Simulator For Performance Prediction Of Reciprocating Considering Various Losses Aditya S. Bawane 1, Dr. V.K. Bhojwani 2, Mitali B. Deshmukh 3 1 (Mechanical Engineering Department, JSCOE, S.P. Pune University, Maharashtra, India) 2 (Mechanical Engineering Department, JSCOE, S.P. Pune University, Maharashtra, India) 3 (Mechanical Engineering Department, JSCOE, S.P. Pune University, Maharashtra, India) ABSTRACT: Reciprocating compressors are widely used in various refrigerating units covering a large range of capacity. With the increasing applications of carbon dioxide (CO2) trans-critical cycles, reciprocating compressor is further gaining the center stage because of its advantages in high pressure operation and good efficiency when running at lower pressure ratio. Computer aided modeling has brought significant enhancement in a large number of engineering disciplines. There is lot of development done in reciprocating compressor to predict the performance. But good simulator models are absent to predict the complete performance of reciprocating compressor along with the consideration of various types of losses (frictional losses, heat transfer, pressure drop, motor losses, etc.). Hence there is need of Simulator for reciprocating compressor which predicts the true performance considering various losses. The planned simulator would estimate instantaneous thermodynamic properties. The simulator will solve second order differential equation to predict, a. Instantaneous position of piston. b. Instantaneous cylinder volume. c. Instantaneous gas density and mass inside the cylinder. d. Instantaneous pressure inside the cylinder. e. Instantaneous temperature inside the cylinder. f. Valve dynamics. g. Mass flow rate of refrigerant in and out of the cylinder. h. Refrigerating effect, compressor power, COP. i. Various losses in the reciprocating compressor. Keywords - Reciprocating compressor, Mathematical Simulator, Losses. 1. INTRODUCTION Simulation is the way of studying the basic behavior of cycle performance, the relative losses in the components, and the interaction of their performance characteristics. Standard science and engineering formulations are applied to describe mathematically the basic processes in compressor. Simulation is the calculation of operating variables (pressure, temperature, energy and fluid flow rates) for a system operating in a steady state such that all energy and mass balances, all equations of state of working substances and performance characteristics are satisfied. Simulation is used when it is not possible or uneconomical to observe the real system. A reciprocating compressor or piston compressor is a positivedisplacement compressor that uses pistons driven by a crankshaft to deliver gases at high pressure. The intake gas enters the suction manifold, then flows into the compression cylinder where it gets compressed by a piston driven in a reciprocating motion via a crankshaft, and is then discharged. An accurate compressor simulation program can provide compressor design engineers with valuable insights. For example, instantaneous position of piston, cylinder volume and pressure inside the cylinder, valve dynamics, refrigerating effect, compressor power, COP, losses can be predicted and basic data for related engineering tasks such as valve analysis can be obtained. Simulator results are validated with experimental results. Advantages of Reciprocating : Operates over a wide range of pressure. Good for small application. Cheap & simple to operate. Installation is simple & easy. 2. SIMULATIONS It is an attempt to model a real life or hypothetical situation on a computer so that it can be studied to see how the system works. By changing the variables in the simulation, prediction may be made about the behavior of the system. ISSN: 2348 8360 www.internationaljournalssrg.org Page 12
2.1 Simulator Potential The developed Simulator has the potential of: 1) Complete analysis of reciprocating compressor will be possible. 2) Dynamic pressure variation inside the cylinder volume. 3) Instantaneous cylinder temperature. 4) Dynamics of suction & discharge valve. 5) Predict the complete cycle performance for given operating conditions. 6) Mass flow rate inside / outside the cylinder. 7) Refrigerating effect, Power & COP. 8) Interfacing with any given refrigerant possible to consider effect of change in refrigerant on performance. 2.2 Features of the Mathematical Simulator Simulator can predicts complete analysis of reciprocating compressor is possible. Estimates instantaneous (variation w.r.t time): 1) instantaneous Cylinder Pressure, 2) instantaneous Cylinder Temperature 3) instantaneous Piston position, 4) instantaneous Cylinder volume 5) Suction and discharge Valve dynamics 6) Mass flow rate inside / outside the cylinder. 7) Refrigerating effect. 8) Power 9) COP 10) Estimation of any refrigerant properties. 2.3 Program Interfaced with REFPROP Program is interfaced with REFPROP. By using this two refrigerant properties transferred to REFPROP and all the necessary refrigerant properties are called in the program. 2.3.1 Potential of REFPROP: REFPROP is standard software which gives refrigerant properties for all available refrigerants, mixtures also. User can create his own refrigerant mixtures and study the properties. 2.4 Total time, time interval and number of cycles The total time, time interval & number of cycles can be determined as described below: 1) User defines: number of cycles, Time Step for discretization. 2) Number of Cycles = 10 Cycles (e.gs) 3) Time Step = 0.01 s 4) Frequency = 50 Hz 5) Total time for which program will run = 10/50 =0.2 s 6) The time progresses in steps of 0.01, 0.02, 0.03., 0.2 s. 7) Program does calculations for each time step till it reaches the final time i.e. 0.2 s or 10 cycles. 8) Program integrates all the variables to be estimated. 9) The Time step is optimized to ensure sufficient accuracy as well as minimum possible time required to run the program. 3. MATHEMATICAL SIMULATORS Mathematical Simulator is proved to be an effective tool to study performance of the reciprocating compressors. The model is useful in the designing of parts and components of a compressor. Model predicts results quiet close to the experimental result. The simulation model can predict well - transient characteristic of the reciprocating hermetic compressor. Mathematical modeling is the most practical way of studying the basic behavior of cycle performance, the relative losses in various components and the interaction of their performance characteristics. Standard science and engineering formulations are applied to describe mathematically the basic processes occurring in the compressor. Mathematical modeling is not an end in itself but is a step towards simulation and optimization. Simulation is the calculation of operating variables (pressures, temperatures, energy and fluid flow rates) for a system operating in a steady state such that all energy and mass balances, all equations of state of working substances and performance characteristics are satisfied. Simulation could also be defined as the prediction of performance with ISSN: 2348 8360 www.internationaljournalssrg.org Page 13
given inputs or simultaneous solution of performance characteristics [1]. 3.1 Mathematical Model Simulation is used when it is not possible or uneconomical to observe the real system. Because of the compressor high rotational speed, the refrigerant compression is quite instantaneous in comparison to the response time of the whole refrigeration system. Therefore, the current model considers the compression process as a quasisteady one [2]. Mathematical simulator solves the following equations to predict the compressor performance: Piston motion equation. Heat transfer equation. Mass flow rate equation. Valve dynamic equation. Mass flow rate equation for leakage. Pressure drop at valve. 3.1.1 The Thermodynamic Modeling The schematic diagram of a reciprocating compressor with spring type suction and discharge valves is shown in Figure 1. The rotary motion of crankshaft is converted to the reciprocating motion of piston by connecting rod. Gas in cylinder is assumed as lump open system. It is assumed that no leakage take place in the compressor. The governing equation for simulating the compressor is presented in this section [2]. 3.2 Energy Equation The cylinder wall, cylinder head and piston end face are considered as boundaries for control volume. The first thermodynamic law is written as follow [3]: =The mass flow rates through the suction and discharge valves (kg/s) respectively. = is the rate of change of the internal energy in the cylinder control volume (J/kg). Figure 1: Schematic of reciprocating compressor 3.2.1 Piston Motion Equation The exact expression for the instantaneous position of the piston displacement from top dead center in terms of the crank angle may be given by = piston displacement (m) ω = angular frequency = L= length of connecting rod (m) Radius of crank (m) 3.2.2 Equation for Cylinder Volume Instantaneous cylinder volume is =Rate of heat flow into the cylinder volume (W). W c =rate of the cylinder work (W). and h d =Specific enthalpies of the suction gas and the discharge gas (J/kg) respectively, = Clearance volume ( D= Diameter (m) Piston displacement (m) 3.2.3 Equation for Suction Gas Temperature The temperature of the suction gas at the conclusion of heat transfer process will be given by as follows: ISSN: 2348 8360 www.internationaljournalssrg.org Page 14
(W) (kg/s) =suction temperature (K) =initial suction temperature (K) = heat transfer rate at discharge valve = mass flow rate at suction valve 3.2.6 Valve Dynamic Equation The dynamics of the automatic reed valve is simplified as a one degree-of-freedom system [3]: Where x is the valve displacement, is the effective force area of the valve, and, and are the equivalent mass, damping coefficient, stiffness of the valve, respectively and Upstream & downstream pressure (Pa) respectively. 3.2.4 Equation for Heat Transfer in Cylinder In the cylinder, periodic heat exchange is taking place between its walls and refrigerant vapor due to considerable temperature variation of the vapor as compared with the almost constant wall temperature and the rate of heat transfer from wall to the vapor during early part of the compression is 3.2.7 Equation For Mass Flow Rate At Suction Valve [4] The equation for mass flow rate at suction valve is (Pa) = pressure drop at suction valve = suction density (kg/ A (t) is the heat transfer area, h(t) is heat transfer coefficient and is wall temperature. Heat transfer area is, Where piston area = = & = Where D is diameter of cylinder volume and TDC. clearance is the piston displacement from 3.2.5 Equation for Cylinder Pressure The pressure inside the cylinder is given by equation 4 LOSSES IN COMPRESSOR There are different types of losses in the reciprocating compressor: loss due to the leakages in the mass flow rate, losses due to heat transfer by conduction, convection and radiation, due to pressure drop across the valves, friction losses and pumping losses. 4.2 Leakage Through [5] The mass flow rate equation for leakage is Where (Pa) Leakage =. ( = no. of cylinder.. m(t) = mass of gas (kg/ V(t) = cylinder volume ( R= gas constant (kj/kg K) 4.3 Heat Transfer Equation [2] Heat transfer due to convection in compression chamber can be calculated as: ISSN: 2348 8360 www.internationaljournalssrg.org Page 15
Where is the heat transfer coefficient, A is surface area in contact with the gas, cylinder gas temperature and is the in is the wall temperature. To calculate convective heat transfer coefficient, the Woschni correlation has been employed. This correlation is originally derived for internal combustion engine. The correlation could also predict the heat transfer rate during compression stage of engine motion. Consequently, it could be used to model heat transfer in a reciprocating compressor. According to the correlation, the heat transfer coefficient is given by: P is instantaneous in-cylinder pressure, T is instantaneous gas temperature, v is the characteristic velocity of gas and D is diameter of the cylinder. According to Woschni correlation, the correlation characteristic velocity for a compressor without swirl is given as: is average velocity of piston. 4.4 Pressure Drop At Valve [5] The equation of pressure drop at valve is ω= p= k=0.002 c= diametrical clearance Electrical losses are considered to cause heat generation and these losses are calculated from the known motor efficiency. The motor efficiency varies from 97% to 80%, depending on the motor speed, which corresponds to the electrical losses of 3 20% [6]. All above equations are solved by the simulator for the given values of input. Equations for cooling capacity, compressor power and COP Refrigerating effect = Mass flow rate * (Enthalpy leaving evaporator Enthalpy entering evaporator) work in Watts = (By integration of PV area) * Frequency COP = RE / work (W /W) 5 FLOW CHART FOR MATHEMATICAL SIMULATOR [3] Where for valve = Swept volume rate ( = 4.5 Mechanical Losses Due To Heat Generation [6] The Mechanical (frictional) losses due to heat generation is given by equation N=speed (rev/min) f=0.326[ Figure 2: Flow chart ISSN: 2348 8360 www.internationaljournalssrg.org Page 16
For a single cylinder refrigerating compressor, a generalized computer simulation program was prepared. Figure 2 shows the outline of flow chart for the main program. It deals with the thermodynamic model. As simultaneous solutions of several models are required, five subroutines as listed below were incorporated in the main program. Main program is: Thermodynamic model Subroutines 1: Kinematic model for slider crank mechanism. 2: Mass transfer (through valves) Model 3: Cylinder heat transfer model 4: Valve dynamics model 5: Valve passage heat transfer model 6: Runge-Kutta solution. The input data required can be classified under the following categories, (i) geometrical description (ii) thermal description (iii) initial conditions (iv) gas properties and (v) experimental information s. The increment is given by crank angle Δθ. The program output provides the time history of the refrigerant as it flows through the compressor by punching out cylinder temperature, pressure and fluid flow rates. Valve displacements are also obtained, from this information; available energy analysis of the compressor cycle can be performed. 6 COMPRESSOR TESTING SETUP: Figure 3: Testing Setup model: KCJ498HAG Frequency: 50Hz ; Refrigerant R134A Displacement: 25.91(CC/rev) The input parameters from the test stand are shown in table1: Table1: Input parameters Sr. No. P suc (bar) P dis (bar) T suc (ºC) T dis (ºC) P evap (bar) T evap (ºC) 1 2.44 13.69 18 91.6 3.12 7 2 2.45 13.55 17.9 88.01 3.14 7.3 3 2.45 13.63 35 103.1 3.11 7.1 4 2.45 13.64 35 103.1 3.12 7.1 5 2.55 13.58 18 89.7 3.26 7 6 2.45 13.64 35 103.1 3.1 7 7 2.44 13.73 18.1 91.1 3.11 7.1 8 2.49 13.73 18 91.2 3.17 7.4 9 2.45 13.6 18 89.9 3.16 7.4 10 2.35 13.6 17.9 89 3.36 7.8 6.1 Mathematical simulation results: ISSN: 2348 8360 www.internationaljournalssrg.org Page 17
The same input data is given to the simulator for performance prediction of reciprocating compressor. The simulator results are: 6.1.1 Stroke (mm) V/s time (s) Figure 6: Instantaneous cylinder pressure (N/ V/s time(s) 6.1.4 Pressure (N/ V/s volume ( Figure 4: Stroke (mm) V/s time (s) The stroke (piston displacement) is seen to be sinusoidal in nature. This is due to fixed motion of piston inside the cylinder. 6.1.2 Instantaneous cylinder volume ( ) V/s time (s) Figure 7: Pressure (N/ V/s volume ( 6.1.5 Temperature (K) V/s time (s) Figure 5: Instantaneous cylinder volume ( time (s) ) V/s 6.1.3 Instantaneous cylinder pressure (N/ V/s time(s) Figure 8: Temperature (K) Vs time (s) ISSN: 2348 8360 www.internationaljournalssrg.org Page 18
7 RESULTS 7.1 Experimental results Sr. No. Table 2: Test stand results Expt. Expt. Cooling Capacity Power (W) (W) Expt. COP 1 960 1596 1.66 2 972 1752 1.8 3 948 1776 1.87 4 960 1824 1.9 5 1032 1848 1.79 6 984 1812 1.9 7 972 1776 1.8 8 984 1680 1.7 9 960 1704 1.77 10 984 1788 1.81 7.2 Simulator results Sr. No. Table 3: Simulator results Simulator Power (W) Simulator Cooling Capacity (W) Simulator COP 1 603.68 1981.6 3.28 2 600.96 2009.83 3.34 3 598.53 2051.27 3.43 4 583.88 2052.82 3.51 5 612 2102 3.433 6 598.79 2049.22 3.42 7 604.67 2006.91 3.319 8 610.81 2031.39 3.33 9 605.89 1993.95 3.29 10 591.7 1929.7 3.27 7.3 Comparison of Experimental results & simulated results Figure 9: Comparison of Power The simulated compressor power & experimental compressor are shown in figure 9. There is difference between the values of simulated & experimental compressor power. This is due to the pressure drop at condenser & evaporator, frictional losses. 7.3.2 Cooling Capacity Figure 10: Comparison of Cooling Capacity Cooling capacity of simulated & experimental is shown in figure 10. There is variation in values due to mass leakage at the valves & heat transfer losses. 7.3.3 COP The comparison of simulated and experimental COP is shown in figure 11. The gap between two COP is due to various losses. 7.3.1 Power ISSN: 2348 8360 www.internationaljournalssrg.org Page 19
Figure 11: Comparison of COP 8. LOSS ANALYSIS 7.3 Pressure drop at condenser A loss in compressor power due to pressure drop at condenser is shown in table 4. Table 4: Loss in compressor power at condenser Expt. No. Pressure drop (bar) Experimental Power (W) Loss in Power due to pressure drop at Condenser (W) 1 0.44 960 57 2 0.72 972 93.3 3 0.56 948 72.53 4 0.56 960 72.53 5 0.8 1032 104 6 0.86 948 72.53 7 0.87 972 112.69 8 0.71 984 92 9 0.46 960 59.58 10 0.87 984 112.69 7.4 Pressure drop at evaporator Loss in compressor power due to pressure drop at evaporator is shown in table 5. Table 5: Loss in compressor power at evaporator Expt. No. Pressure drop (bar) Loss in Power due to pressure drop at Evaporator (W) 1 0.68 88.1 2 0.69 89.4 3 0.66 85.5 4 0.67 86.8 5 0.711 92 6 0.65 84.2 7 0.67 86.8 8 0.68 88.1 9 0.67 86.78 10 1.01 130.82 7.5 Frictional losses Table 6: Losses due to friction Expt. No. Mechanical losses due to friction (W) 1 107.74 2 106.79 3 106.71 4 106.76 5 107.28 6 106.76 7 107.07 8 107.83 9 107.02 10 107.01 7.6 Power Analysis Table 7: Simulated compressor power with losses Expt. No. Experimental Power (W) Simulator Power Results without Losses (W) Simulated Power with Losses 1 960 603.67 856.51 2 972 600.96 890.45 3 948 598.53 863.27 4 960 598.78 864.87 5 1032 612.34 915.62 6 948 598.78 862.24 7 972 604.67 911.24 8 984 610.18 898.11 9 960 605.89 859.27 10 984 591.02 941.53 ISSN: 2348 8360 www.internationaljournalssrg.org Page 20
9. CONCLUSIONS The simulator can predict complete performance of reciprocating compressor. It predicts the ideal behavior of compressor & it also incorporates various losses. There is variation in the values of simulator & experimental compressor power due to the losses. This occurs due to the pressure drop at condenser & evaporator, mechanical losses due to heat generation. The pressure losses accounts 28% of overall compressor power & frictional losses accounts 17%. There is also difference in cooling capacity of simulated & experimental losses. This is because of the leakages in the compressor & heat transfer losses. REFERENCES [1] R. Prakash, R. Singh, Mathematical Modeling and Simulation of Refrigerating s, International Engineering Conference. [2] Mahmood Faezaneh-gord 1, Amir niazmand 2, Mahdi Deymi, Optimizing reciprocating air compressors design parameters based on first law analysis, u.p.b. Sci. Bull., Series d, vol. 75, iss. 4, 2013. [3] W. Zhou, W. Soedel, J. Kim, New Iterative Scheme in Computer Simulation of Positive Displacement s Considering the Effect of Gas Pulsations Journal of Mechanical Design JUNE 2001, Vol. 1. [4] Marie-Eve Duprez1, Eric Dumont1, Marc Fre re* Modelling of reciprocating and scroll compressors International Journal of Refrigeration 30 (2007) 873-886. [5] E. Navarro, E. Granryd A phenomenological model for analyzing reciprocating compressors International Journal of Refrigeration 30 (2007) [6] Kim Tiow Ooi, Heat transfer study of a hermetic refrigeration compressor, Applied Thermal Engineering 23 (2003) 1931 1945. ISSN: 2348 8360 www.internationaljournalssrg.org Page 21