Comment on "Optimum Performance for a Single-Stage Gaseous Ejector"

Abstract

E l has developed a convenient method of calculating the compression ratio of an ejector, based on simple, if somewhat drastic, assumptions. The method was checked by comparing the results with those of a more elaborate computer code believed to be quite accurate. No comparisons of calculated compression ratios with experimental data were given. In his discussion, Emanuel suggests using hydrogen as a driving gas as a way to improve performance. Since the experimental data of Eichacker and Hoge showed that efficiency increases when the molecular weight of the driving gas increases, his suggestion runs counter to our experience. We used a constant-area mixing region, whereas EmanuePs mixing region is assumed to be so designed as to maintain constant pressure. However, it hardly seemed that this difference could completely reverse the dependence on molecular weight. We used the conventional definition of efficiency based on isentropic enthalpy changes, whereas Emanuel compares compression ratios without specifying precisely what is to be held constant. We decided to calculate compression ratios from Emanuel's equations both at constant mass entrainment ratio and at constant molar entrainment ratio to see if the apparent discrepancy between our results and his predictions could be explained. The systems chosen were helium-hydrogen and heliumnitrogen. Both were calculated for a mass entrainment ratio co = 0.1 grams of driven gas per gram of driving gas and for a molar entrainment ratio 12 = 0.05035 mole of driven gas per mole of driving gas. For helium the molecular weight (^=4.004 and the isentropic exponent k= 1.667; for hydrogen ^=2.016 and k= 1.4; for nitrogen W= 28.016 and k= 1.4. The results of the calculations are given in Table 1. Quantities referring to mixtures formed by the driving and driven gas are designated by the subscript m. The Mach number after mixing is Mm. In all cases the Mach number of the driving gas at the beginning of mixing has been taken as 3.5 and the Mach number of the driven gas at the same point is by assumption zero. In the tabulated pressure ratio, P02 is the stagnation pressure of the mixture after compression and Pj is the stagnation pressure of the driven gas as mixing begins (and also the static pressure of the driving gas at the same point). Since we do no.t question the desirability of heating the driving gas and cooling the driven gas, the effects of heating and cooling have been eliminated from the comparison by assuming all stagnation temperatures to be equal, thus excluding irrelevant changes from the comparison. The systems He: H2 and He:N2, compared at co = 0.1, show a higher compression ratio when hydrogen is the driving gas than when nitrogen is the driving gas (10.96 vs 4.728), as predicted by Emanuel. However, when the comparison is made at 12 = 0.05035, the compression ratio when hydrogen is the driving gas is lower than when nitrogen is the driving gas (10.96 vs 13.98). Since the two driving gases have equal values of k, their molar specific heats are equal and the isentropic work of compression between given limits is the same for both gases, to a good approximation. Hence, equal expenditures of work will compress a given amount of driven gas to a higher pressure when the driving gas is N2 than when it is H2. This result, obtained by applying EmanuePs equations at constant molar entrainment ratio, shows that, at least in the situation considered, there is no basic conflict between the calculated results and our published data. However, the recommendation, to use hydrogen as a driving fluid appears to be incorrect, except perhaps in unusual circumstances where the work required to compress the driving gas need not be considered.