Damle, Rashmin

Oliva, Assensi

Perez-Segarra, Carlos D.

Rigola, Joaquim

English

Purdue E-Pubs

Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering2008An Object Oriented Program for the NumericalSimulation of Hermetic Reciprocating CompressorBehaviourRashmin DamleTechnical University of CataloniaJoaquim RigolaTechnical University of CataloniaCarlos D. Perez-SegarraTechnical University of CataloniaAssensi OlivaTechnical University of CataloniaFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlDamle, Rashmin; Rigola, Joaquim; Perez-Segarra, Carlos D.; and Oliva, Assensi, "An Object Oriented Program for the NumericalSimulation of Hermetic Reciprocating Compressor Behaviour" (2008). International Compressor Engineering Conference. Paper 1911.https://docs.lib.purdue.edu/icec/19111402, Page 1An Object Oriented Program for the Numerical Simulation ofHermetic Reciprocating Compressor BehaviourRashmin DAMLE, Joaquim RIGOLA, Carlos D. PÉREZ-SEGARRA, Assensi OLIVACentre Tecnològic de Transferència de Calor (CTTC)Universitat Politècnica de Catalunya (UPC)ETSEIAT, C. Colom 11, 08222 Terrassa (Barcelona), SpainTel. +34-93-739.81.92, Fax: +34-93-739.89.20cttc@cttc.upc.edu, http://www.cttc.upc.eduABSTRACTAn object oriented approach for the numerical simulation of the thermal and fluid dynamic behaviourof hermetic reciprocating compressors is presented in this paper. The compressor domain is formed byconnecting individual elements such as tubes, chambers, compression chambers, valve plates, etc., whichexchange information (pressure, temperature, mass flow etc.) between themselves. The coupled system issolved until convergence is reached. Code verification tests and numerical results of some illustrative casesare presented to show the possibilities offered by the new program.1. INTRODUCTIONA numerical simulation model for the thermal and fluid dynamic behaviour of hermetic reciprocating com-pressors for the analysis of standard domestic/commercial applications has been extensively presented duringseveral Purdue conferences (Pérez-Segarra, et al.,1994), (Escanes, et al.,1996), (Rigola et al.,1998) and pub-lished in detail by (Pérez-Segarra, et al.,2003). These studies were focussed on the improvement of thecompressor design, reduction of power consumption, increasing the compressor efficiency and optimisingthe compressor behaviour. The numerical verification and detailed experimental validation have also beenshown in depth by (Pérez-Segarra, et al.,2003), (Rigola et al.,2003), (Rigola et al.,2004). The numericalmodel analysed the fluid flow based on full integration of the one-dimensional transient governing equations(continuity, momentum and energy) through all the compressor domain in a sequential way.The use of new refrigerants, new compressor circuitry, new designs, some aspects like more than two parallellines, the possibility to work with more than one compression chamber etc., have obliged to develop newmodelling strategies. The thermal and fluid behaviour resolution allowing such flexibility is presented inthis article. The numerical simulation consists of components (tubes, chambers, compression chamber, valveorifices, fixed values), which are interlinked exchanging boundary information from each other. The coupledsystem is solved until the convergence is reached.2. MODULAR COMPRESSOR DOMAINThe compressor domain is divided into separate elements (objects from the C++ point of view) as shown inFigure 1. The following objects are programmed:• “ Tube ”: a tube transporting the gas.• “ Compression chamber ”: a compression chamber.• “ Chamber ”: a chamber as a reservoir.• “ Valve Orifice ”: a valve orifice for valve dynamics.• “ FixedValue ”: a boundary condition object, at fixed pressure and temperature.These objects are linked together to form the compressor domain. Each object is capable of solving it-self for given boundary conditions.19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 2Figure 1: One piston compressor domain formed by different elements (objects)3. DISCRETIZED EQUATIONSEach element of the compressor domain is divided into finite control volumes (CVs). For any CV in whichthe gas is flowing the governing equations (continuity, momentum and energy) can be written in terms oflocal averaged fluid variables, neglecting body forces, axial shear stresses and axial heat conduction in thefollowing form:∂m∂t+Xṁe −Xṁw = 0 (1)∂mv̄∂t+Xṁeve −Xṁwvw = Fs (2)∂m(h̄ + ēc)∂t+Xṁw(hw + ecw)−Xṁe(he + ece) = V∂p̃∂t+ Q̇wall (3)4. NUMERICAL RESOLUTION OF THE COMPRESSOR DOMAINELEMENTS4.1 TubeA tube as shown in the Figure 2a is solved according to the SIMPLEC algorithm (Patankar, 1980) usingstaggered arrangement for velocities. Upwind criteria is used for the convective terms. Inlet and outletFigure 2: (a)Tube with staggered control volumes, (b) Tube with expansion/contractionpressures are linked to the tube boundary pressure (pb) assuming pinlet/outlet=pb ±ρv2P2 . In case of a sudden19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 3expansion or contraction as shown in Figure 2b, when tubes are connected to other tubes or to chambers,the following relation is used to relate the pressures across the expansion/contraction (Morse, 1953).l∂ṁ∂t+˙|m|vP2((SS)2(SII)2−(SS)2(SI)2)+(SSSo−1cc)2= (pi − po)SS (4)The tube gives pressure and mass flow rate as output to the chamber/compression chamber which is usedfor the first pass through the chamber/compression chamber iterative loop at every iteration.4.2 Compression Chamber/ChamberFigure 3: Chamber with multiple inlets and outlets.Pressure correction approach for the compressor chamber is described in the section. The chamber treatmentis similar to that of compression chamber with the volume at the current time step V, equal to that at theprevious instant V0 as the volume of chamber remains constant. The mass flow rate equation for theinlets/outlets of the compression chamber/chamber is written as :ṁk =Nk(pP − pk) + Hk + (lkṁk0t )Mk(5)where, the variables take different values for valve orifices and tubes. The subscript k indicates the differentelements connected to the compression chamber/chamber. From this equation a mass correction is soughtas: ṁ′k = dk(p′P − p′k) where, dk =NkMkand put in the continuity equation (1) to obtain an equation forpressure correction (p′) for compression chamber/chamber. Here, flow entering the chamber is consideredpositive (west) and leaving as negative (east). The compression chamber/chamber gets pressure from thetubes and valve orifices as data. Thus, p′kE = 0 and p′kW = 0. The compression chamber/chamber resolutionconsists of the following steps for every iteration.1. Guess initial p∗P , h∗P and ṁ∗∗k (use the mass flow rate coming from tubes or valve orifices)2. Calculate the density ρ∗P = ρ(p∗P , h∗P )3. Calculate Nk,Hk,Mk for the respective neighbours (tubes or valve orifices) and calculate new ṁ∗k4. Calculate p′P5. Update: pP =p∗P + αrp′P , ρP = ρ∗P + ρ′P6. Solve the energy equation and get new value of hP7. If mass residual > set precision, go to point 2 with p∗P = pP , h∗P = hP and ṁ∗∗k = ṁ∗k4.3 Valve OrificeThe valve orifice object is connected between a chamber and a compression chamber as shown in Figure 4.An equation similar to the expansion/contraction extended to compressible flow used to evaluate mass flow(Browler, 1993), through the valves is:l∂ṁ∂t+˙|m|vP2γ − 1γ1− po/piΠ1/γ −Π= (pi − po)KSs (6)19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 4Figure 4: Valve orifice connected between chamber and compression chamber.It receives pressures (pi and po) on either side of it which are pW and pP for the suction side and pP andpE on the discharge side as shown in Figure 4. The effective area, KSs, is then calculated and in turn themass flow rate. It passes pressures across it and the mass flow rate to its neighbours which is used for thefirst pass through the chamber/compression chamber iterative loop at every iteration.4.4 FixedValueA FixedValue object serves as a boundary condition (fixed pressure and temperature). It only gives thepressure and temperature values as output to the tubes connected to it.5. GLOBAL ALGORITHM OF RESOLUTIONFigure 5: Global algorithm for the simulation of the compressor domainThe global iterative algorithm is shown in the Figure 5. The program control goes through all the elementsonce every iteration. An iteration for the given element at each time step consists of the following steps:1. Get inputs (p, h, ṁ etc.,) from neighbour elements.19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 52. Solve the governing equations of the element.3. Set outputs (p, h, ṁ etc.,) for neighbour elements.The iterations are continued till the maximum number of iterations or the convergence criteria for eachtime step is reached. Transient calculation then continues till steady or cyclic steady state is reached.6. TEST CASES FOR CODE VERIFICATION6.1 One tube vs. two and three tubesMass flow rate at steady state for a tube shown in the Figure 2a is shown in the Table 1. Results for thesame tube solved as two/three different tube objects connected to form a single tube with same geometry (20CVs and a precision of 1e−6) give mass flow rates of 1.490874e−1 kg/s and 1.490874e−1 kg/s respectively.Table 1: Steady state mass flow rate (kg/s) for tube with pinlet=55 bars and poutlet=50 bars: evolution withnumber of nodes (n) and precision (ε).n/εsteady 1e−3 1e−4 1e−5 1e−6 1e−75 1.491375e−1 1.490917e−1 1.490877e−1 1.490873e−1 1.490873e−110 1.491362e−1 1.490879e−1 1.490874e−1 1.490874e−1 1.490874e−120 1.491149e−1 1.490890e−1 1.490876e−1 1.490875e−1 1.490875e−140 1.490832e−1 1.490886e−1 1.490876e−1 1.490875e−1 1.490875e−180 1.491006e−1 1.490888e−1 1.490876e−1 1.490875e−1 1.490875e−16.2 Tube-Chamber-Tube / Chamber with multiple inlets and outletsResults for a chamber connected with two tubes across a pressure difference are shown in the Table 2 whileTable 3 shows results for a chamber with multiple tubes of different diameters across a pressure differenceas in Figure 3. The sum of the mass flow rates entering and leaving tends to zero at steady state.Table 2: Steady state mass flow rate (kg/s) for tube-chamber-tube with pinlet=55 bars and poutlet=50 bars: evolutionwith number of nodes (n) and precision (ε).n/εsteady 1e−4 1e−5 1e−6 1e−7 1e−85 1.210229e−1 1.201000e−1 1.209984e−1 1.209981e−1 1.209982e−110 1.210213e−1 1.209991e−1 1.209968e−1 1.209965e−1 1.209965e−120 1.210205e−1 1.209982e−1 1.209960e−1 1.209957e−1 1.209957e−140 1.210200e−1 1.209978e−1 1.209955e−1 1.209953e−1 1.209953e−180 1.210199e−1 1.209976e−1 1.209953e−1 1.209951e−1 1.209951e−1Table 3: Chamber with 3 tube inlets (with diameters d, 0.2d, 0.6d) and 2 outlets (with diameters d, 0.4d, 0.8d) inletpr=55 bars, outlet pr=50 barsn/εsteady 1e−4 1e−5 1e−6 1e−7 1e−8mass residue 7.621802e−4 7.818611e−5 7.769957e−6 7.715786e−7 7.643355e−8∑ṁin 4.370016e−1 4.373891e−1 4.374283e−1 4.374322e−1 4.374327e−1∑ṁout 4.377638e−1 4.374673e−1 4.374361e−1 4.374330e−1 4.374327e−1time(secs) 14.75 16.63 17.25 19.23 20.7419th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 66.3 One piston compressor domainA single compressor domain without reed valves (valves kept open) is put to equal end pressures in orderto check the cyclic operation of the code. As the end pressures are same the sum of mass flow entering andleaving the compression chamber through suction and discharge ports during a cycle should be zero. Thevalue obtained at cyclic state is 0.59e−6 kg , which is acceptable and verifies the working of the elementsput together as compressor domain. Results for one piston compressor domain as in the Figure 1 operatingbetween 30 bars and 80 bars are shown in Table 4. The compressor capacity is 2.65 cm3 with carbon dioxideas the working fluid.Table 4: Cyclic state parameters for 1 piston assembly working between 30 bars and 80 bars.εt/εcyclic ṁ[kg/hr] ToutoC W (J) avg.iter/cycle time(s)1e−2 29.5939 103.9669 -10.1402 8 2651e−3 29.6028 103.9636 -10.1431 11 3371e−4 29.6027 103.9653 -10.1431 19 4731e−5 29.6026 103.9656 -10.1431 23 6631e−6 29.6026 103.9656 -10.1431 38 9631e−7 29.6026 103.9656 -10.1431 55 13577. ILLUSTRATIVE CASESFigure 6: Different compressor configurations (lp-low pressure, hp-high pressure, cc-compression chamber, c-chamber,rc-resonating chamber, t-tube and vo-valve orifice)Numerical results of some illustrative cases shown in Figure 6 are presented in Table 5. Different configu-rations, working fluids, capacities and pressure ranges have been worked out to show the versatility of thenew program.19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 7Table 5: Results for different compressor configurationsCase Refrigerant Capacity(cm3) Plow(bars) Phigh(bars) ṁ(kg/hr) TinoC ToutoC W (J)a1 R134a 8.095 2 14 10.56 32 108.74 -3.61a2 R134a 8.095 1.14 14 5.38 32 125.84 -2.39b R600a 15.97 1.08 7.72 6.37 32 108.60 -4.78c R744 1.29, 0.95 30 80 15.17 32 99.04 -4.63(a) R134a:case-a1 (b) R134a:case-a2(c) R600a:case-b (d) R744: case-cFigure 7: P-V diagrams of some of the illustrative cases8. CONCLUSIONA new object oriented program for the numerical simulation of the thermal and fluid dynamic behaviourof hermetic reciprocating compressors has been developed. The object oriented approach offers the use ofmultiple paths, several compression chambers in parallel or in series etc., and adapts faster to differentcompressor configurations by adding/removing the required elements. Finally, numerical results of someillustrative cases are presented to show the advantages offered by the new program.REFERENCES1. Pérez-Segarra, C.D., Escanes, F., Oliva, A., 1994, Numerical Study of the Thermal and Fluid-DynamicBehaviour of Reciprocating Compressors, International Compressor Engineering Conference, Purdue Uni-versity, West Lafayette, Indiana, USA, p. 145-150.2. Escanes, F., Pérez-Segarra, C.D., Rigola, J., Serra, J.M., 1996, Numerical Simulation of Reciprocating19th International Compressor Engineering Conference at Purdue, July 14-17, 20081402, Page 8Compressors. Recent Improvements and Experimental Validation, International Compressor EngineeringConference, Purdue University, West Lafayette, Indiana, USA, p. 193-198.3. Rigola, J., Pérez-Segarra, C.D., Oliva, A., Serra, J.M., Escribà, M., Pons, J., 1998, Parametric Study andExperimental Validation of Small Hermetic Refrigeration Compressors Using a Complete Advanced Numeri-cal Simulation Model, International Compressor Engineering Conference, Purdue University, Indiana, USA,Vol. I, p. 737-742.4. Pérez-Segarra C.D., Rigola, J., Oliva, A., 2003, Modelling and numerical simulation of the thermal andfluid dynamic behaviour of hermetic reciprocating compressors. Part 1. Theoretical basis, Int J Heating,Ventilating, Air-Conditioning Refrigerating Res 9, p. 215-236.5. Rigola, J., Pérez-Segarra, C.D., Oliva, A., 2003, Modelling and numerical simulation of the thermal andfluid dynamic behaviour of hermetic reciprocating compressors. Part 2. Experimental investigation, Int JHeating, Ventilating, Air-Conditioning Refrigerating Res 9, p. 237-249.6. Rigola, J., Raush, G., Pérez-Segarra, C.D., Oliva, A., 2004, Detailed Experimental Validation of theTermal and Fluid Dynamic Behaviour of Hermetic Reciprocating Compressors, Int J Heating, Ventilating,Air-Conditioning Refrigerating Res 10, p. 291-306.7. Patankar, S.V., 1980, Numerical Heat Transfer, Hemisphere publishing corporation.8. Morse, P.M., Feshbach, H., 1953, Methods of Theoretical Physics, part 2, McGraw-Hill Book Company.9. Browler, W.B., Eisler, Jr.E., Gonenc, E.J., Plati, C., Stagnitti, J., 1993, On the compressible flow throughan orifice, J. Fluid Engineeering, 115, p. 660-664.NOMENCLATURELatin symbolsp pressure(N/m2) p′pressure correctionh enthalpy(J/kg) m mass(kg)t time(sec) ṁ mass flow rate(kg/sec)CV control volume W work(J)v velocity(m/s) l constriction length(m)ec kinetic energy(J) V Volume(m3)Q̇ heat rate(J/sec) N area(m2)SI , SII areas(m2) of cross-sections i and o M , H terms from momentum equation oftubes and valve orificesSS min(SI , SII) cc expansion/contraction coefficientGreek symbolsφ generic varible(p, h, v) ρ density(kg/m3)ε precision demanded ρ′density correctionΠ compressible flow parameter γ ratio of specific heats of a gasα relaxation factor for p′Superscripts∗ guess value ∗∗ value at previous iteration0 value at previous time stepSubscriptsP central point or CV under consideration W point or CV to left(west) of PE point or CV to right(east) of P k conection index to the chamber(-)overbar integral mass averages over CV (∼)tilde integral volume average over CVw control volume face between W and P e control volume face between P and EACKNOWLEDGEMENTSThe authors gratefully acknowledge the financial support provided by ACC Compressors Spain, S.A. - UnidadHermética division (ref. no. C06244).19th International Compressor Engineering Conference at Purdue, July 14-17, 2008

An Object Oriented Program for the Numerical Simulation of Hermetic Reciprocating Compressor Behaviour

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An Object Oriented Program for the Numerical Simulation of Hermetic Reciprocating Compressor Behaviour

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