According to the October 2015 revision of the Falcon 9 User's Guide, the Falcon 9's first stage Merlin 1D engines have a 70%-100% throttle range, while the second stage Merlin 1D Vac engine has a 38.5%-100% throttle range.

The two engines are very similar; the major difference is that the second stage engine uses a large radiatively cooled nozzle extension which produces substantially higher thrust in vacuum.

The 100% throttle rating for the engines (934kN for the vacuum engine in vacuum, 756kN for the first stage engine at sea level) represents the same fuel flow rate when adjusted for specific impulse.

My question: Why is the upper stage engine so much more deeply throttleable than the first stage engine?

Some of the common problems with deep throttling engines include:

  • Combustion stability
  • Pump flow stability
  • Exhaust flow adhering to one side of the nozzle, causing uneven nozzle erosion and off-center thrust

Given the common design of the pumps and combustion chamber between the engines, the first two seem unlikely.

Is a nozzle operating in vacuum less susceptible to the flow adherence problem?

Does the first-stage engine perhaps require more fuel flow through the regeneratively cooled nozzle to maintain cooling?

  • $\begingroup$ The new rev gives a figure of 170klbf (756kN) for the first stage Merlins, where previously the figure being tossed around was 165klbf (734kN). $\endgroup$ – Russell Borogove Nov 30 '15 at 3:47
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    $\begingroup$ Wouldn't the vacuum operation be a major factor? An atmospheric engine must first overcome the atmospheric pressure, and throttling it lower would cause flameout? Similarly, the same rocket engine can have vastly worse ISp in the atmosphere. $\endgroup$ – SF. Nov 30 '15 at 6:48
  • $\begingroup$ Chamber pressure in the Merlin is about 100 atmospheres, so I wouldn't expect back pressure to be a hard limit. $\endgroup$ – Russell Borogove Nov 30 '15 at 16:28
  • $\begingroup$ I am guessing here, but the throttle is determined by the turbine engine inside the rocket that drives the fuel into the combustion chamber, correct? So I would wager that they intentionally limit the throttle-ability on the first stage for several reasons including to lower risk and lack of practicality (i.e., will the rocket go anywhere if only thrusting at ~38%?) . $\endgroup$ – honeste_vivere Dec 3 '15 at 23:12
  • $\begingroup$ I don't think @SF meant atmospheric pressure backing up into the combustion chamber. I think he meant it could cause the flow separation and uneven erosion of the divergent nozzle. In a vacuum, you have none of these worries. I don't have insider knowledge and haven't run the calculations but operating in a vacuum feels like a major contributing factor to the deep throttle-ability of the engine. $\endgroup$ – Jim2B Dec 18 '15 at 6:41

You are correct, it is the atmospheric pressure at sea level that limits the minimum power setting on the ground started Merlin engines. At atmospheric pressure, the exhaust can only be over expanded up to a point before the engine begins producing negative thrust or very strong oscillating thrust loads (from the exhaust separation from the nozzle walls) which can load the engine past the fatigue life of the nozzle wall and thrust frames.

To help you understand where the cross over point is, here is some math for understanding the gas dynamics inside the nozzle. Essentially, the nozzle is an accelerator, turning omnidirectional static pressure into directional velocity. In vacuum, there is nothing pushing against the exhaust, so this expansion can theoretically be taken to a maximum where the static pressure of the exhaust is zero. However, inside the atmosphere, the outside air pushes against the exhaust flow. As long as the static pressure of the exhaust is higher than atmospheric, the flow accelerates, however, once the flow is expanded past atmospheric, the atmospheric pressure begins to slow down the exhaust. This wouldn't matter so much if the flow in the exhaust were uniformly high. However, this doesn't happen because of something called a boundary layer. A boundary layer is a thin layer of fluid along a wall that brings the flow from full exhaust velocity down to zero at the wall. It is here where the problems of exhaust wall separation start, because this flow begins slowing down then reversing after the nozzle flow static pressure drops below atmospheric. This flow reversal then starts lifting the gas flow off of the wall. Now, due to viscosity, this gas flow will feel shear forces, which spin up eddies in the gas layer. These eddies act like scavenging pumps, helping the gas flow claw its way back to the wall. However, because the gas has mass, this clawing will go too far, alternating between hitting the wall and lifting far off the wall each time, causing an oscillation to start. Because the flow velocity to flow viscosity ratio is really high (this is called the Reynolds Number), this oscillation will grow not die out with time.

A designer has two choices here to ensure this oscillation stays manageable: 1) Minimize the nozzle length so that the oscillation doesn't have a chance to grow too big and generate huge side loads. 2) Shape the nozzle properly to lift the gas flow slightly off the wall to accelerate it by reducing the friction experienced by the flow.

Option 1 is doable up to a point, because the flow will still have to be turned, and that has to be done somewhat gradually to avoid shock wave formation inside the nozzle. The bell nozzle developed by Rocketdyne in the 60's is still the best design for this, but some aerospike nozzle designs have promise to reduce the length further.

Option 2 is where a lot of advancements have been made using unsteady gas dynamics. A class of shapes have been discovered that structure the boundary layer in such a way as to form a series of fluid rollers to behind backward facing steps that lift the flow off the wall and allow it to accelerate, helping delay the point where the flow reversal starts.

Now, if you want to avoid the damaged engines you'll have to go through during testing, it's best to avoid this problem altogether. Hence, it's best to operate the engines at or close to full power (I.E. full chamber pressure) than throttle them deeply within the atmosphere. This is probably why the Merlin engine has a smaller power range in atmosphere than out because SpaceX didn't want to spend the time and money on working out the nozzle geometry through static engines tests.

  • $\begingroup$ Maybe it is also due to reuse of the 1st stage, so not wanting any damage to it. $\endgroup$ – Ian Ringrose May 31 '16 at 15:34

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