Instantaneous Heat Transfer to the Cylinder Wall in Reciprocating Compressors

This study first reviews, discusses, and compares existing correlations for heat transfer in reciprocating compressors and engines. Then after a discussion of the significance of obtaining accurate instantaneous heat transfer data, the authors describe an experimental investigation of the instantaneous heat transfer rates to the cylinder wall of a reciprocating refrigerating compressor. Finally, this report presents an expression which correlates the time averaged data within 20%. INTRODUCTION Previous attempts at describing and predicting the heat transfer occurring in reciprocating engines and compressors have in some cases been moderately successful and in others completely unsuccessfuly. Most of the reported investigations have attempted to predict the instantaneous heat transfer from measured average heat transfer rates [1 through 5]. More recent investigations, however, have been concentrating on the problems of measurement and correlation of instantaneous heat transfer rates [6 through lOJ. All these investigations were carried out on internal combustion engines and, to the authors' knowledge, there has been no previous measurement of instantaneous \eat transfer rates in reciprocating compressors. Thus, this investigation was undertaken with the hope of providing additional insight into the fundamentals of heat transfer processes in reciprocating machinery. The present investigation, which is part of a more extensive research program [11], begins with a review and discussion of the presently available heat transfer correlations. A comparison of these correlations exposes their basic characteristics and differences and is followed by a prediction of the maximum errors introduced when the estimation of compressor efficiencies is b~sed upon a poor knowledge of the 521 instantaneous heat transfer rates. Finally, experimental methods and results are presented together with a correlation of the data obtained. REVIEW OF AVAILABLE HEAT TRANSFER CORRELATIONS The available correlations on cylinder heat transfer have all been developed for internal combustion engines and they can be divided into two main groups according to the choice of variables. Representative for the first group are the correlations by Nusselt [1], Eichelberg [2], and Pflaum [3]. In this group the heat-transfer coefficient chosen is of the following form: h(t) = f[V ,P (t), T (t)] p g g ( 1) where t denotes the instantaneous value of a quantity. Representative of the second group are Woschni [6], Annand [4], Sitkei [5] and LeFeuvre [7]. This group utilizes correlations of the type Nu(t) = f[Re(t), gas properties J. (2) All the correlations in these two groups include constants that have to be determined experimentally and are, therefore, empirical in the first group and semi-empirical in the second. The correlations are given below. First group: Nusselt: h(t)=.0278(1+.38 V )[P (t) 2T (t)]l/3 p g g Eichelberg: h(t)=.0565 V l/3 [P (t)T (t)]l/2 p g g ( 3)