## Thrust Vector Control With Thrust Chamber

Figure 4.23 Nodes for pogo oscillation analysis. (Adapted from Oppenheim and Rubin [11].)

The analysis starts by defining as discrete nodes all the components that are likely to play a role (Fig. 4.23). These include the thrust chambers, propellant pumps, ducts, their junctions, bellows, tanks and their outlets, hydraulic accumulators, and the principal vehicle structural elements. Each node will receive inputs from, and provide inputs to, some other nodes.

It is important to include the elastic compliance of elements such as tank walls and bellows. More difficult is the proper representation of the contributions from thrust chambers and pumps. These are largely empirical. For instance, the representation of the pumps must include the variability of the flow rate-dependent cavitation in the inducer section and the performance changes caused by variations in the blades' angles of attack. The importance of including among the variables the degree of cavitation has long been recognized [11].

The properties of each node are described by first- and second-order, linear differential equations in the state variables, for which convenient choices are the pressures, flow rates, and structural displacements. This coupled system of equations can be analyzed by classical methods that yield the complex eigenfrequencies and eigenmodes of the system.

It has been demonstrated that the pogo instability can be suppressed by introducing hydraulic accumulators ("pogo suppressors") into the propellant feed system. The accumulators are therefore an essential element in the stability analysis.

4.16 Thrust Vector Control

There are several ways to alter the direction of the thrust for steering the rocket. These methods are jointly referred to as thrust vector control.

Most frequently used is a method based on gimballed thrust chambers (Fig. 4.24). The gimbals are on two perpendicular axes that allow independent rotations of the thrust chamber. The maximum rotations allowed by the gimbals are typically angles of about ±7°. The rotations, and therefore the vehicle steering, are imposed by actuators, which, for large motors, are usually hydraulic but can also be pneumatic or electric.

To accommodate the motion of the thrust chamber, the propellant ducts must have the necessary flexibility. This is accomplished by a series of bellows, usually made of stainless steel. Bellows are a critical element of gimballed chambers because their skin must be thin enough to offer only limited

Figure 4.24 Gimbal axes and propellant-line bellows of the LEM engine, NASA. From Ref. 2, Huzel, D. K., et al., "Modern Engineering for the Design of Liquid Propellant Rocket Engines." Courtesy of Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

Figure 4.24 Gimbal axes and propellant-line bellows of the LEM engine, NASA. From Ref. 2, Huzel, D. K., et al., "Modern Engineering for the Design of Liquid Propellant Rocket Engines." Courtesy of Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

resistance to flexing, yet strong enough to withstand the pressure. It is evident that if the motion is limited to, say, ±7° in both directions, the bellows must allow thrust chamber motions of this order of magnitude.

The motions of the hydraulic or pneumatic actuators are controlled by servo-valves, which in turn are controlled by commands from the vehicle's guidance system. Displacement and rate transducers are attached to the actuators. They provide error signals that are the difference between the actual and desired positions and rates. In the control computer, closed-loop control is applied that makes use of the rate signals to ensure stability. In place of rate transducers, digital differentiation of the position signals is also being used.

The figure shows a configuration in which the gimbal axes are placed approximately in the plane of the nozzle throat. Alternatively, they are often placed back of the injection plate and dome (Fig. 4.2).

Figure 4.25 shows the gimbal actuator mounts and articulating propel-lant ducts in the gimbal plane of the U.S. Space Shuttle main engines.

Another means of thrust vector control is by lateral injection into the nozzle. Three such systems are schematically illustrated in Fig. 4.26. In all cases, gas or liquid is injected from the nozzle wall downstream of the throat. A shock front is formed that deflects the main gas stream. The resulting asymmetry of the flow at the nozzle exit plane causes a torque about the center of mass of the vehicle, sufficient to steer it by closed-loop control as commanded by the guidance computer. Four injection ports, each with its servo-valve and spaced 90° apart, are needed. No more than two adjacent injection ports operate at the same time.

Figure 4.25 Articulating ducts in the gimbal plane of the Space Shuttle main engines, NASA. From Ref. 2, Huzel, D. K., et al., "Modern Engineering for the Design of Liquid Propellant Rocket Engines." Courtesy of Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

Figure 4.25 Articulating ducts in the gimbal plane of the Space Shuttle main engines, NASA. From Ref. 2, Huzel, D. K., et al., "Modern Engineering for the Design of Liquid Propellant Rocket Engines." Courtesy of Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

Figure 4.26 Lateral injection systems for thrust vector control: (a) gas chamber tap-off system; (b) bipropellant gas-generator system; (c) liquid system. S, shock front; G, hot gas duct; O, oxidizer; F, fuel duct; L, liquid duct; GV gas valve; GG, gas generator; LV, liquid injection valve.

Figure 4.26 Lateral injection systems for thrust vector control: (a) gas chamber tap-off system; (b) bipropellant gas-generator system; (c) liquid system. S, shock front; G, hot gas duct; O, oxidizer; F, fuel duct; L, liquid duct; GV gas valve; GG, gas generator; LV, liquid injection valve.

In (a), the injected gas is tapped off from the high-pressure region in the combustion chamber. At maximum steering torque, the flow rate of the tap-off gas is typically 1.5 to 2.5% of the primary rocket gas flow. In (b), oxidizer and fuel are combined in gas generators, one for each injection port. A less frequently used scheme in which an inert fluid is injected is illustrated in (c).

Compared with gimballed thrust chambers, a disadvantage of lateral injection is the need to provide ports in a thermally stressed part of the nozzle. This will increase the complexity of providing coolant passages for regenerative cooling. The disadvantage is offset by the simplicity of a fixed mounting of the thrust chamber with rigid propellant ducts.

### 4.17 Engine Control and Operations

The principal function of the engine control is to ensure the correct flowrates of the propellants. In particular, the flow rates must be such as to result in the optimum mixture ratio for the flight condition at the time ("mixture ratio control") . Also, the flow rates need to be controlled so that toward the end of the firing with the tanks nearly empty, the correct ratio of the remaining fuel and oxidizer is maintained in the tanks ("propellant utilization control").

Many rocket motors are designed for a nominally constant thrust, but others allow the thrust to be varied in response to commands from the flight computer ("thrust control"). The principal components needed for the latter type of engine are indicated in the schematic, Fig. 4.27. Omitted for clarity are various secondary controls such as the tank pressurization controls, safety controls, and the controls needed for start-up and shutdown.

The propellant utilization control is based on inputs from transducers that measure the fuel and oxidizer masses in the tanks. Acoustic sensors, capacitance probes, or differential pressure sensors are being used for this purpose. The propellant utilization control is important because there are a number of error sources that can affect the propellant masses actually

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Figure 4.27 Principal components of a typical liquid-propellant control with provision for variable thrust. MR, mixture ratio; PU, propellant utilization.

present in the tanks. These include, for instance, losses of cryogenic pro-pellants from boil-off. Other errors can be present in the initial loading as measured by load cells at the launch site. Without close control, the fuel and oxidizer masses remaining in the tanks toward the end of the firing may significantly deviate from the intended mixture ratio.

The output of the closed-loop propellant utilization control is one of the inputs to the mixture ratio control. Additional inputs are those from the flow meters for fuel and oxidizer. The control is designed to maintain a near-optimum mixture ratio, independent of variations of propellant temperature, density, tank pressure, and vehicle acceleration, although modified, if needed, to satisfy the propellant utilization requirement. In particular, the effect of vehicle acceleration on the mixing ratio can be significant, mostly for the propellant in the forward tank because of the long fluid column connecting it to the engine.

Whereas most engine controls are designed to maintain a near-constant mixture ratio, there can be some advantage in purposely modifying the ratio in flight. The heavier propellant is then used at the early parts of the flight at a rate slightly faster than normal and is used slightly less toward the end. The advantage is a small reduction of the gravity loss.

The output from the mixture ratio control is sent to the vernier actuator, usually on the oxidizer side. It provides the fine adjustment of the mixture ratio.

Engines that allow throttling also require a thrust control. A suitable, although indirect, measurement of the thrust in flight can be obtained from the combustion chamber pressure. A closed-loop control then governs the positions of the main fuel and oxidizer control valves.

Other control schemes are also being used. In all cases is it important to consider the dynamic properties of the components that are being regulated. They can often be characterized by their time delay, for instance, the closing time of valves. Also significant can be the rotational inertia of the turbo pumps and the delay in the pressure buildup of gas generators.

A frequently used type of control is represented by the "proportionalintegral-differential" control law with y as the control variable. Here, e is the error term; k\, k2, k3 are gains; t\ is the integration time; td is the differentiation time; and yo is the desired value of the control variable. The addition of the integral term in this equation eliminates the offset inherent in simple proportional controls (but may also cause overshoots). The addition of the differential term provides a faster transient response to rapidly varying conditions.

Typical start-up and thrust cutoff operations are indicated in Fig. 4.28. At engine start, depending on the type of propellant and the engine cooling method, either the fuel or the oxidizer flow may lead. Safety considerations are essential elements of engine start and engine shutdown. Usually, the propellant cutoff at engine shutdown is such that the condition in the thrust chamber is made fuel rich. Precise thrust cutoff at the time commanded by

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