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Proposes an all liquid version of the Ariane 6 using two Vulcain engines on the core stage instead of just one:
Multi-Vulcain Ariane 6.
https://exoscientist.blogspot.com/2018/ … ane-6.html
SpaceX is making marked strides in the quest towards reusability. The version of the Ariane 6 proposed by the ESA can not be made reusable. Then it may become obsolete by the time it is fielded in 2023.
Instead this proposal is to use two engines on the core stage. This allows it to lift off without the side boosters so that the core stage can return to launch site a la the Falcon 9.
To GW, I need a higher sea level thrust version of the Vulcain engine. I thought I could do this simply by shortening the nozzle. What do your tables say should be the nozzle length for optimized ISP at sea level for a hydrolox engine with a 6 to 1 mixture ratio at a 110 bar chamber pressure? What would that sea level ISP be then?
Bob Clark
Old Space rule of acquisition (with a nod to Star Trek - the Next Generation):
“Anything worth doing is worth doing for a billion dollars.”
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Well, lessee, 110 bar is pretty close to 1600 psia, which I am more familiar with. Pressure ratio at sea is 1600/14.7 = 108.8:1.
I have in my hand an old paper chart for thrust coefficient at specific heat ratio 1.20. At PR = 100, it optimizes at about expansion ratio 12:1, with CF pretty near 1.615. That value already includes the effects of a 15-degree half angle nozzle kinetic energy efficiency, which is 0.983. That’s just the way the chart was pre-calculated. Very handy.
My ancient Pratt & Whitney handbook lists chamber c* = 7950 ft/sec for hydrogen-oxygen at 1000 psia. That’s for an r = 4.0, not 6.0! If the c* exponent were near 0.01, then I would expect c* near 7987 ft/sec at 1600 psia.
The shortcut for Isp is CF c*/gc. For these numbers, that is 400.9 sec. But, that implies no hot chamber gas is tapped off to run the turbopumps! If the gas tap-off rate is 10% of total flow, you have to factor that Isp down, by dividing it by 1.1. That would be 364 sec Isp. If it’s only 2%, factor down by 1.02: some 393.0 sec. At 1000 psia, P&W lists sea level ideal as 388 sec. That sort-of confirms a gas tap-off rate closer to 2% than 10%.
For a given chamber pressure and a given mass flow rate through the nozzle w, the effective throat area you must have is CD At = w c* / Pc gc. Once the throat is known, you can get thrust F = CF Pc At (without the discharge coefficient CD, best determined from empirical correlations, and pretty near unity for any reasonable design). The total feed rate of propellant is nozzle massflow w plus the hot gas tap-off flow rate wtap, for wtot. Isp is effectively F/wtot.
Beware the handbook listings reporting Isp for propellant combinations. These are figured from a thermochemical code with nozzle efficiency 100%, and hot gas tap-off rate 0%. The c* efficiency is also 100%. You get less in the real world, always.
You figure nozzle kinetic energy efficiency as 0.5*(1 + cos(half angle)), where your half angle is the actual geometric value for a conical nozzle, and the average of near-throat and exit lip bell half-angles, if a curved bell. It applies to the mV (momentum) terms in thrust, but not the PA (pressure-area) terms.
You really have to screw up your combustion chamber efficiency in a liquid rocket in order to get very far from 100% c* efficiency, but there are some that do screw this up with too small a contraction area ratio to the throat, and too small an L* parameter = chamber volume/throat area, a crude measure of residence time. In solids and hybrids, non-unity c* efficiency is a very real and significant effect.
GW
Last edited by GW Johnson (2018-03-03 11:47:55)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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Thanks for that. Here are the specs on the Vulcain 2:
http://www.astronautix.com/v/vulcain2.html
The sea level ISP is 318 s compared to the vacuum ISP of 434 s. But as you know a standard bell nozzle being able to have a single expansion ratio is typically overexpanded with respect to sea level pressures to optimize the vacuum ISP.
This though reduces the possible sea level ISP and thrust. The advantages of altitude compensation are frequently spoken of in regards to increasing the vacuum ISP. For instance the Falcon 9 first stage Merlins only have a vacuum ISP of 312 s. But with alt.comp. they could be given the same vacuum ISP of the Merlin Vacuum of 342 s.
But alt.comp. is also important for improving sea level performance. The Vulcain 2 has a sea level thrust of 95.8 metric tons. So two would be about 192 tons sea level thrust, resulting in a poor takeoff T/W ratio, if it could takeoff at all.
But by your estimate of 388 s optimal sea level ISP, the sea level thrust with a sea level optimized nozzle would be 95.8*(388/318) = 116.9 tons, and two would be at 234 tons, giving a much better takeoff T/W.
Then you would use alt.comp. to get also the the optimal vacuum nozzle size. This could be as simple as using a nozzle extension as used on the RL10-B2 for example, but there many ways of accomplishing it as I discussed on my blog.
The same question of improving the sea level thrust occurs in the SpaceX BFR. On various forums is discussed differing options for how many sea level vs. vacuum engines should be included to allow it to takeoff with good T/W ratio yet have good vacuum performance. But with alt.comp. you can have both optimal requirements. You wouldn’t need to have too many sea level engines to takeoff, reducing vacuum ISP. And you wouldn’t need to use too many vacuum engines reducing sea level thrust.
Bob Clark
Old Space rule of acquisition (with a nod to Star Trek - the Next Generation):
“Anything worth doing is worth doing for a billion dollars.”
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There's a limit to just how over-expanded you can be. The flow shock-separates in the nozzle, sometimes almost all the way back to the throat. In extreme cases, the throat unchokes. This utterly kills CF and thrust.
Nozzle separation is not precisely predictable. Everybody has their own favorite empirical correlation for it. Mine is: Psep/Pc = (1.5 Pe/Pc)^0.8333, where Pe/Pc is the ratio of fully-expanded exit plane static pressure Pe to chamber pressure Pc.
If you have a nozzle expansion ratio Ae/At, and you know your gas specific heat ratio (never far from 1.2), then you know Pe/Pc. Psep is the ambient backpressure around the exit at incipient separation conditions. It is the max backpressure you can tolerate for a given Pc.
You cannot separate in the nozzle and still use F = mVe + (Pe - Pamb)Ae to model thrust, even for a negative (Pe-Pamb)Ae term. Once separation happens, Ve falls quite sharply. I don't know about the models you are using, but a lot of the ones I have seen over the years assume no separation, and get the wrong answer (by far) when Pamb/Pc gets too large.
Usually in a launch vehicle, you are most pressed for thrust right at liftoff when the vehicle is heaviest. So you expand to sea level pressure, zeroing the (Pe - Pamb)Ae term, and take off on the mVe term as the min acceptable value. Thrust only rises as you climb, because the (Pe-Pamb)Ae term is always positive. It just doesn't rise to theoretical expansion values.
If you design for expansion at some altitude for the same m and a higher Ve, the mVe gain is offset by the (Pe-Pamb)Ae loss, and you get more limited in achievable takeoff thrust. But you get better thrust as you climb, and on the average, a higher Isp.
In the limit, you design a vacuum nozzle expansion, which gets you much higher Isp out in vacuo, but suffers from a very negative (Pe-Pamb)Ae term throughout most of the climb, and very probably is fully separated at sea level, for no usable thrust at all.
Free-expansion designs like the aerospike improve this a bit, by avoiding the separation issue. But at sea level, the expansion achieved is quite limited, and out in space, the theoretical benefit is killed by so many of the exiting streamlines being essentially sideways, not axial. These free-expansion nozzles do a better job (if you can actually build a survivable version, a big "if"), but only by a single handful of %.
The theoretical benefit is a lot larger than the real-world achievable benefit. Plus you have to have a design that can really be built, and it has to survive incredible heating. The driving temperature difference is pretty near chamber temperature minus hardware temperature, all the way to the exit plane, because viscous dissipation forces the gas to have essentially the total temperature as the turbulent recovery temperature in the thermal boundary layer.
Nozzles are a bitch, ain't they?
GW
Last edited by GW Johnson (2018-03-03 18:52:33)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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This page gives a similar high value for the sea level ISP at 1000 psi, 68 bar, hydrolox combustion chamber pressure:
http://www.braeunig.us/space/propel.htm#liquid
It’s given as 381 s. So for a 110+ bar combustion chamber pressure the optimal sea level ISP very well could be in the range of 388 s.
Bob Clark
Old Space rule of acquisition (with a nod to Star Trek - the Next Generation):
“Anything worth doing is worth doing for a billion dollars.”
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Yep! My numbers certainly indicate that could be feasible, especially if the turbopump bleed faction is under 2%.
GW
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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