英文原文3.1 One Dimensional Mathematical Model 51 The Conservation of Internal Energy （3.1）where is angle of rotation of the main rotor, h = h() is specific enthalpy, m = m () is mass flow rate p = p(), fluid pressure in the working chamber control volume, Q = Q(), heat transfer between the fluid and the compressor surrounding, V = V () local volume of the compressor working chamber. In the above equation the subscripts in and out denote the fluid inflow and outflow.The fluid total enthalpy inflow consists of the following components: (3.2)where subscripts l, g denote leakage gain suc, suction conditions, and oil denotes oil. The fluid total outflow enthalpy consists of: (3.3)where indices l, l denote leakage loss and dis denotes the discharge conditions with m dis denoting the discharge mass flow rate of the gas contaminated with the oil or other liquid injected. The right hand side of the energy equation consists of the following terms which are model The heat exchange between the fluid and the compressor screw rotors and casing and through them to the surrounding, due to the difference in temperatures of gas and the casing and rotor surfaces is accounted for by the heat transfer coefficient evaluated from the expression Nu = 0.023 Re0.8. For the characteristic length in the Reynolds and Nusselt number the difference between the outer and inner diameters of the main rotor was adopted. This may not be the most appropriate dimension for this purpose, but the characteristic length appears in the expression for the heat transfer coefficient with the exponent of 0.2 and therefore has little influence as long as it remains within the same order of magnitude as other characteristic dimensions of the machine and as long as it characterizes the compressor size. The characteristic velocity for the Re number is computed from the local mass flow and the cross-sectional area. Here the surface over which the heat is exchanged, as well as the wall temperature, depend on the rotation angle of the main rotor. The energy gain due to the gas inflow into the working volume is represented by the product of the mass intake and its averaged enthalpy. As such, the energy inflow varies with the rotational angle. During the suction period, gas enters the working volume bringing the averaged gas enthalpy,52 3 Calculation of Screw Compressor Performance which dominates in the suction chamber. However, during the time when the suction port is closed, a certain amount of the compressed gas leaks into the compressor working chamber through the clearances. The mass of this gas, as well as its enthalpy are determined on the basis of the gas leakage equations. The working volume is filled with gas due to leakage only when the gas pressure in the space around the working volume is higher, otherwise there is no leakage, or it is in the opposite direction, i.e. from the working chamber towards other plenums. The total inflow enthalpy is further corrected by the amount of enthalpy brought into the working chamber by the injected oil. The energy loss due to the gas outflow from the working volume is defined by the product of the mass outflow and its averaged gas enthalpy. During delivery, this is the compressed gas entering the discharge plenum, while, in the case of expansion due to inappropriate discharge pressure, this is the gas which leaks through the clearances from the working volume into the neighbouring space at a lower pressure. If the pressure in the working chamber is lower than that in the discharge chamber and if the discharge port is open, the flow will be in the reverse direction, i.e. from the discharge plenum into the working chamber. The change of mass has a negative signand its assumed enthalpy is equal to the averaged gas enthalpy in the pressure chamber. The thermodynamic work supplied to the gas during the compression process is represented by the term pdV d . This term is evaluated from the local pressure and local volume change rate. The latter is obtained from the relationships defining the screw kinematics which yield the instantaneous working volume and its change with rotation angle. In fact the term dV/d can be identified with the instantaneous interlobe area, corrected for the captured and overlapping areas.If oil or other fluid is injected into the working chamber of the compressor, the oil mass inflow and its enthalpy should be included in the inflow terms. In spite of the fact that the oil mass fraction in the mixture is significant, its effect upon the volume flow rate is only marginal because the oil volume fraction is usually very small. The total fluid mass outflow also includes the injected oil, the greater part of which remains mixed with the working fluid. Heat transfer between the gas and oil droplets is described by a first or