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20

Direct measurement is difficult; I've seen some optical methods used but can't put a hand on them at the moment. Here are some calculated inner and outer wall temperatures for the Space Shuttle Main Engine, a regeneratively-cooled booster engine. The X axis is axial distance from the throat. I am pleased to see that both metric and English units are provided....


11

Partial answer: This engine from the 1970s vintage Viking Lander is a liquid engine featuring one combustion chamber and many nozzles. (you can ignore the red arrow, it's from another question). The reason for this design was to prevent exhaust plume erosion of the Martian surface below the lander, to prevent degradation of the science results. Source ...


10

This would not be useful in general. Thermoelectric converters don't convert heat into electrical power, they generate electrical power from the flow of heat across them. You still need to cool the cold side, or the thermoelectric junctions will just burn up. The low efficiency of thermoelectric conversion means you're only removing a small fraction of the ...


8

It's been tried at least once at the research level, as the paper Flight Research of an Aerospike Nozzle Using High Power Solid Rockets details. A comparison was made between conventional and aerospike nozzles on a small solid fueled rocket. The rocket with the conventional nozzle performed better; it had less base drag and better performance. Even though ...


6

Short answer is mixing aerospike and solid fuel is probably not particularly useful The possible advantage of the mass and complexity of an aerospike is efficient operation from sea level to vacuum, useful in a hyperthetical single stage to orbit or space plane design. It is also normally assumed the complexity/cost is recovered by making them re-usable. ...


6

It's not quite a misnomer. Sea level nozzles aren't optimized for sea level, they are designed to be operable at sea level. You can see the "sea level" Raptor for instance produce Mach diamonds due to the overexpanded exhaust being compressed by the surrounding atmosphere. These go away as the vehicle approaches the altitude the nozzle was ...


5

You are omitting an important part of the force exerted by a rocket engine. A better expression is $$F = \dot m v_e + (P_e-P_a)A_e$$ In this expression, $F$ is the force exerted by the engine on the rocket body, $\dot m$ is the mass flow rate of exhaust exiting the engine, $v_e$ is the velocity of the exhaust gas at the exit plane, $P_e$ is the pressure of ...


4

Partial answer to get the ball rolling: The RL-10B-2 and RL-10C-2-1 variants of the venerable RL10 LH2/LO2 upper stage engine feature an expandable nozzle with a 280:11 area ratio and an amazing 465.5 Isp. Aerospaceguide.net RL10 article Image source: Aerojet Rocketdyne Image source: Impact of dynamics on the design of the RL10B-2 extendible carbon-carbon ...


3

A thruster is overexpanded if the nozzle exhaust pressure is less than ambient pressure, ambient if the nozzle exhaust pressure equals ambient pressure, or underexpanded if the nozzle exhaust pressure is greater than ambient pressure. Since ambient pressure is essentially zero in vacuum, any thruster operating in vacuum is by definition an underexpanded ...


3

The answer is much simply presented in the book by John D Anderson - Modern Compressible Flow with historical perspectives. Refer Chapter 5. \begin{equation} \rho = \mbox{density} \end{equation} a = speed of sound, Ma = Mach number, u = speed of fluid, A = area Area velocity relationship can be deduced from the continuity relationship - \begin{equation} \...


3

I would note that the RD-170 and RD-180 designs, while they appear to have two nozzles and two combustion chambers in the assembly, are said to perform as one because there is a pipe from one chamber to the next. I was fascinated to learn that Soviet engineers found they could stabilize the pressure among two or more chambers by doing this. This is the ...


3

One certainly doesn't want a converging nozzle because the flow is already supersonic.  None have made use of converging or converging-diverging nozzles, because the exhaust is typically flowing at supersonic velocities and thus could be choked through the converging cross-section. This would result in a loss of energy that would decrease the overall ...


2

Probably units and the format of eq (7) are the problem. After looking at the referenced website by Nakka, I used the questions information given to get $\dot m= 1.187 kg/s$ (using a rounded off r=12mm/s= .012m/s). Also calculated throat pressure and temperature of 3421000 Pa and 1616 K. Equation (7) should have parentheses around the $ w_t/P_t$,because the ...


2

Just build for the structural needs of your Mars vehicle, the atmosphere there is thin enough that none of the standard Vacuum nozzles will be overexpanded, and for a rocket operating at the surface, the mechanical size limits will be much more stringent. If anyone want to provide a more comprehensive answer, please do so. The true answer is a ridiculously ...


2

The equation shows that the cross-sectional area of the nozzle depends on the local pressure $P$ and values that are constant. So, he expects you to differentiate with respect to $P$, set the result to zero and solve for the value of $P$. Sounds like a fun project. I would let $x=P/P_c$ and take derivative wrt x. Some books go through equations with Mach ...


2

Surely this manuscript on gunpowder-based fireworks rockets by Conrad Haas (1509–1576) qualifies? Or at the very least the followup work on multistage rockets by Johann Schmidlap who published "Künstliche und rechtschaffene Fewrwerck zum Schimpff,” firstly printed in Nuremberg in 1561? That diagram clearly shows a divergent nozzle on a gunpowder rocket....


1

It's not very scientifical, but for candy fuel engines I built when I was younger, I used simple formula to compute area of the nozzle (An) from area of engine (internal diameter) (Ae): An = Ae / K or for radiuses: Rn = sqrt(Re^2 / K) or for diameters: Dn = 2 * sqrt((De/2)^2 / K) for candy fuels, K of around 100 worked for me. So for example if you have ...


1

To have something actually posted in answer form The principle governing the shape of rocket nozzles is in its most reduced form the following: A narrowing passage accelerates subsonic gasses, and decelerates supersonic gasses. A widening passage decelerates subsonic gasses, and accelerates supersonic gasses. It follows that we want the nozzle to become ...


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