Calcul d'éjecteur-pompe à chambre de mélange cylindrique

Abstract

The design of the cylindrical mixing chamber type ejector described in this article is based on the classical mass flow continuity equations and the momentum theorem. The ejector is first considered as consisting solely of the mixing chamber, which is made long enough to ensure that the whole of the driving flow momentum is transferred to the induced flow. It has been found by experience that the length of the mixer should be of the order of 6 tn 7 times the mixer diameter. This being so, owing to the cylindrical shape of the mixer the momentum transfer can be written straight down without any difficulty, wall friction being ignored. The ejector operating equation is then written in non-dimensionless parameters, relating the induced fluid static and total pressure rises Δp and ΔP respectively to the dynamic pressure of the driving fluid: 1 /2 ρu2 (ω = Δp and ρu2/2 and π = ΔP/ρu2/2) and the mean flow velocity of the total mixed discharge v to the driving or inducing flow injection velocity u [w = (v /u)]. Finally, the dilution rate δ relating the total mass flow (m0 + mα) to the driving mass flow δ = [(m0 + mα)/m0] fits in quite naturally and Figure 1 gives the variations of ωδ and πδ in terms of the variable ω which in this case is considered as the fundamental variable in the design of the ejector. This figure, although it concerns a theoretical case, shows that the mixer cross-section should be made large enough to prevent the flow velocity of the total flow being excessively high, the object being to obtain as high an induced fluid pressure as possible. In practice the mixing chamber is generally followed by a diffuser, the objet of which is to transform part of the fluid's kinetic energy into pressure energy as efficiently as possible. This means that the diffuser head loss coefficient k should be taken into account. The operating equation is then applied to the case of the ejector complete with its diffuser, k being combined with the dilution rate δ to give a non-dimensional number kδ, which is taken as a parameter for the sets of curves representing the functions, πδ = πδ (ω, kδ) and : η = η (ω, kδ) η being the thermodynamic efficiency of the mixing operation (Figs. 2 and 3). These sets of curves show very simply the effect of increasing or the dilution rate δ. It is admittedly well known that the value of the coefficient k should be kept as low as possible but these curves also show very clearly that ejectors working at high dilution rates will have very limited thermodynanuc efficiency, as the latter decreases inversely with the dilution rate. Finally, owing to the simple form of these equations the optimum mixer cross-section can be worked out practically straightaway, the maximum value for the product πδ, for a given set of operating conditions, being precisely the same as the ratio v/u which the mixer design must achieve. Two simple applications of this last remark are given to illustrate the use of the method of calculation described in this article.