Resonance expalined - in part!
From the information supplied from this forum and some additional research, I understand the relevant components of the 777 fuel system to be; two AC powered centrifugal booster pumps mounted adjacent on the rear of each wing tank which feed into a common manifold. On the inboard side this manifold extends to become the cross feed (which has two normally closed parallel valves mounted only on the left side of the aircraft) and outboard becomes the fuel delivery pipework which passes through the spar valve, continues to the oil heat exchanger in the fan case and then on to the engine driven HP pump which is fitted with a recirculating bypass to control over pressure.
http://www.eatonaerospaceltd.com/fuel/Resources/021_2_Type9106boostpump777.pdfgives some details of the type of booster pump fitted.
I assume (dangerous?) that this unit is very similar to those fitted to some 747s of which I have better information. In order for it to be possible to service the pump without draining the adjacent fuel tank, a sprung loaded flap valve is located at the inlet of the pump case which is mechanically held fully open by the physical presence of the pump. On the outlet side, a similar flap valve – ie a disc with a hinge on one side perpendicular to the flow – is mounted. This is a typical non return valve which has a soft seat and a weak spring to ensure the valve will close when there is no forward flow and as far as I am aware no means of damping the movement.
Considering just the section of this system between the boosters and HP pump, any physical movement which even slightly changes the shape or concentricity of any part of the pipework also changes the internal volume of the pipe and hence introduces a degree of elasticity.
In the unwanted resonant state, a small surge of fuel progresses towards the engine where it is baulked by the HP pump which by its intended design strictly meters the possible flow. The excess energy contained in this moving column of fuel causes an increase in the local pressure creating a shock wave causing some slight expansion or lateral movement in the pipework which upon contraction returns a reflected shock wave back towards the booster pumps.
The non return valves are held open in proportion to the flow of fuel hence at engine idle the valves will be floating close to their seats. The shock wave hitting the back side of the valves momentarily forces them against the fuel flow direction and towards their seats. This causes a restriction to the flow creating a disparity of a depression on the engine side of the valve and an increase in pressure on the booster side. Once the shock wave has passed, this combined depression and pressure causes the valves to move rapidly to a more open position… causing a surge of fuel to progress towards the engine….
If the many and complex physical characteristics that are an influence allow the continuation of this feed back pattern, this system will continue to oscillate – ie resonate - until something either breaks the loop or as can also happen, exacerbate it although due to the enormous interdependent complexities involved, predetermining what will cause what response may be impossible.
It can be seen that on an increase in demand the HP pump allowing more fuel to pass might reduce the effect of the pressure build up and reflected shockwave and hence damp the effect. Alternately, the greater demand could result in the difference of depression and pressure across the valves causing them to open faster, resulting in an enlarged surge and a growth in the effect.
In the low demand situation with just a small amount of oscillation in the fuel column, the supply seen beyond the HP pump could remain quite adequate to cause no problem or alarm. If however on the increase of demand the oscillation is exacerbated, the supply will become increasingly restricted with all the energy being introduced to the system being absorbed in accelerating and de-accelerating the column of fuel within the pipes, generating shock waves and in accordance with Newton’s 3rd law, powering reactive movements of the mass of fuel line, components and other connected structures.
In this latter circumstance, a point will be reached where the suction of the HP pump causes such a severe pressure differential across the valves that the system will reach a limit where the flaps are moving with such speed and force that they will be bouncing between whatever mechanically limits the maximum open position and the fully closed positions. In this state the liquid managing to get past the valve will be a fraction of the normal full flow and at which time it becomes anyone’s guess as to the state of the fuel – or foam - between the HP pump and valve.
I have omitted a rather critical part of this explanation until now which is ‘So what caused the resonance to start in the first place? The simple answer is that in this particular case I really don’t know! However, if you can understand the explanation and visualise a horizontal column of pressurised liquid passing through a slightly open flap valve and then giving that pipe a little sideways shake perhaps you can see how easily it might start even though there are so many other parameters that have to be ‘just right’ for it to have any chance of self perpetuation.
If this overall scenario as described seems unlikely to begin with, it is made even more so by the fact that there are the two parallel non return valves on the booster pumps and for the effect to develop it is actually essential for them to react simultaneously. In the first instance this may seem absurd but they are both identical, operating close together in an almost identical environment and being induced by the same forces. Even if one valve does slightly lead the other, once even slight pressure variations begin, it is quite feasible that they would operate in perfect unison.
Rather than rewrite the details, I explained in my original post #1165 how once started, this effect could propagate from the right to the left side taking a few seconds to do so.
Still so very many holes all to have to line up…
Regards
JG