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Assessment of pulse-width modulated flow through serial expansion valve/capillary tube arrangements Adriano F. Ronzoni a,*, Christian J.L. Hermes b, Cla´udio Melo a a
POLO Research Laboratories for Emerging Technologies in Cooling and Thermophysics, Department of Mechanical Engineering, Federal University of Santa Catarina, 88040970 Floriano´polis-SC, Brazil b Center for Applied Thermodynamics, Department of Mechanical Engineering, Federal University of Parana´, P.O. Box 19011, 81531990 Curitiba-PR, Brazil
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abstract
Article history:
This paper outlines an experimental and theoretical study on pulse-width modulated
Received 15 February 2012
(PWM) flow of HFC-134a through serial expansion valve/capillary tube arrangements. The
Received in revised form
influence of the operating conditions (inlet pressure, duty cycle, and pulse period) and the
3 September 2012
geometry (valve diameter) on the refrigerant mass flow rate was experimentally evaluated
Accepted 4 September 2012
using a purpose-built testing facility with strict control of all relevant variables. Several
Available online 13 September 2012
experiments were carried out and the results used to calibrate an algebraic first-principles mathematical model. A good agreement between the experimental and calculated data
Keywords:
was achieved, with more than 85% of the data points falling within the 15% error band. It
Expansion valve
was also observed that the model followed the experimental results closely.
Capillary tube
ª 2012 Elsevier Ltd and IIR. All rights reserved.
Experimentation Modeling Household application Hybrid control Two step expansion process
Evaluation de la largeur de l’e´coulement module´ par la largeur des pulsations dans les configurations a` de´tendeur/tube capillaire Mots cle´s : De´tendeur ; Tube capillaire ; Expe´rimentation ; Mode´lisation ; Application domestique ; Re´gulation hybride ; De´tente en deux e´tapes
* Corresponding author. Tel.: þ55 48 3234 5691. E-mail address: [email protected] (A.F. Ronzoni). 0140-7007/$ e see front matter ª 2012 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2012.09.001
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 2 5 8 e2 6 9
Nomenclature Roman A Cv D h L m M p u U v V w x Xv t
1.
cross sectional area, m2 discharge coefficient, dimensionless inner diameter, m specific enthalpy, kJ kg1 length, m mass flow rate, kg s1 refrigerant mass, kg pressure, Pa specific internal energy, kJ kg1 internal energy, kJ specific volume, m3 kg1 volume, m3 pulse width, s vapor quality, dimensionless valve position, dimensionless time, s
Introduction
Household refrigerating appliances consume around 6% of the electrical energy produced worldwide (Melo and Silva, 2010), a number that has pushed both customers and governments towards the development of highly efficient products. However, in spite of the large amount of research effort placed nowadays on the development of more advanced refrigeration systems, only a modest net effect in terms of energy consumption has been achieved in the last few years. This suggests that the conventional vapor compression refrigeration technology is close to its limits (Melo and Silva, 2010). Vapor compression refrigeration systems are usually comprised of a single-speed compressor, a fixed-orifice expansion device, two heat exchangers (i.e., the condenser and the evaporator), and a volatile working fluid. In recent years, small capacity variable-speed compressors have been adopted by many companies in an attempt to match the system cooling capacity with the thermal load for any operating condition (Tassou and Qureshi, 1998; Aprea and Mastrullo, 2002). In addition, it has been advocated in the open literature that the system performance improves further when a variable expansion valve is also employed, since it keeps the evaporator fully activated during most of the compressor runtime (Tassou and Al-Nizari, 1991; Pottker and Melo, 2007). Recent investigations have focused on the development of strategies for the simultaneous control of
Greek F f s
259
capillary coefficient, dimensionless duty cycle (¼w/s), dimensionless pulse period, s
Subscripts c chamber cap capillary tube e exit f flash-point g saturated vapor i inlet l saturated liquid o nominal v valve
variable-speed compressors and variable expansion valves, showing very positive impacts on the system performance (Leducq et al., 2006; Marcinichen et al., 2008; Schurt et al., 2009). Nevertheless, variable expansion valves specifically designed for household refrigerators (cooling capacities w100 W) are not yet available on the market. In a first attempt to address this issue, electric expansion valves (EEVs) originally developed for light commercial refrigeration systems (cooling capacities w1 kW) were used in series with capillary tubes in order to provide suitable refrigerant mass flow rates for household refrigerators (Thiessen and Klein, 2007). This type of valve is driven by a pulse-width modulation (PWM) control strategy, meaning that the capillary tube flow is transient and therefore completely different from the regular capillary tube flow exhaustively studied in the open literature (Hermes et al., 2008; Khan et al., 2009). The aim of this paper is to carry out a comprehensive but not exhaustive experimental and theoretical analysis on the adiabatic flow of HFC-134a through a serial expansion valve/ capillary tube arrangement, as illustrated in Fig. 1. For this arrangement, a purpose-built test facility was constructed and used to study the effect of the operating conditions and valve geometry on the refrigerant mass flow rate. A firstprinciples mathematical model was also developed and validated against an experimental database with 60 data points.
Fig. 1 e Schematic representation of a serial expansion valve/capillary tube arrangement.
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Fig. 2 e Schematic representation of the test rig.
2.
Experimental work
2.1.
Test rig
2.2.
The experimental study was carried out using a purpose-built test rig that is essentially a vapor compression refrigeration loop, as shown in Fig. 2. The refrigerant is firstly pumped by a 10.61 cm3 variable-speed reciprocating compressor (VCC). The discharged refrigerant then passes through two oil separators (OS1, OS2) where it is diverted into two different streams. One stream returns the oil and part of the refrigerant to the suction line, while the other carries the refrigerant to a row of coalescent filters (FC1, FC2, FC3) to guarantee an oil-free circulation of HFC-134a in the high-pressure side of the rig (i.e., the test section). An accumulator is placed after the filters to ensure there is no two-phase refrigerant going into the mass flow meter located at point 2 in Fig. 2. A hot-gas by-pass is used to set the evaporating pressure through the opening of valve VEP01. The refrigerant is condensed in a water-cooled heat exchanger (CONDEN), whose capacity is controlled by the PCV valve that regulates the water flow rate, and subcooled by an additional water-cooled heat exchanger (SC). The refrigerant subcooling at the inlet of the test section is controlled by a PID-driven electric heater. After the expansion, the refrigerant is evaporated in a fan-supplied tubefin evaporator (EVAP) and returns to the compressor, closing the cycle. A liquid accumulator (ACC) is placed at the outlet of the evaporator to avoid any return of liquid to the compressor.
Test section
The variable expansion device under analysis is comprised of a capillary tube of 3.0 m length and 0.83 mm inner diameter mounted in series with a PWM-driven electric expansion valve. This device was placed inside a partially dismountable 20 20 cm2 wooden box, filled with polystyrene blocks that guarantee the necessary thermal insulation (see Fig. 3). The insulation thickness ranges from 100 to 140 mm, thus limiting the heat transfer rate to figures of approximately 1 W. Two couplers (BF1, BF2) ensured that the capillary tube remained straight and in the horizontal position. The valve was fixed as illustrated in Fig. 4. The refrigerant inlet temperature was measured by an immersion T-type thermocouple, while the refrigerant exit temperature and the temperature profile along the tube wall were measured by standard T-type thermocouples (0.13 mm-diameter) with a maximum uncertainty of 0.2 C. The refrigerant inlet and outlet absolute pressures were measured by strain gage pressure transducers with maximum uncertainties of 2 kPa and 1 kPa, respectively. The refrigerant mass flow rate was measured by a Coriolistype mass flow meter with maximum uncertainty of 0.04 kg h1. The expansion valve is driven by an 8.5 W coil (EC) controlled by an electronic module that sets the pulse period (s) and width (w) thus defining the duty cycle (f), i.e., the ratio between the pulse width and period (w/s), as depicted in Fig. 5.
Fig. 3 e Schematic representation of the test section.
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Fig. 4 e Detail of the test section.
2.3.
Test plan
To reduce the number of experimental runs a factorial experimental design was employed (Box et al., 1978). This technique allows the evaluation of the effect of each independent variable as well as the effect of the interactions among them on the dependent variables (e.g., mass flow rate and intermediate pressure). Basically, the factorial design is composed of factors and levels. The former are the controllable independent variables under investigation (i.e., inlet pressure, inlet temperature, pulse period, duty cycle, valve diameter), whereas the latter are the values selected for each independent parameter. The tests were carried out at two inlet pressures (1.1 and 1.5 MPa), two valve diameters (0.4 mm and 1.6 mm), two pulse periods (2 and 8 s) and five duty cycles (10, 25, 50, 75 and 90%). The condenser subcooling and the evaporating pressure were both maintained constant at 8 C, and 0.1 MPa, respectively. This full factorial experiment resulted in 40 experimental data points. Additional tests were also performed with two other valves (0.8 mm and 1.20 mm), but maintaining the period fixed
at 2 s, resulting in 20 experimental data points. In total, 60 experimental data points were gathered in this study, with mass flow rates ranging from 1.5 to 7.5 kg h1. The test conditions are summarized in Table 1, whereas Table 2 provides samples of experimental data for all valves. In addition, it should be noted that the mass flow rate and intermediate pressures do not have a constant value through time due to the fluctuating nature of the PWM valve. Therefore, since the data acquisition system is able to record 51 readings per channel per minute, average values for the mass P flow rate ðm ¼ 1=51 51 k¼1 mk Þ and intermediate pressure P51 ðpi ¼ 1=51 k¼1 pk Þ were adopted, where the superscripted bar stands for the mean values. A particular test was considered to be in steady-state regime when all controlled variables reached the following conditions: sa smax and jyt e y0j 3sa, where sa is the standard deviation, y0 and yt are the variable value at the beginning and end of the test interval, evaluated from a linear best fit to the measured data, and smax is the measurement uncertainty. Approximately 3 h were required to reach the steady-state regime.
3.
Simulation model
In addition to the experimental work, a modeling exercise was also carried out to predict the refrigerant mass flow rate through the expansion device under analysis. The model was divided into three domains, namely expansion valve, capillary tube and intermediate chamber, as described in the next subsections (see Fig. 1). The model considers the refrigerant flow through both the EEV and the capillary tube as quasi-steady, whereas the transient effects related to the refrigerant accumulation in the intermediate chamber were also taken into account.
3.1.
Valve sub-model
The instantaneous mass flow rate through the expansion valve, mv, is calculated from the orifice equation, as follows:
Fig. 5 e Schematic representation of the PWM control.
mv ¼ Cv Av Xv
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pi pc 2 vi
(1)
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Table 2 e Samples of test data (s [ 2 s). Table 1 e Experimental plan and test conditions. Test no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Test no.
Dv [mm]
s [s]
f [%]
pi [bar]
Ti [ C]
pe [bar]
0.4
2
10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90
11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15
35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
8
1.6
2
8
0.8
2
1.2
2
1 2 3 4 5 41 42 43 44 45 51 52 53 54 55 21 22 23 24 25
Dv [mm]
f [%]
pi [bar]
Ti [ C]
pe [bar]
pc [bar]
m [kg h1]
0.4
10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90
11.04 10.96 11.00 11.02 11.03 11.06 11.00 11.00 11.05 11.03 10.99 10.98 11.02 11.01 10.96 10.97 11.07 11.07 11.00 10.95
34.9 34.9 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.1 35.0 35.0 34.9 35.2
0.97 0.98 0.96 0.99 0.99 0.97 0.98 0.98 0.97 1.01 0.98 1.04 1.01 0.96 1.00 1.04 0.99 1.00 1.02 1.03
6.50 8.85 9.62 10.51 10.71 8.56 8.49 9.58 10.28 10.69 8.32 8.87 9.66 10.38 10.68 9.20 8.77 9.74 10.41 10.73
1.98 3.64 4.32 5.16 5.34 3.64 3.96 4.84 5.44 5.79 3.91 4.36 5.08 5.46 5.81 3.93 4.45 4.71 5.33 5.49
0.8
1.2
1.6
where Av is the nominal free flow passage ð¼ pD2v =4Þ, Dv is the valve diameter, Cv is the valve discharge coefficient, Xv is the valve position defined according to the PWM control action on the valve (i.e., “0” when the valve is closed and “1” when it is open), vi is the specific volume at the valve entrance, and pi and pc are the valve inlet pressure and the intermediate pressure, respectively.
3.2.
Capillary tube sub-model
The capillary tube flow was considered adiabatic, thus allowing the mass flow rate, mcap, to be calculated using the explicit algebraic formulation proposed by Hermes et al. (2010),
mcap
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !! u 5 uDcap pc pf pf pe b ape þ b þ 2 ln ¼ Ft þ Lcap vf a a apf þ b
(2)
where Dcap and Lcap are the capillary tube inner diameter and length, respectively, pc is the intermediate pressure, pe is the evaporating pressure, and the subscript “f” denotes the flashpoint. According to Hermes et al. (2010), Equation (2) predicts the experimental data for the subcooled liquid at the capillary inlet with deviations not larger than 10%, when the following values are adopted: F ¼ 6.0, a ¼ vf ð1 kÞ and . b ¼ vf pf k, where k ¼ 1:63$105 p0:72 f When there is two-phase flow at the capillary tube inlet, which is most likely to occur when the capillary tube is placed after an expansion valve, Equation (2) simplifies to: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D5cap pc pe b ape þ b þ 2 ln Lcap a a apc þ b
mcap ¼ F
3.3.
(3)
Intermediate chamber sub-model
The intermediate chamber volume (23 ml for all valves) acts as a buffer which, when combined with the PWM-induced flow, produces mass and pressure oscillations that affect the refrigerant mass flow rate through the expansion device.
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263
Therefore, a time evolving equation for the intermediate pressure, which couples Equation (1) with Equation (3), is required. For this purpose, transient mass and energy balances inside the chamber were invoked, yielding dMc ¼ mv mcap dt
(4)
dUc ¼ mv mcap h dt
(5)
where Mc and Uc are the mass and internal energy of the refrigerant contained in the intermediate chamber. Assuming a two-phase homogeneous flow at the valve outlet, Uc can be written as follows: Uc ¼ Mc ug xc þ ul ð1 xc Þ
(6)
Fig. 6 e Main effect analysis.
Noting that for a homogeneous two-phase flow, the vapor quality can be expressed as follows, xc ¼
vc vl ; vg vl
vg vc vg vl
1 xc ¼
(7)
Equation (6) can then be rewritten as: Uc ¼ Mc
vg ul vl ug ug ul þ Vc ¼ Mc f pc þ Vc g pc vg vl vg vl
(8)
where Vc is the volume of the intermediate chamber. In addition, it can be shown that dMc dUc ¼ f pc þ dt dt
Mc
! df dg dpc þ V c dt dp pc dp pc
(9)
Yielding the following evolving equation for the intermediate pressure: mv mcap h f pc dpc ¼ df dg dt Mc þ Vc dp pc dp pc
(10)
geometry (internal diameter) was assessed using the 40 data points collected during the full factorial experiment (see tests 1 to 40 in Table 1). Fig. 6 shows the main effects of the independent parameters on the mass flow rate, i.e., the average mass flow rate variation when one parameter is changed from its lower to its upper level while all other parameters are held constant. As all parameters were varied between two levels, with the exception of the duty cycle, concurrent analyzes were performed considering the following pair of levels for this parameter: 10/ 25%, 10/50%, 10/75%, and 10/90%. It can be noted that the main trends of the effects are quite similar, independently of the pair of levels adopted for the duty cycle. It can also be observed that the main effect of the duty cycle is predominant, especially when the difference between
The functions f( p) and g( p) were calculated beforehand for HFC-134a and a polynomial fitting to the saturation pressure was performed.
3.4.
Solution scheme
A PWM-wave (see Fig. 5) is the model input that defines whether the valve is opened (Xv ¼ 1) or closed (Xv ¼ 0). Equations (4) and (10) are then integrated over time using a forward (explicit) 1storder scheme with a fixed time-step of s/1000, and with the condensing pressure taken as the initial condition for the intermediate pressure (i.e., pc y pi). At each time-step, the refrigerant mass flow rate through the valve and the capillary tube are computed using Equations (1) and (3), and using the intermediate pressure obtained from Equation (10). The transient simulation is continued until a periodic steady-state regime is achieved.
4.
Discussion
4.1.
Experimental analysis
The sensitivity of the mass flow rate to the operating parameters (duty cycle, pulse period, and inlet pressure) and valve
Fig. 7 e Discharge coefficient as a function of the valve diameter.
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a
Fig. 8 e Predicted vs. measured data using different values of F.
b
the levels is increased, as expected. In contrast, the main effect of the pulse period is minor, meaning that the refrigerant mass flow rate is only slightly affected by this variable. It is also shown that the main effect of the pulse period is negative, that is, the mass flow rate decreases as this parameter increases. Conversely, the main effects of the inlet pressure and valve diameter are both positive and of similar magnitude.
a
Fig. 10 e Comparison between predicted and experimental mass flow rates: (a) Dv [ 0.4 mm and (b) Dv [ 1.6 mm.
4.2.
b
Numerical analysis
All 60 experimental data points were used during the model calibration exercise. Firstly, the valve discharge coefficient was adjusted as a function of the valve diameter by minimizing the squares of the errors between the predicted and measured mass flow rate. It has been found that the discharge coefficient is well represented by Equation (11), with the valve diameter expressed in [mm], as illustrated in Fig. 7. Cv ¼ 0:516$D1:18 v
Fig. 9 e Model predictions: (a) mean mass flow rate and (b) mean intermediate pressure.
(11)
Secondly, the capillary tube model F-coefficient was also adjusted in order to better match the experimental data. As shown in Fig. 8, the model underestimates the measured data by 10% when F ¼ 6 is used. However, the model predictions are significantly improved when F ¼ 7 is adopted. One should note that Hermes et al. (2010) reported that their model underestimates the refrigerant mass flow rate up to 10% for low subcooling degrees, which explains the change experienced by F in the present work. Fig. 9 compares the predicted averaged mass flow rates and intermediate pressures with their experimental counterparts for various valve diameters and duty cycles. As can be seen, in comparison with the experimental data, 70% and 85% of the
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265
Fig. 11 e Time evolution of the valve and capillary tube instantaneous mass flow rates: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
266
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Fig. 12 e Zoomed view of evolution over time of the valve and capillary tube instantaneous mass flow rates: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
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267
Fig. 13 e Evolution over time of the instantaneous intermediate pressure: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
268
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model predictions lie within the 10% and 15% error bands, respectively. Fig. 10 depicts the mass flow rate as a function of the duty cycle, inlet pressure, pulse period and valve diameter, revealing that the experimental trends are reasonably well predicted by the model. Fig. 11 shows the evolution over time of the instantaneous refrigerant mass flow rate through the expansion device mounted with a 1.6 mm (I.D.) valve, when the duty cycle was varied from 10% (Fig. 11a) to 90% (Fig. 11e) and the pulse period was kept at 8 s. These results are repeated (zoomed view) in Fig. 12. It may be noted that for duty cycles lower than 10% the valve and the capillary tube mass flow rates never match, indicating that most of time the intermediate chamber is not completely filled with liquid refrigerant. From a duty cycle of 25% onward the valve and the capillary tube mass flow rates match for longer periods as the valve duty cycle increases. It may also be observed that the peak in the valve mass flow rate for low duty cycles, soon after the valve opening, is higher when compared to high duty cycles. This is so because the intermediate pressure immediately before the valve opening is higher in the latter case (see Fig. 13). It also worth mentioning that the valve mass flow rate is zero when the valve is closed, although the capillary tube mass flow rate is not, as refrigerant flows due to the pressure difference between the intermediate chamber and the evaporator.
a
8.0 Dv= 1.6 mm
Mass flow rate [kg·h-1]
7.0 6.0 5.0
5.
4.0 3.0
Dcap = 1.00 mm Dcap = 0.83 mm (Original)
2.0
Dcap = 0.70 mm
1.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.9
1.0
Duty cycle
b
8.0 Dv = 1.6 mm
7.0 Mass flow rate [kg·h-1]
Fig. 13 shows the behavior of the instantaneous intermediate pressure over time. It may be seen that as the duty cycle is increased, the intermediate pressure tends toward the condensing pressure, forming a plateau where the valve and capillary tube mass flow rates are equal and the chamber is completely filled with liquid refrigerant. Fig. 14 shows the effect of the inner diameter of the capillary tube (Fig. 14a) and intermediate chamber volume (Fig. 14b) on the refrigerant mass flow rate, for a pulse period of 8 s. It can be seen that the expansion device becomes less sensitive to the duty cycle as the inner diameter of the capillary tube decreases. It can also be noted for low duty cycles (<10%), the hydraulic restriction relies mostly on the valve, so that the intermediate chamber is not flooded with liquid refrigerant. However, for higher duty cycles (>10%), the governing hydraulic resistance is mostly due to the capillary tube, so that the chamber is flooded with liquid refrigerant. Therefore, one can conclude that the capillary tube governs the expansion process for duty cycles greater than 10%. Furthermore, it can be observed that the expansion device under analysis can provide a broad range of refrigerant mass flow rates, ranging from 0 to 6 kg s1 (0.83 mm) and 0e7.5 kg s1 (1.0 mm). The effect of the volume of the intermediate chamber on the refrigerant mass flow rate was also explored by doubling and halving the original value. It can be observed that for duty cycles lower than 5% and higher than 90%, the refrigerant mass flow rate is almost unaffected by the chamber volume. However, the chamber volume tends to increase the refrigerant mass flow rate within the duty cycle range of 5e90%, since in this region the intermediate pressure is kept at a higher level.
6.0 5.0 4.0
2·Vc Vc
3.0
0.5·Vc
2.0 1.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Duty cycle
Fig. 14 e Effect of (a) capillary tube inner diameter and (b) chamber volume on mean mass flow rate.
Conclusions
An experimental facility was designed and constructed to investigate the pulsating refrigerant flow through serial PWMdriven expansion valve-capillary tube arrangements. In total, 60 experimental data points were gathered for various operating (inlet pressure, duty cycle, pulse period) and geometric (valve diameter) conditions. The dataset was used to assess the effect of the independent parameters on the resulting mass flow rate, and it was found that the duty cycle plays a dominant role, followed by the valve diameter and the inlet pressure. On the other hand, the pulse period showed no relevant effect. The dataset was also used to calibrate an algebraic quasisteady model for predicting the refrigerant mass flow rate through such an expansion device. The valve mass flow rate was calculated from the orifice equation, with empirical discharge coefficients derived from the experimental data. A strict relationship was found between the discharge coefficient and the valve diameter. The capillary tube mass flow rate was obtained from an explicit analytical approach, where the intermediate pressured was calculated assuming a twophase homogeneous flow at the valve outlet. The model results were compared with the experimental data and it was verified that more than 70% and 85% of the mass flow rate and intermediate pressure data predicted by the model lay within 10% and 15% error bands, respectively.
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The experimental trends were also reasonably well predicted by the model. A numerical analysis carried out with a 1.6 mm (I.D.) valve revealed that the valve and the capillary tube mass flow rates never match for a duty cycle lower than 10%, indicating that the intermediate chamber under this condition never becomes completely filled with refrigerant. From a duty cycle of 25% onward, the valve and the capillary tube mass flow rates match for longer periods as the duty cycle increases.
Acknowledgments This study was carried out at the POLO Labs under National Grant No. 573581/2008-8 (National Institute of Science and Technology in Refrigeration and Thermophysics) funded by the Brazilian Government Agency CNPq. Financial support from the company Embraco S.A. is also duly acknowledged. Thanks are also addressed to Mr. E. A. Grein, former undergraduate student at the POLO Labs, for his valuable support with the experiments.
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Aprea, C., Mastrullo, R., 2002. Experimental evaluation of electronic and thermostatic expansion valves performances using R22 and R407C. Appl. Thermal Eng. 22, 206e218. Box, G.E.P., Hunter, W.G., Hunter, J.S., 1978. Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. John Wiley & Sons, New York, USA. Hermes, C.J.L., Melo, C., Gonc¸alves, J.M., 2008. Modeling of nonadiabatic capillary tube flows: a simplified approach and
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comprehensive experimental validation. Int. J. Refrigeration 31, 1358e1367. Hermes, C.J.L., Melo, C., Knabben, F.T., 2010. Algebraic solution of capillary tube flows, part I: adiabatic capillary tubes. Appl. Thermal Eng. 30, 449e457. Khan, M.K., Kumar, R., Sahoo, P.K., 2009. Flow characteristics of refrigerants flowing through capillary tubes e a review. Appl. Thermal Eng. 29, 1426e1439. Leducq, D., Guilpart, J., Trystram, G., 2006. Non-linear predictive control of a vapour compression cycle. Int. J. Refrigeration 29, 761e772. Marcinichen J.B, Holanda T.N, Melo C., 2008, A dual SISO controller for a vapor compression refrigeration system, 12th Int. Refrig. Conf. at Purdue, West Lafayette-IN, USA, Paper 2444. Melo C, Silva L.W., 2010, A Perspective on Energy Savings in Household Refrigerators, Sustainable Refrigeration and Heat Pump Technology Conference, Stockholm, Sweden. Pottker G, Melo C., 2007, A Study on the Relationship between Compressor Speed and Expansion Valve Opening in Refrigeration Systems, Conf. on Compressors and their Systems, London, UK, Paper C658. Schurt, L.C., Hermes, C.J.L., Trofino Neto, A., 2009. A model-driven multivariable controller for vapor compression refrigeration systems. Int. J. Refrigeration 32, 1672e1682. Tassou, S.A., Al-Nizari, H., 1991. Investigation of the steady state and transient performance of reciprocating chiller equipped with an electronic expansion valve. Heat Recovery Syst. CHP 11, 541e550. Tassou, S.A., Qureshi, T.Q., 1998. Comparative performance evaluation of positive displacement compressors in variablespeed refrigeration applications. Int. J. Refrigeration 21, 29e41. Thiessen M.R, Klein F.H., 2007, Flow rate control system in refrigeration circuits, method for controlling a refrigeration system, World Intellectual Property Organization, Patent WO 2007/118293 A2.
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Assessment of pulse-width modulated flow through serial expansion valve/capillary tube arrangements Adriano F. Ronzoni a,*, Christian J.L. Hermes b, Cla´udio Melo a a
POLO Research Laboratories for Emerging Technologies in Cooling and Thermophysics, Department of Mechanical Engineering, Federal University of Santa Catarina, 88040970 Floriano´polis-SC, Brazil b Center for Applied Thermodynamics, Department of Mechanical Engineering, Federal University of Parana´, P.O. Box 19011, 81531990 Curitiba-PR, Brazil
article info
abstract
Article history:
This paper outlines an experimental and theoretical study on pulse-width modulated
Received 15 February 2012
(PWM) flow of HFC-134a through serial expansion valve/capillary tube arrangements. The
Received in revised form
influence of the operating conditions (inlet pressure, duty cycle, and pulse period) and the
3 September 2012
geometry (valve diameter) on the refrigerant mass flow rate was experimentally evaluated
Accepted 4 September 2012
using a purpose-built testing facility with strict control of all relevant variables. Several
Available online 13 September 2012
experiments were carried out and the results used to calibrate an algebraic first-principles mathematical model. A good agreement between the experimental and calculated data
Keywords:
was achieved, with more than 85% of the data points falling within the 15% error band. It
Expansion valve
was also observed that the model followed the experimental results closely.
Capillary tube
ª 2012 Elsevier Ltd and IIR. All rights reserved.
Experimentation Modeling Household application Hybrid control Two step expansion process
Evaluation de la largeur de l’e´coulement module´ par la largeur des pulsations dans les configurations a` de´tendeur/tube capillaire Mots cle´s : De´tendeur ; Tube capillaire ; Expe´rimentation ; Mode´lisation ; Application domestique ; Re´gulation hybride ; De´tente en deux e´tapes
* Corresponding author. Tel.: þ55 48 3234 5691. E-mail address: [email protected] (A.F. Ronzoni). 0140-7007/$ e see front matter ª 2012 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2012.09.001
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 2 5 8 e2 6 9
Nomenclature Roman A Cv D h L m M p u U v V w x Xv t
1.
cross sectional area, m2 discharge coefficient, dimensionless inner diameter, m specific enthalpy, kJ kg1 length, m mass flow rate, kg s1 refrigerant mass, kg pressure, Pa specific internal energy, kJ kg1 internal energy, kJ specific volume, m3 kg1 volume, m3 pulse width, s vapor quality, dimensionless valve position, dimensionless time, s
Introduction
Household refrigerating appliances consume around 6% of the electrical energy produced worldwide (Melo and Silva, 2010), a number that has pushed both customers and governments towards the development of highly efficient products. However, in spite of the large amount of research effort placed nowadays on the development of more advanced refrigeration systems, only a modest net effect in terms of energy consumption has been achieved in the last few years. This suggests that the conventional vapor compression refrigeration technology is close to its limits (Melo and Silva, 2010). Vapor compression refrigeration systems are usually comprised of a single-speed compressor, a fixed-orifice expansion device, two heat exchangers (i.e., the condenser and the evaporator), and a volatile working fluid. In recent years, small capacity variable-speed compressors have been adopted by many companies in an attempt to match the system cooling capacity with the thermal load for any operating condition (Tassou and Qureshi, 1998; Aprea and Mastrullo, 2002). In addition, it has been advocated in the open literature that the system performance improves further when a variable expansion valve is also employed, since it keeps the evaporator fully activated during most of the compressor runtime (Tassou and Al-Nizari, 1991; Pottker and Melo, 2007). Recent investigations have focused on the development of strategies for the simultaneous control of
Greek F f s
259
capillary coefficient, dimensionless duty cycle (¼w/s), dimensionless pulse period, s
Subscripts c chamber cap capillary tube e exit f flash-point g saturated vapor i inlet l saturated liquid o nominal v valve
variable-speed compressors and variable expansion valves, showing very positive impacts on the system performance (Leducq et al., 2006; Marcinichen et al., 2008; Schurt et al., 2009). Nevertheless, variable expansion valves specifically designed for household refrigerators (cooling capacities w100 W) are not yet available on the market. In a first attempt to address this issue, electric expansion valves (EEVs) originally developed for light commercial refrigeration systems (cooling capacities w1 kW) were used in series with capillary tubes in order to provide suitable refrigerant mass flow rates for household refrigerators (Thiessen and Klein, 2007). This type of valve is driven by a pulse-width modulation (PWM) control strategy, meaning that the capillary tube flow is transient and therefore completely different from the regular capillary tube flow exhaustively studied in the open literature (Hermes et al., 2008; Khan et al., 2009). The aim of this paper is to carry out a comprehensive but not exhaustive experimental and theoretical analysis on the adiabatic flow of HFC-134a through a serial expansion valve/ capillary tube arrangement, as illustrated in Fig. 1. For this arrangement, a purpose-built test facility was constructed and used to study the effect of the operating conditions and valve geometry on the refrigerant mass flow rate. A firstprinciples mathematical model was also developed and validated against an experimental database with 60 data points.
Fig. 1 e Schematic representation of a serial expansion valve/capillary tube arrangement.
260
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Fig. 2 e Schematic representation of the test rig.
2.
Experimental work
2.1.
Test rig
2.2.
The experimental study was carried out using a purpose-built test rig that is essentially a vapor compression refrigeration loop, as shown in Fig. 2. The refrigerant is firstly pumped by a 10.61 cm3 variable-speed reciprocating compressor (VCC). The discharged refrigerant then passes through two oil separators (OS1, OS2) where it is diverted into two different streams. One stream returns the oil and part of the refrigerant to the suction line, while the other carries the refrigerant to a row of coalescent filters (FC1, FC2, FC3) to guarantee an oil-free circulation of HFC-134a in the high-pressure side of the rig (i.e., the test section). An accumulator is placed after the filters to ensure there is no two-phase refrigerant going into the mass flow meter located at point 2 in Fig. 2. A hot-gas by-pass is used to set the evaporating pressure through the opening of valve VEP01. The refrigerant is condensed in a water-cooled heat exchanger (CONDEN), whose capacity is controlled by the PCV valve that regulates the water flow rate, and subcooled by an additional water-cooled heat exchanger (SC). The refrigerant subcooling at the inlet of the test section is controlled by a PID-driven electric heater. After the expansion, the refrigerant is evaporated in a fan-supplied tubefin evaporator (EVAP) and returns to the compressor, closing the cycle. A liquid accumulator (ACC) is placed at the outlet of the evaporator to avoid any return of liquid to the compressor.
Test section
The variable expansion device under analysis is comprised of a capillary tube of 3.0 m length and 0.83 mm inner diameter mounted in series with a PWM-driven electric expansion valve. This device was placed inside a partially dismountable 20 20 cm2 wooden box, filled with polystyrene blocks that guarantee the necessary thermal insulation (see Fig. 3). The insulation thickness ranges from 100 to 140 mm, thus limiting the heat transfer rate to figures of approximately 1 W. Two couplers (BF1, BF2) ensured that the capillary tube remained straight and in the horizontal position. The valve was fixed as illustrated in Fig. 4. The refrigerant inlet temperature was measured by an immersion T-type thermocouple, while the refrigerant exit temperature and the temperature profile along the tube wall were measured by standard T-type thermocouples (0.13 mm-diameter) with a maximum uncertainty of 0.2 C. The refrigerant inlet and outlet absolute pressures were measured by strain gage pressure transducers with maximum uncertainties of 2 kPa and 1 kPa, respectively. The refrigerant mass flow rate was measured by a Coriolistype mass flow meter with maximum uncertainty of 0.04 kg h1. The expansion valve is driven by an 8.5 W coil (EC) controlled by an electronic module that sets the pulse period (s) and width (w) thus defining the duty cycle (f), i.e., the ratio between the pulse width and period (w/s), as depicted in Fig. 5.
Fig. 3 e Schematic representation of the test section.
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Fig. 4 e Detail of the test section.
2.3.
Test plan
To reduce the number of experimental runs a factorial experimental design was employed (Box et al., 1978). This technique allows the evaluation of the effect of each independent variable as well as the effect of the interactions among them on the dependent variables (e.g., mass flow rate and intermediate pressure). Basically, the factorial design is composed of factors and levels. The former are the controllable independent variables under investigation (i.e., inlet pressure, inlet temperature, pulse period, duty cycle, valve diameter), whereas the latter are the values selected for each independent parameter. The tests were carried out at two inlet pressures (1.1 and 1.5 MPa), two valve diameters (0.4 mm and 1.6 mm), two pulse periods (2 and 8 s) and five duty cycles (10, 25, 50, 75 and 90%). The condenser subcooling and the evaporating pressure were both maintained constant at 8 C, and 0.1 MPa, respectively. This full factorial experiment resulted in 40 experimental data points. Additional tests were also performed with two other valves (0.8 mm and 1.20 mm), but maintaining the period fixed
at 2 s, resulting in 20 experimental data points. In total, 60 experimental data points were gathered in this study, with mass flow rates ranging from 1.5 to 7.5 kg h1. The test conditions are summarized in Table 1, whereas Table 2 provides samples of experimental data for all valves. In addition, it should be noted that the mass flow rate and intermediate pressures do not have a constant value through time due to the fluctuating nature of the PWM valve. Therefore, since the data acquisition system is able to record 51 readings per channel per minute, average values for the mass P flow rate ðm ¼ 1=51 51 k¼1 mk Þ and intermediate pressure P51 ðpi ¼ 1=51 k¼1 pk Þ were adopted, where the superscripted bar stands for the mean values. A particular test was considered to be in steady-state regime when all controlled variables reached the following conditions: sa smax and jyt e y0j 3sa, where sa is the standard deviation, y0 and yt are the variable value at the beginning and end of the test interval, evaluated from a linear best fit to the measured data, and smax is the measurement uncertainty. Approximately 3 h were required to reach the steady-state regime.
3.
Simulation model
In addition to the experimental work, a modeling exercise was also carried out to predict the refrigerant mass flow rate through the expansion device under analysis. The model was divided into three domains, namely expansion valve, capillary tube and intermediate chamber, as described in the next subsections (see Fig. 1). The model considers the refrigerant flow through both the EEV and the capillary tube as quasi-steady, whereas the transient effects related to the refrigerant accumulation in the intermediate chamber were also taken into account.
3.1.
Valve sub-model
The instantaneous mass flow rate through the expansion valve, mv, is calculated from the orifice equation, as follows:
Fig. 5 e Schematic representation of the PWM control.
mv ¼ Cv Av Xv
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pi pc 2 vi
(1)
262
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Table 2 e Samples of test data (s [ 2 s). Table 1 e Experimental plan and test conditions. Test no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Test no.
Dv [mm]
s [s]
f [%]
pi [bar]
Ti [ C]
pe [bar]
0.4
2
10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90
11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15 11 11 11 11 11 15 15 15 15 15
35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47 35 35 35 35 35 47 47 47 47 47
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
8
1.6
2
8
0.8
2
1.2
2
1 2 3 4 5 41 42 43 44 45 51 52 53 54 55 21 22 23 24 25
Dv [mm]
f [%]
pi [bar]
Ti [ C]
pe [bar]
pc [bar]
m [kg h1]
0.4
10 25 50 75 90 10 25 50 75 90 10 25 50 75 90 10 25 50 75 90
11.04 10.96 11.00 11.02 11.03 11.06 11.00 11.00 11.05 11.03 10.99 10.98 11.02 11.01 10.96 10.97 11.07 11.07 11.00 10.95
34.9 34.9 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.1 35.0 35.0 34.9 35.2
0.97 0.98 0.96 0.99 0.99 0.97 0.98 0.98 0.97 1.01 0.98 1.04 1.01 0.96 1.00 1.04 0.99 1.00 1.02 1.03
6.50 8.85 9.62 10.51 10.71 8.56 8.49 9.58 10.28 10.69 8.32 8.87 9.66 10.38 10.68 9.20 8.77 9.74 10.41 10.73
1.98 3.64 4.32 5.16 5.34 3.64 3.96 4.84 5.44 5.79 3.91 4.36 5.08 5.46 5.81 3.93 4.45 4.71 5.33 5.49
0.8
1.2
1.6
where Av is the nominal free flow passage ð¼ pD2v =4Þ, Dv is the valve diameter, Cv is the valve discharge coefficient, Xv is the valve position defined according to the PWM control action on the valve (i.e., “0” when the valve is closed and “1” when it is open), vi is the specific volume at the valve entrance, and pi and pc are the valve inlet pressure and the intermediate pressure, respectively.
3.2.
Capillary tube sub-model
The capillary tube flow was considered adiabatic, thus allowing the mass flow rate, mcap, to be calculated using the explicit algebraic formulation proposed by Hermes et al. (2010),
mcap
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !! u 5 uDcap pc pf pf pe b ape þ b þ 2 ln ¼ Ft þ Lcap vf a a apf þ b
(2)
where Dcap and Lcap are the capillary tube inner diameter and length, respectively, pc is the intermediate pressure, pe is the evaporating pressure, and the subscript “f” denotes the flashpoint. According to Hermes et al. (2010), Equation (2) predicts the experimental data for the subcooled liquid at the capillary inlet with deviations not larger than 10%, when the following values are adopted: F ¼ 6.0, a ¼ vf ð1 kÞ and . b ¼ vf pf k, where k ¼ 1:63$105 p0:72 f When there is two-phase flow at the capillary tube inlet, which is most likely to occur when the capillary tube is placed after an expansion valve, Equation (2) simplifies to: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D5cap pc pe b ape þ b þ 2 ln Lcap a a apc þ b
mcap ¼ F
3.3.
(3)
Intermediate chamber sub-model
The intermediate chamber volume (23 ml for all valves) acts as a buffer which, when combined with the PWM-induced flow, produces mass and pressure oscillations that affect the refrigerant mass flow rate through the expansion device.
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263
Therefore, a time evolving equation for the intermediate pressure, which couples Equation (1) with Equation (3), is required. For this purpose, transient mass and energy balances inside the chamber were invoked, yielding dMc ¼ mv mcap dt
(4)
dUc ¼ mv mcap h dt
(5)
where Mc and Uc are the mass and internal energy of the refrigerant contained in the intermediate chamber. Assuming a two-phase homogeneous flow at the valve outlet, Uc can be written as follows: Uc ¼ Mc ug xc þ ul ð1 xc Þ
(6)
Fig. 6 e Main effect analysis.
Noting that for a homogeneous two-phase flow, the vapor quality can be expressed as follows, xc ¼
vc vl ; vg vl
vg vc vg vl
1 xc ¼
(7)
Equation (6) can then be rewritten as: Uc ¼ Mc
vg ul vl ug ug ul þ Vc ¼ Mc f pc þ Vc g pc vg vl vg vl
(8)
where Vc is the volume of the intermediate chamber. In addition, it can be shown that dMc dUc ¼ f pc þ dt dt
Mc
! df dg dpc þ V c dt dp pc dp pc
(9)
Yielding the following evolving equation for the intermediate pressure: mv mcap h f pc dpc ¼ df dg dt Mc þ Vc dp pc dp pc
(10)
geometry (internal diameter) was assessed using the 40 data points collected during the full factorial experiment (see tests 1 to 40 in Table 1). Fig. 6 shows the main effects of the independent parameters on the mass flow rate, i.e., the average mass flow rate variation when one parameter is changed from its lower to its upper level while all other parameters are held constant. As all parameters were varied between two levels, with the exception of the duty cycle, concurrent analyzes were performed considering the following pair of levels for this parameter: 10/ 25%, 10/50%, 10/75%, and 10/90%. It can be noted that the main trends of the effects are quite similar, independently of the pair of levels adopted for the duty cycle. It can also be observed that the main effect of the duty cycle is predominant, especially when the difference between
The functions f( p) and g( p) were calculated beforehand for HFC-134a and a polynomial fitting to the saturation pressure was performed.
3.4.
Solution scheme
A PWM-wave (see Fig. 5) is the model input that defines whether the valve is opened (Xv ¼ 1) or closed (Xv ¼ 0). Equations (4) and (10) are then integrated over time using a forward (explicit) 1storder scheme with a fixed time-step of s/1000, and with the condensing pressure taken as the initial condition for the intermediate pressure (i.e., pc y pi). At each time-step, the refrigerant mass flow rate through the valve and the capillary tube are computed using Equations (1) and (3), and using the intermediate pressure obtained from Equation (10). The transient simulation is continued until a periodic steady-state regime is achieved.
4.
Discussion
4.1.
Experimental analysis
The sensitivity of the mass flow rate to the operating parameters (duty cycle, pulse period, and inlet pressure) and valve
Fig. 7 e Discharge coefficient as a function of the valve diameter.
264
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a
Fig. 8 e Predicted vs. measured data using different values of F.
b
the levels is increased, as expected. In contrast, the main effect of the pulse period is minor, meaning that the refrigerant mass flow rate is only slightly affected by this variable. It is also shown that the main effect of the pulse period is negative, that is, the mass flow rate decreases as this parameter increases. Conversely, the main effects of the inlet pressure and valve diameter are both positive and of similar magnitude.
a
Fig. 10 e Comparison between predicted and experimental mass flow rates: (a) Dv [ 0.4 mm and (b) Dv [ 1.6 mm.
4.2.
b
Numerical analysis
All 60 experimental data points were used during the model calibration exercise. Firstly, the valve discharge coefficient was adjusted as a function of the valve diameter by minimizing the squares of the errors between the predicted and measured mass flow rate. It has been found that the discharge coefficient is well represented by Equation (11), with the valve diameter expressed in [mm], as illustrated in Fig. 7. Cv ¼ 0:516$D1:18 v
Fig. 9 e Model predictions: (a) mean mass flow rate and (b) mean intermediate pressure.
(11)
Secondly, the capillary tube model F-coefficient was also adjusted in order to better match the experimental data. As shown in Fig. 8, the model underestimates the measured data by 10% when F ¼ 6 is used. However, the model predictions are significantly improved when F ¼ 7 is adopted. One should note that Hermes et al. (2010) reported that their model underestimates the refrigerant mass flow rate up to 10% for low subcooling degrees, which explains the change experienced by F in the present work. Fig. 9 compares the predicted averaged mass flow rates and intermediate pressures with their experimental counterparts for various valve diameters and duty cycles. As can be seen, in comparison with the experimental data, 70% and 85% of the
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265
Fig. 11 e Time evolution of the valve and capillary tube instantaneous mass flow rates: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
266
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Fig. 12 e Zoomed view of evolution over time of the valve and capillary tube instantaneous mass flow rates: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
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267
Fig. 13 e Evolution over time of the instantaneous intermediate pressure: (a) 10%, (b) 25%, (c) 50%, (d) 75% and (e) 90%.
268
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model predictions lie within the 10% and 15% error bands, respectively. Fig. 10 depicts the mass flow rate as a function of the duty cycle, inlet pressure, pulse period and valve diameter, revealing that the experimental trends are reasonably well predicted by the model. Fig. 11 shows the evolution over time of the instantaneous refrigerant mass flow rate through the expansion device mounted with a 1.6 mm (I.D.) valve, when the duty cycle was varied from 10% (Fig. 11a) to 90% (Fig. 11e) and the pulse period was kept at 8 s. These results are repeated (zoomed view) in Fig. 12. It may be noted that for duty cycles lower than 10% the valve and the capillary tube mass flow rates never match, indicating that most of time the intermediate chamber is not completely filled with liquid refrigerant. From a duty cycle of 25% onward the valve and the capillary tube mass flow rates match for longer periods as the valve duty cycle increases. It may also be observed that the peak in the valve mass flow rate for low duty cycles, soon after the valve opening, is higher when compared to high duty cycles. This is so because the intermediate pressure immediately before the valve opening is higher in the latter case (see Fig. 13). It also worth mentioning that the valve mass flow rate is zero when the valve is closed, although the capillary tube mass flow rate is not, as refrigerant flows due to the pressure difference between the intermediate chamber and the evaporator.
a
8.0 Dv= 1.6 mm
Mass flow rate [kg·h-1]
7.0 6.0 5.0
5.
4.0 3.0
Dcap = 1.00 mm Dcap = 0.83 mm (Original)
2.0
Dcap = 0.70 mm
1.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.9
1.0
Duty cycle
b
8.0 Dv = 1.6 mm
7.0 Mass flow rate [kg·h-1]
Fig. 13 shows the behavior of the instantaneous intermediate pressure over time. It may be seen that as the duty cycle is increased, the intermediate pressure tends toward the condensing pressure, forming a plateau where the valve and capillary tube mass flow rates are equal and the chamber is completely filled with liquid refrigerant. Fig. 14 shows the effect of the inner diameter of the capillary tube (Fig. 14a) and intermediate chamber volume (Fig. 14b) on the refrigerant mass flow rate, for a pulse period of 8 s. It can be seen that the expansion device becomes less sensitive to the duty cycle as the inner diameter of the capillary tube decreases. It can also be noted for low duty cycles (<10%), the hydraulic restriction relies mostly on the valve, so that the intermediate chamber is not flooded with liquid refrigerant. However, for higher duty cycles (>10%), the governing hydraulic resistance is mostly due to the capillary tube, so that the chamber is flooded with liquid refrigerant. Therefore, one can conclude that the capillary tube governs the expansion process for duty cycles greater than 10%. Furthermore, it can be observed that the expansion device under analysis can provide a broad range of refrigerant mass flow rates, ranging from 0 to 6 kg s1 (0.83 mm) and 0e7.5 kg s1 (1.0 mm). The effect of the volume of the intermediate chamber on the refrigerant mass flow rate was also explored by doubling and halving the original value. It can be observed that for duty cycles lower than 5% and higher than 90%, the refrigerant mass flow rate is almost unaffected by the chamber volume. However, the chamber volume tends to increase the refrigerant mass flow rate within the duty cycle range of 5e90%, since in this region the intermediate pressure is kept at a higher level.
6.0 5.0 4.0
2·Vc Vc
3.0
0.5·Vc
2.0 1.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Duty cycle
Fig. 14 e Effect of (a) capillary tube inner diameter and (b) chamber volume on mean mass flow rate.
Conclusions
An experimental facility was designed and constructed to investigate the pulsating refrigerant flow through serial PWMdriven expansion valve-capillary tube arrangements. In total, 60 experimental data points were gathered for various operating (inlet pressure, duty cycle, pulse period) and geometric (valve diameter) conditions. The dataset was used to assess the effect of the independent parameters on the resulting mass flow rate, and it was found that the duty cycle plays a dominant role, followed by the valve diameter and the inlet pressure. On the other hand, the pulse period showed no relevant effect. The dataset was also used to calibrate an algebraic quasisteady model for predicting the refrigerant mass flow rate through such an expansion device. The valve mass flow rate was calculated from the orifice equation, with empirical discharge coefficients derived from the experimental data. A strict relationship was found between the discharge coefficient and the valve diameter. The capillary tube mass flow rate was obtained from an explicit analytical approach, where the intermediate pressured was calculated assuming a twophase homogeneous flow at the valve outlet. The model results were compared with the experimental data and it was verified that more than 70% and 85% of the mass flow rate and intermediate pressure data predicted by the model lay within 10% and 15% error bands, respectively.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 2 5 8 e2 6 9
The experimental trends were also reasonably well predicted by the model. A numerical analysis carried out with a 1.6 mm (I.D.) valve revealed that the valve and the capillary tube mass flow rates never match for a duty cycle lower than 10%, indicating that the intermediate chamber under this condition never becomes completely filled with refrigerant. From a duty cycle of 25% onward, the valve and the capillary tube mass flow rates match for longer periods as the duty cycle increases.
Acknowledgments This study was carried out at the POLO Labs under National Grant No. 573581/2008-8 (National Institute of Science and Technology in Refrigeration and Thermophysics) funded by the Brazilian Government Agency CNPq. Financial support from the company Embraco S.A. is also duly acknowledged. Thanks are also addressed to Mr. E. A. Grein, former undergraduate student at the POLO Labs, for his valuable support with the experiments.
references
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