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The flow quantity defines the impeller inlet and outlet areas according to the equation of continuity. The diameters obtained from this equation should be in the proportion indicated by the diagrams for a given specific speed in Table 10-2. The continuity equation for an incompressible liquid is where the subscripts refer to the impeller inlet and outlet sections, all areas being measured normal to their respective flow velocity. The inlet velocity ranges usually between 2 and 6 m/sec or 6.5 to 20 ft/sec and the outlet velocity v2 between 3 and 15 m/sec or 10 to 70 ft/sec. For a compressible liquid, such as liquid hydrogen, the density will change with pressure. The continuity equation then is:

The head developed by the pump will then also depend on the change in density.

The pump performance is limited by cavitation, a phenomenon that occurs when the static pressure at any point in a fluid flow passage becomes less than the fluid's vapor pressure. The formation of vapor bubbles causes cavitation. These bubbles collapse when they reach a region of higher pressure, that is, when the static pressure in the fluid is above the vapor pressure. In centrifugal pumps cavitation is most likely to occur behind the leading edge of the pump impeller vane at the inlet because this is the point at which the lowest absolute pressure is encountered. The excessive formation of vapor causes the pump discharge mass flow to diminish and fluctuate and can reduce the thrust and make the combustion erratic and dangerous (see Ref. 10-10).

When the bubbles travel along the pump impeller surface from the low-pressure region (where they are formed) to the downstream higher-pressure region, the bubbles collapse. The sudden collapses create local high-pressure pulses that have caused excessive stresses in the metal at the impeller surface. In most rocket applications this cavitation erosion is not as serious as in water or chemical pumps, because the cumulative duration is relatively short and the erosion of metal on the impeller is not usually extensive. It has been a concern with test facility transfer pumps.

The required suction head (HS)R is the limit value of the head at the pump inlet (above the local vapor pressure); below this value cavitation in the impeller will not occur. It is a function of the pump and impeller design and its value increases with flow as can be seen in Fig. 10-6. To avoid cavitation the suction head above vapor pressure required by the pump (HS)R must always be less than the available or net positive suction head furnished by the line up to the pump (.Hs)a, that is, (Hs)r < (Hs)a. The required suction head above vapor pressure can be determined from the suction specific speed S :

The suction specific speed S depends on the quality of design and the specific speed Ns, as shown in Table 10-2. The suction specific speed S has a value between 5000 and 60,000 when using ft-lbf units. For pumps with poor suction characteristics it has values near 5000, for the best pump designs without cavitation it has values near 10,000 and 25,000, and for pumps with limited and controllable local cavitation it has values above 40,000. In Eq. 10-7 the required suction head (HS)R is usually defined as the critical suction head at which the developed pump discharge head has been diminished arbitrarily by 2% in a pump test with increasing throttling in the suction side. Turbopump development has, over the last several decades, led to impeller designs which can operate successfully with considerably more cavitation than the arbitrary and commonly accepted 2% head loss limit. Inducers are now designed to run stably with extensive vapor bubbles near the leading edge of their vanes, but these bubbles collapse at the trailing end of these vanes. Inducers now can have S values above 80,000. A discussion of the design of impeller blades can be found in Ref. 10-9.

The head that is available at the pump suction flange is called the net positive suction head or available suction head above vapor pressure (HS)A. It is an absolute head value determined from the tank pressure (the absolute gas pressure in the tank above the liquid level), the elevation of the propellant level above the pump inlet, the friction losses in the line between tank and pump, and the vapor pressure of the fluid. When the flying vehicle is undergoing accelerations, the head due to elevation must be corrected accordingly. These various heads are defined in Fig. 10-7. The net positive suction head (HS)A is the maximum head available for suppressing cavitation at the inlet to the pumps:

{Hs)A — #tank + -^elevation — ^friction — ^vapor (1O-8)

To avoid pump cavitation, (HS)A has to be higher than (HS)R. If additional head is required by the pump, the propellant may have to be pressurized by external means, such as by the addition of another pump in series (called a booster pump) or by gas pressurization of the propellant tanks. This latter method requires thicker tank walls and, therefore, heavier tanks, and a bigger gas-pressurizing system. For example, the oxygen tank of the German V-2 was pressurized to 2.3 atm, partly to avoid pump cavitation. For a given value of (HS)A, propellants with high vapor pressure require correspondingly higher tank pressures and heavier inert tank masses. For a given available suction head (HS)A, a pump with a low required suction pressure usually permits designs with high shaft speeds, small diameter, and low pump inert mass. A small value of (HS)R is desirable because it may permit a reduction of the requirements for tank pressurization and, therefore, a lower inert tank mass. The value of (HS)R will be small if the impeller and fluid passages are well designed and if the shaft speed N is low. A very low shaft speed, however, requires a large diameter pump, which will be excessively heavy. The trend in

Tank pressure gage C\;

Fluid level

Gage tank gas pressure

Gas pressure

Atmospheric pressure

Absolute tank_ pressure, H^

Gage tank gas pressure

Gas pressure

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