Molten Salt Steam Engine

[intrepidpursuit]

I've been thinking about the possibility of a new rocket engine design that uses molten salt to heat water into steam in a de Laval nozzle.

Water expands at a ratio of 1:1600 plus when it is converted to steam. From what I understand, typical steam rocket engines store the heat in pressurized water and then release the water. Some of that water converting to steam as it is released is what provides thrust. The problem with that is water is almost uncompressable and can't store enough heat by itself to convert all the mass to steam. Molten Salt has around 19x the heat capacity of water.

So, if you treat this like a bi-propellant engine and have a tank of almost boiling water and a tank of molten salt heated right before launch to about 1000c. Then feed a small flow of molten salt into the chamber of the nozzle and spray water at it at a 19:1 ratio. The molten salt would heat the water almost immediately into steam, producing an incredible amount of pressure and converting nearly all the water mass into steam. This should be able to surpass the chamber pressure of a Merlin engine. In a fine tuned engine, the water should stay supercritical in the reaction chamber and actually expand a little more as the temperature and pressure reduce in the bell.

These temperatures are within the limits of stainless steel, so a vacuum insulated molten salt tank within a larger water tank should be viable. The water tank will have very little pressure and no extreme temperatures. It could almost be made of plastic (though probably not). The temperature in the reaction chamber would not be extreme to the levels of combustion engines either, so pressure tubes could feed directly from the chamber to the water and salt tanks to provide back pressure, with valves on these to control throttle and mixture.

I am an electrical acoustical engineer by trade, so I couldn't be less qualified to design something like this. But from the math I know how to do, this seems like a decent little engine. It may be buildable as a hobby project since it does not require exotic materials or cryogenics. It would be a great headline project because you could heat the salt with solar energy and call it "the world's first solar powered rocket". There is a lot of math here that I haven't wrapped my head around yet that would determine the actual performance of this thing, but I can determine that as I go by learning the math and by trial and error. Or if anyone thinks this might be fun and wants to apply their expertise, I'd be grateful.

This also may not be the correct section, or even the correct forum for this. So please correct and forgive me. I'm to the point where I'm going to start making spreadsheets and 3D models, so I thought I'd share. Let me know what you think.

[speedevil]

I've been thinking about the possibility of a new rocket engine design that uses molten salt to heat water into steam in a de Laval nozzle.

Water expands at a ratio of 1:1600 plus when it is converted to steam. From what I understand, typical steam rocket engines store the heat in pressurized water and then release the water. Some of that water converting to steam as it is released is what provides thrust. The problem with that is water is almost uncompressable and can't store enough heat by itself to convert all the mass to steam. Molten Salt has around 19x the heat capacity of water.

Molten salt has - as I understand it - around a third of the heat capacity of water per C, and a couple of hundred joules per gram or so heat of fusion.
Neglecting everything else, cooling from 1000C gives you 200kJ/kg from fusion, and 2000kJ/kg or so from the cooling.
Call it 2.5MJ/kg, which coincidentally is almost precisely enough to boil an equal weight of water.

And is compared to the 15MJ/kg or so which combustion achieves.
In addition, water at 1000C will quite enthusiastically become steam if you let it go.

There is also a reason nobody uses steam rockets, they have simply terrible performance and are very heavy.

[johnfwhitesell]

I'm generally a nuclear skeptic but if your goal is to generate a bunch of heat, it sounds like a job for nuclear fission.

[intrepidpursuit]

I've been thinking about the possibility of a new rocket engine design that uses molten salt to heat water into steam in a de Laval nozzle.

Water expands at a ratio of 1:1600 plus when it is converted to steam. From what I understand, typical steam rocket engines store the heat in pressurized water and then release the water. Some of that water converting to steam as it is released is what provides thrust. The problem with that is water is almost uncompressable and can't store enough heat by itself to convert all the mass to steam. Molten Salt has around 19x the heat capacity of water.

Molten salt has - as I understand it - around a third of the heat capacity of water per C, and a couple of hundred joules per gram or so heat of fusion.
Neglecting everything else, cooling from 1000C gives you 200kJ/kg from fusion, and 2000kJ/kg or so from the cooling.
Call it 2.5MJ/kg, which coincidentally is almost precisely enough to boil an equal weight of water.

And is compared to the 15MJ/kg or so which combustion achieves.
In addition, water at 1000C will quite enthusiastically become steam if you let it go.

There is also a reason nobody uses steam rockets, they have simply terrible performance and are very heavy.

The various units used to measure heat capacity and energy required to change states confuse me a bit and I'm not sure how to do math around them. The water in this case is already nearly boiling, so it only needs to go up by 10s of degrees to convert fully to steam. The salt is MUCH hotter than the water, so even if it cools at the same rate the water heats, it can convert many times the amount its mass in water before it cools too much. Controlling the flow rate of the salt to ensure minimal usage to get 99% vapor conversion on the water should give the best efficiency.

It is not true that no one uses steam rockets. I'm not trying to compete with electron. Steam engines are the most common rockets used around people in the hobbyist world. But every steam rocket I've seen uses only the water to store the heat. Using molten salt as a reactant should make a much more energetic reaction and I think it will increase the ISP enough to be worth it even with the extra mass of the salt. I just have to figure out the formula for how much salt I need for how much water and then what the thrust would be, from there I should be able to calculate ISP and put it into a rocket equation and figure out how much delta-v an engine like this could provide.

The idea is to make a unique hobby project that improves on something. Sugar rockets are fun but I have a hard time getting into just copying something that's been done. I like engineering problems. 

[intrepidpursuit]

I'm generally a nuclear skeptic but if your goal is to generate a bunch of heat, it sounds like a job for nuclear fission.

The nuclear powered steam "tea kettle" engines in the Expanse are what got me thinking about this. I don't have access to a nuclear reactor though, so I started looking for something that would store heat really well. Salt is where I landed.

[Gliderflyer]

The main drivers of specific impulse are the exhaust temperature and molecular weight; you want the exhaust to as light and hot as possible. While it may increase the temperature slightly, the salt is going to hurt your molecular weight. In the end, the Isp will probably be in the same ~50 second range as traditional steam rockets.

I haven't run the numbers yet, but the Atomic Rockets website and NASA SP-125 should have the equations you need. I would suggest sticking with a traditional steam rocket for simplicity, but it should be a fun hobby project in either case.

[hkultala]

The salt is MUCH hotter than the water, so even if it cools at the same rate the water heats, it can convert many times the amount its mass in water before it cools too much.

No, it cannot.

Vaporizing liquid water into steam takes a LOT of energy, 2.26 MJ/kg. This is as much as heating it about 1200  kelvins(or celcius).

If your molten salt is cooling from 900 to 100 celcius, for each kilogram of water you need about 4.5 kilograms of molten salt.

[intrepidpursuit]

The main drivers of specific impulse are the exhaust temperature and molecular weight; you want the exhaust to as light and hot as possible. While it may increase the temperature slightly, the salt is going to hurt your molecular weight. In the end, the Isp will probably be in the same ~50 second range as traditional steam rockets.

I haven't run the numbers yet, but the Atomic Rockets website and NASA SP-125 should have the equations you need. I would suggest sticking with a traditional steam rocket for simplicity, but it should be a fun hobby project in either case.

Why does temperature directly impact ISP? A rocket is all about throwing mass out the back to push the rocket forward. You run out of mass eventually so you want to throw that mass at the maximum possible exhaust velocity. That is why in a liquid engine the chamber pressure is tied directly to the ISP, because the higher the pressure the faster the mass is moving as it exits. Though temperature is important in combustion engines, in an ION thruster the temperature of the reaction mass is irrelevant.

So what I am attempting to do is to significantly increase the expansion ratio of water by adding an additional heat source. In this case that heat source is adding weight without adding its own thrust, so it has to reduce the water flow by at least the rate of its own flow for the same amount of thrust. Based on its uses in solar plants and the additional energy that would be put into the rocket before launch, it seems like a small percentage of molten salt at high temperatures should add additional energy.

Any experimenting I do will have to keep a traditional steam rocket configuration as a control. I do need to figure out some of this math though before I go machining a stainless steel injector.

EDIT: As I research this there are some rules about hotter materials moving faster. The above should be taken as a question because I'm well aware that I don't understand big chunks of rocket science. The chemistry in particular.

[intrepidpursuit]

The salt is MUCH hotter than the water, so even if it cools at the same rate the water heats, it can convert many times the amount its mass in water before it cools too much.

No, it cannot.

Vaporizing liquid water into steam takes a LOT of energy, 2.26 MJ/kg. This is as much as heating it about 1200  kelvins(or celcius).

If your molten salt is cooling from 900 to 100 celcius, for each kilogram of water you need about 4.5 kilograms of molten salt.

But in this case most of that heating is already done. The water isn't starting at room temperature, it is on the edge of vaporization already. The salt is just super heating that steam for more complete expansion.

[TommiR]

Heating water from 273K to 373K needs only about 20% (419kJ/kg) of energy needed for vaporization - so basically only thing that matters is vaporization energy.

[intrepidpursuit]

Heating water from 273K to 373K needs only about 20% (419kJ/kg) of energy needed for vaporization - so basically only thing that matters is vaporization energy.

I see. The water actually cools a bit when some of the volume vaporizes because there is energy associated with the vaporization itself rather than just the temperature change. That explains some of the math I didn't understand. I'm sure someone told me this in high school.

Is there similar energy associated with the salt turning solid? Probably nowhere near as much if so.

[DistantTemple]

Heating water from 273K to 373K needs only about 20% (419kJ/kg) of energy needed for vaporization - so basically only thing that matters is vaporization energy.

I see. The water actually cools a bit when some of the volume vaporizes because there is energy associated with the vaporization itself rather than just the temperature change. That explains some of the math I didn't understand. I'm sure someone told me this in high school.

Is there similar energy associated with the salt turning solid? Probably nowhere near as much if so.

Homework help! https://www.enotes.com/homework-help/how-much-heat-necessary-melt-175-32-g-nacl-801-122485

How much heat is necessary to melt 175.32 g of NaCl at 801 degree Celsius? (heat of fusion NaCl=28.16 kJ/mol)  The answer is 84.5 kJ but I don't know how to find it.

My working "The latent heat of fusion of NaCl is given as 28.16 kJ/mol"

I will use 1000g as the mass of NaCl as its 1Kg (as ppl above are talking in Kg)

We can convert this mass in grams to mass in mol by dividing it by molecular weight of NaC, which we know to be 58.4428. (see link for detail)

1000/58.4428 = 17.11 mol

so to melt 1 Kg of NaCl (at constant temperature and pressure, i.e. not including energy for raising temperatue, just changing state) is 28.16 kJ/mol x 17.11 mol = 482 KJ

(And the same energy is given out/removed when/to solidify.)

Edit: However the salt will not be solidifying.... if you are spraying it into boiling water. I don't know what will happen, ... mmmm perhaps it will as it can't exactly dissolve in steam?  So thats another detail to clarify.

[john smith 19]

My working "The latent heat of fusion of NaCl is given as 28.16 kJ/mol"

I will use 1000g as the mass of NaCl as its 1Kg (as ppl above are talking in Kg)

We can convert this mass in grams to mass in mol by dividing it by molecular weight of NaC, which we know to be 58.4428. (see link for detail)

1000/58.4428 = 17.11 mol

so to melt 1 Kg of NaCl (at constant temperature and pressure, i.e. not including energy for raising temperatue, just changing state) is 28.16 kJ/mol x 17.11 mol = 482 KJ

(And the same energy is given out/removed when/to solidify.)

Edit: However the salt will not be solidifying.... if you are spraying it into boiling water. I don't know what will happen, ... mmmm perhaps it will as it can't exactly dissolve in steam?  So thats another detail to clarify.

Note that number 482KJ/Kg IE 0.482MJ/Kg
Versus 2.26MJ/Kg to turn 100c water into 100c steam.

water has a very high SHC and a pretty high Heat of solidification.

Incidentally most people would class this as a High School level Physic problem. 

[intrepidpursuit]

My working "The latent heat of fusion of NaCl is given as 28.16 kJ/mol"

I will use 1000g as the mass of NaCl as its 1Kg (as ppl above are talking in Kg)

We can convert this mass in grams to mass in mol by dividing it by molecular weight of NaC, which we know to be 58.4428. (see link for detail)

1000/58.4428 = 17.11 mol

so to melt 1 Kg of NaCl (at constant temperature and pressure, i.e. not including energy for raising temperatue, just changing state) is 28.16 kJ/mol x 17.11 mol = 482 KJ

(And the same energy is given out/removed when/to solidify.)

Edit: However the salt will not be solidifying.... if you are spraying it into boiling water. I don't know what will happen, ... mmmm perhaps it will as it can't exactly dissolve in steam?  So thats another detail to clarify.

Note that number 482KJ/Kg IE 0.482MJ/Kg
Versus 2.26MJ/Kg to turn 100c water into 100c steam.

water has a very high SHC and a pretty high Heat of solidification.

Incidentally most peopel would class this as a High School level Physic problem.

Yeah, I mentioned my own forgotten education above. Thanks for the help everyone!

[DistantTemple]

Don't be put off by the "High school physics problem" comment. There are rocket scientists here, but I bet there are plenty of others who need to revise specific heat etc, and others that never covered it! And some of the rocket scientist don't know chemicals manufacturing or life support design etc.... or Martian concrete etc. let alone growing plants in containers. And it is supposed to be inclusive to people learning!

[hkultala]

The salt is MUCH hotter than the water, so even if it cools at the same rate the water heats, it can convert many times the amount its mass in water before it cools too much.

No, it cannot.

Vaporizing liquid water into steam takes a LOT of energy, 2.26 MJ/kg. This is as much as heating it about 1200  kelvins(or celcius).

If your molten salt is cooling from 900 to 100 celcius, for each kilogram of water you need about 4.5 kilograms of molten salt.

But in this case most of that heating is already done. The water isn't starting at room temperature, it is on the edge of vaporization already. The salt is just super heating that steam for more complete expansion.

No, it's not.

The energy I was talking about is the vaporization energy. Not heating energy.

[Hominans Kosmos]

The main drivers of specific impulse are the exhaust temperature and molecular weight; you want the exhaust to as light and hot as possible. While it may increase the temperature slightly, the salt is going to hurt your molecular weight. In the end, the Isp will probably be in the same ~50 second range as traditional steam rockets.

I haven't run the numbers yet, but the Atomic Rockets website and NASA SP-125 should have the equations you need. I would suggest sticking with a traditional steam rocket for simplicity, but it should be a fun hobby project in either case.

Why does temperature directly impact ISP?

If you'll take a look at the equation 

Ve = sqrt( ((2 * k) / (k - 1)) * ((R' * Tc) / M) * ( 1 - (Pe/Pc)^((k-1)/k) ) )

you will find that exhaust velocity is proportional to: 

square root of absolute nozzle inlet temperature, 

while the effect of nozzle inlet to nozzle outlet pressure ratio on exhaust velocity is proportional to: 

square root of one minus (pressure ratio to the power of 0,248[1]).

What does this mean? 
sqrt(1-(1bar/10bar)^0.248)*constant=0.659*constant 
sqrt(1-(1bar/100bar)^0.248)*constant=0.825*constant 
or an exhaust velocity 1.25 times higher for ten times higher nozzle entrance pressure against 
sqrt(400Kelvin)*constant=20*constant 
sqrt(4000Kelvin)*constant=63.2*constant 
which gives you 3.16 times the exhaust velocity increase. 

Temperature directly impacts specific impulse because rocket nozzle exhaust velocity is more sensitive to nozzle inlet temperature than it is to nozzle inlet pressure. 

https://en.wikipedia.org/wiki/Rocket_engine_nozzle#One-dimensional_analysis_of_gas_flow_in_rocket_engine_nozzles 
https://en.wikipedia.org/wiki/Specific_impulse#Specific_impulse_as_a_speed_(effective_exhaust_velocity) 
[1]{(1.330-1)-1.330} https://en.wikipedia.org/wiki/Heat_capacity_ratio 

[ulm_atms]

Would it not be more efficient(simpler) just to construct a heat exchange and use the salt as a heat battery for the water instead of trying to inject the hot salt into the water stream before exit?  Depending on how much heat you can exchange, you can get that steam up to some pretty high temps and pressures before it goes out the nozzle.  This would keep your molecular weight lower buy not exhausting the salt too and would simplify the engine by not having to mess with any type of salt injection.

See attached.

[Hominans Kosmos]

Would it not be more efficient(simpler) just to construct a heat exchange and use the salt as a heat battery for the water instead of trying to inject the hot salt into the water stream before exit?  Depending on how much heat you can exchange, you can get that steam up to some pretty high temps and pressures before it goes out the nozzle.  This would keep your molecular weight lower buy not exhausting the salt too and would simplify the engine by not having to mess with any type of salt injection.

See attached.

This whole thread has been explaining how and why salt is an inefficient method for storing heat for a flying vehicle. I'm not sure about the numbers, but you might find yourself trading the low vapor pressure of molten salt holding the heat, against your propellant tank being a pressure vessel that can take more than 3.3 bar (48 psi) as it holds 410 Kelvin liquid.

0.6256 km/s

435 Kelvin + 6.48 bar water gets you up to 0.7752 km/s

Now if you're working down to a vacuum these temperatures start looking interesting Ve goes nearly double. The pressure+temperature pairs are eyeballed from a water phase diagram. 

No clue how fast your above boiling point pressurized water propellant tank freezes when you open the tap, tho.