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
Liquid Slugging Measurements in Reciprocating Compressors
Several different methods of measuring cylinder pressures generated during liquid slugging in Hermetic and Semi-Hermetic compressors have been devised. The methods are discussed and compared, and test results are presented. Some interesting aspects of liquid slugging are also discussed. An empirical relation for predicting maximum cylinder pressure aa a function of compressor power, bore size, and stroke length is presented.
Positive Rights and State Constitutions: The Limits of Federal Rationality Review
INTRODUCTION ............................................................................................................................. 1132 I. STATE CONSTITUTIONAL WELFARE PRACTICE ............................................................. 1144 A. A Mandatory Obligation: The New York Example .................................................. 1144 B. A Typology of Current State Court Decisions .......................................................... 1145 IT. RECONSIDERING FEDERAL RATIONALITY REVIEW IN STATE CONSTITUTIONAL WELFARE CASES ................................................................................ 1153 A. Rationality Review and Positive Rights .................................................................. 1155 B. Rationality Review and Democratic Legitimacy .................................................... 1157 C. Rationality Review and Judicial Finality ............................................................. xi61 D. Rationality Review and Federalism ......................................................................... i166 E. Rationality Review Revisited .................................................................................... 1169 III. TOWARD A NEW STANDARD OF REVIEW ......................................................................... 1169 A. The Need for Judicial Review .................................................................................. 1170 B. Institutional Competence and Welfare Litigation ................................................... 1175 I. State Courts as Fact Gatherers ......................................................................... 1175 2. State Courts as Policymakers ......................................................................... " 179 3. State Courts as Rights Enforcers ..................................................................... 1182 C. A Jurisprudence of Consequences .............................................................................. 1183 D. Why Education and Not Welfare? ........................................................................... i86 E. Implications for Welfare Litigation ........................................................................... i9i IV. CONCLUSION ........................................................................................................................ 1194