Calling all Engineers

[Chris LaPanse]

So basically that idea would mean you fill the tank partially of water and heat it till its all vapor? Then release it throught the valve and nozzle? Wouldnt that limit the amount of vapor you could produce? If you have a full tank of water and transform that all to steam you could almost double the amount of steam. If you only partially fill the tank you would only get a fraction of steam.

That’s exactly what I mean. You could get it substantially hotter in the chamber this way, which would help bring that exit temp up to keep the steam from condensing. In addition, for a given chamber pressure and nozzle area expansion ratio, the exit mach is constant, which means that the exit velocity (and thus the ISP) is substantially improved by the increase in chamber temperature.

As I said above (and as you said as well), you can’t hold nearly as much propellant this way, since as you said, if you filled the tank all the way to the top, you could get a lot more steam. As I said though, I don’t see any way to do that without having much too cold of a temperature in the nozzle (since if you raised the tank temperature, the pressure would go up as well due to the water vapor pressure increase with temperature).

[Chris LaPanse]

What equations are you using for those numbers? I cant even start to understand the dynamics books I looked at.

Well the equations are fairly complicated, so the easy way is to use tables (which is what I did). However, I can give you the equations if you want. Have you had any fluid mechanics by any chance, especially dealing with compressible or high speed flows (I’m guessing not)? The equations do require a bit of background, and if you haven’t had any, I can try to type out an explanation (as best I can) in addition to the equations…

[Kyle Parsons]

No dynamics yet, only in my first year. If you could just copy over the equations that would be fine. The only problem with trying to make steam in the upper conatiner is now we have to find a new way of pressurizing the tank. We were going to use a water pump so little to no air would be used. Now that half the tank is going to be empty before heating. How can we pressurize it? If we use air then were going to have to take in consideration the volume of air that we are going to have to put in. Then when we open the valve some of the thrust will come from the vapor being pushed out by the air which is inefficient.

[Chris LaPanse]

Why would you need to pressurize the tank? When you heat the tank, it will pressurize itself.

(By the way, just out of curiosity, which school are you going to?)

[Chris LaPanse]

OK, here are the equations, with somewhat of an explanation. For a nozzle flow, the key defining factor is known as choked flow. When you have choked flow through a nozzle, the flow in the nozzle throat is at mach 1, and the mass flow through the nozzle is at its maximum. As a result of this, some parameters show up in the equations with a star after them. Star parameters are conditions at the throat of the nozzle (for example A* is the throat area of the nozzle). Parameters with no subscript or superscript are local parameters, and can vary depending on location in the nozzle, and parameters with a subscripted zero on them (or, if I’m writing just on the forum here, with a full size zero after them) are what are known as stagnation values. They are the values which the flow would have if you slowed it down to zero speed with no losses. In an ideal nozzle, they are also basically equal to the chamber conditions (so, for a nozzle flow, P0 is chamber pressure, T0 is chamber temperature, etc). M is local mach number (obviously), and finally, but certainly not least, is gamma. Gamma is the ratio of specific heats of a gas, but that doesn’t tell you a whole lot about what it actually means. Basically, gamma tells you the way a gas behaves when compressed or expanded (which is obviously happening in a nozzle). It tells you how much the gas heats up when the pressure is increased compared to how much it increases in density for example. In addition, because of some equations that I don’t want to get into right now, it tells you things like how fast pressure waves propagate through the gas. For air, gamma is usually considered to be 1.4 (although it can vary a bit at high temperature), and for water vapor, gamma is around 1.33. You can find a table of values for various gases here: http://www.kayelaby.npl.co.uk/general_physics/2_3/2_3_6.html

When using these equations, probably the best place to start is to chose a set of chamber conditions (temperature and pressure), as well as an exit pressure. For most solid rocket motors, the exit pressure is slightly above the ambient pressure, but as far as the equations are concerned, the only real restriction is that Pexit must be less than 1/2 of P0. You then plug these into the pressure equation and find out what your exit mach number is. Once you have your exit mach number, you can plug that into the area ratio and temperature ratio equations to find exit area and temperature. Once you have the exit temperature, you can calculate the speed of sound in the gas at the exit, and then multiply that by the exit mach number to get the exit velocity.

Oh, and remember this: you absolutely MUST use absolute temperatures or it will not work. T can be in Kelvin or Rankine, but not in C or F.

[Kyle Parsons]

How could we heat water hot enough to create that much pressure? Wouldnt those temperatures be extremely high? Which would then limit valves we could use and even how to heat it to such a high temp?

[Chris LaPanse]

You can figure out the appropriate temperature and pressure fairly easily from the phase diagram of water. The numbers I used before (1000 PSI at 550F) are actually attainable using the heating-only method. Also, given my calculations, you’ll likely need to get substantially hotter than that (550F) in order to have an acceptable exhaust temperature. I’d guess you’d need a chamber temp on the order of 1300-1500F to get an acceptable exhaust temperature with a thousand PSI in the chamber. Lower chamber pressure would require less temperature, but I think that’ll be the real concern as far as temperature goes, not the pressurization (since, as I indicated earlier, you can achieve tens of thousands of PSI just by heating water to around 800F).

Oh, and the reason I asked which school you were going to was because if you’re at CU, then I could meet up with you in person to discuss this sometime. Otherwise, you can disregard that question…

[Bruce R. Schaefer]

Sorry, Shredder, just an initial glance at your project. Mean is not in my nature. You guys are really making my day! However, Chris is still right in everything he’s said. Gas out of a nozzle cannot change. HOWEVER, how that Mach 1 gas escapes can. Think about it.

[Kyle Parsons]

Alright that sounds good. Well start working on numbers once I get back from spring break. Chris I go to Mesa State in Grand Junction, and you have more then helped me, pretty much saved your asses. Ill post the progress of the project and any more questions that I come upon.

Thanks Chris

[Kyle Parsons]

Anyone know a way that we could heat the tank? To temperatures of about 700 degrees? Heater blankets, even a burner.

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