Effects Of Leakage Flow Model On The Thermodynamic Performance Of A Scroll Compressor

A computer program for thermodynamic performance of a scroll compressor was developed. The thermodynamic model assumes that the compression volumes of the scroll compressor are separated and interact only through leakages between them. The continuity and energy equations are used to calculate the pressure and temperature of the compression volumes. A leakage flow model is used to simulate the mass flow rate through all leakages. In this study, two different leakage models, isentropic and Fanno flow model, were studied to see its effects on the thermodynamic performance of the scroll compressor. The isentropic flow model shows a larger mass flow rate, compared with the Fanno flow model. CFD solutions obtained by using FLUENT show that the Fanno flow model is more accurate. The difference between the two leakages models grows larger as the clearance increases. NOMENCLATURE A: cross sectional area of a leakage passage Cf: skin friction coefficient h: scroll height m: mass of the compression chamber p: pressure of compression chamber R: gas constant T: temperature of compression chamber V: volume of compression chamber y: lift of a check valve α : involute start angle φ: orbiting angle ε: orbiting radius ρ: density of compression chamber θε: involute maximum angle ω: natural frequency of check valve ξ: damping coefficient of check valve subscript 1 : inside scroll profile (involute) 2 : outside scroll profile(involute) ι: inflow o : outflow INTRODUCTION Scroll compressor is widely used in various industries due to its high efficiency and low noise characteristics, compared with conventional rotary and reciprocating compressors. So, a bunch of papers on its thermal, mechanical and dynamic analysis and design were already published in various conferences [1-3]. However, most thermal model of a scroll compressor use simple one-dimensional isentropic flow model to simulate the leakage flow in the scroll compressor. But, research on the leakage flow model is not sufficiently performed to validate the use of the isentropic flow model. Present study aims to evaluate the accuracy of the isentropic flow model in a very practical way and suggest an alternative model that is more accurate. We developed a thermal analysis program to predict the performance of a scroll compressor and used this program to show effects of leakage flow model on the thermodynamic performance of a scroll. The accuracy of the leakage flow models is also checked using a commercial CFD code. We use FLUENT, a commercial CFD code, to compute the fluid flow through a leakage. PREDICTION OF THERMODYNAMIC PERFORMANCE Each compression volume of a scroll compressor was modeled as a separate system having its own mass as shown in Fig. 1. Its volume changes as the scroll orbits and can be expressed with respect to the orbiting angle. For example, the volume of the suction chamber (#1 in Fig. 1) can be expressed as The mass, temperature and pressure of each volume is determined by solving the continuity, energy, and state equation summarized in the following: The scroll compressor used in this paper has a check at discharge port. We modeled it as a mass spring system. So, its motion can be determined by computing the following equation: Leakage flow models The leakage flow through a clearance in the scroll compressor should be modeled to complete the thermodynamic model. There are two different kinds of clearance in the scroll as shown in Fig. 2. One is called radial clearance, and it causes the leakage flow in the circumferential direction. The other one is called tip clearance, and it leads to the leakage flow in the radial direction. In this paper, two leakage flow models are tried and evaluated by using the commercial CFD code FLUENT[4]. The isentropic flow model assumes that the leakage flow rate can be calculated by the following equation[5]: The second leakage flow model is a kind of Fanno flow[5]. It takes account of viscous effect in the leakage passage. We assume that the leakage passage has a constant area, and then the mass flow rate can be determined by solving the following equation: where the function f(M) is defined as CFD evaluation We used FLUENT, a commercial CFD code, to evaluate the leakage flow models. Fig. 3 shows a model of a tip clearance. The inlet and outlet conditions, pressure and temperature, are results of the thermodynamic performance prediction. Computed mass flow rate is used to evaluate the mass flow rate predictions obtained by eqs. (5) and (6). , (1) )} cos 1 ( 2 2 ) 2 sin( ) 2 1 ( sin ) 1 e ( 2 ) 2 1 e 2 ( { 2 a h V φ φ α α π φ α π θ α α π φ θ φ ε − + + − − − − − − − − − = (4) RT p ) 3 ( ] m dt dm mT dt dm T dt dm m 1 dt dV V 1 [ T dt dT ) 2 ( dt dm dt dm dt dm