Rocket Propellant Line Waterhammer Transients In a Variable-G Environment
AFT Impulse™ Technical Paper
Authors: Trey Walters, P.E., Applied Flow Technology, USA
PPresented at the Winter Annual Meeting of the American Society of Mechanical Engineers, Dallas, TX, November 1990
ABSTRACT
Waterhammer pressure transients are generated in liquid-filled pipes when the velocity of the liquid is increased or decreased. Rapid velocity changes (such as an instantaneous valve closure) can lead to very high pipe pressures that may damage the piping system. The fundamental equations of waterhammer can be found in standard references (1, 2. ~. and their solution by the method of characteristics has become a straightforward process when performed on a digital computer.
To simplify the solution, the equations are generally written in terms of piezometric head, which assumes a constant acceleration due to gravity. An application of the equations to waterhammer occurring in a rocket propellant line required that the equations be formulated so as to include varying system acceleration levels. This formulation was incorporated into a computer program, and comparisons with flight data show good agreement.
CONCLUSION
A method for modeling waterhammer transients with the method of
characteristics in systems with variable-g environments is described. A comparison of predictions with this technique to flight data for a rocket propellant line shows good agreement. The general use of this technique for modeling systems with variable-g environments can remove unnecessary conservatism in predictions.
It is evident that the predicted pressure peak at 0.33 second in Figures 4 and 5 was not supported by the data. This may be due to the difficulty in predicting the engine flow rate decay in this region by the engine manufacturer. Although the slope of the AC-60 flowrate decay shown in Figure 2 steepens at 0.3 second, the real change in slope at this point may not be quite as severe.
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Background
BACKGROUND
Waterhammer in a variable acceleration environment can occur in
any fluid system that is not stationary. Because the fluid system is often the method of propulsion in a moving vehicle, rapid changes in vehicle acceleration often occur simultaneously with rapid fluid velocity changes in the vehicle propulsion system. Systems where this may occur include automobiles, aircraft, missiles, and launch vehicles. What is meant by a “variable-g environment” is an acceleration experienced equally by the entire system that varies in magnitude but not direction.
This is generally the case for launch vehicles, but may not be the case for the other vehicle systems just mentioned. The modeling of systems where the system acceleration vector varies with direction is beyond the scope of this paper.
APPLICATION FOR VARIABLE-G WATERHAMMER
Waterhammer pressure transients were investigated in an Atlas/
Centaur expendable launch vehicle liquid oxygen (LO2) propellant line during in-flight booster engine cutoff (BECO). The Atlas II, a new version of Atlas/Centaur currently in development, required a propellant line waterhammer analysis at BECO. For an Atlas Il, BECO occurs about 170 seconds after liftoff. Figure 1 depicts an Atlas II vehicle and its
LO2 line, which feeds three engines. During BECO the two booster engines (Bl and B2) are shut down while the sustainer engine continues to burn, resulting in a rapid system acceleration decay from 5.5 to 0.85 g’s due to the reduction in thrust. 1bis g decay and the flowrate decay of the booster engines are shown in Figure 2. The waterhammer pressure transients generated in the LO2 line due to engine shutdown occur in this rapidly changing acceleration field.
Initial analyses conservatively assumed a constant 5.5 g’s at BECO,
but the magnitude of the predicted pressure transients exceeded the 132 MPa (192 psi) allowable in the line. An analytical technique was therefore developed to model the variable-g environment, which resulted in acceptable line pressure predictions. Figure 3 shows the predicted pressures at the B2 engine inlet when assuming a constant 5.5 g’s, and also shows the pressures when the variable-g curve shown in Figure 2 is modeled. It can be seen that the variable-g model prediction is below the LO2 line pressure allowable, while the constant 5.5 g model exceeds it. This variable-g approach helped avoid a costly redesign of the LO2 line