In view of the widespread application of pumps, ejectors, and turbines, in which liquid-gas mixtures are the working medium, the determination of the speed of sound in such media has been getting special attention.In the simplest case, the liquid-gas mixture is considered as a continuous homogeneous medium with averaged characteristics. The temperature of the phase in such a medium is the same and mass exchange is assumed not to occur between the phases [ 1 ].Despite the simplicity of the model adopted for the mixture, familiar relations for determining the speed of sound were obtained after additional assumptions that limit their range of application. Samoilovich [ 1 ], for example, assumes that the density is constant, which corresponds to an infinite speed of sound in a liquid.In [2] Wallace determines the speed of sound a for two possible cases of flow: isothermal and isentropic. In the second case, isentropic compression of the gas medium is assumed to occur. Accordingly, the following relations are obtained for a low concentration of the liquid phase, e.g., less than 10%:where p is the mean density of the medium; p is the pressure; kg is the isentropic exponent of the gas; T is the temperature ; and S is the entropy. Experiments carried out with a mass concentration of air below 3-10 -3 showed that the speed of sound agrees well with the values found from Eq. (1). Strictly speaking, however, Eqs. (1) and (2) are incorrect. The speed of sound in a homogeneous medium should be determined in the same way as for a pure gas, i.e., from the condition of conservation of the entropy of the mixture, a= (~p~ s or a=4k p,where k is the entropy exponent of the mixture.Let us consider the solution of the problem of the speed of sound in a homogeneous liquid-gas medium without any additional assumptions. That solution, therefore, is valid for any concentration of phases and any ratios of the liquid and gas densities Pliq and pgof a homogeneous medium.Conservation of entropy during propagation of a sound wave means that the heat removed from the gas is equal to the heat transferred to the liquid phase, dqg= dqliq. Obviously, dqliq= (1 -(P)CliqdT, where q) = m~(rng + mli q) is the mass concentration of the gas; mg and mti q are the masses of the gas and liquid, respectively; and Cli q is the heat capacity of the liquid.Moscow State University of Engineering Ecology.
No abstract
Several features of hydrogen turboexpanders, which markedly distinguish them from more popular air turboexpanders, stem from significant differences in physical properties of hydrogen and air. For instance, at 293 K and 0.1 MPa pressure the gas constant R and heat capacity % of hydrogen are roughly 14 times, the kinematic viscosity coefficient 1, is 1.4 times, and the coefficient of thermal conductivity k is 6.6 times higher than those of air. Hydrogen turboexpanders operate, as. a rule, at inlet temperatures T O = 80-35 K, whereas air turboexpanders operate at To = 170-118 K (depending on the pressure in the cycle).These differences between hydrogen and air predetermine, at an identical degree of expansion 8 = Po/l~ (here, Po is the inlet pressure and i)2 is the outlet pressure), divergent peripheral velocities u~ at the inlet to the impellers of hydrogen and air turboexpanders.In order to analyze, we shall take average turboexpander inlet temperatures as T0H 2 = 60 K and T0a -145 K (here and hereafter, H2 refers to parameters of a hydrogen turboexpander and a to parameters of an air turboexpander). Then, at the same values of the dimensionless parameter x,, which is one of the key similarity criteria that equals
Deep-well centrifugal pumps (DCP) with a delivery of 50-1000 m3/day and a head of 7000-18,000 m are used widely in oil extraction. Depending on the head, the number of stages in the pump reaches 140-360. These pumps differ from the conventional multistage centrifugal pumps by a limited radial dimension of the stage (from 90 to 138 ram) and the special design of its flow part because, irrespective of the greatly restricted radial dimensions, the stage must ensure a high head and delivery in order to remove large amounts of the liquid from the well.As indicated by Fig. 1, the pump does not contain the axial part of the diffusor, and the flow behind the wheel rotates by almost 180" at a relatively high speed level. The external diameter of the working wheel 1 is increased to the maximum value and occupies almost the entire space of the stage. The exit edge of the blade of the wheel is bevelled in the axial direction. The experiments show [1] that the rotating part of the flow from the channel of the wheel into the reversed channel of the guiding section 2 is the main source of losses (the losses in this section equal 40-60% of the total losses).Analysis of the design of the DCP shows that it is possible to increase the head of the stages while increasing at the same time their efficiency, for example, by increasing the exit angle of the working blades of the wheel with the change of the flow part of the interblade channels. We shall examine the method of increasing the head and efficiency of the stage by changing the geometry of the flow part with an allowance made for the design special features of the DCP.One of the main shortcomings of the standard stage is the constricted section at the exit from the wheel (Fig. 2a) and, consequently, the increase of the losses when the flow rotated behind the wheel and in the entry into the guide section.However, the increase of the flow-passage section as a result of additional machining of the outlet edges of the wheel blade (Fig. 2b) reduces the mean external diameter of the working wheel and it is therefore highly undesirable. As shown by experiments, carried out by the authors, the increase of the flow-passage section to the normal value (this corresponds to the constant meridional protection of the speed) increases the efficiency but the head decreases by two percent. This shortcoming is eliminated when using blades of a constant diameter at the exit (Fig. 2c) with a simultaneous increase of the flow-passage section as a result of machining the back disk of the wheel.Experimental verification of this variant of the design showed that k is efficient, as indicated by the results (Fig. 3). Comparative tests of a 1EtsN5F-250-1000 plant pump (185 stages) and of a pump with a changed flow part in accordance with Fig. 2c were carried out in a test well [2]. Figure 3 shows that in the calculated operating regime the head increases by 5 % and the efficiency by 1.3%; the shape of the wheel and the dimensions of the stage remained unchanged.
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