Liquid and solid propellant rocket engines provide the power to boost launch vehicles into space. Figure 1 shows the Space Transportation System (STS) at Solid Rocket Booster (SRB) separation. At liftoff, both the SRBs and the main engines are ignited. When the SRBs have expended the propellant they are jettisoned and the main engine continues to operate and carry the Space Shuttle into orbit.
A rocket engine produces thrust by combining stored fuel (e.g. gaseous hydrogen, kerosene, solid rubber) and oxidizer (e.g. oxygen, nitrous oxide) at extremely high pressures and temperatures inside a chamber where they are combusted to produce a high velocity flow through a converging/diverging nozzle. [Click here to learn more about rocket propulsion.] This combustion process produces large forces in a wide band of frequencies, where the exact time history cannot be predicted. These types of forces are called "random loads."
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At the same time, turbomachinery is required to pump the fuel and oxidizer to the required pressure, and this turbomachinery produces substantial vibrational forces at specific frequencies, which are called "harmonic loads." Both the random and the harmonic loads propagate through every component on the engine and last throughout engine operation.
To design an engine that will survive these loads, the structural dynamics engineer must apply every analysis tool available, including frequency analysis, modal testing, finite element modeling, shock response analysis, random analysis, transient analysis, and fluid/structure interaction. In addition, substantial interaction with other design team members in the areas of rotor dynamics, stress analysis, computational fluid dynamics, and design is also required. For these reasons, structural dynamic analysis of rocket engines is a challenging, well-paid field requiring lifelong learning. |
In many structures, the modes of vibration are essentially only used in a mathematical sense to find the response to an arbitrary dynamic loading. In turbomachinery, though, there are large harmonic excitation mechanisms that cause resonant response of individual modes, so the identification, characterization, and analysis of the modes themselves become substantially more important. This makes turbomachinery structural dynamics especially interesting because of its direct, physical application.
These harmonics occur for two reasons. First, as the rotor spins, there is an unavoidable unbalance in the rotor which causes forces at 1, 2, and 4 times the rotational speed of the rotor. Secondly, the items on the rotor (e.g., turbine blades, inducer blades) cause a rotational flow distortion at very high multiples of the rotor speed. These harmonic forces have caused cracking in items both up and downstream of the flow distortion.
This phenomenon was first discovered by W. Campbell in a landmark paper in 1910. He published the well-known "Campbell Diagram" which is used in the design of all turbomachinery. An example, shown in Figure 5, is the diagram for the Space Shuttle Main Engine High Pressure Fuel Turbopump turbine blades. The axes of the plot are frequency in hertz vs. engine operating speed in revolutions per minute. The plot indicates resonance by showing where a "triple crossover" occurs between the mode, which for blades is a slightly slanted horizontal line indicating the natural frequency adjusted for temperature (which drops with operating speed), vs. multiples of the operating speed that correspond to the number of up or downstream distortions in the flow field (e.g. the number of stator vanes). Since the distortions do not cause perfectly sinusoidal excitations, multiples of these excitations are also included to qualitatively account for the spectral (frequency) content. These types of excitations have caused cracking in turbines blades for modes above 20,000 Hz, much higher than frequencies generally examined in the structural dynamics world.
(Click here for more information-"Campbell Diagram")
In a failure investigation, one of the chief methods for identifying if a modal resonance is the cause of the failure is to compare the crack location with a plot of the normalized "modal stresses," which is identical to a mode shape plot except that the response parameter is stress instead of displacement (see Figure 6). Other important techniques include performing a Fourier decomposition of a computational fluid dynamics (CFD) generated forcing function to identify its harmonic content and therefore which modes could be excited. Finally, many turbomachine components contain axisymmetric structures whose modes can be described by the number of "nodal diameters," or circumferential waves. Campbell, using the principle of orthogonality, showed that these modes can only be excited by an engine rotational order multiple with the same number of waves. The analysis of these structures therefore requires a description of the mode and identification of the mode as a circle on the Campbell diagram rather than a line, which indicates that it can only be excited by one excitation line (i.e., with the same excitation shape) rather than any that cross the line (i.e., that have only the same frequency).
In addition to the main combustion chamber that feeds the rocket engine nozzle, there are several other combustion devices in a rocket engine. These generally are used to provide the hot gas that drives the turbomachinery. Each of these devices produces a random load that propagates throughout the engine. In addition, a complex fluid/structure interaction phenomena that occurs in the main nozzle due to separation during the start and shutdown transient or during sea-level testing (generally called the "side-load" phenomena) can generate a harmonically shaped forcing function that is tied to the first ovalization mode of the nozzle. This load is so powerful that it has caused failures in tests of numerous engines around the world, most recently in Japan, and must be accounted for in the engine design. The phenomenon is very poorly understood, though, and so it is an area with substantial ongoing research.
The random and harmonic drivers specified above can not only cause high dynamic stress in components very close to the driver, but also propagate throughout the rest of the engine both due to mechanical vibration and acoustic noise. Some of the components most affected by these global forces are the many fuel and oxidizer ducts. In order to evaluate the effect of these loads, a system model of the entire engine is created and evaluated against these forces.
The methodology to accomplish this, however, has not been optimized. It is especially difficult to obtain accurate "loads" in the design process because the magnitude and frequency of these forces can only be guessed at by comparison with hot-fire testing of previous engines. The generally accepted conservative method has been to apply measured acceleration as "enforced accelerations" onto either specific engine zones one at a time or all at once on the system model and determine the random and harmonic response. This method usually results in stresses much larger than actually experienced, but a rigorous alternative has not yet been determined.
As with most complex engineering systems, mathematical simulation and analysis is limited in accuracy by many factors. In addition, the prediction of certain interactions of engine components cannot even be attempted. For these reasons, all engine structural dynamics calculations have to be verified with test. There are several different kinds of testing that are frequently applied. The first is modal testing, which verifies the basic structural dynamic characteristics (natural frequencies and modes) of a structure. This information is used to either verify or improve an existing computer model. A second type of testing is cold-flow subcomponent testing, such as a turbomachinery rig or a sub-scale nozzle air-flow facility. These tests verify the functionality of the component and identify any component-specific problems.
The final verification is a full-blown hot-fire test, in which a complete engine is tested on a stand in a complete flight simulation. The hot-fire test is used not only to verify functionality of the entire engine system, but through the use of extensive strain-gage and accelerometer instrumentation, is used to verify the system loads prediction and to update the system model.
Click here to view the Hot-Fire Test of FASTRAC Rocket Engine.
The study and application of rocket engine dynamics is a demanding yet rewarding field of engineering. A thorough knowledge of all areas of structural dynamics, from finite element modeling to spectral and signal analysis, is required to ensure that components in the engine do not fail due to the large dynamic environment. In addition, accurate yet not over-conservative calculations are necessary since weight is a critical item for any space vehicle component. Tremendous awards await successful analysis, though, as there's nothing like seeing one's work pay off in a fury of "fire and smoke."
Contributed by: Andrew M. Brown, Ph.D
NASA Marshall Space Flight Center
