An Investigation of Compressor Slugging Problems
Mathematical models have been popularly applied to study the compression processes of superheated refrigerant vapor in compressors. As to the case when refrigerant enters a compressor cylinder in the state of liquid and vapor mixture, however, the availability of fundamental studies is very limited. -A mathematical model is presented to simulate the compression processes of two-phase saturated refrigerant mixture. Factors leading to slugging are analyzed. It is explained why certain types of compressors are less prone to slug. Introduction Under nonnal operation of compressors, refrigerant is drawn into compressor cylinders in the state of super heated vapor. However, liquid refrigerant, or a portion of liquid refrigerant, can enter compressor cylinders under certain circumstances, such as during the cold start of a compressor. In some of the scroll compressor applications [13], refrigerant liquid is even deliberately injected into the gas pockets to decrease the discharge gas temperature under high compression ratios and thereby to extend the operating range of such compressors. Liquid refrigerant entering compressor cylinders has been a concern for a long time. However, not enough has been achieved from the view point of mathematical modeling. An extensive literature review was done in this area, but no satisfactory thennodynamic model, which could be used to simulate the compressor cylinder processes, was found. Simpson and Lis [4] measured cylinder pressures during compressor liquid ingestion in reciprocating compressors and presented an empirical relation for predicting the maximum cylinder pressure in terms of compressor power, bore size, and stroke length. Singh, Nieter, and Prater [5-6] applied the polytropic equation to simulate compressor cylinder pressure, but the polytropic index in their model is considered as a variable and can be chosen arbitrarily. It is necessary to develop a mathematical model to predict the cylinder refrigerant thermodynamic properties instantaneously and to study the effects of liquid entering the cylinder on the compressor performance by simulating the thermodynamic process of compressing the liquid and vapor mixture. Slugging problems are detrimental to compressors. Under extreme conditions, the compressor cylinder pressures could be as high as ten times the peak pressures under normal operations [5], due to the incompressibility of liquid, consequently damaging the compressor valves and reducing the reliability and lifetime of compressors. These effects should always be avoided, if possible. Does the liquid and vapor mixture entering compressor cylinders necessarily lead w a slugging problem? It depends on the quality (the ratio of vapor mass to the total mass of the liquid and vapor mixture) of the refrigerant entering the compressor cylinders, the kinematics of the compressor, and whether the compressor is a high side design or a low side design. For compressors with low side design, since the compressor shell is filled with cool suction gas and the cylinder temperature is not very hot, a slugging problem is likely to happen because of the lack of heat transfer from the cylinder to the liquid-vapor mixture, especially during the cold start. On the other hand, the cylinder of the compressor in a high side design is heated by the relatively high temperature discharge gas, therefore the possibility of liquid slugging is reduced. Common sense tells us that slugging is more likely to occur in compressors when refrigerant of low quality flows into the cylinders. However, the influence of the kinematics of a compressor on the possibility of slugging is not so obvious, and has to be studied through mathematical modeling. Thermodynamic Model
Prediction of Slugging-Induced Cylinder Overpressures
In typical refrigerant compressors, peak cylind er pressures under liquid slugging conditions are as high as 10 times the peak pressures during the normal operation. In this paper we model this phenomenon by considering the compression process with a separated gas and liquid media in the cylinder. Two cases of this model for various liquid fractions are simulat ed. Even though time histories corresponding to both cases are sl ightly different, both models yield very high peak pressures, similar to those measured, when the compressor is "pumping" mostly liquid. Various aspects of the problem are discussed here. NOMENCLATURE A flow area b slider-crank length C coefficient of discharge gc gravitational constant k ratio of isentropic specific heat capacities m mass flow rate n polytropic index
Mathematical Modeling of Scour and Deposition
Electronic computers are opening up the field of sedimentation engineering by permitting the analysis of problems which heretofore have required too much time and effort. Movable stream bed profiles are being calculated in addition to water surface profiles. The initial gradation of sediment material in the stream bed may be prescribed to facilitate the calculation of an armor layer. This gradation is continually changed by the computer program in response to sediment particles being deposited on the stream bed and material on the stream bed being removed to satisfy transport capacity. Hydraulic sorting of sediment by grain size is accomodated. The stream bed does not have to be represented by a single grain size. Retardance of motion because of armor layer is calculated.