Optimization of Compressor Design Including Economic Factors

A new approach to choosing the optimum design of reciprocating compressors is discussed. Economic criteria ore included together with optimisation procedures which account far thermodynamic criteria of performance, These procedures are applied to a mathematical model of a compressor to produce a "best" design. Such factors as initial cost, interest rates, depreciation, inflation, running costs, I oad factors and compressor I ife can either be app I ied to the results of a completed optimisation based on thermodynamic criteria only or incorporated directly into the procedures and permitted to affect the optimisation during the "search" phose. It is demonstrated that economic factors affect the "best" design and that thermodynamic efficiency may require to be sacrificed to achieve the optimum overall efficiency. INTRODUCTION To quote from reference (1). "The compressor design process is a complex procedure. The designer must select values for the design variables, i.e. bore and stroke sizes, valve port diameters and locations, etc, to produce a compressor of specified capacity with highest Coefficient Of Performance (COP) and lowest cost. The interacting effects of the variables are not simple and thus determining the "best" values of the variables is a complex task. To analyse the compressor design, the designer has historically resorted to building a prototype compressor. Using his experience and intuition, the designer successively modified the compressor and retested it. This "cut and try" sequence generally required several stages before an acceptable compressor was developed and was expensive and time consuming. To reduce the amount of compressor testing and development time, compressor designers are now using compressor modelling and simulations to reduce the amount of testing. The simulations allow the design engineer to evaluate design decisions quickly. The logical next step in compressor design has been the use of univariant searches to attempt to optimize the compressor design in terms of improved performance or some other objective. Univariant searches consist of keeping all design variables fixed except one. The simulation is then run for different 24 values of the free variable. Once the optimum value of the free variable is found it is fixed and the un ivoriant search is repeated with another variable as the free variable. This process is then repeated until all variables have been searched. Univariant searches do not continuously account for the interaction of design variables. To achieve the true optimum it is more efficient to consider all the variables simultaneously with the variable interactions taken into accourt continuously. Optimi:z:ation or "non( inear programming" technology permits an analysis of this rype. The objective function and constraint functions can be highly non I ineor functions of several design variables thus making nonlinear programming an efficient way to consider the many variables of the compressor simu lotion." Papers presented at Purdue Compressor Technology Conferences (1 1 2, 3 1 4, 5) have considered the optimisation of compressor design to meet thermodynamic criteria (within the practical constraints which must be imposed). If the thermodynamic performance and reliability of compressors from various manufacturers show little difference in thermodynamic performance then economic considerations become dominant, The present paper is an initial attempt to involve economic criteria. ECONOMIC FACTORS The inclusion of economic factors was approached from two standpoints, an indirect method and a direct method. In the indirect method an adequate mathematical model of the compressor is used with an appropriate search routine to maximise an objective function which, within the constraints imposed, gives the "best" thermodynamic design; economic factors are then applied to the results of the search. With the direct method both economic and thermodynamic criteria are included in an overall objective function, Hence both-economic and thermodynamic variables are permitted to influence the design during the search. Based on the premise that economic factors are likely to change more rapidly due to market conditions than thermodynamic criteria and constraints, the indirect method has the advantage that a design optimised on thermodynamic criteria con be considered as completed and can have changing or different economic factors accounted for at a later date without expensive computer resources. In the direct method all the variables are permitted to interact during the search to achieve the best overall design; if the economic criteria change then the whole optimisation procedure has to be rerun. The direct method presupposes that all the relevant variables con be identified and guantified at the outset, together with the constraints on them. It was shown (5) that it is difficult to specify a suitable objective function even when the indirect method is used wherein only thermodynamic criteria hove to be defined; the problem is even greater with the direct method. Since market forces increasingly press for better thermodynamic performance at less cost, it is considered that either or both of the methods will be applied increasingly.