when the discharge coefficient equals 1. Smooth and well-rounded entrances to the injection holes and clean bores give high values of the discharge coefficient and this hole entry design is the most common.

When an oxidizer and a fuel jet impinge, the resultant momentum can be calculated from the following relation, based on the principle of conservation of momentum. Figure 8-7 illustrates a pair of impinging jets and defines y0 as the angle between the chamber axis and the oxidizer stream, y/ as the angle between the chamber axis and the fuel stream, and 8 as the angle between the chamber axis and the average resultant stream. If the total momentum of the two jets before and after impingement is equal, tan S =

m0v0 sin y0 — rrifVf sin yj-m0v0 cos y0 + rhfVf cos yf

Line of resultant jet momentum

Line of resultant jet momentum

FIGURE 8-7. Angular relation of doublet impinging-stream injection pattern.

Good performance is often obtained when the resultant momentum of impinging streams is approximately axial. If the resultant momentum is along the chamber axis, <5 = 0, tan S = 0, and the angular relation for an axially directed jet momentum is given by m0v0 sin y0 — rhjVf sin yj- (8—7)

From these equations the relation between yj-, y0, and S can be determined. A sample injector analysis is shown in Section 8.6.

Factors Influencing Injector Behavior

A complete theory relating injector design parameters to rocket performance and combustion phenomena has not yet been devised, and therefore the approach to the design and development of liquid propellant rocket injectors has been largely empirical. Yet the available data indicate several important factors that affect the performance and operating characteristics of injectors; some of these are briefly enumerated here.

Propellant Combination. The particular combination of fuel and oxidizer affects such characteristics as the relative chemical reactivity, the ease and speed of vaporization, the ignition temperature, the diffusion of hot gases, the volatility, or the surface tension. Hypergolic (self-igniting) propellants generally require injector designs somewhat different from those required by propellants that must be ignited. Injector designs that perform well with one combination generally do not work too well with a different propellant combination.

Injection Orifice Pattern and Orifice Size. With individual holes in the injector plate, there appears to be an optimum performance and/or heat transfer condition for each of the following parameters; orifice size, angle of impingement, angle of resultant momentum, distance of the impingement locus from the injector face, number of injection orifices per unit of injector face surface, flow per unit of injection orifice, and distribution of orifices over the injector face. These parameters are largely determined experimentally or from similar earlier successful injectors.

Transient Conditions. Starting and stopping may require special provisions (temporary plugging of holes, accurate valve timing, insertion of paper cups over holes to prevent entry of one propellant into the manifold of the other propellant, or check valves) to permit satisfactory transient operation.

Hydraulic Characteristics. The orifice type and the pressure drop across the injection orifice determine the injection velocity. A low pressure drop is desirable to minimize the weight of the feed system or the pumping power and improve the overall rocket efficiency, yet high pressure drops are used often to increase the rocket's resistance to combustion instability and enhance atomization of the liquids.

Heat Transfer. Injectors influence the performance and the heat transferred in rocket thrust chambers. Low heat transfer rates have been obtained when the injection pattern resulted in an intentionally rich mixture near the chamber walls. In general, the higher performance injectors have a higher heat-transfer rate to the walls of the combustion chamber, the nozzle, and the injector face.

Structural Design. The injector is highly loaded by pressure forces from the combustion chamber and the propellant manifolds. During transition (starting or stopping) these pressure conditions can cause stresses which sometimes exceed the steady-state operating conditions. The faces of many modern injectors are flat and must be reinforced by suitable structures which nevertheless provide no obstructions to the hydraulic manifold passages; the structure must also be sufficiently flexible to allow thermal deformations caused by heating the injector face with hot combustion gases or cooling by cryogenic propellants. The injector design must also provide for positive seals between fuel and oxidizer manifolds (an internal leak can cause manifold explosions or internal fires) and a sealed attachment of the injector to the chamber. In large, gimbal-mounted thrust chambers the injector also often carries the main thrust load, and a gimbal mount is often directly attached to the injector, a shown in Figs. 6-1 and 8-1.

Combustion Stability. The injection hole pattern, impingement pattern, hole distribution, and pressure drop have a strong influence on combustion stability; some types are much more resistant to pressure disturbances. As explained in Section 9-3, the resistance to vibration is determined experimentally, and often special antivibration devices, such as baffles or resonance cavities, are designed directly into the injector.

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