In order to investigate the performance of variable thickness scroll compressors, a detail mathematical modeling based on energy and mass balances is established in this two-part. In part I, the geometric modeling and thermodynamic modeling are developed. The profile based on circle involute, high order curve, and arc is built up using the base line method. The volume of working chambers from suction to discharge is defined. Thereafter, the evolution and derivative of the working chamber volume with respect to the orbiting angle are discussed. The energy and the mass balance for working chamber are described. Suction gas heating, radial and flank leakage, heat transfer between the working fluid, scroll wraps and plates are considered in the thermodynamic modeling. The established geometric modeling and thermodynamic modeling can provide better understanding of the variable thickness scroll compressor working process. The dynamical modeling and model validation are reported in part II.
Bush JW, Beagle WP and Housman ME. Maximizing scroll compressor displacement using generalized wrap geometry. In: Proceedings of international compressor engineering conference 1994, Purdue University, West Lafayette, IN, 1994, pp.205–210. IN: Ray W. Herrick Laboratories Press.
4.
WangLCChenJZhangXM. Study on geometry theory of variable wall thickness scroll profiles and shape optimization based on functional theory. China Mech Eng2010; 21: 1898–1901.
5.
WangJLiXQ. Construction of tapered thickness wrap profile for twin wrap scroll machinery. J China Univ Petrol (Ed Nat Sci)2008; 32: 128–132.
6.
GravesenJHenriksenC. The geometry of the scroll compressor. SIAM Rev2001; 43: 113–126.
7.
ShafferBRGrollEA. Variable wall thickness scroll geometry modeling with use of a control volume approach. Int J Refrigeration2013; 36: 1809–1820.
8.
LiuYGTangYJChangYC. Optimum design of scroll profiles created from involute of circle with variable radii by using finite element analysis. Mech Mach Theory2012; 55: 1–17.
9.
LiuYGHungCHChangYC. Study on involute of circle with variable radii in a scroll compressor. Mech Mach Theory2010; 45: 1520–1536.
10.
Morishita E, Sugihara M, Inaba T, et al. Scroll compressor analytical model. In: Proceedings of international compressor engineering conference 1984, Purdue University, West Lafayette, IN, 1984, pp.487–495. IN: Ray W. Herrick Laboratories Press.
11.
Ishii N, Fukushima M, Sano K, et al. A study on dynamic behavior of a scroll compressor. In: Proceedings of international compressor engineering conference 1986, Purdue University, West Lafayette, IN, 1986, pp.901–916. IN: Ray W. Herrick Laboratories Press.
12.
Sunder S. Thermodynamic and heat transfer modeling of a scroll pump. PhD Thesis, Massachusetts Institute of Technology, 1996.
13.
ScheinCRadermacherR. Scroll compressor simulation model. J Eng Gas Turbines Power2001; 123: 217–225.
14.
LeeGH. Performance simulation of scroll compressors. Proc IMechE, Part A: J Power and Energy2002; 216: 169–179.
15.
Halm NP. Mathematical modeling of scroll compressors. Master of Science Thesis, Purdue University, 1997.
16.
ChenYHalmNPGrollEA. Mathematical modeling of scroll compressors—part I: compression process modeling. Int J Refrigeration2002; 25: 731–764.
17.
ChenYHalmNPGrollEA. Mathematical modeling of scroll compressors—part II: overall scroll compressor modeling. Int J Refrigeration2002; 25: 751–764.
18.
ParkYCKimYCChoHY. Thermodynamic analysis on the performance of a variable speed scroll compressor with air injection. Int J Refrigeration2002; 25: 1072–1082.
19.
WinandyESaavedraOCLebrunJ. Experimental analysis and simplified modeling of a hermetic scroll refrigeration compressor. Appl Therm Eng2002; 22: 107–120.
20.
KimTOZhuJ. Convective heat transfer in a scroll compressor chamber: a 2-D simulation. Int J Therm Sci2004; 43: 677–688.
21.
ZhaoYYLiLSWuHG. Theoretical and experimental studies of water-injection scroll compressor in automotive fuel cell systems. Energy Conversion Manage2005; 46: 1379–1392.
22.
WangBLLiXTShiWX. A general geometrical model of scroll compressors based on discretional initial angles of involute. Int J Refrigeration2005; 28: 958–966.
23.
ChenRWangW. Discussion on leaking characters in meso-scroll compressor. Int J Refrigeration2009; 32: 1433–1441.
24.
SunSHZhaoYYLiLS. Simulation research on scroll refrigeration compressor with external cooling. Int J Refrigeration2010; 33: 897–906.
25.
Rovira J, Rigola J, Perez-segarra CD, et al. Numerical simulation of wrap scroll temperature for refrigeration and air conditioning compressors. In: Proceedings of international compressor engineering conference 2012, Purdue University, West Lafayette, IN, 2012, 1380, pp.1–8. IN: Ray W. Herrick Laboratories Press.
26.
Bell IH, Groll EA, Braun JE, et al. Derivation of optimal scroll compressor wrap for minimization of leakage losses. In: Proceedings of international compressor engineering conference 2012, Purdue University, West Lafayette, IN, 2012, 1371, pp.1–8. IN: Ray W. Herrick Laboratories Press.
27.
Bell IH, Groll EA, Braun JE, et al. A computationally efficient hybrid leakage model for modeling leakage in positive displacement compressors. In: Proceedings of international compressor engineering conference 2012, Purdue University, West Lafayette, IN, 2012, 1103, pp.1–10. IN: Ray W. Herrick Laboratories Press.
28.
Diniz MC, Pereira ELL and Deschamps CJ. A lumped thermal parameter model for scroll compressors including the solution of the temperature distribution along the scroll wraps. In: Proceedings of international compressor engineering conference 2012, Purdue University, West Lafayette, IN, 2012, 1341, pp.1–10. IN: Ray W. Herrick Laboratories Press.
29.
Pereira ELL and Deschamps CJ. A numerical study of convective heat transfer in the compression chambers of scroll compressors. In: Proceedings of international compressor engineering conference 2012, Purdue University, West Lafayette, IN, 2012, 1274, pp.1–6. IN: Ray W. Herrick Laboratories Press.
30.
QiangJGPengBLiuZQ. Dynamic model for the orbiting scroll based on the pressures in scroll chambers—part I: analytical modeling. Int J Refrigeration2013; 36: 1–20.
31.
QiangJGPengBLiuZQ. Dynamic model for the orbiting scroll based on the pressures in scroll chambers—part II: investigations on scroll compressors and model validation. Int J Refrigeration2013; 36: 1850–1865.
32.
PengBSunYZhangL. Geometrical and frictional loss model for scroll compressor with variable scroll thickness. J Lanzhou Univ Technol2012; 38: 34–38.
33.
LemmonEWJacobsenRTPenoncelloSG. Thermodynamic properties of air and mixtures of nitrogen, argon, and oxygen from 60 to 2000 K at pressures to 2000 MPa. J Phys Chem Ref Data2000; 29: 331–385.
34.
FoxRWMcDonaldAT. Introduction to fluid mechanics, New York, NY: John Wiley & Sons, 1992.
35.
IncroperaFPDewittDP. Fundamentals of heat and mass transfer, New York, NY: John Wiley & Sons, 1996.
36.
KakacSShahRK. Handbook of single-phase convective heat transfer, New York, NY: John Wiley & Sons, Inc, 1987.
37.
RajavelRSaravananK. Heat transfer studies on spiral plate heat exchanger. Therm Sci2008; 12: 85–90.
38.
JangKJeongS. Experimental investigation on convective heat transfer mechanism in a scroll compressor. Int J Refrigeration2006; 29: 744–753.
