where kc is the coefficient characterizing the deflection of particle motion from the rectilinear with a flow around the intake portion of the nozzle; Ap/p% 8 4 2 0 100 200 300 400 With a total deceleration of particles the error attains a maximum value The maximum error for air, depending on the velocity of the flow, is presented on Figure 40 (kc = 1). According to reference [54], the distance at which the velocity of a particle in an immobile gas lowers to zero is = For example, in it where co 100 m/sec Zmax = 2 mm where d = 1 μπ and Zmax = 50 mm where d = 5 μm. Since the length of the intake portion of a Pitot tube does not usually exceed several mm, then where d > 6 μm it is possible to ignore deceleration of the particles in the nozzle, and consequently even an error in the measureHowever, with large particles it is possible that the liquid phase striking the intake portion of the nozzle and the conduit leading to the measuring instrument may influence the results of the Therefore axial or cylindrical nozzles are usually provided with a drainage opening (Fig. 41) and also provide for blowing air through them. measurements. Still greater difficulties arise in measuring the temperature of the gas phase, since a thermocouple in a double-phase flow with liquid particles is covered by a film isolating it from the external flow. Insofar as particle temperature may greatly differ from the gas temperature, thermocouple readings will not be reliable. In the majority of cases the temperature of the gas phase is determined by calculation (for example, according to the heat balance equation) or by a translation of the temperature measured in the zones protected from the action of the liquid phase. Selection of tests of a double-phase flow must be conducted in such a way that the velocity in the intake portion of the intake valve remains equal to the velocity of the basic flow (isokinetic test selection). In this case error due to deviation of the trajectories of the particles in front of the intake valve will be minimal (Fig. 42). Such an equality of velocities can be obtained by maintaining static pressure inside the intake valve equal to the static pressure in the external flow. CHAPTER 3 THE OPERATION OF A TURBINE ON A DOUBLE-PHASE FLOW §1. Basic Characteristics of the Operation of the As experimental studies show, the flow of a double-phase mixture with liquid particles in the flow portion of a turbine is of a very complex nature and possesses the following characteristics: (1) The flow is characterized by sharp reversals and great acceleration. Therefore, the particles, due to their own inertia, noticeably lag behind the gas; as a result of the losses due to friction of the gas on the particles arising here, the flow process is irreversible. (2) The flow is accompanied by a redistribution in the concentration of phases along a section of the flow portion due to the inertial lag of the particles behind the gas flow. This redistribution is especially intensive in the blade apparatus where the velocity of the gas sharply changes in volume and direction, and also in the axial clearance between the nozzle and working blades under the influence of the great vortex of the flow. (3) All the elements of the flow portion of the turbine (in particular, its nozzle apparatus) are covered with a film formed by particles precipitating from the flow. Large particles (d> 10 μm) precipitate out under the action of inertial forces; precipitation of small particles (d < 1 μm) is of a turbulent diffuse nature. Moreover, thermophoretic precipitation of particles may take place in cooled blade rims. (4) The film surface, under the action of turbulent flow pulsations and the impact of particles striking it, acquires a wave-like form, whereby the height of the crest, the waveforms and velocity of their motion depends in the first place upon the viscosity, surface tension and thickness of the layer of liquids, velocity and density of the flow, nature of the boundary layer and upon the curvature of the wall along which the film flows. It has still not been possible to establish the precise dependence of height and form of the waves upon the basic parameters determining the flow. However, it is known from experiments that the height of the crest increases with an increase in the mean thickness of the layer, viscosity of the liquid and whirling of the boundary layer and decreases with an increase in the density and velocity of the gas flow. In conduits with cooled walls with a temperature near the freezing point of the liquid phase, the liquid phase "freezes" on the walls, which leads to a further deterioration of the flow condition. (5) Tearing away from the exit edges of the nozzle blades and also from the internal and peripheral surfaces of the flow portion, a film under the action of gas forces is fragmented into secondary drops, the diameter of which may reach several tenths of a milli meter. Such drops substantially lag behind the gas flow and strike the working blades under large negative angles of attack, causing a decrease in the effectiveness of the turbine, and with prolonged exploitation, even erosional wear of the working blades. (6) In the expansion process of a double-phase flow, heat exchange between the phases takes place in which heat is conducted 'from the particles to the gas. Therefore, the effectiveness of the gas phase is somewhat increased. With a moderate degree of expansion (2) and a particle concentration gk < 0.1 the increase in the effectivenss may be from 1 to 2.5%. /89 However, due to intensive precipitation of particles on the walls of the flow portion, the surface of the division (heat exchange) is sharply curtailed. And although due to the low velocity of the film flow equal to (0.05 - 0.15)cr, the time the liquid phase remains in the flow portion is significantly increased, and the coefficient of heat emission from the liquid to the gas increases due to the increase in the relative velocity of the liquid and the gas, and the total amount of transmittable heat may decrease by several times. As a result of this, in the majority of cases, especially with a moderate concentration of the liquid phase and a particle diameter d > 10 μm, the increase in efficiency of a gas phase due to heat exchange with particles may be ignored in first approximation. In turbines operating on double-phase flows with liquid particles, supplementary losses appear. These losses may be classifed in the following way. (1) Losses in the nozzle apparatus accumulating from: (a) losses due to friction of the gas on the particles; (b) losses with the separation of particles onto the nozzle blades (the kinetic energy of the particles is almost completely lost when they precipian immobile surface); (c) losses due to friction of the gas on the liquid undulating film covering the nozzle blades, as well as the internal and peripheral surface, bounding the flow protions of the nozzle apparatus. (2) Losses in the axial clearance between the nozzle and working blades, consisting of: (a) losses due to friction of gas on the particles; (b) losses with precipitation of the particle onto the peripheral wall; (c) losses due to friction of the gas on the liquid undulating flim, covering the internal and external surface in the axial clearance. /90 (3) Losses in the working wheel, the majority being losses due to impact of the liquid particles on the input edge of the working blades, and due to scattering of the liquid phase toward the periphery. It is possible to ignore the increase in profile losses on the working blades, since the film is directly scattered by centripetal forces to the periphery, and therefore its thickness on the working blades does not exceed several hundredths of a millimeter, even when the fluid is very viscous. However, in blades having erosional wear profile losses can be significant. (4) Losses in the radial clearance. The viscous liquid phase, separated out onto the peripheral surface in nozzles and in the axial clearance in front of the working wheel, flows out under the action of gas forces in the radial clearance above the working wheel. With a small concentration of the liquid phase, this leads to a decrease in radial clearance and, consequently, to a certain increase in the effectiveness of the turbine. However, with great expenditures of the liquid phase the end of the working blades may touch the wave crests. This leads to a decrease in turbine effectiveness, and also may cause an increase in vibrational strains in the working blades. Therefore the radial clearance must be chosen in such a way that the ends of the blades do not touch the wave crests of the liquid film in all operational regimens. Therefore it is necessary to consider the possible deterioration of the parameters of turbine operation due to a decrease in the nozzle flow sections and a change in the reactivity of its stages. With a very viscous liquid the flow sections of the turbine may be decreased by 5-10%, which will lead to a decrease in gas expenditure through the turbine in comparison with a turbine operating on a pure gas. In the case of such a turbine working in a gas turbine system or in a stationary gas turbine installation system, this may a decrease in the margin of stable operation and even to compressor stalling. Therefore, in calculating the effectiveness of turbines on double-phase mixtures it is necessary to consider the clogging of flow sections by a viscous liquid film. In the case of a liquid phase of low viscosity such as water or kerosene in a moderate concentration (gk≤ 5%), it is possible to ignore clogging of the flow section stages. A change in the reactivity of the stage depends upon flow section clogging in the nozzle apparatus by a film which decreases the reactivity of the stage and upon the interaction between the gas and the particles in the exhaust process, which increases its reactivity. Actually, with the same pressure drop, the exhaust velocity of a mixture is less than the exhaust velocity of a pure gas. Therefore, with an invariable circumferential velocity, the flow angle B1 and, consequently, even the geometric configuration of the film in the |