Optimization of a Valve Using a Genetic Algorithm

A numerical optimization of the suction valve of a large reciprocating compressor has been carried out as a case study, using a combination of a compressor simulation program and a genetic optimization algorithm. This optimization algorithm is based on the theory of biological evolution: survival of the fittest. The compressor simulation program solves the mass and energy conservation laws for the suction chamber, cilinder and discharge chamber. The dynamics of the valves are described by Newtonian motion and the piping system is partly taken into account as flow restrictions. A set of optimal designs has been generated by assigning different combinations of weight factors to the volumetric efficiency, the isentropic efficiency and the impact velocity of the valve. These performance data were used for judging the compressor quality. This procedure can be applied as an effective design tool when a considerable number of parameters is involved, especially when analytical optimization is either impossible or too complex. INTRODUCTION The object of the investigation presented here is to establish the feasibility of numerical optimization as a design tool for reciprocating compressors. The work is done in a co-operation between Grasso Products B.V. and the Delft University of Technology. As the subject of this case study the suction valve of the Grasso RC11 compressor was chosen, mainly because detailed geometrical and experimental data were available. The genetic optimization algorithm was selected because the only constraint it imposes, on the function it optimizes, is that it exists and because it does not get trapped by local optima: it always searches for the global optimum. PARAMETERS AND OBJECTIVE FUNCTION The suction valve of the RCll is a ring valve (fig. 1). The geometry can therefore be defined by the thickness ( hv), the inner diameter ( dv) and the outer diameter ( Dv). The inner diameter depends on the cylinder diameter and is therefore not a parameter. The thickness itself is not an input parameter for the compressor model, but it is added as an independent parameter in order to describe the volume and mass of the valve. The valve is loaded with sinusoidal springs, which can be represented by an exponential characteristic (fig. 2). It is parameterized by the force (Fmin) at zero lift and the force (Fmax) at maximum lift (xmax)· Table 1 shows the parameters and their ranges. Parameter RCll Range Unit Dv 200 180 ... 240 mm hv 1.0 0.5 ... 5.0 mm X max 2.6 1.5 .. .4.0 mm Fmin 18 10 .. .40 N Fmaz 137 40 ... 240 N Tab. 1 The parameters with their values for the RCJJ compressor and the ranges used during optimization. These parameters will be fed into the compressor simulation program, which calculates the performance data that are used to judge the quality of the compressor. Initially an economic optimization was intended. It should minimize the total costs of operation including depreciation, interest, energy requirements and costs of maintenance. But the economical optimization was abandoned because it turned out that the quantification of some costs was too complex. As an alternative a technical judgement is used, constructed of three quantities: the isentropic efficiency ( TJ), the volumetric efficiency (A) and the maximum impact velocity of the suction valve (vmax)The latter was added because it is the main influence