Discharge, gallons per minute
FIGURE 10-6. Water test performance curves of the centrifugal pumps of the German V-2 rocket engine. The propellants are diluted 75% ethyl alcohol and liquid oxygen.
pumps. The negative slope on the head versus flow curve indicates a stable pump behavior. References 10-7 and 10-8 describe the development of a smaller turbopump and the testing of a spiral high-speed first-stage impeller, called an inducer.
A shrouded impeller has a shroud or cover (in the shape of a surface of revolution) on top of the vanes as shown in Figs. 10-1, 10-3, and 10-5. This type usually has higher stresses and lower leakage around the impeller. In an unshrouded impeller or turbine the vanes are not covered as seen in the turbine vanes in Fig. 10.2.
Pump Parameters. This section outlines some of the important parameters and features that have to be considered in the design of rocket propellant centrifugal pumps under steady flow conditions.
The required pump flow is established by the rocket design for a given thrust, effective exhaust velocity, propellant densities, and mixture ratio. In addition to the flow required by the thrust chamber, the propellant consumption of the gas generator, and in some designs also a bypass around the turbine and auxiliaries have to be considered in determining the pump flows. The required pump discharge pressure is determined from the chamber pressure and the hydraulic losses in valves, lines, cooling jacket, and injectors (see Eq. 6-15). To obtain the rated flow at the rated pressure, an additional adjustable pressure drop for a control valve or orifice is usually included which permits a calibration adjustment or change in the required feed pressure. A regulation of the pump speed can also change the required adjustable pressure drop. As described in Section 10.6, this adjustment of head and flow is necessary to allow for hydraulic and performance tolerances on pumps, valves, injectors, propellant density, and so on.
It is possible to predict the pump performance at various speeds if the performance is known at any given speed. Because the fluid velocity in a given pump is proportional to the pump speed N, the flow quantity or discharge Q is also proportional to the speed and the head H is proportional to the square of the speed. This gives the following relations:
Q (flow) ~ N (rpm or rad/sec) H (pump head) ~ N2 (10-1)
From these relations it is possible to derive a parameter called the specific speed Ns. It is a dimensionless number derived from a dimensional analysis of pump parameters as shown in Ref. 10-9.
Any set of consistent units will satisfy the equation: for example, N in radians per second, Q in m3/s, g0 as 9.8 m/sec2, and H in meters. The subscript e refers to the maximum efficiency condition. In U.S. pump practice it has become the custom to delete g0, express N in rpm, and Q in gallons per minute or ft3/sec. Much of the existing U.S. pump data is in these units. This leads to a modified form of Eq. 10-2, where Ns is not dimensionless, namely
The factor 21.2 applies when N is in rpm, Q is in ft3/sec, and H is in feet. For each range of specific speed, a certain shape and impeller geometry has proved most efficient, as shown in Table 10-2. Because of the low density, hydrogen can be pumped effectively by axial flow devices.
The impeller tip speed in centrifugal pumps is limited by design and material strength considerations to about 60 to 450 m/sec or roughly 200 to 1475 ft/sec. With titanium (lower density than steel) and machined unshrouded impellers a tip speed of over 2150 ft/sec is now possible and used on the pumps shown in Fig. 10-2. For cast impellers this limiting value is lower than for machined impellers. This maximum impeller tip speed determines the maximum head that can be obtained from a single stage. The impeller vane tip speed u is the product of the shaft speed, expressed in radians per second, and the impeller radius and is related to the pump head by u - ifj2gQAH (10-4)
where r/r has values between 0.90 and 1.10 for different designs. For many pumps, x/r = 1.0.
TABLE 10-2. Pump Types
Radial Francis Mixed flow Near axial Axial
Above 8000 Above 2.5
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