Several years back I suggested a type of compensating nozzle that should be inexpensive to build and test. Unfortunately the ones I made for demonstration with compressed air were hit and miss as I didn’t have the theory quite right. Hit and miss is not good enough for serious companies, so I mostly dropped the idea for a while. I thought a few of my acquaintances in the business might do something with the idea for a while. Now I think the idea has  been mostly forgotten as unworkable.
A few years back I did finally find the missing part of the concept and did nothing about it as I thought at the time that others had picked it up and moved on. Since I don’t think that has happened, I am going to repost the concept.
On the left is the engine with the notch showing on the right side. The notch allows the atmosphere to enter the bell to compensate for over expansion at lower altitudes. At higher altitudes and in vacuum the exhaust gradually uses the whole bell with some losses through the notch. This will allow a nozzle to be optimum at sea level when most are over expanded. It will also be nearly as good as a full diameter high expansion nozzle in regimes with the exhaust under expanded.
The missing ingredient in the prior concept was appreciation for the momentum of the exhaust at the notch site. The momentum, especially with the rounded notches that I was advocating before, would prevent the atmosphere from entering the notch in a controlled manner. The addition of a sharp edge at the notch to assure a clean break and a slight reverse on the notch edge to direct the exhaust inwards controls the momentum of the exhaust in a manner that allows the atmosphere to interact and provide pc/pa compensation at a range of back pressures.
A compensating nozzle allows lower pressure engines to operate more efficiently in a launch vehicle. They should allow a payload increase of 1-5% depending on the vehicle and the assumptions going in. For a VTVL that wants to operate at very low pressures in the landing phase, a compensating nozzle would be a very important upgrade, though the successes of Blue and SpaceX take some of the edge off that argument.
This is a public domain concept as I described it here years ago. So anyone that wants to see what I am talking about can build a quick and dirty nozzle to use with shop air. The ones have done were an air chuck and fiberglass. About $10.00 in materials. I know it works at 135 psi. Then you can try a higher pressure gas if it might be useful to you or someone you know.
johnhare
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I think the element you’re missing is the nozzle turning the gas flow between throat and exhaust. Something like a sector cut from an E-D nozzle. Of course the angle the flow turns will vary with throttle and ambient pressure, requiring gimbal correction or a second nozzle oriented to cancel the shift.
Something along that line I rendered after reading your earlier presentation, https://lh3.googleusercontent.com/tthR1tbhHu99UpfatvYGec0UtVGtJ1pOMiQks-ORR7AtdALEJmiYH50AJ2L6OLM6UWPKs1GM2zBXl6V85Lxxf9Ms9EpWT80HKybbzwMGdZXy4ZLOQNXU1RTywbf1hRCk6ooJxEa5kaHaa55zRF99-8DFqBToqg5CXGzr-R3uzIxDDB-22CqelNz9XIRML7sTW_bSjqiARaVgISfSpQSunKDcGB5n2r0F1Odiz8IeG1pd-73X5HCAZjwkaUQ1nlf2vPsQ2WAQhWP24dTD9qVQ9OWB5iivid_J2gSJtLluX8j5jlQwMJYiztWT8Q6TJOOJdqf6jsCXENnDr1-7RKk-edS79Ia72Tb4ljCXi3L68c5EMGr739tQ_GdIL9AVDkhvb10zHFuUUxv0DWuJ9eZJEmXQJV26oZ8j3lweRAJ6SRIgzvXR_Up9dFV3RcL_edT3N8s4fpeoX3XKpdcvlIZfQe71NjkpaoCmdG5Sftm6-Ing3QLE3XIePV2kmK89EF6A2T9DgswIn27VYmDNW2G-NExvhpEqbPbfmfIH1i5XvqNC5sr6XGwQfKW6ef2Xdi5ltmzx6iRPjnC1Myf3u9-LS6qZrw=w640-h480-no
No, it is the same as the short side of the aerospike nozzle which has the short reverse. The way I sketched it now works.
I remember this. Interesting. Really.
My preference had always been for an ejectable nozzle insert optimized for the lower atmosphere. An ablative nozzle inserted in a high expansion regenerative nozzle, and ejected after the boost phase. That is a patented concept, and has never been used in practice, I believe.
Neat idea.
It looks like the thrust is going to be off-axis and the direction of the thrust vector is going to change as pressure goes down and the plume fills the whole bell. Do you think that’s right?
Probably not a problem for a vehicle with multiple engines arranged symmetrically, but I suppose it could be a problem for a single engine vehicle.
Would two notches on opposite sides of the bell fix the thrust asymmetry?
Even for multiple engines it would be desirable to gimbal to keep the thrust vector through the center of mass. Thrust should shift toward center with increasing altitude as you suggest.
I don’t have a handle on twin notches. Perhaps after somebody proves the original it might be worth investigating.
I was thinking about how big the notch should be, and I came up with this idea. The notch should start at the point in the nozzle where it is properly expanded at the highest ambient pressure it will see. Then below that, the un-notched surface area of the nozzle should remain constant to produce no additional expansion at that ambient pressure.
But then I had another thought. Below that ambient pressure, there will be additional expansion that will spill out of the notch. You will get additional thrust because the un-notched surface area will be at higher pressure than ambient, but not as much thrust as if the notch were smaller. So I think there is still a trade-off to be made where a smaller notch performs worse at sea level and better in vacuum. The trade is probably not as stark as changing the expansion ratio of a traditional no-notch nozzle.
I agree except that the reverse kicks the exhaust back into the bell to some extent. Extrapolating from the linear aerospike that informs this concept, most of the expansion will be in the solid bell.
The flap necessary to deflect flow away from the notch, if constructed anything close to as drawn, would produce some nasty shock waves in the exhaust flow.
It hasn’t worked that way in practice.