Wednesday, August 18, 2021

Propellant Ullage Problem and Solutions

For liquid rockets employing free-surface tanks sitting on the launch pad or in thrusted flight,  the propellants in the tanks are pushed by gravity or the vehicle acceleration into the same position covering the drains into the engine pumps.  But between burns,  the vehicle is essentially in free-fall.  The propellants,  because they no longer fill the entire volume,  get pulled by surface tension into multiple spherical globules floating around inside the tanks.

This situation essentially removes the propellants from the inlets to the engine pumps.  The engines cannot be restarted without correcting this situation.  Nor could a ship-to-ship refueling operation be conducted,  as the drain pipe inlets are dry.  No pump of any kind can pull propellant out of tanks if the pump inlet has only vapor in it.

Initially,  rocket stages needing to ignite in free fall were the upper stages of multi-stage launch vehicles.  The first solution to this problem was adding small solid propellant rocket cartridges called “ullage motors” to the stage.  This is depicted in Figure 1.  The solid propellant cartridges were entirely unaffected by either gravity or its total absence.

When the ullage motors fired,  their total thrust accelerated the vehicle by an amount equal to total thrust divided by vehicle mass.  After a period of time,  the globules settled into pools of liquid in the tank bottoms,  as depicted in the figure.  This has a long history of success with both storable liquids and with cryogenics,  over fairly short time intervals.  Attitude thrusters can also be used for this.

Figure 1 – The Ullage Problem and the Ullage Motor Solution

A “time constant” for this process would be the time for a globule to fall from one end of the tank to the other,  under the small acceleration induced by the ullage thrust. A figure-of-merit for the settling time into a pool with no voids in it,  would be roughly three times the time constant.  That plus the time it takes to get the engine fully ignited and stabilized,  is the min burn time required of the ullage motors.

The pressure at the main engine pump inlet (for each line) is the pressure inside the tank,  plus an increment that is the depth shown  in the figure times the liquid density times the vehicle acceleration.  That pressure divided by Earth gravity-times-the-density must equal or exceed the “net positive suction head” specified for the engine (or refill) propellant pump.  The pressure in the tank is that of the vapor,  plus that of any injected pressurant gas.

The first ullage motors were solid propellant devices,  but that is not the only way to provide ullage thrust.  Liquid propellant attitude thrusters can be used for this purpose,  if designed to operate in free-fall.  These are usually bladdered-tank systems such as those in Figures 2 and 3 (discussed just below),  and which are almost universally pressure-fed instead of pumped.

Bladdered tank designs contain the liquid inside a bladder,  in turn inside the tank.  Pressurant gas injected between the tank and bladder squeezes it to the liquid,  preventing the formation of void space in which free-floating globules can form.  The difference in pressure between the pressurant gas and engine pump inlet drives the expulsion of liquid from the bladdered tank.  This has a long history of success with near-room-temperature storable liquid propellants,  but none with cryogenics.

Figure 2 – The Bladdered Tank Solution,  Done As Axial Eversion

This can be done in pretty much any geometry,  but such a bladder as it crushes under pressure will crumple and wrinkle,  which significantly lowers the liquid expulsion efficiency of the design.  Expulsion efficiency is defined here as volume expelled / volume loaded.  A way to achieve high expulsion efficiency is to “evert” the bladder,  so that one half of it collapses inside the other half.  If the symmetry of this eversion can be preserved,  the expulsion efficiency can theoretically be very nearly perfect.  There are two eversion geometries for cylindrical tanks:  axial (Figure 2),  and lateral (Figure 3).

Figure 3 – The Bladdered Tank Solution,  Done As Lateral Eversion

The axial eversion path offers propellant expulsion from a tank end with a centered connection,  but offers a long eversion path,  increasing the probability of asymmetric eversion with wrinkles.  That leads to less expulsion from the tank than desired.  The shorter lateral eversion path offers higher symmetric eversion probability,  for higher expulsions nearer those desired.  However,  it requires side feed and expulsion connections.

Both geometries require the bladder be bonded to the tank on one side or one end.  Both feature a very sharp bend with a very short radius of curvature indeed,  at the eversion point.  The trick for reusability is to ensure the strain at the eversion point is elastic,  otherwise,  the bladder will become the wrong shape,  and will no longer fit the tank correctly.  That guarantees wrinkles and lower expulsion than design.  It also increases the likelihood of bladder failure.  Note also that the eversion point moves!

Key here is very large elastic strain values for the bladder material.  Generally speaking,  with most elastomers,  these strain capabilities are quite large at ordinary temperatures,  but quite low at cryogenic temperatures.  That is why this bladdered expulsion propellant system has historically been used with more-or-less room temperature storable propellants,  but not with cryogens!  If the right material with the right properties can be found,  it would then work with cryogens.

Corrosiveness of the propellant is also an issue to consider.  This is especially important with the nitric acid systems,  and to some extent with the hydrazines.  Reliability of the design,  especially if it is to be reusable,  is extremely important.  This is especially true for very toxic propellants such as NTO and the hydrazines.  Leaks simply cannot be tolerated.

In any event,  the pressure of the expulsion gas that is fed in must exceed whatever propellant pressure exists within the bladder.  If not otherwise controlled,  the rate of propellant expulsion is proportional to the square root of the difference between the feed gas pressure and the tank pressure inside the bladder.  It is also proportional to the propellant outlet area.

The feed gas volume flow rate at pressure,  must be as large as the volume rate of flow of expelled propellant,  while still providing that expulsion pressure difference.  This is generally a rather significant pressure difference,  in order to achieve useful expulsion rates.

The bladder material must be able deform easily,  so that it does not resist this pressure difference,  instead just resting against the liquid while the gas moves them both. It therefore cannot be stiff,  despite whatever thickness it must have,  to survive.   We are talking about materials with high tensile strength,  very low Young’s modulus,  and truly enormous elastic strain capability,  at all the cryogenic temperatures it will see in service.

The radius of curvature at the eversion point,  right on the inside of that eversion bend,  is essentially zero.  That puts the outer side of the bend into considerable tensile stress and strain.  If the material is going to split,  that is where it will happen.  The thicker the bladder has to be,  the worse this eversion point bend-splitting risk is.

Piston-Driven Displacement

About the only remaining alternative approach for positive expulsion would be a gas-driven piston,  essentially a syringe.  This is depicted in Figure 4.  As far as I know,  this approach has never been used in a flying system,  other than as an engine start primer.

There are multiple constraints on this type of design for a rocket vehicle.  One tank dome has to be inverted,  in order for there to be a place to locate the piston skirt,  when the tank is full,  such that max liquid volume is obtained.  The piston must have such a skirt,  in order to remain properly aligned,  and not jam.

At the other end of the piston travel,  the piston face must match the contour of that dome,  so that maximum liquid volume may be expelled.

The piston skirt and side must be of nontrivial thickness in order to house the groove (or grooves) for the O-ring seals.  Remembering that the square edges of the grooves are stress concentrators,  there must be enough “meat” to sustain the loads on the piston,  repeatedly for reusability.

The depth of the groove plus the wall clearance has to be such that the O-ring seal(s) is compressed radially enough to seal.  That compression distance is small if the O-ring is hard,  but the compression force is high.  The compression force is low if the O-ring is soft,  but the O-ring may not be compressed enough to effectively seal,  if this is taken too far.

High compression force is high friction force to move the piston.  In particular,  the static friction is typically much higher than sliding friction,  leading to slip-and-jerk behavior characteristics,  which are quite undesirable.

The width of the O-ring groove has to be wide enough not to compress the O-ring,  so that pressurant gas can fill one side of the groove evenly,  and force the O-ring against the other side,  thus effecting the seal.  This works correctly if there is only one O-ring.

If there are multiple O-ring seals,  pressurant gas cannot reach those seals further away from the pressurant gas side.  If such seals are installed,  their grooves must be narrower,  so that radial compression forces deform the O-ring enough to seal against both sides of the groove.  This requires high radial pressures,  obtaining large friction values,  and causing severe slip-and-jerk behavior.  Net result:  multiple-seal redundancy is not always a good idea!

Figure 4 – Positive Displacement With A Piston

Venting Boiloff Vapors With Cryogens

All the issues and observations made so far apply to near-room-temperature storable liquid propellants.  The boiloff behavior of cryogenic propellant materials introduces yet another very complicated issue to deal with:  adequate venting of boiloff vapors.

In the free-surface tank where ullage thrust is used,  the tank venting system is located on the forward dome.  The tank may be filled fully at launch,  or very nearly so,  but when in free-fall,   there will be considerably more physical tank volume than there is liquid volume inside it.  Vapors add to the atmosphere not occupied by liquid,  which must be vented periodically,  if tank pressure is not to rise rapidly. The forward dome location is the logical place to install such venting equipment.

When venting,  ullage thrust must be applied to resettle the globules into a pool of liquid,  with a separate vapor atmosphere.  Otherwise,  liquid as well as vapor will be vented.

We may conclude that free-surface tanks with ullage thrust are inherently compatible with cryogenic propellants.  History bears that conclusion out.  Periodic venting will also require ullage thrust,  in addition to engine ignitions and propellant transfer operations.

Using cryogenics in the bladdered tank approach is going to require a flexible vent line between the bladder and a location on the tank shell.  The equipment to control tank venting can be mounted at the shell location.  But,  there are two very serious problems:  (1) the vent line is quite long,  essentially full tank length,  if axial eversion is used,  and (2) how does one ensure that only vapor enters the vent line,  when vapor can form essentially anywhere within the bladder?

Problem 1 can be reduced in severity by using lateral eversion.  The vent line is much shorter,  but must still be flexible,  and it will affect the everting bladder geometry,  requiring an inconvenient pocket in the tank shell to hold it,  when the bladder is filled.  There is no practical way to put the vent line back into the pocket during tank refill,  without opening the tank at the pocket location,  and physically flaking the flexible vent line in place.

Problem 2 has no known solution,  yet,  other than the application of ullage thrust.  But if you add ullage thrust,  you might as well just build a simple free-surface tank!

The flexible vent line is as severe a cryogenic elastic strain capability problem,  as is the bladder itself.  These are technologies requiring development and demonstration.  They are not ready to apply!

We may therefore conclude that neither bladdered tank approach is compatible in any practical way with a boiloff vapor vent,  which is absolutely required if cryogenic propellants are to be used.  There are materials technologies that must be developed and demonstrated to enable this design approach.

The piston displacement approach will require a venting installation on the piston itself,  as there is no other feasible place to put it.  This may prevent the piston from recessing fully into the forward dome when the tank is full,  thus lowering the volume of liquid propellant that could otherwise be loaded into a tank of a given volume.

It also requires a long flexible vent line from the piston to the forward dome,  where the venting controls can be mounted.  This flexible line will also act to hold the piston off the forward dome.  There is no way to flake this vent line into position between the piston and forward dome during refill,  without opening an access port in that forward dome.

This idea also suffers the cryogenic elastic strain capability problem for the vent line,  which the piston was supposed to eliminate by eliminating the bladder.  And,  it still suffers the same problem with how to ensure only venting vapor,  when liquid is inherently adjacent to the piston,  and the vapor can form throughout the liquid volume.  As with the bladder tank,  you could apply ullage thrust,  but then it would be easier just to build a free-surface tank.

The flexible line technology at cryogenic temperatures requires development and demonstration.  It is not ready to apply!

We may therefore conclude that the displacement piston approach is also incompatible with a boiloff vapor vent,  which is required if cryogenic propellants are to be used.  There are materials technologies that must be developed and demonstrated to enable this design approach.

Bottom Line:

The most practical solution to the ullage problem when using cryogenic propellants,  is the free-surface tank with ullage thrust provided.  This is also the historically-proven solution,  and all the technologies to enable it are ready to apply.  It is compatible with boiloff vapor venting.  Ullage thrust must be supplied for every free-fall engine ignition,  every tank refill in free fall,  and every boiloff vapor venting event.

The bladdered tank and piston displacement approaches are not compatible with boiloff vapor venting installations,  which are required,  and they run severe cryogenic elastic strain capability risks for the various structures that are required to be flexible at cryogenic temperatures.  Such materials technologies are not yet ready to apply.

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Update 2 October 2021

There is another option for providing an ullage solution in a free-surface tank with cryogenic propellants.  That is to spin the tank to provide “artificial gravity”,  so that a free surface forms again.  The dynamics of spinning objects are stable only about those axes with maximum and minimum mass moments of inertia.  For objects that are cylindrical,  that would be spinning end-over-end (like a baton) at maximum moment of inertia,  or spinning about the long axis like a rifle bullet,  for minimum inertia.

The two geometries are quite different in their effects. If you spin end-over-end,  the result is as illustrated in Figure 5.  The moving tank walls “intercept” the floating globules,  enforcing their acceleration into the spinning motion.  The result is the formation of a new free surface inside the tank,  reflecting the direction of the centrifugal force of the spinning motion.   It is likely there will be one tank on each side of the center of gravity,  so that propellants are slung to opposite ends of the tanks,  as illustrated.  The drain and vent roles will be reversed for at least one set of tank plumbing connections.

Because the mass moment of inertia is maximum for this spin direction,  a maximum torque-time product is required to spin-up the vehicle to any given rotation speed.  However far the spin-up thruster is from the center of gravity is the moment arm for the torque that thruster provides.  The torque-time product divided by the moment arm length is the thrust time product (total impulse) required of the thruster to spin-up the vehicle for ullage.  A similar total impulse is required to de-spin.  Note that engine restarts cannot be done successfully while the vehicle is spinning,  although propellant transfers might be.

Figure 5 – What Happens With End-Over-End Spin

The other option is rifle-bullet spin,  as illustrated in Figure 6.  This one slings the propellants radially outward against the periphery,  as shown,  to form a cylindrical free surface inside each tank.  The total impulse required to spin-up and de-spin is less,  because this is the minimum mass moment of inertia.  The pre-existing vent connections can still serve that role in both tanks,  as long as they are near the center of the tank dome.  The drain connections will require a second set of drains along the tank peripheries,  where the liquid pools are located,  in addition to the aft dome center connections,  used when under thrust.  It would best preserve spin stability to install the periphery drain connections in a symmetrical manner.  Otherwise cross products of inertia become large instead of zero.

There is one other problem to solve,  associated specifically with this spin direction.  There are no surfaces that “intercept” the globules when you spin-up the vehicle!  In effect,  you spin-up the hardware,  but not the propellant.  Only the random motions of the globules bring them into contact with the moving tank wall.  Friction forces collect some of the spatter from those collisions onto the wall.  In this way,  eventually the propellant finally gets “spun up” and affixed to the tank wall.  But this random and inefficient process takes a very long time indeed!

The solution is a set of radially-oriented perforated baffles,  similar to anti-slosh baffles.  When you spin-up the hardware,  these baffles “intercept” the floating globules,  forcing their immediate spin-up,   and thus their immediately getting slung outward against the tank wall.  This is shown in Figure 7

This solution costs some extra inert mass in the form of the extra peripheral drain connections,  and the radial perforated baffles.  But it does reduce the mass of spin and de-spin thruster propellant that needs to be budgeted.  Given a fast switch from peripheral to aft dome drains,  this rifle-bullet spin geometry might possibly serve for engine reignitions as well as for propellant transfers.  For transfers,  the very convenient nose-to-nose or tail-to-tail docking geometry could serve.   See Figure 8

Figure 6 – What Happens With Rifle-Bullet Spin

Figure 7 – Spinning-Up the Propellant As Well As the Hardware

Figure 8 – Using Rifle-Bullet Spin For Propellant Transfers Between Two Docked Vehicles

Updated Bottom Line:

The rifle-bullet spin technique could easily supplant the application of ullage thrust for propellant transfers between docked vehicles.  It might not serve as well for engine reignitions,  where simple ullage thrust is already well-proven and easily had.   While this spin technique needs demonstration,  there is nothing here to suggest that it wouldn’t be a successful and short effort.

The obvious application here is the tanker problem for refilling SpaceX “Starships” on-orbit.  Such is not required for low orbit operations,  but it is required for high-orbit operations,  and for outside-of-orbit operations.  That last includes trips to the moon and to Mars (or anywhere else outside of Earth orbit).  This spin technique may help make possible the otherwise-very attractive tanker scenarios I have already explored in multiple other articles on this site.

A not-so-obvious (but still important) application would be for an on-orbit propellant depot facility.  Such a depot would have to serve a variety of vehicles,  and so would have to store a variety of propellant combinations.  Some of those are going to be cryogenics.  The bladdered tank solutions in Figures 2 and 3 apply to the storable materials,  but the cryogenic materials s could be stored in tanks that spin like rifle bullets.  That is an idea worth exploring further,  perhaps in a future article.

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