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Feasibility study of a bowtie compressor with novel capacity modulation
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International Journal of Refrigeration 30 (2007) 1427e1438 www.elsevier.com/locate/ijrefrig
Feasibility study of a bowtie compressor with novel capacity modulation Jun-Hyeung Kim*, Eckhard A. Groll School of Mechanical Engineering, Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907, USA Received 14 November 2006; received in revised form 27 February 2007; accepted 21 March 2007 Available online 28 March 2007
Abstract A novel refrigeration compressor with an integrated method of capacity modulation for use in domestic refrigerators/freezers is proposed and analyzed here. The compressor is called bowtie compressor due to its two sector-shaped, opposing compression chambers forming a bowtie. The bowtie compressor modulates the cooling capacity by changing the piston stroke without changes of the clearance volume for better thermodynamic efficiency. The new compressor includes a unique off-center-line mechanism so that the piston stroke can be varied without creating an extra clearance volume. To investigate the feasibility of the proposed compressor, a simulation model has been developed. A detailed description of the bowtie compressor and its simulation model are presented in this paper. In addition, parametric studies have been carried out to see how the proposed compressor performance can be improved. Ó 2007 Elsevier Ltd and IIR. All rights reserved. Keywords: Domestic refrigerator; Design; Compressor; Oscillating compressor; Capacity reduction; Simulation; Performance
Compresseur « nœud de papillon » muni d’un nouveau dispositif de modulation : E´tude de faisabilite´ Mots cle´s : Re´frige´rateur domestique ; Conception ; Compresseur ; Compresseur oscillant ; Re´duction de puissance ; Simulation ; Performance
1. Introduction The compressor of typical domestic refrigerators/ freezers is designed to deliver the full cooling capacity at
* Corresponding author. Tel.: þ1 765 496 5143; fax: þ1 765 496 0787. E-mail addresses: [email protected] (J.-H. Kim), [email protected] (E.A. Groll). 0140-7007/$35.00 Ó 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.03.006
a single speed. Since the cooling capacity of domestic refrigerators/freezers varies throughout their operation, the capacity of the compressor has to be modulated to match the cooling loads. Conventional compressors are designed to operate at the maximum cooling load. As a result, they cycle on and off in response to the change of the cooling load. This on-and-off operation is not efficient and consumes unnecessary amounts of energy whenever the compressors are turned back on. One way to increase the efficiency of the compressors is to continuously modulate the compressor capacity based on the demand of the cooling load.
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Nomenclature A AðtÞ BDC CD Cv D h hðtÞ ks KðtÞ l m meq m_ P Q_ r01 r02 r24 r25 R ! R !01 R !13 R 25 rpm t T TDC Upiston V d V x
area (m2) time-dependent heat transfer area (m2) bottom-dead-center drag coefficient specific heat at constant volume (J kg1 K1) diameter (m) enthalpy (J kg1) heat transfer coefficient (W m2 K1) spring stiffness (N m1) thermal conductivity of the gas (W m1 K1) initial length between the centers of the crank and the journal shafts (m) refrigerant mass (kg) equivalent mass of the plate spring (kg) mass flow rate (kg s1) pressure (Pa) heat transfer rate (W) length of the eccentricity (m) length of the ground vector (m) length of the journal shaft vector (m) length of the vane vector (m) thermal resistance (K W1) eccentricity vector connecting rod vector vane vector rotation per minute time (s) temperature (K) top-dead-center mean piston speed (m s1) velocity (m s1) volume (m3) x directional coordinate or x distance or control length (cm)
Greek letters g specific heat ratio h efficiency mðtÞ dynamic viscosity of the gas (Pa s) v specific volume (m3 kg1) u angular velocity (s1) u12 angular velocity of the journal shaft (s1) un;1 natural frequency at the first mode shape (s1) r density (kg m3) q angle (radian)
A typical method for continuous capacity modulation is variable speed control in which a variable speed motor controls the speed of the piston stroke to match the cooling loads. Theoretical studies by Holdcack-Janssen and Kruse [1], and Zubair and Bahel [2] reported that variable speed control is the most energy efficient capacity control method at full and part load conditions in comparison to on/off
q01 q02 q12
angle of the eccentricity vector (radian) angle of the ground vector (radian) angle of the connecting rod vector (radian)
Superscript / vector e average Subscripts amb ambient cir circumference of the valve comp compression cond condensing cv clearance volume cyl cylinder dis discharge evap evaporating f flux force flow effective flow of the port friction friction gas gas high high-side in into the cylinder leak leakage loss loss low low-side m mechanical motor motor o total oil oil o,s,c overall isentropic compressor out out of the cylinder p pressure force piston piston port port rad radiation shell in the shell suct suction super superheating swept swept th throat of a valve port tr transitional v volumetric valve valve wall cylinder wall
control, hot gas bypass, clearance volume control, and cylinder unloading. In addition, variable speed control introduces the following other advantages: (1) precise thermal control is possible; (2) the reliability of the compressor is improved due to the reduced number of on/off cycles; (3) the response time for set conditions is fast. However, variable speed control is the most expensive method among the other capacity
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control methods due to the extra cost associated with electronic speed controllers. In comparison, compressors that do not use variable speed motors, but are able to operate with capacity modulation, can be thought of as cost-effective alternatives to variable speed compressors. The desired features of a compressor with mechanical capacity control are as follows: (1) the thermal efficiency should be as high as that of variable speed motor-driven compressors; (2) the compressor controls the cooling capacity at significantly lower cost than variable speed compressors; (3) the compressor is able to deliver continuous capacity modulation; and (4) the compressor structures are simple and reliable. This paper explores a compressor with novel capacity modulation. The new compressor is based on the conceptual design of the BeardePennock variable-stroke compressor [3], but includes significant modifications, such as a unique off-center-line mechanism. By using the new off-center-line
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mechanism and an inexpensive controller, the compressor can change the piston stroke while keeping the same clearance volume for better thermodynamic efficiency. The compressor uses an inexpensive fixed speed motor and does not need a rotational change of the crankshaft. An embodiment of the new compressor, named ‘‘Bowtie Compressor’’, is presented in detail, and its simulation model, the simulation results, and parametric studies are discussed in this paper. 2. Description of the bowtie compressor 2.1. Description of the capacity control The new compressor concept is shown in Fig. 1. It provides an ideal solution to achieve capacity modulation. The crankshaft rotates counter-clockwise, and the piston rod makes the piston reciprocate axially and not linearly. Thus, two compressions take place at the same time. The
Fig. 1. Diagram of the proposed design.
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crankshaft, piston rod, and piston are arranged in such a way that the piston rod is perpendicular to the crankshaft when the piston reaches the top-dead center as shown in the top schematic of Fig. 1. The cylinder is placed in the sliding chamber with mechanical springs and pressurized on both ends by the suction and the discharge gases. The cylinder is allowed to slide based on the difference of the two pressure forces. When more capacity is demanded, the difference between the two pressure forces increases. Thus, the force on the right side of the cylinder increases. As a result, the cylinder moves to the left creating a longer stroke which increases the compression volume as shown in the bottom schematic of Fig. 1. It has to be noted that the cylinder movement does not create an extra clearance volume. Thus, the capacity modulation is achieved solely by changing the piston stroke. Two-step capacity modulation can be realized more easily than multi-step capacity modulation. When more capacity is needed, the high-side pressure is introduced to the right side of the sliding cylinder, and the pressure force moves the cylinder all the way to the left end until it reaches some stopping mechanism. As a consequence, the piston stroke and thus the capacity are increased. On the other hand, when the normal capacity is required, the introduced pressure is vented out so that the mechanical spring pulls the sliding cylinder back to the right hand side, its initial position. Thus, the stroke and capacity are decreased. 2.2. Description of the prototype design Based on the new compressor concept, a prototype compressor is proposed. Fig. 2 shows a cylinder module which consists of six main parts. The module creates two volumetric chambers when all parts are fully assembled. Each chamber produces a volume of 11 cm3. The module is designed so that at most 4.696 cm3 out of the 11 cm3 will be used for the compression process, and the other volume will serve as an intermediate pocket for the incoming refrigerant. Part 4,
which can be considered the vane, is a flat rectangular rod with two suction valves on each side. Thus, the suction valves and the rod circumferentially reciprocate together. The discharge valves are installed in Part 3, and are concealed by two pockets on the bottom of Part 5. On the top of Part 5, there are two refrigerant inlets and two outlets. Thus, the refrigerant flows into the compressor from the inlets of Part 5, and passes through the pockets in Part 2, the suction valves, the compression chamber, the discharge valves, and the pockets in Part 5, and finally flows out of the outlets on Part 5. Part 6 has two rectangular holes so that Part 4 can be inserted in the middle and the connecting rod can be inserted at the bottom. Four panels are put together to linearly guide the cylinder module as shown in an embedded figure at the bottom, right side of Fig. 2. The module is spring-biased so that in default mode, the module is pushed to the right end, and can slide from the right end to the left end by using the actuator. At startup, the actuator is off so that the compressor operates with a smaller swept volume. When more capacity is needed, some of the discharge gas is bypassed to activate the actuator. Thus, it results in moving the module to the left end, which creates a larger swept volume. 3. Theoretical analysis To simulate the proposed bowtie compressor, the processes that contribute most to the performance of the bowtie compressor are analyzed. 3.1. Analysis of the kinematics The analysis of the kinematics of the bowtie compressor is based on the work of Beard and Pennock [3]. Unlike the vector analysis done by Beard and Pennock, a complex analysis is used for the analysis of the kinematics of the bowtie compressor. The complex analysis is more mathematically concise and easier to use than the vector analysis when analyzing the kinematics of a compressor. A vector diagram using an off-center-line mechanism is shown in Fig. 3. The
R25
12
0, r01
3
r01
R12
R01 1
2 12
01
0
R02
l
x, r01
Connectinf Rod & Journal shaft Parts
02
0, 0 Crank Shaft Parts
l Fig. 2. Views of the cylinder module.
R24
Fig. 3. Vector diagram of the proposed design.
x
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! eccentricity vector, R 01 , rotates counter-clockwise. When ! the eccentricity vector, R 01 , is at 90 , the vane vector, ! R 25 , reaches the top-dead-center, TDC. When the eccentric! ity vector, R 01 , further rotates to the point where the angle ! between the eccentricity vector, R 01 , and the connecting ! ! rod vector, R 13 , reaches 90 , the vane vector, R 25 , reaches the bottom-dead-center, BDC. The difference between these two points creates the swept volume of the compressor. The swept volume per unit depth, d V cyl cyl, of the cylinder is determined by: 2 2 q12 pr24 ð1Þ d V cyl ¼ pr25 2p Using a complex analysis, q12 and u12 can be calculated as: r02 sinq02 r01 sinq01 q12 ¼ tan1 ð2Þ r02 cosq02 r01 cosq01 dq12 1 dq01 u12 ¼ r ¼ 01 sec2 q12 dt dt # " r02 ðcosq01 cosq02 þ sinq01 sinq02 Þ r01 ð3Þ ðr02 cosq02 r01 cosq01 Þ2 Thus, the speed of the vane end is determined as r25 u12 . 3.2. Analysis of the dynamics The methodology for the force analysis is based on the work by Beard and Pennock [3]. A force analysis of the proposed design is performed by making the following assumptions: (1) no friction; (2) constant angular velocity of the crankshaft. Using Newton’s second law and equations of angular motion, effective forces in the proposed design are determined [4]. 3.3. Conservation of mass and energy The mass change with time inside the cylinder is determined from the conservation of mass as: dmcyl dmsuct dmleak;in dmdisc dmleak;out ¼ þ dt dt dt dt dt
ð4Þ
The first law of thermodynamics is applied to derive the temperature change with time in the cylinder [5]. The resulting equation is as follows: dmleak;in dTcyl 1 dmsuct ¼ hsuc hcyl þ hleak;in hcyl mcyl Cv dt dt dt vPcyl dmcyl dV dcyl dQcyl;wall þTcyl þ ð5Þ vcyl vTcyl v dt dt dt There is no heat transfer coefficient available for the bowtie compressor. However, since the vane is reciprocating circumferentially, the heat transfer coefficient [6] for reciprocating compressors is adopted for the instantaneous heat
1431
transfer rate from the refrigerant to the cylinder wall, Q_ cyl;wall in Eq. (5). Todescat et al. [7] recommended that the heat transfer coefficient is multiplied by a factor of three for a better prediction of the heat transfer rate. The resulting equation is as follows: 0:7 KðtÞ rðtÞUpiston Dpiston hðtÞ ¼ 3 0:7 ð6Þ Dpiston mðtÞ where KðtÞ, rðtÞ, and mðtÞ are thermal conductivity, density, and dynamic viscosity of refrigerant, respectively. Dpiston is the diameter of the piston, and Upiston is the mean piston velocity (¼2 stroke rpm/60). Modifications are needed in determining the piston diameter and stroke since the swept volume of the vane is not in a cylindrical shape and the stroke of the vane changes with the radius. Thus, a hydraulic diameter and a mean stroke are calculated and used instead. Then, the instantaneous heat transfer from the refrigerant to the cylinder wall is determined as:
Q_ cyl;wall ¼ hðtÞAðtÞ Tcyl ðtÞ Twall ð7Þ where AðtÞ and Twall are the heat transfer area and the mean wall temperature. It should be noted that the cylinder wall temperature is assumed to be constant. Adair et al. [8] reported that the cylinder wall temperature for a reciprocating compressor changed to less than 0.6 K from its time average temperature. Thus, a constant cylinder wall temperature is assumed here as well. 3.4. Dynamic valve model It is assumed that the gas in the cylinder is at uniform temperature and pressure and that the gas flow through the valve port is isentropic, compressible, and ideal. With these assumptions, the mass flow rates of the discharge and the suction valves can be determined by using the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t m_ valve ¼ Aflow 2rhigh Phigh Phigh g 1 Phigh ð8Þ The flow area, Aflow , is strongly related to the valve plate lift and can be determined by an experimental test [9,10]. However, a theoretical analysis also provides the means of determining the relationship of the valve plate lift and the flow area. It can be recognized that there are two dominant regions when a valve opens and closes dynamically. These are a pressure-force dominant region in which the differential pressure force on the valve is the main driving force, and a mass-flux-force dominant region where the pressure forces cancel each other out so that the mass-flux-force is the dominant force as shown in Fig. 4. The mass flow rates at each
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1432 Plow
p m_ valve ¼ m_ vavle;f ¼ rth Vth D2port 4
Plow
cir C.V. Phigh
Po
Po
C.V. Phigh Po th
Plow
Plow
cir
0
x
Pressure Force Dominant Region
The valve plate lift can be determined by analyzing the dynamics of a valve plate. The plate valve is modeled as onedegree of mass and spring [11]. The natural frequency of the plate spring at the first mode is determined [12], and the equivalent mass of the plate spring is calculated as: meq ¼
0 x Flux Force Dominant Region
Fig. 4. Schematic of a valve.
region can be approximately determined by using the following equations: m_ valve;p ¼ rcir Vcir Acir where rcir ¼ f1 Phigh ; Plow and Vcir ¼ f2 Phigh ; Plow vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t ð9Þ ¼ Acir 2rhigh Phigh g 1 Phigh Phigh m_ valve;f ¼ rth Vth Ath where rth ¼ f1 Phigh ; Plow and Vth ¼ f2 Phigh ; Plow vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t ¼ Ath 2rhigh Phigh g 1 Phigh Phigh ð10Þ where m_ valve; p and m_ valve;f are the mass flow rate in the pressure-force dominant and the mass-flux-force dominant regions, respectively. It is assumed that most of the flow inside the square box drawn in the pressure dominant region is stagnant since the leak created by the valve lift is relatively small to the port area. Thus, rcir and Vcir are functions of Phigh and Plow . By recognizing that rcir and Vcir are the same as rth and Vth from Eqs. (9) and (10), the transitional valve lift, xtr , above which the flow area is independent of the valve lift (i.e., the flow area is the port area), can be calculated by letting m_ valve; p to be the same as m_ valve;f : p rcir Vcir ðpDvalve xtr Þ ¼ rth Vth D2port 4 ð11Þ 1 D2port xtr ¼ 4 Dvalve Thus, when the valve lift is less than the transitional valve lift, the valve mass flow rate is determined as: m_ valve ¼ m_ valve; p ¼ rcir Vcir ðpDvalve xÞ
ð12Þ
When the valve lift is larger than and equal to the transitional valve lift, the valve mass flow rate does not change with the valve lift, and it is calculated as:
ð13Þ
ks u2n;1
ð14Þ
The main acting forces on the valve plate are a pressure force, a spring force, a drag force and a mass-flux-force. Other forces, such as the viscous damping force, the oil sticking force and the spring preload force, are neglected due to complexities in identifying them theoretically. For the pressure-force dominant region, the pressure on the left side of the valve obviously decreases from Phigh at the center to Plow at the circumference. However, since the valve area is almost the same as the port area, the dominant pressure on the left side of the valve is assumed to be Phigh . The governing dynamic equation for the pressure force dominant region is derived as: 1 meq €x þ ks x ¼ Phigh Plow Avalve þ CD rth Vth2 Avalve 2
ð15Þ
where CD is a drag coefficient for a round plate, which is 1.17. For the mass-flux-force dominant region, the pressure forces cancel out each other since the control volume is in the same low pressure, Plow . Instead, the mass-flux-force is added. As a result, the governing dynamic equation is given as: 2 1 meq €x þ ks x ¼ rth Vth x_ Aport þ CD rth Vth2 Avalve 2
ð16Þ
3.5. Leakage model The Ishii et al. leakage model [13] is adopted for the compressor simulation. The main reasons are as follows: (1) fairly good agreements between the experimental data and theoretical results; (2) minimal use of experimental coefficients, which can only be acquired by an actual experiment; (3) the computer calculations are not extensive, i.e., only a small number of iterations are needed. In this model, it is assumed that the leakage flow is incompressible, viscous, and turbulent. Five possible leakage passages are identified as shown in Fig. 5: (1) leakage through the radial clearance, m_ leak;01 ; (2) leakage over the vane, m_ leak;02 ; (3) leakage between the side vane and the journal shaft, m_ leak;03 ; (4) leakage between the journal bearing and the journal shaft, m_ leak;04 ; and (5) leakage between the top vane and the journal shaft, m_ leak;05 . Leakage from the valves is not considered because no experimental information is available to determine how the valve clearance changes with change in pressure difference. In addition, in
J.-H. Kim, E.A. Groll / International Journal of Refrigeration 30 (2007) 1427e1438
1433 Qrad,dis,shell
Tgas Tcyl,in
Tsuc Tevap
Tsuper
Tcyl,out
T
Q
wall
Tamb
Tshell
Qshell,amb
Tdis
Qrad,wall,shell dis,gas
Q
wall,gas
Qgas,shell Q friction loss Tgas
Wcomp Wshaft
Qmotor loss
Qoil,gas
Qrad,shell,amb Qoil,shell
Toil Welec
Twall Rwall,gas
Qcyl,wall
Tgas Tshell
Fig. 5. Leakage passages. Tamb
Rgas,shell Qrad,shell,amb
Qmotor loss
Qfriction loss
Qrad,wall,shell
Qrad,dis,shell
Qdis,gas
Rshell,amb
Roil,shell Roil,gas
comparison to the leakage from the vane, the valve leakage is much smaller due to smaller leakage area.
Toil
Fig. 6. Overall compressor energy flows and equivalent thermal resistance network for the bowtie compressor.
3.6. Friction loss model The mechanical friction losses of the bearings are determined using Reynolds Lubrication Equation [14] with the following assumptions: Newtonian flow, incompressible flow, constant dynamic viscosity, negligible inertia effects, no squeeze motion, and negligible pressure variation across the oil film. The friction analysis is performed on five parts of the compressor: the vane, the journal shaft in the cylinder block, the sliding bearing, the journal bearing at the end of the eccentricity rod and the crank shaft journal bearing [4]. The friction model neglects the variation of the oil viscosity with pressure and only considers the variation of oil viscosity as a function of temperature by using Kauzlarich’s correlation [15] for polyol ester oil with an ISO VG number of 22. 3.7. Overall compressor analysis An overall energy balance among the motor, the shell, the gas in the shell, the cylinder module, and the ambient air is considered. The overall energy balance model is developed based on the work presented by Chen et al. [16] by considering a resistance network. The resistance network considered for the bowtie compressor is shown in Fig. 6. Based on the current theoretical model, a simulation code has been developed in Visual Cþþ 6.0 in conjunction with REFPROP 7.0 [17] for thermal properties. GNU Scientific Library [18] that is compiled for Visual Cþþ 6.0 is extensively used for numerical calculations, such as solving linear algebra and finding the roots of nonlinear equations. The
current simulation model requires the following seven initial guess values: (1) the shell temperature; (2) the refrigerant vapor temperature in the shell; (3) the cylinder wall temperature; (4) the discharge temperature; (5) the compressor cylinder outlet temperature; (6) the oil temperature in the oil sump; and (7) the motor RPM. The simulation model continues to iterate until the residuals of each of the seven values are met within an absolute error of 1E02. Fig. 7 shows the flow chart of solving the compressor model starting with the seven initial guess values and an initial step angle. 4. Simulation model validation At this point, a prototype bowtie compressor has not been built and thus, no experimental data are available for model validation. However, in order to validate the model predictions, the model was modified to predict the performance of a conventional hermetic reciprocating compressor for use in domestic refrigerators and freezers. A detailed description of the model modifications and the comparison between experimental results and model predictions are shown in Kim and Groll [19]. The comparisons of the simulation results to the calorimeter data and the compressor map showed that the simulation methodology of the reciprocating compressor model is appropriate. Since the bowtie compressor model is similar to the reciprocating compressor model in many ways, the bowtie compressor model is assumed to be validated in order to
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Initial angle and guess values θi = θi + Δθ
Analysis of Kinematics Analysis of Dynamics Instaneous Heat Transfer Model Leakage Flow Model
dvcyl dθ dmcyl dθ dTcyl dθ
Valve Model
m(θ, vcyl, mcyl, Tcyl) T(θ, vcyl, mcyl, Tcyl)
Do Until One Cyle, where θi = θ0 + 2π Y Overall Energy Balance
N
Vane height Vane thickness Connecting rod length Suction port diameter Leakage clearances Vane radius Cylinder journal bearing radius Eccentricity rod Discharge port diameter
15 mm 4.4 mm 80 mm 8.0 mm 2.5 mm 35 mm 10 mm 10 mm 4.5 mm
5.1. Effect of changes of the swept volume
v(θ, vcyl, mcyl, Tcyl)
Friction Loss Model
N
Table 1 Bowtie compressor geometric parameters
Guess values converged?
The swept volume can increase by up to 55% from 3.04 cm3 to 4.70 cm3. This can be achieved by increasing the control length, x, from the reference point, where the minimum swept volume occurs, to 2.0 cm. The proposed compressor will always startup with the minimum swept volume because the cylinder module is spring-biased. Thus, at default, the cylinder module is positioned at x ¼ 0 cm. While the clearance volume stays unchanged, the swept volume increases with the control distance. Consequently, the compressor work, the enclosed area of a pressureevolume diagram, increases. The predictions of the volumetric, clearance volume and motor efficiencies are plotted in Fig. 8. Two important predictions have to be pointed out. First, the volumetric and clearance volume efficiencies decrease with the swept volume. The main reason for this behavior is that the volume during the suction process and the refrigerant volumetric flow rate at the cylinder inlet decrease as the swept volume decreases. However, it should be noted that since the clearance volume stays constant and less expansion volume is
Y END
Tcond=54.4°C & Tevap=-23.3°C 84
Fig. 7. Flow chart for the compressor simulation model.
80
5. Simulation model results The bowtie compressor is simulated using R-134a as the refrigerant at the operating conditions of Tcond ¼ 54.4 C, Tevap ¼ 23.3 C, and Tamb ¼ Tsuct ¼ 32.2 C. While the compressor swept volume is varied from 3.04 cm3 to 4.70 cm3 in each chamber, the clearance volume for each chamber is fixed at 0.12 cm3. All leakage clearances are set to 2.5 mm. Table 1 lists the geometric parameters of the bowtie compressor that are used in the simulation unless indicated otherwise.
76
Efficiency (%)
conduct the theoretical bowtie compressor performance analysis.
72 68 64 60 56
ηmotor
52
ηcv ηv
48 3.0
3.5
4.0
4.5
5.0
Swept Volume (cm3) Fig. 8. Effect of swept volume on volumetric, clearance volume, and motor efficiencies.
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Mass Flow Rate ηo.s.c -4.3%
1.2
-17.5%
1.0
-31.4% -42.8%
0.8 -52.0% 0.6 3.0
3.5
4.0
90
Frictional Power Loss (W)
88 16
86 14
84 3.0
4.5
5.0
Swept Volume (cm3)
3.5
4.0
4.5
Fig. 10. Effect of swept volume on frictional power loss and mechanical efficiency.
compressor shaft power decreases as well. This explains that the mechanical efficiency decreases even though the frictional power loss decreases. 5.2. Effect of changes of the clearances of the leakage passages The bowtie compressor is simulated with the same geometric parameters listed in Table 1 except that the leakage clearances are varied from 0.5 to 5.0 mm. Fig. 11 shows the fractional leakage flow rate, which is defined as a ratio of average leakage flow rate to actual compressor flow rate. The fractional leakage flow rates through the five leakage flow paths are stacked up for each case of leakage clearance. The total fractional leakage flow rate decreases from
leak01 leak05 leak04 leak03
30
leak02
20
10
0
0.5
1.0
1.5
2.0
2.5
3.8
Clearance ( m) Fig. 9. Effect of swept volume on mass flow rate and overall isentropic compressor efficiency.
5.0
Swept Volume (cm3)
Fractional Leakage Flow Rate (%)
Mass Flow Rate (g/sec)
65 60 55 50 45 40 35 30 25 20 15 10 5 0
Overall Isentropic Compressor Efficiency (%)
1.4
-9.2%
me
18
40
1.6 -14.8% -20.6%
Frictional Power Loss
Mechanical Efficiency (%)
required, the bowtie compressor should have a lower rate of decreases in volumetric and clearance volume efficiencies than typical variable stroke compressors. It should also be noted that the clearance volume efficiency is different from the volumetric efficiency. The clearance volume efficiency does not consider the gas density at the cylinder inlet. Second, the motor efficiency decreases from 83% to 76.2%. This shows that for the given capacity modulation mode, the current motor of the bowtie compressor operates away from the plateau of the motor map, where changes in the motor efficiency are very small. Fig. 9 presents the prediction of the compressor mass flow rate and the overall isentropic compressor efficiency as a function of the swept volume. At these operating conditions, the model of the bowtie compressor predicts a 52% reduction in compressor mass flow rate from 1.504 g/s to 0.722 g/s with an approximately 21% decrease in overall isentropic compressor efficiency from 59.65% to 47.38%. One reason for the decrease in overall isentropic compressor efficiency is that the motor runs off its optimum efficiency at the low capacity conditions. This is not unexpected given that fixed motors are optimized for a certain range where the maximum cooling capacity can be achieved. The compressor mass flow rate decreases almost linearly with the swept volume. This indicates that a linear controller as the actuator can be used to achieve continuous capacity modulation. The frictional power loss and the mechanical efficiency are presented in Fig. 10. The frictional power loss and the mechanical efficiency decrease approximately 22% from 17.2 W to 13.5 W and approximately 5% from 89% to 84.6%, respectively. It is observed that both the frictional power loss and the mechanical efficiency decrease with a reduction in swept volume. When the swept volume decreases, the swept area where friction occurs reduces, which causes less frictional power loss. However, at the same time, the
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Fig. 11. Effect of clearance on leakage.
5.0
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36% to 0.6% when the clearance is reduced from 5.0 to 0.5 mm. The results show that the largest leakage occurs in Leak02, i.e., leakage over the vane. It comprises approximately 73% of the total leakage flow for each case of clearance. The frictional loss and compressor mass flow rate as a function of leakage clearance are shown in Fig. 12. The figure indicates that the mass flow rate starts to increase and then flattens out at a clearance of 1.0 mm when the leakage clearance is varied from 5.0 to 0.5 mm. Meanwhile, the frictional loss slowly increases and then shoots up dramatically at a clearance of 1.5 mm when the leakage clearance is varied from 5.0 to 0.5 mm. These trends strongly indicate that the performance gain by an increase in mass flow rate with smaller clearances could be eliminated at some point due to the increase in frictional losses. The increase in frictional losses implies that the viscous shear stress in the leakage path is more sensitive to changes in the Couette flow than in the Poisson flow. Fig. 13 presents the clearance volume and volumetric efficiencies as a function of leakage clearance. The figure indicates that the clearance volume efficiency and volumetric efficiency have opposite trends when the leakage clearance increases. The clearance volume efficiency increases by 7.2% to a value of 78.5% whereas the volumetric efficiency decreases approximately 20.6% to a value of 53.5% as the leakage clearance increase from 0.5 to 5.0 mm. The reason for the decreasing volumetric efficiency is that the mass flow rate decreases. The increasing trend in the clearance volume can be explained by considering trapped refrigerant mass in the clearance volume. As the clearance increases, less amount of refrigerant is trapped in the clearance volume due to the increased leakage. As a result, the expansion volume decreases. Thus, the clearance volume efficiency increases since the clearance volume and swept volume are kept the same. Fig. 14 shows the overall isentropic efficiency as a function of leakage clearance. The figure shows that there is an
80 75
Efficiency (%)
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70 cv v
65 60 55 50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Clearance ( m) Fig. 13. Effect of clearance on ‘‘clearance volume and volumetric efficiencies’’.
optimum leakage clearance where the best compressor performance can be achieved. The figure indicates that in a clearance range of 1.0e5.0 mm the compressor tends to perform better with smaller clearance because the performance gain of the increased mass flow rate offsets the performance loss due to the increased frictional loss. The overall isentropic compressor efficiency is improved by approximately 22% when the leakage clearance is decreased from 5.0 to 1.0 mm. However, as the leakage clearance is further reduced to 0.5 mm, the overall isentropic efficiency decreases because the performance loss due to the increased frictional loss is larger than the gain of the increased flow rate. 5.3. Effect of a ratio of the vane radius to height The bowtie compressor is simulated by using ratios of the vane radius to the vane height as shown in Table 2 while
32
Friction Loss (W)
28
1.6
1.5
26 24 1.4
22 20
1.3
18
Mass Flow Rate (g/sec)
30
Friction Loss Mass Flow Rate
Overall Isentropic Compressor Efficiency (%)
62 34
60 58 56 54 52 50
16 14
1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Clearance ( m)
Clearance ( m) Fig. 12. Effect of clearance on friction loss and mass flow rate.
Fig. 14. Effect of clearance on overall isentropic compressor efficiency.
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Table 2 Ratio of the vane radius to the vane height Swept volume ¼ 4.696 cm3, swept angle ¼ 30.05 , clearance volume ¼ 0.12 cm3, leakage clearance ¼ 2.5 mm Ratio 0.5 0.75 1 1.25 1.5 1.75 2 Vane radius (mm) 21.99 24.73 26.95 28.84 30.5 31.99 33.35 Vane height (mm) 43.98 32.98 26.95 23.07 20.33 18.28 16.67
2.25 34.6 15.38
2.5 35.77 14.31
Swept volume ¼ 4.696 cm3, swept angle ¼ 25.05 , clearance volume ¼ 0.12 cm3, leakage clearance ¼ 2.5 mm Ratio 0.5 0.75 1 1.25 1.5 1.75 2 Vane radius (mm) 23.57 26.57 28.99 31.05 32.86 34.49 35.97 Vane height (mm) 47.14 35.43 28.99 24.84 21.91 19.71 17.99
2.25 37.34 16.59
2.5 38.61 15.44
maintaining the same swept volume and angle. Fig. 15 presents that the mass flow rate and overall efficiency at two different swept angles as a function of the ratio of the vane radius to the vane height. The figure shows that in each case of swept angle the compressor mass flow rate and the overall isentropic efficiency have maximum values at the same ratio of 1.25. In each case of swept angle, it is observed that the minimum leakage occurs at the ratio of 1.25. This explains why the maximum compressor mass flow rate is achieved at that ratio. Consequently, the results show that there is an optimum combination of the vane radius and vane height to achieve the maximum compressor performance at fixed leakage clearance and swept volume. It is shown that the optimum ratio does not change with swept angles. 6. Conclusions A new compressor concept that changes the piston stroke by simple mechanical means while keeping the same
59.0 2.75
59.2
1.470 2.50
59.4
1.475 2.25
59.6
1.480
2.00
59.8
1.485
1.75
60.0
1.490
1.50
60.2
1.495
1.25
60.4
1.500
1.00
60.6
1.505
0.75
60.8
1.510
0.50
61.0
1.515
0.25
1.520
Overall Isentropic Compressor Efficiency (%)
Compressor Mass Flow Rate (g/sec)
Mass Flow Rate, Swept Angle = 25.05° Mass Flow Rate, Swept Angle = 31.89° o.s.c, Swept Angle = 25.05° o.s.c, Swept Angle = 31.89°
Ratio of Vane Radius and Height Fig. 15. Effect of a ratio of the vane radius and height on compressor mass flow rate and overall isentropic compressor efficiency at the swept angles of 25.05 and 31.89 .
clearance volume for better thermodynamic efficiency is proposed here. The new compressor is called bowtie compressor, which uses a unique off-center-line mechanism so that the piston stroke can be varied without changes in clearance volume. The concept of a bowtie compressor was described in detail. Subsequently, a prototype design of the bowtie compressor was proposed and discussed. The proposed bowtie compressor has some innate features: (1) the cooling capacity can be controlled inexpensively by using a simple on/off solenoid valve without using premium variable speed motors; (2) the compressor always starts with the shorter piston stroke in default mode which results in a smooth startup due to the reduced motor torque; (3) the overall compressor efficiency is improved by keeping the clearance volume constant at all times; and (4) continuous capacity modulation can be easily realized by replacing the simple solenoid valve with a more complex valve controller, which leads to further improvement of the overall compressor efficiency. A simulation model of the proposed compressor was presented to investigate the feasibility of the bowtie compressor. Furthermore, parametric studies were carried out to investigate the effects of using different geometric parameters on compressor performance. The effects of leakage clearances and the ratio of the vane radius to the vane height while keeping the swept volume constant on compressor performance were studied. The result showed that the bowtie compressor is able to control its mass flow rate (and thus, its cooling capacity) from 50% to 100% using an electronic control valve. Since the proposed compressor has more leakage paths than conventional reciprocating compressors, the effect of changes of the leakage clearance was studied. The simulation results showed that the compressor performance improved as the leakage clearance decreased from 5.0 to 1.0 mm. The reduction in leakage clearance adversely increased the friction loss and decreased the mechanical efficiency, but the overall isentropic compressor efficiency improved because the reduced leakage flow rate increased the mass flow rate of the compressor. However, as the leakage clearance is further reduced to 0.5 mm, the compressor performance decreased. At that point, the increased mass flow rate could not compensate the performance loss by the increased frictional loss. Even though the model
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predicted that the maximum compressor performance would occur at the clearance of 1.0 mm, it has to be noted that reducing the clearance to 1.0 mm may not be practical due to manufacturing costs and challenges. Instead, it would be more feasible to increase the vane thickness so that the maximum compressor performance occurs at larger leakage clearance than 1.0 mm. The study of using different ratios of the vane radius to the vane height while maintaining the same swept volume demonstrated that there is an optimum ratio of vane radius to vane height to achieve the maximum compressor performance at a given swept volume. The optimum ratio of the studied bowtie compressor with the swept volume of 4.7 cm3 is found to be 1.25 and does not change with different swept angles. Although the presented results are solely based on theoretical models and need to be verified using experimental data, it is reasonable to believe that these results capture trends of the actual bowtie compressor performance. The current simulation model can be used as a tool to prototype a bowtie compressor. Acknowledgements The authors would like to express their gratitude to Tecumseh Products Company, who sponsored this study. The authors also thank Joaquim Rigola at Technical University at Catalonia, Spain, for sharing the test data of a reciprocating compressor.
References [1] H. Holdcack-Janssen, H. Kruse, Continuous and discontinuous capacity control for high speed refrigeration compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1984, pp. 67e75. [2] S.M. Zubair, V. Bahel, Compressor capacity modulation scheme, Heating/Piping/Air Conditioning 61 (1989) 135e143. [3] G.R. Pennock, J.E. Beard, The BeardePennock variable-stroke compressor, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1988, pp. 599e607. [4] J.-H. Kim, Analysis of a Bowtie Compressor with Novel Capacity Modulation, Ph.D. thesis, Purdue University, West Lafayette, IN, 2005. [5] S.Y. Sun, T.R. Ren, New method of thermodynamic computation for a reciprocating compressor: computer simulation of working process, International Journal of Mechanical Science 37 (4) (1995) 343e353. [6] W.J.D. Annad, Heat transfer in the cylinder of reciprocating internal combustion engines, Institution of Mechanical Engineering 177 (36) (1963) 973e996.
[7] M.L. Todescat, F. Fagotti, A.T. Prata, R.T.S. Ferreira, Thermal energy analysis in reciprocating hermetic compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1992, pp. 1419e1428. [8] R.P. Adair, E.R. Qvale, J.T. Pearson, Instantaneous heat transfer to the cylinder wall in reciprocating compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1972, pp. 521e526. [9] W. Soedel, Introduction to computer simulation of positive displacement type compressors, Ray W. Herrick Laboratories, 1972. [10] R.T.S. Ferreira, J.L. Driessen, Analysis of the influence of valve geometric parameters on the effective flow and force areas, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1986, pp. 632e646. [11] K. Suefuji, S. Nakayama, Practical method for analysis and estimation of reciprocating hermetic compressor performance, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1980, pp. 15e23. [12] R.D. Blevins, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York, 1979. [13] N. Ishii, K. Bird, K. Sano, M. Oono, S. Iwanura, T. Otokura, Refrigerant leakage flow evaluation for scroll compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1996, pp. 633e638. [14] O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil, Philosophical Transactions of the Royal Society of London 177 (1886) 157e234. [15] J.J. Kauzlarich, Viscosity times density equations for five classes of lubricants, Proceedings of the Institution of Mechanical Engineers Part J: Journal of Engineering Tribology 212 (3) (1998) 235e239. [16] Y. Chen, N.P. Halm, E.A. Groll, J.E. Braun, 2002, Mathematical modeling of scroll compressors e part II: overall scroll compressor modeling, International Journal of Refrigeration 25 (2002) 751e764. [17] REFPROP 7.0, NIST Standard Reference Database 23: NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) version 7.0, National Institute of Standard and Technology, Gaithersburg, Maryland, 2002. [18] M. Galassi, J. Davies, J. Theiler, B. Gough, G. Junqman, M. Booth, F. Rossi, GNU Scientific Library Reference Manual, second ed., Network Theory Ltd., 2003, ISBN 0954161734. [19] J.-H. Kim, E.A. Groll, Bowtie compressor with novel capacity modulation e part II: model validation and parametric studies, in: Proceedings of the International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 2006, p. C151.
International Journal of Refrigeration 30 (2007) 1427e1438 www.elsevier.com/locate/ijrefrig
Feasibility study of a bowtie compressor with novel capacity modulation Jun-Hyeung Kim*, Eckhard A. Groll School of Mechanical Engineering, Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907, USA Received 14 November 2006; received in revised form 27 February 2007; accepted 21 March 2007 Available online 28 March 2007
Abstract A novel refrigeration compressor with an integrated method of capacity modulation for use in domestic refrigerators/freezers is proposed and analyzed here. The compressor is called bowtie compressor due to its two sector-shaped, opposing compression chambers forming a bowtie. The bowtie compressor modulates the cooling capacity by changing the piston stroke without changes of the clearance volume for better thermodynamic efficiency. The new compressor includes a unique off-center-line mechanism so that the piston stroke can be varied without creating an extra clearance volume. To investigate the feasibility of the proposed compressor, a simulation model has been developed. A detailed description of the bowtie compressor and its simulation model are presented in this paper. In addition, parametric studies have been carried out to see how the proposed compressor performance can be improved. Ó 2007 Elsevier Ltd and IIR. All rights reserved. Keywords: Domestic refrigerator; Design; Compressor; Oscillating compressor; Capacity reduction; Simulation; Performance
Compresseur « nœud de papillon » muni d’un nouveau dispositif de modulation : E´tude de faisabilite´ Mots cle´s : Re´frige´rateur domestique ; Conception ; Compresseur ; Compresseur oscillant ; Re´duction de puissance ; Simulation ; Performance
1. Introduction The compressor of typical domestic refrigerators/ freezers is designed to deliver the full cooling capacity at
* Corresponding author. Tel.: þ1 765 496 5143; fax: þ1 765 496 0787. E-mail addresses: [email protected] (J.-H. Kim), [email protected] (E.A. Groll). 0140-7007/$35.00 Ó 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.03.006
a single speed. Since the cooling capacity of domestic refrigerators/freezers varies throughout their operation, the capacity of the compressor has to be modulated to match the cooling loads. Conventional compressors are designed to operate at the maximum cooling load. As a result, they cycle on and off in response to the change of the cooling load. This on-and-off operation is not efficient and consumes unnecessary amounts of energy whenever the compressors are turned back on. One way to increase the efficiency of the compressors is to continuously modulate the compressor capacity based on the demand of the cooling load.
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Nomenclature A AðtÞ BDC CD Cv D h hðtÞ ks KðtÞ l m meq m_ P Q_ r01 r02 r24 r25 R ! R !01 R !13 R 25 rpm t T TDC Upiston V d V x
area (m2) time-dependent heat transfer area (m2) bottom-dead-center drag coefficient specific heat at constant volume (J kg1 K1) diameter (m) enthalpy (J kg1) heat transfer coefficient (W m2 K1) spring stiffness (N m1) thermal conductivity of the gas (W m1 K1) initial length between the centers of the crank and the journal shafts (m) refrigerant mass (kg) equivalent mass of the plate spring (kg) mass flow rate (kg s1) pressure (Pa) heat transfer rate (W) length of the eccentricity (m) length of the ground vector (m) length of the journal shaft vector (m) length of the vane vector (m) thermal resistance (K W1) eccentricity vector connecting rod vector vane vector rotation per minute time (s) temperature (K) top-dead-center mean piston speed (m s1) velocity (m s1) volume (m3) x directional coordinate or x distance or control length (cm)
Greek letters g specific heat ratio h efficiency mðtÞ dynamic viscosity of the gas (Pa s) v specific volume (m3 kg1) u angular velocity (s1) u12 angular velocity of the journal shaft (s1) un;1 natural frequency at the first mode shape (s1) r density (kg m3) q angle (radian)
A typical method for continuous capacity modulation is variable speed control in which a variable speed motor controls the speed of the piston stroke to match the cooling loads. Theoretical studies by Holdcack-Janssen and Kruse [1], and Zubair and Bahel [2] reported that variable speed control is the most energy efficient capacity control method at full and part load conditions in comparison to on/off
q01 q02 q12
angle of the eccentricity vector (radian) angle of the ground vector (radian) angle of the connecting rod vector (radian)
Superscript / vector e average Subscripts amb ambient cir circumference of the valve comp compression cond condensing cv clearance volume cyl cylinder dis discharge evap evaporating f flux force flow effective flow of the port friction friction gas gas high high-side in into the cylinder leak leakage loss loss low low-side m mechanical motor motor o total oil oil o,s,c overall isentropic compressor out out of the cylinder p pressure force piston piston port port rad radiation shell in the shell suct suction super superheating swept swept th throat of a valve port tr transitional v volumetric valve valve wall cylinder wall
control, hot gas bypass, clearance volume control, and cylinder unloading. In addition, variable speed control introduces the following other advantages: (1) precise thermal control is possible; (2) the reliability of the compressor is improved due to the reduced number of on/off cycles; (3) the response time for set conditions is fast. However, variable speed control is the most expensive method among the other capacity
J.-H. Kim, E.A. Groll / International Journal of Refrigeration 30 (2007) 1427e1438
control methods due to the extra cost associated with electronic speed controllers. In comparison, compressors that do not use variable speed motors, but are able to operate with capacity modulation, can be thought of as cost-effective alternatives to variable speed compressors. The desired features of a compressor with mechanical capacity control are as follows: (1) the thermal efficiency should be as high as that of variable speed motor-driven compressors; (2) the compressor controls the cooling capacity at significantly lower cost than variable speed compressors; (3) the compressor is able to deliver continuous capacity modulation; and (4) the compressor structures are simple and reliable. This paper explores a compressor with novel capacity modulation. The new compressor is based on the conceptual design of the BeardePennock variable-stroke compressor [3], but includes significant modifications, such as a unique off-center-line mechanism. By using the new off-center-line
1429
mechanism and an inexpensive controller, the compressor can change the piston stroke while keeping the same clearance volume for better thermodynamic efficiency. The compressor uses an inexpensive fixed speed motor and does not need a rotational change of the crankshaft. An embodiment of the new compressor, named ‘‘Bowtie Compressor’’, is presented in detail, and its simulation model, the simulation results, and parametric studies are discussed in this paper. 2. Description of the bowtie compressor 2.1. Description of the capacity control The new compressor concept is shown in Fig. 1. It provides an ideal solution to achieve capacity modulation. The crankshaft rotates counter-clockwise, and the piston rod makes the piston reciprocate axially and not linearly. Thus, two compressions take place at the same time. The
Fig. 1. Diagram of the proposed design.
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crankshaft, piston rod, and piston are arranged in such a way that the piston rod is perpendicular to the crankshaft when the piston reaches the top-dead center as shown in the top schematic of Fig. 1. The cylinder is placed in the sliding chamber with mechanical springs and pressurized on both ends by the suction and the discharge gases. The cylinder is allowed to slide based on the difference of the two pressure forces. When more capacity is demanded, the difference between the two pressure forces increases. Thus, the force on the right side of the cylinder increases. As a result, the cylinder moves to the left creating a longer stroke which increases the compression volume as shown in the bottom schematic of Fig. 1. It has to be noted that the cylinder movement does not create an extra clearance volume. Thus, the capacity modulation is achieved solely by changing the piston stroke. Two-step capacity modulation can be realized more easily than multi-step capacity modulation. When more capacity is needed, the high-side pressure is introduced to the right side of the sliding cylinder, and the pressure force moves the cylinder all the way to the left end until it reaches some stopping mechanism. As a consequence, the piston stroke and thus the capacity are increased. On the other hand, when the normal capacity is required, the introduced pressure is vented out so that the mechanical spring pulls the sliding cylinder back to the right hand side, its initial position. Thus, the stroke and capacity are decreased. 2.2. Description of the prototype design Based on the new compressor concept, a prototype compressor is proposed. Fig. 2 shows a cylinder module which consists of six main parts. The module creates two volumetric chambers when all parts are fully assembled. Each chamber produces a volume of 11 cm3. The module is designed so that at most 4.696 cm3 out of the 11 cm3 will be used for the compression process, and the other volume will serve as an intermediate pocket for the incoming refrigerant. Part 4,
which can be considered the vane, is a flat rectangular rod with two suction valves on each side. Thus, the suction valves and the rod circumferentially reciprocate together. The discharge valves are installed in Part 3, and are concealed by two pockets on the bottom of Part 5. On the top of Part 5, there are two refrigerant inlets and two outlets. Thus, the refrigerant flows into the compressor from the inlets of Part 5, and passes through the pockets in Part 2, the suction valves, the compression chamber, the discharge valves, and the pockets in Part 5, and finally flows out of the outlets on Part 5. Part 6 has two rectangular holes so that Part 4 can be inserted in the middle and the connecting rod can be inserted at the bottom. Four panels are put together to linearly guide the cylinder module as shown in an embedded figure at the bottom, right side of Fig. 2. The module is spring-biased so that in default mode, the module is pushed to the right end, and can slide from the right end to the left end by using the actuator. At startup, the actuator is off so that the compressor operates with a smaller swept volume. When more capacity is needed, some of the discharge gas is bypassed to activate the actuator. Thus, it results in moving the module to the left end, which creates a larger swept volume. 3. Theoretical analysis To simulate the proposed bowtie compressor, the processes that contribute most to the performance of the bowtie compressor are analyzed. 3.1. Analysis of the kinematics The analysis of the kinematics of the bowtie compressor is based on the work of Beard and Pennock [3]. Unlike the vector analysis done by Beard and Pennock, a complex analysis is used for the analysis of the kinematics of the bowtie compressor. The complex analysis is more mathematically concise and easier to use than the vector analysis when analyzing the kinematics of a compressor. A vector diagram using an off-center-line mechanism is shown in Fig. 3. The
R25
12
0, r01
3
r01
R12
R01 1
2 12
01
0
R02
l
x, r01
Connectinf Rod & Journal shaft Parts
02
0, 0 Crank Shaft Parts
l Fig. 2. Views of the cylinder module.
R24
Fig. 3. Vector diagram of the proposed design.
x
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! eccentricity vector, R 01 , rotates counter-clockwise. When ! the eccentricity vector, R 01 , is at 90 , the vane vector, ! R 25 , reaches the top-dead-center, TDC. When the eccentric! ity vector, R 01 , further rotates to the point where the angle ! between the eccentricity vector, R 01 , and the connecting ! ! rod vector, R 13 , reaches 90 , the vane vector, R 25 , reaches the bottom-dead-center, BDC. The difference between these two points creates the swept volume of the compressor. The swept volume per unit depth, d V cyl cyl, of the cylinder is determined by: 2 2 q12 pr24 ð1Þ d V cyl ¼ pr25 2p Using a complex analysis, q12 and u12 can be calculated as: r02 sinq02 r01 sinq01 q12 ¼ tan1 ð2Þ r02 cosq02 r01 cosq01 dq12 1 dq01 u12 ¼ r ¼ 01 sec2 q12 dt dt # " r02 ðcosq01 cosq02 þ sinq01 sinq02 Þ r01 ð3Þ ðr02 cosq02 r01 cosq01 Þ2 Thus, the speed of the vane end is determined as r25 u12 . 3.2. Analysis of the dynamics The methodology for the force analysis is based on the work by Beard and Pennock [3]. A force analysis of the proposed design is performed by making the following assumptions: (1) no friction; (2) constant angular velocity of the crankshaft. Using Newton’s second law and equations of angular motion, effective forces in the proposed design are determined [4]. 3.3. Conservation of mass and energy The mass change with time inside the cylinder is determined from the conservation of mass as: dmcyl dmsuct dmleak;in dmdisc dmleak;out ¼ þ dt dt dt dt dt
ð4Þ
The first law of thermodynamics is applied to derive the temperature change with time in the cylinder [5]. The resulting equation is as follows: dmleak;in dTcyl 1 dmsuct ¼ hsuc hcyl þ hleak;in hcyl mcyl Cv dt dt dt vPcyl dmcyl dV dcyl dQcyl;wall þTcyl þ ð5Þ vcyl vTcyl v dt dt dt There is no heat transfer coefficient available for the bowtie compressor. However, since the vane is reciprocating circumferentially, the heat transfer coefficient [6] for reciprocating compressors is adopted for the instantaneous heat
1431
transfer rate from the refrigerant to the cylinder wall, Q_ cyl;wall in Eq. (5). Todescat et al. [7] recommended that the heat transfer coefficient is multiplied by a factor of three for a better prediction of the heat transfer rate. The resulting equation is as follows: 0:7 KðtÞ rðtÞUpiston Dpiston hðtÞ ¼ 3 0:7 ð6Þ Dpiston mðtÞ where KðtÞ, rðtÞ, and mðtÞ are thermal conductivity, density, and dynamic viscosity of refrigerant, respectively. Dpiston is the diameter of the piston, and Upiston is the mean piston velocity (¼2 stroke rpm/60). Modifications are needed in determining the piston diameter and stroke since the swept volume of the vane is not in a cylindrical shape and the stroke of the vane changes with the radius. Thus, a hydraulic diameter and a mean stroke are calculated and used instead. Then, the instantaneous heat transfer from the refrigerant to the cylinder wall is determined as:
Q_ cyl;wall ¼ hðtÞAðtÞ Tcyl ðtÞ Twall ð7Þ where AðtÞ and Twall are the heat transfer area and the mean wall temperature. It should be noted that the cylinder wall temperature is assumed to be constant. Adair et al. [8] reported that the cylinder wall temperature for a reciprocating compressor changed to less than 0.6 K from its time average temperature. Thus, a constant cylinder wall temperature is assumed here as well. 3.4. Dynamic valve model It is assumed that the gas in the cylinder is at uniform temperature and pressure and that the gas flow through the valve port is isentropic, compressible, and ideal. With these assumptions, the mass flow rates of the discharge and the suction valves can be determined by using the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t m_ valve ¼ Aflow 2rhigh Phigh Phigh g 1 Phigh ð8Þ The flow area, Aflow , is strongly related to the valve plate lift and can be determined by an experimental test [9,10]. However, a theoretical analysis also provides the means of determining the relationship of the valve plate lift and the flow area. It can be recognized that there are two dominant regions when a valve opens and closes dynamically. These are a pressure-force dominant region in which the differential pressure force on the valve is the main driving force, and a mass-flux-force dominant region where the pressure forces cancel each other out so that the mass-flux-force is the dominant force as shown in Fig. 4. The mass flow rates at each
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1432 Plow
p m_ valve ¼ m_ vavle;f ¼ rth Vth D2port 4
Plow
cir C.V. Phigh
Po
Po
C.V. Phigh Po th
Plow
Plow
cir
0
x
Pressure Force Dominant Region
The valve plate lift can be determined by analyzing the dynamics of a valve plate. The plate valve is modeled as onedegree of mass and spring [11]. The natural frequency of the plate spring at the first mode is determined [12], and the equivalent mass of the plate spring is calculated as: meq ¼
0 x Flux Force Dominant Region
Fig. 4. Schematic of a valve.
region can be approximately determined by using the following equations: m_ valve;p ¼ rcir Vcir Acir where rcir ¼ f1 Phigh ; Plow and Vcir ¼ f2 Phigh ; Plow vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t ð9Þ ¼ Acir 2rhigh Phigh g 1 Phigh Phigh m_ valve;f ¼ rth Vth Ath where rth ¼ f1 Phigh ; Plow and Vth ¼ f2 Phigh ; Plow vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " gþ1 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu u g Plow g2 Plow g t ¼ Ath 2rhigh Phigh g 1 Phigh Phigh ð10Þ where m_ valve; p and m_ valve;f are the mass flow rate in the pressure-force dominant and the mass-flux-force dominant regions, respectively. It is assumed that most of the flow inside the square box drawn in the pressure dominant region is stagnant since the leak created by the valve lift is relatively small to the port area. Thus, rcir and Vcir are functions of Phigh and Plow . By recognizing that rcir and Vcir are the same as rth and Vth from Eqs. (9) and (10), the transitional valve lift, xtr , above which the flow area is independent of the valve lift (i.e., the flow area is the port area), can be calculated by letting m_ valve; p to be the same as m_ valve;f : p rcir Vcir ðpDvalve xtr Þ ¼ rth Vth D2port 4 ð11Þ 1 D2port xtr ¼ 4 Dvalve Thus, when the valve lift is less than the transitional valve lift, the valve mass flow rate is determined as: m_ valve ¼ m_ valve; p ¼ rcir Vcir ðpDvalve xÞ
ð12Þ
When the valve lift is larger than and equal to the transitional valve lift, the valve mass flow rate does not change with the valve lift, and it is calculated as:
ð13Þ
ks u2n;1
ð14Þ
The main acting forces on the valve plate are a pressure force, a spring force, a drag force and a mass-flux-force. Other forces, such as the viscous damping force, the oil sticking force and the spring preload force, are neglected due to complexities in identifying them theoretically. For the pressure-force dominant region, the pressure on the left side of the valve obviously decreases from Phigh at the center to Plow at the circumference. However, since the valve area is almost the same as the port area, the dominant pressure on the left side of the valve is assumed to be Phigh . The governing dynamic equation for the pressure force dominant region is derived as: 1 meq €x þ ks x ¼ Phigh Plow Avalve þ CD rth Vth2 Avalve 2
ð15Þ
where CD is a drag coefficient for a round plate, which is 1.17. For the mass-flux-force dominant region, the pressure forces cancel out each other since the control volume is in the same low pressure, Plow . Instead, the mass-flux-force is added. As a result, the governing dynamic equation is given as: 2 1 meq €x þ ks x ¼ rth Vth x_ Aport þ CD rth Vth2 Avalve 2
ð16Þ
3.5. Leakage model The Ishii et al. leakage model [13] is adopted for the compressor simulation. The main reasons are as follows: (1) fairly good agreements between the experimental data and theoretical results; (2) minimal use of experimental coefficients, which can only be acquired by an actual experiment; (3) the computer calculations are not extensive, i.e., only a small number of iterations are needed. In this model, it is assumed that the leakage flow is incompressible, viscous, and turbulent. Five possible leakage passages are identified as shown in Fig. 5: (1) leakage through the radial clearance, m_ leak;01 ; (2) leakage over the vane, m_ leak;02 ; (3) leakage between the side vane and the journal shaft, m_ leak;03 ; (4) leakage between the journal bearing and the journal shaft, m_ leak;04 ; and (5) leakage between the top vane and the journal shaft, m_ leak;05 . Leakage from the valves is not considered because no experimental information is available to determine how the valve clearance changes with change in pressure difference. In addition, in
J.-H. Kim, E.A. Groll / International Journal of Refrigeration 30 (2007) 1427e1438
1433 Qrad,dis,shell
Tgas Tcyl,in
Tsuc Tevap
Tsuper
Tcyl,out
T
Q
wall
Tamb
Tshell
Qshell,amb
Tdis
Qrad,wall,shell dis,gas
Q
wall,gas
Qgas,shell Q friction loss Tgas
Wcomp Wshaft
Qmotor loss
Qoil,gas
Qrad,shell,amb Qoil,shell
Toil Welec
Twall Rwall,gas
Qcyl,wall
Tgas Tshell
Fig. 5. Leakage passages. Tamb
Rgas,shell Qrad,shell,amb
Qmotor loss
Qfriction loss
Qrad,wall,shell
Qrad,dis,shell
Qdis,gas
Rshell,amb
Roil,shell Roil,gas
comparison to the leakage from the vane, the valve leakage is much smaller due to smaller leakage area.
Toil
Fig. 6. Overall compressor energy flows and equivalent thermal resistance network for the bowtie compressor.
3.6. Friction loss model The mechanical friction losses of the bearings are determined using Reynolds Lubrication Equation [14] with the following assumptions: Newtonian flow, incompressible flow, constant dynamic viscosity, negligible inertia effects, no squeeze motion, and negligible pressure variation across the oil film. The friction analysis is performed on five parts of the compressor: the vane, the journal shaft in the cylinder block, the sliding bearing, the journal bearing at the end of the eccentricity rod and the crank shaft journal bearing [4]. The friction model neglects the variation of the oil viscosity with pressure and only considers the variation of oil viscosity as a function of temperature by using Kauzlarich’s correlation [15] for polyol ester oil with an ISO VG number of 22. 3.7. Overall compressor analysis An overall energy balance among the motor, the shell, the gas in the shell, the cylinder module, and the ambient air is considered. The overall energy balance model is developed based on the work presented by Chen et al. [16] by considering a resistance network. The resistance network considered for the bowtie compressor is shown in Fig. 6. Based on the current theoretical model, a simulation code has been developed in Visual Cþþ 6.0 in conjunction with REFPROP 7.0 [17] for thermal properties. GNU Scientific Library [18] that is compiled for Visual Cþþ 6.0 is extensively used for numerical calculations, such as solving linear algebra and finding the roots of nonlinear equations. The
current simulation model requires the following seven initial guess values: (1) the shell temperature; (2) the refrigerant vapor temperature in the shell; (3) the cylinder wall temperature; (4) the discharge temperature; (5) the compressor cylinder outlet temperature; (6) the oil temperature in the oil sump; and (7) the motor RPM. The simulation model continues to iterate until the residuals of each of the seven values are met within an absolute error of 1E02. Fig. 7 shows the flow chart of solving the compressor model starting with the seven initial guess values and an initial step angle. 4. Simulation model validation At this point, a prototype bowtie compressor has not been built and thus, no experimental data are available for model validation. However, in order to validate the model predictions, the model was modified to predict the performance of a conventional hermetic reciprocating compressor for use in domestic refrigerators and freezers. A detailed description of the model modifications and the comparison between experimental results and model predictions are shown in Kim and Groll [19]. The comparisons of the simulation results to the calorimeter data and the compressor map showed that the simulation methodology of the reciprocating compressor model is appropriate. Since the bowtie compressor model is similar to the reciprocating compressor model in many ways, the bowtie compressor model is assumed to be validated in order to
J.-H. Kim, E.A. Groll / International Journal of Refrigeration 30 (2007) 1427e1438
1434
Initial angle and guess values θi = θi + Δθ
Analysis of Kinematics Analysis of Dynamics Instaneous Heat Transfer Model Leakage Flow Model
dvcyl dθ dmcyl dθ dTcyl dθ
Valve Model
m(θ, vcyl, mcyl, Tcyl) T(θ, vcyl, mcyl, Tcyl)
Do Until One Cyle, where θi = θ0 + 2π Y Overall Energy Balance
N
Vane height Vane thickness Connecting rod length Suction port diameter Leakage clearances Vane radius Cylinder journal bearing radius Eccentricity rod Discharge port diameter
15 mm 4.4 mm 80 mm 8.0 mm 2.5 mm 35 mm 10 mm 10 mm 4.5 mm
5.1. Effect of changes of the swept volume
v(θ, vcyl, mcyl, Tcyl)
Friction Loss Model
N
Table 1 Bowtie compressor geometric parameters
Guess values converged?
The swept volume can increase by up to 55% from 3.04 cm3 to 4.70 cm3. This can be achieved by increasing the control length, x, from the reference point, where the minimum swept volume occurs, to 2.0 cm. The proposed compressor will always startup with the minimum swept volume because the cylinder module is spring-biased. Thus, at default, the cylinder module is positioned at x ¼ 0 cm. While the clearance volume stays unchanged, the swept volume increases with the control distance. Consequently, the compressor work, the enclosed area of a pressureevolume diagram, increases. The predictions of the volumetric, clearance volume and motor efficiencies are plotted in Fig. 8. Two important predictions have to be pointed out. First, the volumetric and clearance volume efficiencies decrease with the swept volume. The main reason for this behavior is that the volume during the suction process and the refrigerant volumetric flow rate at the cylinder inlet decrease as the swept volume decreases. However, it should be noted that since the clearance volume stays constant and less expansion volume is
Y END
Tcond=54.4°C & Tevap=-23.3°C 84
Fig. 7. Flow chart for the compressor simulation model.
80
5. Simulation model results The bowtie compressor is simulated using R-134a as the refrigerant at the operating conditions of Tcond ¼ 54.4 C, Tevap ¼ 23.3 C, and Tamb ¼ Tsuct ¼ 32.2 C. While the compressor swept volume is varied from 3.04 cm3 to 4.70 cm3 in each chamber, the clearance volume for each chamber is fixed at 0.12 cm3. All leakage clearances are set to 2.5 mm. Table 1 lists the geometric parameters of the bowtie compressor that are used in the simulation unless indicated otherwise.
76
Efficiency (%)
conduct the theoretical bowtie compressor performance analysis.
72 68 64 60 56
ηmotor
52
ηcv ηv
48 3.0
3.5
4.0
4.5
5.0
Swept Volume (cm3) Fig. 8. Effect of swept volume on volumetric, clearance volume, and motor efficiencies.
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Mass Flow Rate ηo.s.c -4.3%
1.2
-17.5%
1.0
-31.4% -42.8%
0.8 -52.0% 0.6 3.0
3.5
4.0
90
Frictional Power Loss (W)
88 16
86 14
84 3.0
4.5
5.0
Swept Volume (cm3)
3.5
4.0
4.5
Fig. 10. Effect of swept volume on frictional power loss and mechanical efficiency.
compressor shaft power decreases as well. This explains that the mechanical efficiency decreases even though the frictional power loss decreases. 5.2. Effect of changes of the clearances of the leakage passages The bowtie compressor is simulated with the same geometric parameters listed in Table 1 except that the leakage clearances are varied from 0.5 to 5.0 mm. Fig. 11 shows the fractional leakage flow rate, which is defined as a ratio of average leakage flow rate to actual compressor flow rate. The fractional leakage flow rates through the five leakage flow paths are stacked up for each case of leakage clearance. The total fractional leakage flow rate decreases from
leak01 leak05 leak04 leak03
30
leak02
20
10
0
0.5
1.0
1.5
2.0
2.5
3.8
Clearance ( m) Fig. 9. Effect of swept volume on mass flow rate and overall isentropic compressor efficiency.
5.0
Swept Volume (cm3)
Fractional Leakage Flow Rate (%)
Mass Flow Rate (g/sec)
65 60 55 50 45 40 35 30 25 20 15 10 5 0
Overall Isentropic Compressor Efficiency (%)
1.4
-9.2%
me
18
40
1.6 -14.8% -20.6%
Frictional Power Loss
Mechanical Efficiency (%)
required, the bowtie compressor should have a lower rate of decreases in volumetric and clearance volume efficiencies than typical variable stroke compressors. It should also be noted that the clearance volume efficiency is different from the volumetric efficiency. The clearance volume efficiency does not consider the gas density at the cylinder inlet. Second, the motor efficiency decreases from 83% to 76.2%. This shows that for the given capacity modulation mode, the current motor of the bowtie compressor operates away from the plateau of the motor map, where changes in the motor efficiency are very small. Fig. 9 presents the prediction of the compressor mass flow rate and the overall isentropic compressor efficiency as a function of the swept volume. At these operating conditions, the model of the bowtie compressor predicts a 52% reduction in compressor mass flow rate from 1.504 g/s to 0.722 g/s with an approximately 21% decrease in overall isentropic compressor efficiency from 59.65% to 47.38%. One reason for the decrease in overall isentropic compressor efficiency is that the motor runs off its optimum efficiency at the low capacity conditions. This is not unexpected given that fixed motors are optimized for a certain range where the maximum cooling capacity can be achieved. The compressor mass flow rate decreases almost linearly with the swept volume. This indicates that a linear controller as the actuator can be used to achieve continuous capacity modulation. The frictional power loss and the mechanical efficiency are presented in Fig. 10. The frictional power loss and the mechanical efficiency decrease approximately 22% from 17.2 W to 13.5 W and approximately 5% from 89% to 84.6%, respectively. It is observed that both the frictional power loss and the mechanical efficiency decrease with a reduction in swept volume. When the swept volume decreases, the swept area where friction occurs reduces, which causes less frictional power loss. However, at the same time, the
1435
Fig. 11. Effect of clearance on leakage.
5.0
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36% to 0.6% when the clearance is reduced from 5.0 to 0.5 mm. The results show that the largest leakage occurs in Leak02, i.e., leakage over the vane. It comprises approximately 73% of the total leakage flow for each case of clearance. The frictional loss and compressor mass flow rate as a function of leakage clearance are shown in Fig. 12. The figure indicates that the mass flow rate starts to increase and then flattens out at a clearance of 1.0 mm when the leakage clearance is varied from 5.0 to 0.5 mm. Meanwhile, the frictional loss slowly increases and then shoots up dramatically at a clearance of 1.5 mm when the leakage clearance is varied from 5.0 to 0.5 mm. These trends strongly indicate that the performance gain by an increase in mass flow rate with smaller clearances could be eliminated at some point due to the increase in frictional losses. The increase in frictional losses implies that the viscous shear stress in the leakage path is more sensitive to changes in the Couette flow than in the Poisson flow. Fig. 13 presents the clearance volume and volumetric efficiencies as a function of leakage clearance. The figure indicates that the clearance volume efficiency and volumetric efficiency have opposite trends when the leakage clearance increases. The clearance volume efficiency increases by 7.2% to a value of 78.5% whereas the volumetric efficiency decreases approximately 20.6% to a value of 53.5% as the leakage clearance increase from 0.5 to 5.0 mm. The reason for the decreasing volumetric efficiency is that the mass flow rate decreases. The increasing trend in the clearance volume can be explained by considering trapped refrigerant mass in the clearance volume. As the clearance increases, less amount of refrigerant is trapped in the clearance volume due to the increased leakage. As a result, the expansion volume decreases. Thus, the clearance volume efficiency increases since the clearance volume and swept volume are kept the same. Fig. 14 shows the overall isentropic efficiency as a function of leakage clearance. The figure shows that there is an
80 75
Efficiency (%)
1436
70 cv v
65 60 55 50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Clearance ( m) Fig. 13. Effect of clearance on ‘‘clearance volume and volumetric efficiencies’’.
optimum leakage clearance where the best compressor performance can be achieved. The figure indicates that in a clearance range of 1.0e5.0 mm the compressor tends to perform better with smaller clearance because the performance gain of the increased mass flow rate offsets the performance loss due to the increased frictional loss. The overall isentropic compressor efficiency is improved by approximately 22% when the leakage clearance is decreased from 5.0 to 1.0 mm. However, as the leakage clearance is further reduced to 0.5 mm, the overall isentropic efficiency decreases because the performance loss due to the increased frictional loss is larger than the gain of the increased flow rate. 5.3. Effect of a ratio of the vane radius to height The bowtie compressor is simulated by using ratios of the vane radius to the vane height as shown in Table 2 while
32
Friction Loss (W)
28
1.6
1.5
26 24 1.4
22 20
1.3
18
Mass Flow Rate (g/sec)
30
Friction Loss Mass Flow Rate
Overall Isentropic Compressor Efficiency (%)
62 34
60 58 56 54 52 50
16 14
1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Clearance ( m)
Clearance ( m) Fig. 12. Effect of clearance on friction loss and mass flow rate.
Fig. 14. Effect of clearance on overall isentropic compressor efficiency.
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Table 2 Ratio of the vane radius to the vane height Swept volume ¼ 4.696 cm3, swept angle ¼ 30.05 , clearance volume ¼ 0.12 cm3, leakage clearance ¼ 2.5 mm Ratio 0.5 0.75 1 1.25 1.5 1.75 2 Vane radius (mm) 21.99 24.73 26.95 28.84 30.5 31.99 33.35 Vane height (mm) 43.98 32.98 26.95 23.07 20.33 18.28 16.67
2.25 34.6 15.38
2.5 35.77 14.31
Swept volume ¼ 4.696 cm3, swept angle ¼ 25.05 , clearance volume ¼ 0.12 cm3, leakage clearance ¼ 2.5 mm Ratio 0.5 0.75 1 1.25 1.5 1.75 2 Vane radius (mm) 23.57 26.57 28.99 31.05 32.86 34.49 35.97 Vane height (mm) 47.14 35.43 28.99 24.84 21.91 19.71 17.99
2.25 37.34 16.59
2.5 38.61 15.44
maintaining the same swept volume and angle. Fig. 15 presents that the mass flow rate and overall efficiency at two different swept angles as a function of the ratio of the vane radius to the vane height. The figure shows that in each case of swept angle the compressor mass flow rate and the overall isentropic efficiency have maximum values at the same ratio of 1.25. In each case of swept angle, it is observed that the minimum leakage occurs at the ratio of 1.25. This explains why the maximum compressor mass flow rate is achieved at that ratio. Consequently, the results show that there is an optimum combination of the vane radius and vane height to achieve the maximum compressor performance at fixed leakage clearance and swept volume. It is shown that the optimum ratio does not change with swept angles. 6. Conclusions A new compressor concept that changes the piston stroke by simple mechanical means while keeping the same
59.0 2.75
59.2
1.470 2.50
59.4
1.475 2.25
59.6
1.480
2.00
59.8
1.485
1.75
60.0
1.490
1.50
60.2
1.495
1.25
60.4
1.500
1.00
60.6
1.505
0.75
60.8
1.510
0.50
61.0
1.515
0.25
1.520
Overall Isentropic Compressor Efficiency (%)
Compressor Mass Flow Rate (g/sec)
Mass Flow Rate, Swept Angle = 25.05° Mass Flow Rate, Swept Angle = 31.89° o.s.c, Swept Angle = 25.05° o.s.c, Swept Angle = 31.89°
Ratio of Vane Radius and Height Fig. 15. Effect of a ratio of the vane radius and height on compressor mass flow rate and overall isentropic compressor efficiency at the swept angles of 25.05 and 31.89 .
clearance volume for better thermodynamic efficiency is proposed here. The new compressor is called bowtie compressor, which uses a unique off-center-line mechanism so that the piston stroke can be varied without changes in clearance volume. The concept of a bowtie compressor was described in detail. Subsequently, a prototype design of the bowtie compressor was proposed and discussed. The proposed bowtie compressor has some innate features: (1) the cooling capacity can be controlled inexpensively by using a simple on/off solenoid valve without using premium variable speed motors; (2) the compressor always starts with the shorter piston stroke in default mode which results in a smooth startup due to the reduced motor torque; (3) the overall compressor efficiency is improved by keeping the clearance volume constant at all times; and (4) continuous capacity modulation can be easily realized by replacing the simple solenoid valve with a more complex valve controller, which leads to further improvement of the overall compressor efficiency. A simulation model of the proposed compressor was presented to investigate the feasibility of the bowtie compressor. Furthermore, parametric studies were carried out to investigate the effects of using different geometric parameters on compressor performance. The effects of leakage clearances and the ratio of the vane radius to the vane height while keeping the swept volume constant on compressor performance were studied. The result showed that the bowtie compressor is able to control its mass flow rate (and thus, its cooling capacity) from 50% to 100% using an electronic control valve. Since the proposed compressor has more leakage paths than conventional reciprocating compressors, the effect of changes of the leakage clearance was studied. The simulation results showed that the compressor performance improved as the leakage clearance decreased from 5.0 to 1.0 mm. The reduction in leakage clearance adversely increased the friction loss and decreased the mechanical efficiency, but the overall isentropic compressor efficiency improved because the reduced leakage flow rate increased the mass flow rate of the compressor. However, as the leakage clearance is further reduced to 0.5 mm, the compressor performance decreased. At that point, the increased mass flow rate could not compensate the performance loss by the increased frictional loss. Even though the model
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predicted that the maximum compressor performance would occur at the clearance of 1.0 mm, it has to be noted that reducing the clearance to 1.0 mm may not be practical due to manufacturing costs and challenges. Instead, it would be more feasible to increase the vane thickness so that the maximum compressor performance occurs at larger leakage clearance than 1.0 mm. The study of using different ratios of the vane radius to the vane height while maintaining the same swept volume demonstrated that there is an optimum ratio of vane radius to vane height to achieve the maximum compressor performance at a given swept volume. The optimum ratio of the studied bowtie compressor with the swept volume of 4.7 cm3 is found to be 1.25 and does not change with different swept angles. Although the presented results are solely based on theoretical models and need to be verified using experimental data, it is reasonable to believe that these results capture trends of the actual bowtie compressor performance. The current simulation model can be used as a tool to prototype a bowtie compressor. Acknowledgements The authors would like to express their gratitude to Tecumseh Products Company, who sponsored this study. The authors also thank Joaquim Rigola at Technical University at Catalonia, Spain, for sharing the test data of a reciprocating compressor.
References [1] H. Holdcack-Janssen, H. Kruse, Continuous and discontinuous capacity control for high speed refrigeration compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1984, pp. 67e75. [2] S.M. Zubair, V. Bahel, Compressor capacity modulation scheme, Heating/Piping/Air Conditioning 61 (1989) 135e143. [3] G.R. Pennock, J.E. Beard, The BeardePennock variable-stroke compressor, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1988, pp. 599e607. [4] J.-H. Kim, Analysis of a Bowtie Compressor with Novel Capacity Modulation, Ph.D. thesis, Purdue University, West Lafayette, IN, 2005. [5] S.Y. Sun, T.R. Ren, New method of thermodynamic computation for a reciprocating compressor: computer simulation of working process, International Journal of Mechanical Science 37 (4) (1995) 343e353. [6] W.J.D. Annad, Heat transfer in the cylinder of reciprocating internal combustion engines, Institution of Mechanical Engineering 177 (36) (1963) 973e996.
[7] M.L. Todescat, F. Fagotti, A.T. Prata, R.T.S. Ferreira, Thermal energy analysis in reciprocating hermetic compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1992, pp. 1419e1428. [8] R.P. Adair, E.R. Qvale, J.T. Pearson, Instantaneous heat transfer to the cylinder wall in reciprocating compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1972, pp. 521e526. [9] W. Soedel, Introduction to computer simulation of positive displacement type compressors, Ray W. Herrick Laboratories, 1972. [10] R.T.S. Ferreira, J.L. Driessen, Analysis of the influence of valve geometric parameters on the effective flow and force areas, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1986, pp. 632e646. [11] K. Suefuji, S. Nakayama, Practical method for analysis and estimation of reciprocating hermetic compressor performance, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1980, pp. 15e23. [12] R.D. Blevins, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York, 1979. [13] N. Ishii, K. Bird, K. Sano, M. Oono, S. Iwanura, T. Otokura, Refrigerant leakage flow evaluation for scroll compressors, in: Proceedings of International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 1996, pp. 633e638. [14] O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil, Philosophical Transactions of the Royal Society of London 177 (1886) 157e234. [15] J.J. Kauzlarich, Viscosity times density equations for five classes of lubricants, Proceedings of the Institution of Mechanical Engineers Part J: Journal of Engineering Tribology 212 (3) (1998) 235e239. [16] Y. Chen, N.P. Halm, E.A. Groll, J.E. Braun, 2002, Mathematical modeling of scroll compressors e part II: overall scroll compressor modeling, International Journal of Refrigeration 25 (2002) 751e764. [17] REFPROP 7.0, NIST Standard Reference Database 23: NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) version 7.0, National Institute of Standard and Technology, Gaithersburg, Maryland, 2002. [18] M. Galassi, J. Davies, J. Theiler, B. Gough, G. Junqman, M. Booth, F. Rossi, GNU Scientific Library Reference Manual, second ed., Network Theory Ltd., 2003, ISBN 0954161734. [19] J.-H. Kim, E.A. Groll, Bowtie compressor with novel capacity modulation e part II: model validation and parametric studies, in: Proceedings of the International Compressor Engineering Conference, Purdue University, West Lafayette, USA, 2006, p. C151.