The effect of the lubricating oil on heat transfer in a hermetic reciprocating compressor
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Abstract
In some types of hermetic refrigeration reciprocating compressors, the oil circulation pattern inside the crankcase produces an oil falling film on the inner wall of the compressor shell. The conjugate heat transfer between the shell and the oil affects the heat dissipation from the internal components to the external environment and, consequently, the compressor thermal profile. A differential model is proposed to calculate the oil film and compressor shell temperature distributions. This model is incorporated into an existing compressor model based on integral forms of the energy balances for its components. The combined (integrated) model results are verified against experimental data for the temperature of the components and of the compressor shell. The model can be used to predict the compressor performance as a function of the suction and discharge pressures, the total oil flow rate and the fraction of this flow rate flowing as a film on the shell.
Keywords
Lubricating oil Heat transfer Reciprocating compressor Differential modelList of symbols
- \(A\)
Area (m\(^{2}\))
- \(c_\mathrm{p}\)
Specific heat capacity at constant pressure (J kg\(^{-1}\) \(^{\circ}\)C\(^{-1}\))
- \(c_\mathrm{v}\)
Specific heat capacity at constant volume (J kg\(^{-1}\) \(^{\circ }\)C\(^{-1}\))
- COP
Coefficient of performance (-)
- \(d\)
Equivalent diameter of the shaft helical channel (m)
- \(G_\mathrm{or}\)
Mass flow rate per unit area (Eq. 6) (kg m\(^{-2}\) s\(^{-1}\))
- \(h\)
Specific enthalpy (J kg\(^{-1}\))
- \(\hbar\)
Convection coefficient (W m\(^{-2}\) \(^{\circ }\)C\(^{-1}\))
- \(k\)
Thermal conductivity (W m\(^{-1}\) \(^{\circ }\)C\(^{-1}\))
- \(m\)
Mass (kg)
- \(\dot{m}\)
Refrigerant mass flow rate (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{o}\)
Total oil mass flow rate (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{oh}\)
Oil mass flow rate on the compressor shell (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{or}\)
Oil mass flow rate on the compressor components (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{des}\)
Refrigerant mass flow rate (discharge) (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{rdes}\)
Refrigerant mass flow rate (backflow discharge) (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{rsuc}\)
Refrigerant mass flow rate (backflow suction) (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{suc}\)
Refrigerant mass flow rate (suction) (kg s\(^{-1}\))
- \(\dot{m}_\mathrm{spc}\)
Refrigerant mass flow rate (clearance leakage) (kg s\(^{-1}\))
- \(p\)
Pressure (Pa)
- \(\dot{Q}\)
Heat transfer rate (W)
- \(q''\)
Heat flux (W m\(^{-2}\))
- \(r\)
Radial coordinate (m)
- \(R\)
Equivalent radius of the crankcase (m)
- \(t\)
Time (s)
- \(T\)
Temperature (\(^{\circ }\)C)
- \(\langle T_\mathrm{g} \rangle\)
Cycle average cylinder gas temperature (\(^{\circ }\)C)
- \(\overline{\mathrm{UA}}\)
Thermal conductance (W \(^{\circ }\)C\(^{-1}\))
- \(v\)
Specific volume (m\(^{3}\) kg\(^{-1}\))
- \(V\)
Volume (m\(^{3}\))
- \(\dot{W}\)
Power (W)
- \(x\)
Oil flow fraction (compressor shell) (-)
- \(z\)
Axial coordinate (m)
- \(Z\)
Length of the flange (m)
Greek
- \(\delta\)
Thickness (m)
- \(\theta\)
Crank angle (rad)
- \(\omega\)
Angular velocity (rad s\(^{-1}\))
- \(\xi\)
Shaft helical channel coordinate (m)
Subscripts
- \(\text{bf}\)
Base of the flange (fin analogy)
- \({\text{d}{-}\mathrm{or}}\)
Between discharge plenum and oil on components
- \({\text{d}{-}\mathrm{sh}}\)
Between discharge plenum and shaft channel
- dc
Discharge plenum
- des
discharge
- ee
External environment
- ele
Electrical
- \(\text{f}\)
Flange
- \(\text{g}\)
Gas in the cylinder
- \(\text{h}\)
Compressor shell
- he
Shell/external environment interface
- io
Crankcase gas/oil film interface
- ie
Crankcase gas
- in
Inlet of control volume
- \({\text{l}{-}\mathrm{or}}\)
Between discharge line and oil on components
- \({\text{l}{-}\mathrm{sh}}\)
Between discharge line and shaft channel
- \(\mathrm{ld}\)
Discharge line
- \(\text{m}\)
Electric motor/stator
- \({\text{m}{-}\mathrm{or}}\)
Between motor and oil on components
- \({\text{m}{-}\mathrm{sh}}\)
Between motor and shaft channel
- \(\text{o}\)
Oil
- oc
Oil sump
- oee
Oil entering the reed pump
- oh
Oil film/shell interface
- or
Oil flow on the components
- ot
Oil in the shaft channel
- out
Outlet of control volume
- ose
Oil leaving the shaft
- ps
Inlet tubing
- \({\text{s}{-}\mathrm{or}}\)
Between suction muffler and oil on components
- \({\text{s}{-}\mathrm{sh}}\)
Between suction muffler and shaft channel
- suc
suction muffler
- \({\text{v}{-}\mathrm{or}}\)
Between discharge mufflers and oil on components
- \({\text{v}{-}\mathrm{sh}}\)
Between discharge mufflers and shaft channel
- vb
Discharge muffler
- \(\text{w}\)
Cylinder wall
- \({\text{w}{-}\mathrm{or}}\)
Between cylinder wall and oil on components
- \({\text{w}{-}\mathrm{sh}}\)
Between cylinder wall and shaft channel
Notes
Acknowledgments
The material presented in this paper is a result of a long-standing technical-scientific partnership between the Federal University of Santa Catarina (UFSC) and Embraco. The authors are indebted to FINEP and CNPq through Grant No. 573581/2008-8 (National Institute of Science and Technology in Refrigeration and Thermophysics).
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