. [38] F.P. Incropera, Fundamentals of heat and mass transfer, Chapter 8, Seventh ed., John Wiley, Hoboken, NJ, 2011. [39] W. Schlösser, Mathematical model for displacement pump and motors, Hydraulic Power Trans. (1961) 252–257. [40] A. S. Gosal, Modelling and control of a hydrostatic transmission for a load haul dump underground mining machine 2004. University of British Columbia, MASc Thesis. [41] H. S. Jason, Statistical analysis of multiple hydrostatic pump flow loss models 2014. Iowa State University, MSc Thesis. [42] J.-F. Oudkerk, S. Quoilin, S. Declaye, L. Guillaume, E. Winandy, V. Lemort, Evaluation of the energy performance of an organic rankine cycle-based micro combined heat and power system involving a hermetic scroll expander, J. Eng. Gas Turbines Power 135 (2013) 042306, https://doi.org/10.1115/1.4023116.
[9] Eric Winandy, Claudio Saavedra, Jean Lebrun, Experimental analysis and simplified modelling of a hermetic scroll refrigeration compressor, Appl. Therm. Eng. 22 (2) (2002) 107–120. [10] A. Giuffrida, Modelling the performance of a scroll expander for small organic Rankine cycles when changing the working fluid, Appl. Therm. Eng. 70 (2014) 1040–1049, https://doi.org/10.1016/j.applthermaleng.2014.06.004. [11] V. Lemort, S. Quoilin, C. Cuevas, J. Lebrun, Testing and modeling a scroll expander integrated into an organic Rankine cycle, Appl. Therm. Eng. 29 (2009) 3094–3102, https://doi.org/10.1016/j.applthermaleng.2009.04.013. [12] V. Lemort, V.I. Teodorese, J. Lebrun, Experimental study of the integration of a scroll expander into a heat recovery rankine cycle, International Compressor Engineering Conference, (2006) Paper 1771. [13] E. Yun, D. Kim, M. Lee, S. Baek, S.Y. Yoon, K.C. Kim, Parallel-expander organic Rankine cycle using dual expanders with different capacities, Energy. 113 (2016) 204–214, https://doi.org/10.1016/j.energy.2016.07.045. [14] B. Twomey, P. Jacobs, H. Gurgenci, Dynamic performance estimation of small-scale solar cogeneration with an organic Rankine cycle using a scroll expander, Appl. Therm. Eng. 51 (2013) 1307–1316, https://doi.org/10.1016/j.applthermaleng. 2012.06.054. [15] D. Ziviani, S. Gusev, S. Lecompte, E. Groll, J. Braun, W. Horton, et al., Characterizing the performance of a single-screw expander in a small-scale organic Rankine cycle for waste heat recovery, Appl. Energy 181 (2016) 155–170, https:// doi.org/10.1016/j.apenergy.2016.08.048. [16] M. Ibarra, A. Rovira, D.-C. Alarcón-Padilla, J. Blanco, Performance of a 5kWe organic Rankine cycle at part-load operation, Appl. Energy 120 (2014) 147–158, https://doi.org/10.1016/j.apenergy.2014.01.057. [17] L.C. Mendoza, J. Navarro-Esbrí, J.C. Bruno, V. Lemort, A. Coronas, Characterization and modeling of a scroll expander with air and ammonia as working fluid, Appl. Therm. Eng. 70 (2014) 630–640, https://doi.org/10.1016/j.applthermaleng.2014. 05.069. [18] L.C. Mendoza, Caracterización y modelización de un expansor scroll de pequeña potencia. integración en sistemas de absorciónpara producción de energía mecánica y refrigeración 2013. URV Tarragona, PhD Thesis. [19] D.S. Ayou, J.C. Bruno, R. Saravanan, A. Coronas, An overview of combined absorption power and cooling cycles, Renew. Sustain. Energy Rev. 21 (2013) 728–748, https://doi.org/10.1016/j.rser.2012.12.068. [20] I. Borde, M. Jelinek, N. Daltrophe, Absorption system based on the refrigerant R134a, Int. J. Refrig 18 (1995) 387–394, https://doi.org/10.1016/0140-7007(95) 98161-d. [21] EES, Engineering equation solver, F-Chart Software. < http://www.fchart.com > . 2016. [22] Hydra-Cell Pump, (accessed 27.09.17). < http://www.hydra-cell.com/product/ D35-hydracell-pump.html > . [23] Sanden scroll compressors, (accessed 30.09.17). < http://www.sanden.com/ scrollcompressors.html > . [24] S. Emhardt, G. Tian, J. Chew, A review of scroll expander geometries and their performance, Appl. Therm. Eng. 141 (2018) 1020–1034. [25] S. Quoilin, M.V.D. Broek, S. Declaye, P. Dewallef, V. Lemort, Techno-economic survey of Organic Rankine Cycle (ORC) systems, Renew. Sustain. Energy Rev. 22
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Research Paper
Modelling of scroll expander for different working fluids for low capacity power generation
T
⁎
J. Muyea, G. Praveen Kumarb, J.C. Brunoa, R. Saravananb, , A. Coronasa a b
Universitat Rovira i Virgili, Department of Mechanical Engineering, CREVER, Avda Països Catalans 26, 43007 Tarragona, Spain Anna University, College of Engineering, Department of Mechanical Engineering, Guindy, Chennai, Tamil Nadu 600 025, India
H I GH L IG H T S
characterization of a scroll expander using R-134a and Ammonia. • Experimental of a general semi empirical model of a scroll expander for several fluids. • Development of the model generalization procedure performed with experimental data. • Validation model accurately predicts mass flow rate, shaft power and exhaust temperature. • The • This model can save time and material resources in experimental procedures.
A R T I C LE I N FO
A B S T R A C T
Keywords: Scroll expander Working fluid Modelling Leakage loss Mechanical loss
This paper presents the experimental investigation and development of a general semi empirical scroll expander model for different working fluids. Initially, the characterization and modelling of a scroll expander with R134a working fluid is performed. The influence of key operating variables on the main performance indicators such as isentropic efficiency, filling factor and specific power are investigated. The proposed semi empirical model for the scroll expander predicts mass flow rate, mechanical shaft power and exhaust temperature at accuracies of 3%, 9% and 2 K respectively. The developed semi empirical model is then modified to accommodate different working fluids; validation of the generalization procedure is performed with experimental data using ammonia/ water mixture and ammonia as working fluids. The generalized semi-empirical model predicts mass flow rate, mechanical shaft power and exhaust temperature to be less than 5%, 7% and 4 K error margin for both ammonia/water and pure ammonia working fluids. Therefore, the simulation model presented in this study can save the time and material resources for the selected scroll expander solely as a consequence of a change in the working fluid to predict the main performance indicators.
1. Introduction The world today is mostly dependent on fossil fuel for power generation. This dependency on fossil fuel is leading the world into a multifaceted crisis comprising the insecurity of supplies, environment impact and also the fluctuation of fuel price. In order to tackle this crisis, scientists are shifting their interest on new energy sources like biomass resources, solar, tidal and geothermal energies. Cost efficient power generation from low temperature heat sources requires an optimal usage of the available heat achieved through employing economical technologies [1–2]. The overall cost and thermodynamic performance of any low grade heat transforming system strongly correlates with that of its unitary
⁎
components, especially the expander. The selection of the expander is usually related to the size and the design of the system. Two main types of expanders can be distinguished: the dynamic (velocity/kinetic/ turbo) type, such as axial turbine expander, and positive displacement (volume) type, such as screw expander and scroll expanders [3–4]. Various reviews on expanders [5–6] have highlighted that the volumetric expanders are preferred for small capacity (up to 50 kW) low grade heat conversion applications. Since the scroll machine technology has become more and more matured in the residential and commercial markets (for air conditioning and refrigeration) it is therefore not surprising that currently, the majority of scroll expanders integrated into the low-grade energy utilization systems are mostly modified from refrigerant scroll compressors. This practice ensures that the expander
Corresponding author. E-mail address: [email protected] (R. Saravanan).
https://doi.org/10.1016/j.applthermaleng.2019.113932 Received 19 December 2018; Received in revised form 3 April 2019; Accepted 6 June 2019 Available online 06 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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π ρ τ φ
Nomenclature Variables
A AU Cp D h K L ṁ N Nu P Pr Q̇ R Re T u U v̇ V V̇ w Ẇ X
area, m2 heat transfer coefficient, W K−1 specific heat at constant pressure, J kg−1 K−1 hydraulic diameter, m specific enthalpy, J kg−1 friction coefficient length, m mass flow rate, kg s−1 rotational speed, Hz Nusselt number pressure, Pa Prandtl number heat transfer rate, W ratio Reynolds number temperature, K velocity, m s−1 thermal transmittance, W m−2 K−1 specific volume, m3 kg−1 volume, m3 volumetric flow rate, m3/s specific power, J kg−1 power, W Concentration of ammonia in the ammonia/water mixture
Subscripts
amb calc com coul esp ex exp global hydro in int is leak loss max meas min nom p shaft shell su sw total v visc
Greek symbols
u Δ Σ η λ μ
3.1416 density, kg m−3 torque, N m filling factor
velocity, m s−1 change of value Summation Efficiency thermal conductivity, W m−1 K−1 dynamic viscosity, Pa s
ambient calculated compressor couloumb specific exhaust expander Overall hydrodynamic into internal isentropic leakage power loss maximum measured minimum nominal isobaric, pressure prime mover cover, wall supply swept summed up volumetric viscous
Acronym ORC
Organic Rankine Cycle
small capacity low-grade energy utilization systems. Lemort et al. [11] proposes an eight parameter semi-empirical simulation model of a scroll expander using R123 as working fluid. The losses considered by the model include: supply pressure drop loss, exhaust and ambient heat transfer losses, internal leakage loss, friction and expansion losses. The model, with its parameters identified, can predict the mass flow rate, the shaft power and the exhaust temperature with an accuracy of 2%, 5% and 3 K respectively. Because of its accuracy, low computational time, robustness and ease of integration into a thermodynamic cycle simulation, several researchers have studied the eight parameter semiempirical model for different working fluids (Water [12], Air [12], R245fa [3,13,14,15], R134a [14] and Solkatherm SES36 [15]). In the theoretical study of the performance of an Organic Rankine Cycle (ORC) at part load operation with R245fa and Solkatherm SES36 working fluids, Ibarra et al. [16] adopted a simplified four parameter semi empirical model. The simplification is a result of neglecting the supply pressure drop loss and the three thermal losses. Since the study is theoretical, the prediction accuracy of the models is not provided. Later, Mendoza et al. [17] also implements the simplified four parameter semi-empirical model for their experimental study of an open drive scroll expander with ammonia working fluid. Using this semiempirical model, the deviations in the calculated mechanical power, exhaust temperature and supply mass flow rate are ± 9%, ± 4 K and ± 5% respectively. The non-deterministic nature of the semi-empirical model ensures that the model is intrinsic to the particular expander and the working fluid that was used for calibrating and testing.
costs are kept low and thus contributing favourably to the overall cost effectiveness of the low grade energy conversion system. Many researchers have extensively reported experimental and numerical results on the scroll expander performance for various organic working fluids. In 1988, Yanagisawa et al. [7] carried out a performance test on a scroll expander that modified from off-the-shelf automotive scroll compressor. The adiabatic efficiency of the scroll expander reached up to 60–75% for the corresponding shaft speed of 1000–4000 rpm. Zanelli and Favrat [8] carried out an experimental study on hermetic scroll expander-generator modified from standard hermetic compressor fed with refrigerant R134a. The peak overall isentropic efficiencies are reported in the range of 63% to 65% for varying shaft rotation between 2400 and 3600 rpm. Eric et al. [9] proposed a simplified four-parameter model is proposed to predict the scroll compressor discharge temperature and mass flow rate of working fluid. In addition, driven electric power of compressor the predicted by using three-parameter model such as built in volume ratio, constant power loss and a power coefficient. Giuffrida [10] reports that up until recently, technical papers dealing with small-size power production systems did not always consider a specific modelling for the expander. In such theoretical works, the expander efficiency was taken constant in spite of variable operating conditions, such as fluid pressure and temperature at the inlet of the machine, expansion pressure ratio, type of working fluid and speed of rotation. Recent literature reports on scroll expanders nonetheless suggests that scientists have been developing and using thermodynamic models to simulate expander performance in 2
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To address the working fluid constraint resulting from rigidity of the model, Giuffrida [10] starts from the original eight parameter R123 scroll expander model [11] developed by Lemort et al. and outlines a thermodynamically realistic procedure to generalize the model to simulate the expander performance with fluids other than R123. Because of the theoretical nature of the study and a lack of experimental data, Giuffrida [10] was only able to perform a preliminarily verification of the generalization procedure against the results of previous experimental studies from the literature with the expander efficiency as the single mean of comparison. Clearly, this verification technique could not offer a qualitative validation of the proposed model generalization approach. The current investigation is performed with the aim of: (1) to study the influence of four independent input parameters on the behavior of an open drive scroll expander with R134a working fluid; (2) to propose a six parameter semi empirical model for the scroll expander operating with R134a; (3) present an improved expander model generalization approach for the six parameter model to facilitate adaptability to any working fluid and (4) to use experimental data obtained presently in this research work and also from the literature ([17;18]) to validate the generalised six parameter model with ammonia and ammonia/water working fluids. Eventually, the findings from this investigation will be very helpful in the study and design of low grade energy utilization systems such as ORCs and combined absorption power and cooling cycles [19] where researchers will not be forced to develop new semi empirical models for every time a switch in working fluid is required. The logic behind the selection of the working fluids employed in this study (R134a, ammonia and ammonia/water) is to ensure that the developed model captures a broad assortment of working fluids classifications: natural vs organic, dry vs wet etc. Furthermore, the selected working fluids cover a wide range of application systems especially when the absorption technology is also extended to R134a [20]. Engineering Equation Solver [21] software is used to simulate the behavior of the working fluids. Thermodynamic properties for R134a and ammonia are retrieved from the internal thermo-physical data base of the software while those for the ammonia/water mixture are sourced from the external routines database. The paper is structured as follows. In Section 1 (current section) the background and justification of the work performed with their objectives was explained. In Section 2 the characteristics of the experimental setup are described. This setup is used to measure the performance of an expander using R-134a (Section 3). A modified 6-parameter
empirical model is presented in Section 4 to model this expander with R-134a. In Section 5 a methodology is proposed to extend the model to other working fluids that is validated in Section 6 for ammonia and ammonia/water working fluids. The main findings are summarized as conclusions.
2. Experimental methods 2.1. Test bench description For this study, the expander test bench developed by Mendoza et al. [17], has been utilized with slight modifications in instrumentation and complete removal of the lubrication network as shown in Fig. 1. The test rig comprises of a diaphragm pump (Wanner Hydra-Cell), three plate heat exchangers (Alfa Laval), two 17 L steel vessels, the scroll device (Sanden, TRSA05) and an electrical brake. Working fluid from the expander (stream 7) is condensed by the chiller (stream 1) then fed to a liquid reservoir (stream 2) before being sub-cooled by the glycol based chiller (stream 3) and eventually pumped (stream 4) to the evaporator. From the evaporator (stream 5), the working fluid goes through a vapor tank (stream 6) and then straight to the scroll expander for power generation. The temperature of the working fluid at the inlet of the expander is controlled by the external boiler. Pressure at the expander inlet is provided by the pump whereas the condenser temperature sets the pressure at the exit of the expander. The electrical brake connected to the expander is used to control its rotational speed. A pulley and belt mechanism provides coupling of the electrical brake to the expander at a ratio of 1:3.08. It is true that this is transmission could provide a lower efficiency than a direct shaft connection but is a solution implemented in many open-drive automotive A/C compressors adapted as expanders [5]. Both the pump and the electrical brake are manually controlled by frequency drives. The vapor tank is fitted with a pressure relief valve which is activated at 2500 kPa and the hot water from the boiler is limited to temperatures below 403 K. Ambient temperature limits the water based chiller (condenser temperature) whereas the glycol based chiller (sub-cooler temperature) is limited to temperatures above 277 K as per pump specifications [22]. Steel piping was used to ensure compatibility with both ammonia/water and R134a working fluids.
Fig. 1. Schematic diagram of the scroll expander test bench. 3
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2.2. Measuring devices
3.2. Influence of supply temperature and pressure
Temperatures and pressures in the test rig are measured by resistance thermometers (in 4 wire configuration) and piezo-resistive (silicon) transducers, respectively. A Coriolis flow meter provides the density and mass flow rate of the working fluid while the rotational frequency and torque are measured by an integrated torque and speed transducer fitted on the shaft of the electrical brake. A data acquisition unit from Agilent technologies (34970A) is used for logging all the measured data. Table 1 shows the main characteristics of transducers in the test rig.
Dincer et al. [27] highlight that friction and leakage losses contribute the highest portion of irreversibilities in a scroll expander. The effect of these two losses is especially predominant when pressure ratio remains constant. The filling factor (Eq. (4)) can be redefined as:
φexp = 1 +
ṁ leak ṁ in
(5)
Therefore, a filling factor closer to unity implies low leakage losses and consequently suggests a desirable volumetric performance. However, the isentropic efficiency provides a measure for all the losses. Isentropic efficiency and filling factor exhibit no sensitivity to the supply temperature, they remain constant at 0.4 and 1.7 respectively. This suggests that both frictional and leakage irreversibilities remain constant when the supply temperature is varied. Conversely, a 19 K increase in the supply temperature leads to a 0.7 kJ/kg increase in specific power as a result of the increased enthalpy. The effect of supply pressure on the expander performance was found to be negligible. According to Lemort and Legros [28], leakages are due to the pressure gradients that are applied across leakage paths resulting from clearances between moving elements and friction losses result from the axial force that tends to separate the two scrolls. Therefore, a constant pressure ratio ensures that the proportion of these two losses remain virtually unchanged even under varying supply temperature and pressure conditions.
2.3. Scroll expander The Sanden, model TRSA05 open-drive scroll compressor (normally used in automotive refrigeration systems) was modified and operated in expander mode. According to the manufacturer, the volumetric displacement per revolution of the scroll device in compressor mode is 53.9 cm3, and it can withstand a maximum of 3500 kPa and 166 Hz of pressure and rotational speed respectively [23]. The built-in volume ratio is 1.9, calculated by measuring the cross section area at the suction and exhaust chambers [17]. This is a low pressure expander device according to the classification based on built-in volume ratio: low (< 2), medium (2-3) and high built-in volume ratio expanders (> 3) [24]. 3. Characterisation of the scroll expander with R134a
3.3. Influence of pressure ratio and rotational speed
Since the expander was adopted from a scroll compressor, performance and eventual characterization of such an expander can only be determined experimentally. Four independent input variables (supply pressure and temperature, pressure ratio and rotational speed) were identified and the effect they have on the expander performance (mechanical shaft power, global isentropic efficiency and filling factor) was investigated to facilitate an in-depth understanding of the expander behavior at different operating conditions with R134a working fluid. The experiments were carried out at: Tsu = 355–378 K; Psu = 850–1450 kPa; Rp = 1.3–1.8 and Nexp = 13–32 Hz.
Fig. 2 highlights the influence of varying pressure ratios on the scroll expander performance. An increase in both isentropic efficiency and filling factor is observed with an increase in pressure ratio. It is an indication that the volumetric performance of the device declines with increasing pressure ratio because as predicted by Lemort et al. [26] increasing the pressure gradient also increases leakage. As expected a clear improvement in specific power is observed with increasing pressure ratio. Therefore, the increasing isentropic efficiency suggests that when increasing the pressure ratio, the specific power increases at a faster rate than leakage and friction losses. On the contrary, a decrease in both the isentropic efficiency and filling factor is observed with an increase in the expander rotational speed as illustrated in Fig. 3. Similarly, increasing the expander rotational speed reduces the specific power. At lower rotational speeds, the filling factor is high, consequently the working chamber is overfilled by the working fluid and leakage occurs, thus the rotational speed improves the volumetric performance of the scroll expander [15]. However, increasing the rotational speed leads to increasing frictional losses on account of the increasing axial force which translates to the gradual reductions in isentropic efficiency and specific power. Fig. 4 shows the influence of pressure ratio and rotational speed on mechanical power loss and leakage loss of the TRSA05 scroll expander. It reveals that performance of scroll expander strongly depends on pressure ratio and rotational speed, since friction and leakage losses contribute highest portion of irreversibility.
3.1. Performance indices The three performance parameters of interest in the characterisation of the scroll device are the specific power, isentropic efficiency and filling factor. Specific power is the measured output power divided by the measured mass flow rate:
wesp =
Ẇshaft , meas ṁ su, meas
(1)
where
Ẇshaft , meas = 2π × τexp, meas × Nexp, meas
(2)
The global isentropic efficiency of the scroll expander can be defined as the ratio of the measured output power divided by the isentropic expansion power [25]:
ηis, global =
Table 1 Measuring ranges and uncertainties of the transducers in the test rig.
Ẇshaft , meas ṁ su, meas (hsu − hex , is )
(3)
The filling factor can be used to express the volumetric performance of the scroll machinery, it is the ratio of the measured mass flowrate and the mass flowrate theoretically displaced by the expander [26]:
φexp = ṁ su, meas
̇ Vsu ̇ , exp Vsw
(4) 4
Variable
Range
Uncertainty
Pressure Temperature Mass flow Density Torque Rotational speed
0 … 2500 kPa −33 … 573 K Max. 330 kg/h Max. 5000 kg/m3 0.1 … 50 N m 1 … 166 Hz
± 5 kPa ± 0.5 K ± 0.10% ± 0.2 kg/m3 < ± 0.075 N m ± 0.017 Hz
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Fig. 3. Effect of varying rotational speed on the (a) filling factor, (b) global isentropic efficiency and (c) specific power of the scroll expander.
Fig. 2. Effect of varying pressure ratio on the (a) filling factor, (b) global isentropic efficiency and (c) specific power of the scroll expander.
exhaust temperature, but do not significantly alter the calculation of mass flow rate and mechanical power [28]. The scroll device being studied in this investigation is not insulated, therefore the expander shell exchanges heat with the environment and should not be assumed as adiabatic. Therefore, in addition to including exhaust heat transfer, the proposed six-parameter semi empirical model shown in Fig. 5 also acknowledges ambient heat transfer. The flow of working fluid from the expander supply to exhaust can be theoretically simplified by the following processes:
4. Scroll expander semi empirical model for R134a working fluid 4.1. Model description The semi-empirical scroll expander simulation model proposed by Lemort et al. [11] required eight parameters to predict three outputs. To reduce the computational time and improve the robustness of the model some authors [15,16] have suggested a four parameter model which neglects irreversibilities caused by supply pressure drop and thermal losses. Thermal losses mostly influence prediction the fluid
• Isobaric heat exchange between the imaginary shell and the inlet 5
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Fig. 4. Influence of (a) Pressure ratio and (b) rotational speed on leakage area and mechanical power loss.
fluid stream and an imagined expander shell (su to su1)
fluid stream (su → su1)
• Isentropic internal leakage of the working fluid (su1 → leak) • Isentropic expansion of the working fluid to the device internal pressure (in → int) • Isochoric adaptation of the working fluid to the external pressure (int → ex ) • Isobaric adiabatic mixing of the leaked and the expanded working fluid streams (ex → ex ) • Isobaric heat exchange between the imaginary shell and the exhaust
̇ = ṁ su (hsu − h su1) = {1 − exp−AUsu / ṁ su Cp } ṁ su Cp (Tsu − Tshell ) Qex
The working fluid stream supplied to expander (ṁ su1) is split into two: a work producing stream (ṁ in ) and a non-work producing stream (ṁ leak ) which leaks between the scrolls.
2
2
(6)
ṁ in + ṁ leak = ṁ su1
1
(7)
The leaked mass flow is directly proportional to a theoretical leakage area (Aleak) as shown in Eq. (8) [17]. The leakage area comprises of all leakage routes aggregated into one imaginary leakage path linking the expander inlet and outlet ports.
fluid stream (ex1 → ex)
Detailed thermodynamic description of the processes can be found in refs. [3], [10], [11], [12], [15] and [17]. The process descriptions provided here will only highlight the salient expressions. To begin, a constant pressure heat exchange takes place between the
ṁ leak = ρleak Aleak 2(hsu − hleak )
(8)
The work producing stream is then expanded in a two stage process: the 6
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Fig. 5. Process diagram for the proposed semi-empirical scroll expander model.
first being isentropic (from in to int) then followed by an isochoric process (int to ex2 ). Internal pressure (Pint) is a limitation of the built in volume ratio (Rv).
̇ = ṁ in {(hin − hint ) + vint (Pint − Pex2)} Wexp
The four empirical parameters are determined using 45 steady state points. As hinted by Figs. 2 and 3 in Section 3.3, the leakage area and mechanical power loss are found to have strong correlations with pressure ratio and rotational speed. Correlations proposed to simulate leakage area and mechanical work loss are shown in Table 2. These correlations are fitted with experimental data to a linear model and achieve coefficients of determination of 90% and 93% respectively.
(9)
Reducing the total expander power produced (Eq. (9)) by all the mechanical power losses yields the shaft power available for use. Sources of mechanical power loss include friction in scrolls, bearings, transmission pulley and hydrodynamic effects.
̇ − Ẇloss, total Ẇshaft = Wexp
(10)
After the two stage expansion and eventually a power reduction processes, adiabatic mixing of the two streams (ṁ leak andṁ in ) occurs atex1.
ṁ leak hleak + ṁ in h ex2 = ṁ su h ex1
(11)
(12)
The overall exhaust heat conductance AUex is a function of mass flow based on the Reynolds analogy of turbulent pipe flow [10,11]:
AUex = AUex , nom (ṁ su / ṁ su, nom )0.8
(13)
where the nominal exhaust heat conductance AUex , nom is an empirical parameter and ṁ su, nom is a fixed nominal mass flow. Since the expander is not insulated, it is important to simulate the heat exchange between the fictitious expander shell and ambient.
̇ Qamb = AUamb (Tshell − Tamb)
(16)
Ẇloss, total = −3.19 × 10−1 + 8.83 × 10−3 (Nexp) + 1.38 × 10−1 (Rp)
(17)
At higher filling factors (meaning lower rotational speeds, Fig. 3(a)), the leakages become predominant because the working chamber is overfilled and the working fluid has the time to leak [11]; thus the leakage area decreased with increase in speed. A slight increase of the filling factor with supply pressure or pressure ratio increases internal leakages [29]. The effect of the pressure in leakage area is also taken into account in the calculation of the leakage area by other authors [30]. According to Lemort and Legros [28], leakages are due to the pressure gradients that are applied across leakage paths resulting from clearances between moving elements and friction losses result from the axial force that tends to separate the two scrolls. Therefore, a constant pressure ratio ensures that the proportion of these two losses remain virtually unchanged even under varying supply temperature and pressure conditions. The two heat conductance parameters are evaluated by minimizing a global deviation function that accounts for deviations between the
Finally, a constant pressure heat exchange takes place between the fluid stream and an imagined expander shell (ex1 to ex) [11].
̇ = ṁ su (hex − h ex1) = {1 − exp−AUex / ṁ su Cp } ṁ su Cp (Tshell − Tex1) Qex
Aleak = 5.36 × 10−6 − 7.18 × 10−8 (Nexp) + 2.48 × 10−7 (Rp)
(14)
The mechanical power loss is assumed to be completely dissipated in the expander shell, thus performing a steady state energy balance across the shell results to:
̇ ̇ − Qsu ̇ Ẇloss, total = Qamb + Qex
(15)
4.2. Parameter identification A block schematic of the six parameter semi-empirical model is illustrated in Fig. 6. It shows that the model requires six parameters and four independent variables (Psu, Tsu, Pex , Nexp ) to predict three output variables (Ẇshaft , ṁ su , Tex ). The six semi-empirical model parameters can be obtained in three ways: (1) from manufacture’s data (Vsw, com ); (2) from geometrical measurements (Rv ) and (3) experimental tests ( AUex , nom , AUamb , Aleak , Ẇloss, total ).
Fig. 6. Six parameter semi-empirical model block schematic. 7
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Table 2 The six model parameters for the scroll expander with R134a. Parameter
Value
Nominal exhaust heat conductance, UAex , nom (kW/K) Overall ambient heat conductance, UAamb (kW/K) Swept volume in compressor mode, Vsw, com (cm3) Built-in volume ratio, Rv (-) Leakage area, Aleak (m2)
0.06482 0.00469 53.9 1.9
5.36 × 10−6 − 7.18 × 10−8 (Nexp) + 2.48 × 10−7 (Rp)
Power loss, Ẇ loss, total (kW)
− 3.19 × 10−1 + 8.83 × 10−3 (Nexp) + 1.38 × 10−1 (Rp)
measured and calculated values of the three output variables (mass flow rate, mechanical shaft power and discharge temperature) [9,26,29 ]. To determine exhaust heat conductance, a nominal mass flow rate value of 0.07 kg/s was used. Equal weights are assigned to all the variables as shown in Eq. (18):
employing a different approach in the simulation of internal leakage and friction irreversibilities to accommodate the fluid alteration. Furthermore, this study presents a comprehensive validation of the generalized semi-empirical model with ammonia and ammonia/water working fluids. The assumptions used to extend the six-parameter semi-empirical scroll expander model to different fluids are the following: Parameters Vsw,com and Rv define the built in volumes of the suction and discharge chambers of the scroll machinery; they are fixed and are not altered when the working fluid is changed. On the other hand, the leakage area parameter is solely dependent of the operating conditions (Rp and Nexp) imposed on the scroll device as shown in correlation given in Table 2. Thus a fluid switch is not expected to modify Aleak. The overall ambient heat conductance (AUamb) is also independent of the working fluid since it simulates heat exchange between the scroll expander shell and the ambient. The same is not true for nominal exhaust heat conductance (AUex,nom) because it predicts heat transfer between the working fluid and expander casing. Finally, the friction losses which are represented by the work loss function (Table 2) are reliant on both the operating conditions (Rp and Nexp) and working fluid imposed on the scroll expander as discussed in Section 5.3.
Deviation = 1/3
/3
/3
⎧ ⎨ ⎩
⎧ ⎨ ⎩ ⎧ ⎨ ⎩
n
ṁ su − ṁ su, meas ⎞2 ⎫ +1 ṁ su ⎝ ⎠ ⎬ ⎭
∑⎛ ⎜
1 n
⎟
2 Ẇshaft − Ẇshaft , meas ⎞ ⎫ +1 ⎟ Ẇshaft ⎝ ⎠ ⎬ ⎭
∑ ⎛⎜ 1 n
2
Tex − Tex , meas ⎞⎟ ⎫ − T ex , meas _ max ex . meas _ min ⎝ ⎠ ⎬ ⎭
∑ ⎛T ⎜
1
(18)
Table 2 summarizes the six parameters of the semi-empirical model for Sanden TRSA05 scroll expander with R134a working fluid. 4.3. Semi-empirical scroll expander model validation A total of 100 steady state points are used to check the validity of the semi-empirical model, this includes the 45 points which were used to tune the model. The 55 extra states guarantee the model for noncalibrated points. Fig. 7 displays a graphical collation of the measured and calculated values of the three output variables: displaced mass flow, mechanical shaft power and exhaust temperature. Absolute disparities of 3%, 9% and 2 K are found between measured and calculated values of mass flow, mechanical shaft power and exhaust temperature respectively. The instrumentation availability and limited power values makes the absolute disparities of 9% in mechanical shaft power prediction. However, the achieved accuracies compare well with those reported in other studies using semi-empirical models as shown in Table 3.
5.1. Leakage area The Sanden TRSA05 scroll device is designed to be operated with lubrication. Introducing a substantial amount of lubrication oil into a scroll device enhances the internal sealing and improves its volumetric performance [34–35]. The main drawback of most volumetric expanders is the need for lubrication even though it has been demonstrated that oil free expanders are technically feasible [36] with marginally low performance. The oil effect in scroll expander modelling aspects is quite complex [37]. Due to some technical difficulties experienced with R134a (oil foaming and obsolete oil separator) and ammonia/water (water retention in oil separator and melting of oil pump discharge valve) working fluids, the authors were compelled to operate the expander oil-free. The data compiled by Mendoza et al. [17] for pure ammonia characterizes the same scroll expander at a lubrication rate of 2%. Therefore it is critical to quantify the influence of the 2% lubrication on the leakage area of the expander in order to include the data compiled by ref. [18] in the model validation campaign. The authors define the oil seal factor as the fraction of the leakage area that is unavailable (sealed off) to facilitate leakage as a result of lubrication oil. Thus, during oil-free operation the oil seal factor is nonexistent. Fig. 8 shows that the oil seal factor is approximately 30% when a 2% lubrication is applied. To estimate the leakage area for ammonia with 2% lubrication using the leakage area calculated for R134a (oilless operation) requires consideration of the 30% oil sealing:
5. Generalization of the six parameter semi empirical model for any working fluid The non-deterministic nature of the semi-empirical model ensures that the model is intrinsic to the particular expander and the working fluid that was used for calibrating and testing. In the past researchers have been forced to calibrate the semi-empirical models for every time a switch in working fluid is required. Consequently, the calibration process can be labor intensive, time consuming and financially costly since it requires experimental data. The six-parameter semi-empirical scroll expander model generalization procedure presented here is inspired by work performed by Byrne et al. [32] and Duprez et al. [33] on scroll compressors and later adopted for the scroll expander by Giuffrida [10]. Because of the theoretical nature of the study and a lack of experimental data, Giuffrida [10] was only able to perform a preliminarily verification of the generalization procedure against the results of previous experimental studies from the literature with the expander efficiency as the single mean of comparison. The current paper introduces novel features to the models available in the literature by
Aleak, NH3 = 0.7(Aleak, R134a )
(19)
In the case of ammonia/water, since the operation of the scroll expander was oil-free (same as with R134a), the leakage areas are equivalent:
Aleak, NH3/ H2 0 = Aleak, R134a 8
(20)
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Table 3 Estimation of accuracies for semi-empirical models from various authors. Parameters in model
Prediction accuracies
Literature source
[–]
ṁ su [±%]
Ẇ loss, total [±%]
Tex [±°C]
8 8 8 8 8 4 6
2 4 2 4 5 5 3
6 10 5 20 10 9 9
2 – 3 5 5 4 2
[26] [3] [30] [31] [15] [18] This study
Oil seal factor [-]
0.4
0.35
0.3
0.25
0.2 0
1
2
3
4
5
6
7
8
9
Rate of Lubrication [%] Tsu=352 K; Psu=1000 kPa; R p=1.46; Nexp =33 Hz Tsu=350 K; Psu=1000 kPa; R p=1.45; Nexp =25 Hz Fig. 8. The influence of lubrication on leakage gap sealing [18].
by a fluid through a surface. It can be used to evaluate the overall heat transfer coefficient of a fluid: (21)
U = Nu. λ / l
In 1930, Dittus and Boelter proposed a convective heat transfer correlation for turbulent flows in smooth tubes (10,000 < Re < 12,000 and 0.7 < Pr (1 2 0). This correlation is recommended only for rather small differences between tube wall (shell) and fluid temperatures [38].
n = 0.3(Tshell < Tfluid ) Nu = Re 0.8 Pr n ⎧ ⎨ n = 0.4(Tshell > Tfluid ) ⎩
(22)
Re = ρ . u. D / μ
(23)
Pr = Cp. μ/ λ
(24)
The characteristic length (L), hydraulic diameter (D) and fluid velocity (u) are all functions of the scroll expander physical make-up and will not be altered by fluid swapping. By combining Eq. (20)–(24), the heat conductance of the new fluid can be evaluated:
ρfluid ⎞0.8 ⎛ μR134a ⎞ AUfluid = AUR134a ⎜⎛ ⎟ ⎜ ⎟ ⎝ ρR134a ⎠ ⎝ μfluid ⎠ Fig. 7. Experimental and predicted magnitudes of (a) mass flow rate, (b) mechanical shaft power and (c) discharge temperature.
0.8 − n
n 1−n ⎛⎜ Cpfluid ⎞⎟ ⎛ λ fluid ⎞ ⎝ CpR134a ⎠ ⎝ λR134a ⎠ ⎜
⎟
(25)
Reflecting from Reynolds analogy, a nominal mass flow is required to evaluate heat conductance. To determine the overall exhaust heat conductance for ammonia/water and ammonia working fluids, nominal mass flow rate values of 0.0135 kg/s (ammonia) and 0.0162 kg/s (ammonia/water) are used.
It should be noted that for simplicity, the influence of the 2% lubrication on thermodynamic and transport properties of ammonia has been neglected.
5.3. Mechanical power loss 5.2. Heat conductance The mechanical power losses of the expander are dependent on torque losses and the rotational speed as shown:
Nusselt number compares convective and conductive heat transfers 9
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Ẇloss = 2. π . Nexp. τloss
mixing when determining the dynamic viscosity and thermal conductivity of ammonia/water. The improved prediction in shaft power however only implies that the model becomes more accurate when simulating power production in excess of 0.5 kW and should not be interpreted as a merit of the generalization procedure.
(26)
Schlösser [39] proposed a physical model to simulate the torque losses in a positive displacement machine by addressing the three main sources of frictional losses: viscous friction, coulomb friction and hydrodynamic friction. 5/3 τloss = Kvisc μωVsw, com + K coul ΔPVsw, com + Khydro ρω2Vsw . com
(27)
6.2. Ammonia
The first term in the torque loss equation (Eq. (24)) represents viscous friction arising from viscous forces between moving parts due to the presence of a film of fluid and the second term (coulomb friction) describes a pressure dependent dry friction. Lastly, the third term predicts the effects of fluid density on the machine performance. For this research, the viscous and coulomb friction terms are neglected because they simulate torque losses in laminar flow [40–41]. The mechanical power losses model could be improved considering the additional viscous and coulomb parameters but in this case the extension of the model to other working fluids could be more complicated [10]. Therefore, the density dependent turbulent loss term (hydrodynamic friction) is sufficient to relate torque losses and their respective working fluids:
τloss, hydro _fluid/ τloss, hyro_R134a = ρfluid / ρR134a
To test the accuracy of the generalized model for pure ammonia, the data utilized is from literature [18] for experiments performed on the same scroll device with 2% lubrication. This exercise employed 36 steady state points at: Tsu = 330–357 K; Psu = 1000–1400 kPa; Rp = 1.3–2.0 and Nexp = 25–50 Hz. As shown in Fig. 10, the accuracy
(28)
Mendoza et al. [17] established the mechanical losses exclusively generated by friction in the moving parts of the uncharged experimental system (scroll expander with coupling pulley and belt) shown in Fig. 1 to be:
Ẇloss, mech = 1.27 × 10−1 + 5.18 × 10−3 (Nexp)
(29)
Hydrodynamic friction losses can be estimated by subtracting the component of power loss that is generated exclusively by friction in the moving parts (Eq. (29)) from the total mechanical power loss:
Ẇloss, hydro = Ẇloss, total − Ẇloss, mech
(30)
From Eq. (28) it is clear that for a given scroll expander at a set pressure ratio and speed of rotation, the effect of hydrodynamic friction resulting from a change in the working fluid can be accounted for by a constant equivalent to the density ratio of the concerned fluids.
Ẇloss, hydro _fluid = Ẇloss, hydro_R134a ρfluid / ρR134a
(31)
The resulting expression for total mechanical losses adjusted to accommodate a fluid change can be denoted as:
Ẇloss, total _fluid = Ẇloss, hydro_fluid + Ẇloss . mech
(32)
6. Validating the generalized six parameter semi empirical model Proving the legitimacy of the proposed generalized six parameter semi empirical model involves comparing predicted and measured values for mass flow, mechanical shaft power and exhaust temperature for different working fluids and using the same expander. 6.1. Ammonia/water A total of 50 steady state points are collected at the following ranges: Tsu = 357–385 K; Psu = 1100–2000 kPa; X = 0.95–0.99; Rp = 1.3–2.0 and Nexp = 25–45 Hz. Fig. 9 illustrates that the accuracy of the generalized model to predict mass displacement, mechanical shaft power and discharge temperature for ammonia/water working fluid is 5%, 7% and 3 K respectively. Prediction of shaft power by the generalized model is improved by 2% (Fig. 9b) whereas exhaust temperature (Fig. 9) and mass displacement (Fig. 9a) simulation deteriorates by 1 K and 2% respectively when compared to the original R134a model. A decrease in the accuracy of simulating discharge temperature could be the effect of assuming ideal
Fig. 9. Accuracy of the generalized model to predict (a) mass displacement, (b) mechanical shaft power and (c) discharge temperature for ammonia/water working fluid. 10
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This error threshold is well within the range recorded by other researchers applying the original “non-generalized” semi empirical model [3,12,13,14,17,15,42]. Therefore, the generalization procedure presented in this study is thermodynamically sound and it should hold true for any working fluid. 7. Conclusion The development and experimental investigation of a general semi empirical scroll expander model for any working fluid has been presented. This paper can be organized in three sections. The first section deals with the characterization, modelling and eventual testing of a sixparameter semi-empirical model for R134a working fluid. The resulting model reports absolute disparities of 2 K, 3% and 9% between measured and calculated values of exhaust temperature, displaced mass flow and mechanical shaft power respectively. The second section presents a procedure for adopting the R134a semi-empirical model to operate with any working fluid. Of the six parameters employed in the model, only the nominal exhaust heat conductance and mechanical power loss are found to be fluid dependent. Finally, the last part involves testing the proposed generalized six parameter semi empirical model with different working fluids (ammonia/water and pure ammonia) to prove its validity (it reports the simulation errors for mass flow rate, mechanical shaft power and exhaust temperature to be less than 5%, 7% and 4 K respectively for both working fluids). In conclusion, the generalized semi-empirical model presented in this paper is simple, with a reduced computational time and a level of accuracy comparable with the original “non-generalized” semi-empirical models. Therefore, this simulation tool can save the time and material resources that are committed in the experimental and analytical procedures involved each time a semi empirical model has to be developed for a particular scroll expander solely as a consequence of change in the working fluid. Acknowledgements This work was supported by FEDER, Spanish Ministry of Economy and Competiveness (grant DPI2015-71306-R), Spain and Government of India-Department of Science and Technology (grant DST/TM/SERI/ 2K12/74(G)), India. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.113932. References [1] S. Shafie, A review on paddy residue based power generation: energy, environment and economic perspective, Renew. Sustain. Energy Rev. 59 (2016) 1089–1100, https://doi.org/10.1016/j.rser.2016.01.038. [2] H. Mergner, T. Weimer, Performance of ammonia–water based cycles for power generation from low enthalpy heat sources, Energy 88 (2015) 93–100, https://doi. org/10.1016/j.energy.2015.04.084. [3] F. Ayachi, E.B. Ksayer, P. Neveu, A. Zoughaib, Experimental investigation and modeling of a hermetic scroll expander, Appl. Energy 181 (2016) 256–267, https:// doi.org/10.1016/j.apenergy.2016.08.030. [4] G. Qiu, H. Liu, S. Riffat, Expanders for micro-CHP systems with organic Rankine cycle, Appl. Therm. Eng. 31 (2011) 3301–3307, https://doi.org/10.1016/j. applthermaleng.2011.06.008. [5] P. Song, M. Wei, L. Shi, S.N. Danish, C. Ma, A review of scroll expanders for organic Rankine cycle systems, Appl. Therm. Eng. 75 (2015) 54–64, https://doi.org/10. 1016/j.applthermaleng.2014.05.094. [6] M. Imran, M. Usman, B.-S. Park, D.-H. Lee, Volumetric expanders for low grade heat and waste heat recovery applications, Renew. Sustain. Energy Rev. 57 (2016) 1090–1109, https://doi.org/10.1016/j.rser.2015.12.139. [7] T. Yanagisawa, T. Shimizu, M. Fukuta, T. Handa, Study on fundamental performance of scroll expander, Trans. Jpn. Soc. Mech. Eng. Ser. B 54 (1988) 2798–2803. [8] R. Zanelli, D. Favrat, Experimental investigation of a hermetic scroll expandergenerator, in: Proceedings of the International Compressor Engineering Conference at Purdue, 1994, pp. 459–464.
Fig. 10. Accuracy of the generalized model to predict (a) mass displacement, (b) mechanical shaft power and (c) discharge temperature for pure ammonia working fluid.
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