## Tuesday, October 27, 2009

### The Stick Does Not Pogo

With the upcoming test flight of the Ares IX, there is lots of talk about high vibration levels and design problems with the big solid first stage. One common misconception I've noticed (and pointed out) a couple times is that folks think Ares I might have pogo oscillations. Pogo oscillations are a specific type of propulsion-structure interaction that occurs in liquid rockets, not solids.

Here's a succinct description of what pogo is (Rubin, 1970, emphasis mine):
Many liquid rocket vehicles have experienced longitudinal vibration because of an instability arising from interaction of the vehicle structure with the propulsion system. The vibrations, nicknamed pogo'' after the jumping stick, have occurred principally in the first longitudinal structural mode during operation of the first liquid-propellant stage of a launch vehicle.

From the same report, here's a figure of the accelerations characteristic of pogo.

The dynamic instability being described here is not simply resonant forcing. There is a positive feedback loop.
A block diagram of the positive feedback process which can lead to instability is shown in figure 2. Structural vibratory accelerations induce the propulsion system to generate forces which can then intensify the original vibration. When the system becomes unstable, oscillations will appear spontaneously.

--Rubin (1970), emphasis mine

Rubin gives a further description of the two types of pogo.
Two basic kinds of propulsion-system behavior have produced pogo instability. The common form of pogo, called engine-coupled pogo, has been experienced to a significant degree on certain configurations of the Thor, Titan, and Saturn space vehicles. This form results from the action of the tank-to-engine propellant feed-lines and the engine itself (fig 3.) When the vehicle vibrates longitudinally, the pump and the propellant in the flexible tank undergo oscillatory motions. These two motions produce oscillating flow in the feed-line and in the pump's discharge line. The flow oscillations lead to oscillations in engine thrust and in pressure at the pump inlet, which then act as regenerative forcing functions on the vehicle structure. The feedback loop is thereby closed. Although a pump is included in figure 3, pogo can also occur in pressure-fed systems.

A much less common form of pogo results from the pneumatic behavior of an active pressurization system for the propellant tank ullage. This form is known as ullage-coupled pogo, and has been experienced only on Atlas vehicles immediately after liftoff. It has also been referred to as pneumatic-coupled pogo, or bloating''. A simplified schematic of an active pneumatic system for pressurizing a tank is shown in figure 4. When the vehicle vibrates longitudinally, the tank ullage pressure oscillates because of oscillation of the ullage-volume boundaries. The sense line transmits the pressure oscillation to the regulator. The regulator responds by producing an oscillatory flow of pressurant (i.e., the pressurizing gas) into the supply line which regenerates the ullage-pressure oscillation that acts as an axial forcing function on the vehicle structure, and again the feedback loop is closed.

The big SRB being contemplated for use in Ares I probably does have lots of combustion instabilities which will cause some wicked forcing on the rocket. It may even couple well to the rocket's lower longitudinal modes, but that is not pogo. There is no positive feedback there, just lots of hammering on the structure (and the astronauts).

1. The Crucial Role of Error Correlation for Uncertainty Modeling of CFD-Based Aerodynamics Increments, Abstract: The Ares I ascent aerodynamics database for Design Cycle 3 (DAC-3) was built from wind-tunnel test results and CFD solutions. The wind tunnel results were used to build the baseline response surfaces for wind-tunnel Reynolds numbers at power-off conditions. The CFD solutions were used to build increments to account for Reynolds number effects. We calculate the validation errors for the primary CFD code results at wind tunnel Reynolds number power-off conditions and would like to be able to use those errors to predict the validation errors for the CFD increments. However, the validation errors are large compared to the increments. We suggest a way forward that is consistent with common practice in wind tunnel testing which is to assume that systematic errors in the measurement process and/or the environment will subtract out when increments are calculated, thus making increments more reliable with smaller uncertainty than absolute values of the aerodynamic coefficients. A similar practice has arisen for the use of CFD to generate aerodynamic database increments. The basis of this practice is the assumption of strong correlation of the systematic errors inherent in each of the results used to generate an increment. The assumption of strong correlation is the inferential link between the observed validation uncertainties at wind-tunnel Reynolds numbers and the uncertainties to be predicted for flight. In this paper, we suggest a way to estimate the correlation coefficient and demonstrate the approach using code-to-code differences that were obtained for quality control purposes during the Ares I CFD campaign. Finally, since we can expect the increments to be relatively small compared to the baseline response surface and to be typically of the order of the baseline uncertainty, we find that it is necessary to be able to show that the correlation coefficients are close to unity to avoid over-inflating the overall database uncertainty with the addition of the increments.

Haven't had time to read this one in detail, but looks interesting.

2. A version of Titan II was being developed by the Air Force for use as the booster for NASA's Gemini (two-man) spacecraft. As flight testing proceeded, a problem of what was called �pogo' instability developed. It turns out pogo had always been present in the ICBM version to some degree, but those longitudinal vibrations were simply integrated by the guidance system and didn't affect the payload or other mechanical components. However, male human bodies were another matter, and pogo proved to have serious consequences for testicles. The problem had to be fixed, and there was only one or two remaining unmanned test flights. One of the Aerospace analysts, Sheldon Rubin, a Caltech Ph.D. (BS '53 ME, MS '54 ME, PhD '56 ME), did an absolutely fantastic job of tracking down the problem, and prepared a first class mathematical model. The vibrations depended on a feedback with the first stage liquid rocket engines, and Aerojet was able to take high-speed motion pictures of transparent pump volutes that showed a clear cavitation problem in the eye of the pump which would account for a feedback mechanism. The cure for the problem, absent a new pump design which was out of the question in a schedule sense, was to increase the propellant tank pressure. This was not without a performance penalty, but the overall performance remained within the envelope. So the fix was to go into the next flight. About this time, an senior experienced bozo who ran the Aerospace flight test operation facility down at Canaveral came up with some crazy theory for the problem which was supported by nothing. He insisted that Rubin's solution would make the problem worse, and the Gemini program would crash and burn. Because this fellow was an old acquaintance of the company president, the Engineering Division took his warning seriously and a major in-house review meeting was called to decide whether the scheduled flight test should go.
Sheldon Rubin and the Pogo Instability

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