A New Correlation for Instantaneous Heat Transfer Between Gas and Cylinder in Reciprocating Compressors

The heat transfer process that takes place in the inteiface between the working fluid and the cylinder walls is one of the most relevant effect regarding reciprocating compressor peiformance. The fast transients and the limitations in terms of space to install transducers imply severe restrictions to the experimental analysis of this phenomenon. On the other hand, it is always desired to develop simple correlations to describe mathematically this heat transfer process, in order to permit its use in simulation programs without computational time penalties. The main objective of this work is to evaluate existing correlations to the Nusselt number that represent the heat transfer on the above mentioned inteiface, including complex number formulations. The emphasis is to introduce a new correlation to substitute correlations currently used in compressor simulation programs. The proposed formulation is based on the difference between the gas mean temperature and the cylinder wall temperature, as usual, but it also considers the gas temperature derivative. A simulation program that solves the transient fluid flow and heat transfer inside the cylinder via Finite Volume Method, generated results to corroborate the hypothesis regarding the use of mean gas temperature and pressure and the correlation itself The validation of the theory is achieved by comparing results of the simulation programs with experimental data, and the evaluation of compressor thermodynamic losses. INTRODUCTION Accurate information about heat transfer processes play a significant role in simulation and design of reciprocating machines. In particular, the instantaneous heat transfer between the in-cylinder gas and the solid walls is of crucial importance, due to its paramount influence on the thermodynamic performance of those equipments. This has been recognized since the thirties (Eichelberg, 1939) and a large number of experimental and theoretical studies have been performed in this field. In general, the main objective of all works is to develop simple correlations to predict the Nusselt number for the gas-cylinder interface as a function of global properties. This characteristic is of particular importance when developing compressor simulation programs, because of the requirements that arise from the balance between computational time and accuracy. In Fagotti et al. (1994), some of the most important correlations proposed in the literature to determine the gasto-wall heat transfer have been analyzed through a pragmatic approach, although not strictly precise. The correlations were implemented in a compressor simulation code, in order to determine which one best fitted the experimental data relative to a small hermetic reciprocating compressor for domestic appliances. Due to the intrinsic difficulties to install transducers with adequate time response to measure directly the in-cylinder process, only global compressor running characteristics were taken into account. In this aspect, the main restrictions are the narrow spaces available to install probes and the required fast-response time. In this scenario, one should reach a compromise between lack of precision in the measurements and uncertainties due to changes in the characteristics of the set up configuration relative to the real compressor. Both, enlarging the dimensions or diminishing the cycle period would require scaling factors, difficult to predict and to deal with. The correlations proposed by Annand (1963) and Adair et al. {1974) led to the best results, the later with a slightly lower precision. Both Annand's and Adair's correlations are widely used in reciprocating compressors simulation. Like almost all the models developed up to now, they assume that heat transfer follows Newton's law. However it has long being observed (Pfriem, 1943) that during in-cylinder gas transformations due to reciprocating movement, the