Furnace temperature and pressure math

The data used was collected in version 0.2.2800. It was obtained with regular furnaces only, the advanced furnace is untested. If there is any difference between them, it would probably be the internal volume, the regular furnace holds 1000 L.

Furnace behaviour

• Only the gas inside the furnace have temperature, the furnace itself does not and absorbs no heat
• Combustion will consume 95% of the limiting ingredient, O2 or H2 (if there is 10 mol O2, and excess H2, 0.5 mol O2 will remain afterwards)
• For a combustion to occur, there must be at least 5% of either O2 or H2
• Reaction formula: 1 O2 + 2 H2 -> 6 CO2 + 3 X + 595kJ
• No side reactions with other gases have been observed so far
• The inlet pipe will only allow gas to enter the furnace, it will only do so if the pressure in the pipe is higher than the pressure inside the furnace.
• The outlet pipe will allow gas to pass both ways, the direction depends on the pressure in the pipe and in the furnace. So it can be used as an alternative inlet point.

Using perfect 2:1 fuel

Temperature peak

• T(after) = (T(before) * 61.9 + 0.95 * 595k) / (243.6 * 0.95 + 61.9 * 0.05)
  • Temperature in Kelvin (Celsius + 273)
  • 61.9 = heat capacity before combustion (based on reaction formula, so 3 moles total) = sum(specific heat * moles of each gas before) = 21.1 + 2*20.4
  • 243.6 = heat capcity for gas after combustion = sum(specific heat * moles of each gas after) = 0.05*(21.1 + 2*20.4) + 0.95*(6*28.2 + 3*24.8)
  • 0.95 and 0.05 refers to the 95% combustion efficiency
• The number of moles combusted doesn't matter under perfect conditions, the temperature increase is the same since the reagent/product ratio determines this outcome. The number of moles will however effect how quickly the gas cools.

Pressure peak

• P = nRT/V
  • n = total moles
  • R = 8314
  • V = 1000
• P (before) = n(before) * 8314 * T(before) / 1000
• P (after) = n(before) * (0.05*1 + 0.05*2 + 0.95*6 + 0.95*3) / (1 + 2) * 8314 * T(after) / 1000

Using diluted fuel

Unreactive gases can be added before the ignition to increase pressure and decrease temperature. An excess of either O2 or H2 also counts as unreactive. The outcome can be calculated like this.

Temperature peak

1. O2 moles reacted = min(moles O2, moles H2 * 0.5) * 0.95
2. released energy = O2 moles reacted * 595k
3. heat capacity (before) = sum(specific heat * moles of each gas (before))
4. heat capacity (after) = heat capacity (before) + O2 moles reacted * 181.7†
5. thermal energy (before) = temp (before) * heat capacity (before)
6. thermal energy (after) = thermal energy (before) + released energy
7. temperature (after) = thermal energy (after) / heat capacity (after)

† 181.7 comes from 243.6 - 61.9 (the change in the heat capacity for the gas before and after combustion, see above)

Pressure peak

1. total moles (before) = pressure(Pa) * 1000 / (8314 * Temp (before)
2. total moles (after) = total moles (before) + O2 moles reacted * 6†
3. Pressure (after) = total moles (after) * 8314 * Temperature (after) / 1000

†6 comes from 9 - 3, combustion consumes 3 moles and produces 9 moles

Using Ice(Oxite) and Ice(Volatiles)

There is a minor difference between which ice is added first. One can also observe a fluctuation in the combustion efficiency compared to when a furnace is fueled with gas. The end result also matters a little bit on how fast the ignition button is pressed when the first ice type is added while doing larger batches.

small batch, oxite first

• Adding 1 oxite + 1 volatile, in that order
  • Temperature: 2222K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 1 oxite + 2 volatiles, in that order
  • Temperature: 2514K, Pressure: 4.13MPa, moles of O2/H2 combusted: 22/43, Combustion ratio (H2): 98%

small batch, volatiles first

• Adding 1 volatile + 1 oxite, in that order
  • Temperature: 2224K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 2 volatiles + 1 oxite, in that order
  • Temperature: 2432K, Pressure: 3.93MPa, moles of O2/H2 combusted: 21/42, Combustion ratio (H2): 95%

large batch, oxite first

• Adding 5 oxite + 10 volatiles, in that order
  • Temperature: 2463K, Pressure: 18.76MPa, moles of O2/H2 combusted: 96/190, Combustion ratio (H2): 86%
• Adding 8 oxite + 16 volatiles, in that order
  • Temperature: 2537K, Pressure: 33.28MPa, moles of O2/H2 combusted: 172/344, Combustion ratio (H2): 98%

The difference in combustion efficiency is a mystery. Fuel temperature doesn't seem to matter (seen by furnace tests with 2:1 gas on both Mars and Europa). One possibility is that this deviation is a result of multiple consecutive ignitions. Whatever the reason, using ice in a furnace creates some unpredictability.

Furnace cooling rate

unknown

Observations

• the rate of cooling is temperature dependent, hotter cools faster (furnace temp - surrounding temp? how do vaccum behave?)
• the rate of cooling is time dependent (game tick speed is once per 0.5 seconds)
• the rate of cooling is mol dependent (small amounts cool faster, appears to be a linear correlation)
• adding ores decreases the temperature (do melting cost energy? or is this just from heating the trapped gases inside the ore?)

Possible experimental setup to measure dT/dt

• Hold a tablet with an atmos cartridge in the right hand (so it can be read when the game is paused). Aim the tablet against the furnace and pause with ESC, double tap ESC to move the game forward one tick, record the temperatures.
• Remember to record the total amount of moles as well

Resetting the furnace

Since only gas have temperature, evacuating all gas means resetting the temperature

Calculating how to reach a desired Temperature and Pressure on ignition

To freely control the temperature and pressure, the fuel must be diluted with a non-combustable gas. This can be added either before or after ignition, doing so before ignition makes it alot easier to predict, since doing so after ignition is more of an art than a science. The method prefered here is to add the non-combustable gas before ignition. It is possible to force gas into the furnace via the exhaust pipe too, so it's not necessary to dilute the fuel inside the fuelpipes to do this.

There are only 4 variables required for this calculation.

1. Intial fuel mix temperature (furnace temperature before ignition)
2. Desired temperature on ignition (you choose)
3. Desired pressure on ignition (you choose)
4. The specific heat value of the gas used to dilute the fuel (if a mix of gases is used, the specific heat to use is the average specific heat per mol, example calculation below)

The equations will give these results

1. The ratio(fuel) in the fuel-dilutant mix. (0.75 means 75% perfect 1:2 fuel mols (O2 and H2 added together)†, the other 25% will be dilutant gas mols, making it a 1:2:1 mix of O2:H2:dilutant)
2. The pressure of the fuel mix inside the furnace before ignition

†It's important to separate out the fuel part like this to allow an excess of either O2 or H2 to be the dilutant gas if so desired

Diluting the fuel correctly isn't hard, but if there are issues one can easily double check if the mix is correct by using the tablet and looking at the mol% values for the fuel mix. The fuel ratio calculated with the big equation below uses the sum of the moles in the fuel, to get the individual ratios for O2 and H2, they must calculated separately.

Calculating the fuel ratio

• ratio(fuel) = n(fuel)/(n(fuel)+n(dilutant)) = s*(T(after) - T(before)) / ( T(before)*(61.9/3-s) + (0.95*595000/3) - T(after)*(61.9-s) - T(after)*(0.95*181.7/3) )
  • s = specific heat of diluting gas
    • if the dilutant is a mix of gases, calculate the average specific heat in the mix per mol
    • example: 8 mol N2 and 17 mol CO2 as dilutant -> specific heat = (8*20.6 + 17*28.2) / (8+17) = 25.77
  • n(fuel) = total mols of fuel = n(O2)+n(H2) together (always in the perfect 1:2 ratio, if either O2 or H2 are in excess the extra amount is considered a dilutant)
  • n(dilutant) = total mols of non-combusting gas (this can be an excess of O2 or H2 if that is used as dilutant)
  • ratio(fuel), 1 = 100% fuel = 33.3% O2 and 66.7% H2, no dilutant present

Diluting the fuel

• ratio(O2) = ratio(fuel)/3
  • The desired O2 ratio, use this one when there is an excess of H2
• ratio(H2) = ratio(fuel)*2/3
  • The desired H2 ratio, use this one when there is an excess of O2

Calculating the pressure before ignition

• P(before) = P(after)*R*T(before) / ( R*T(after) * (1 + ratio(fuel)*2*0.95) )
  • r(fuel) is the result from the temperature calculation above
  • R = 8314
  • P(after) = desired value, in Pa
  • T(before) = temperature of fuel mix in the furnace before ignition
  • T(after) = the chosen value used in the temperature calculation above

Mixing fuel inside the furnace

• Fuel and dilutant must have the same temperature (this is because pressure is used as an indirect way to measure moles via PV=nRT, if the temperature is different, more pressure no longer means more moles)
• First add fuel via the fuel pipe into the furnace
  • Fuel pressure in furnace = ratio(fuel) * P(before)
• Then add the dilutant via the exhaust pipe until the pressure inside the furnace reaches P(before) (if the fuel pipe is used, flush the remaining fuel before adding the dilutant)

Example calculation

It's a warm and sunny day on Europa and a stationeer wants to make some invar. The desired temperature and pressure will be chosen as be the upper limit for invar, so 1500K and 20MPa. Adding ore to the furnace will reduce its temperature and increase the amount of gas (and pressure) inside of it, but the stationeer is pretty sure that making just 100g of invar should be doable. The furnace is exposed to the atmosphere and will be loosing temperature and pressure fairly fast which could be an issue, but making the alloy should be quick enough. The dilutant gas will be pure O2 from the atmosphere, which has a specific heat value of 21.1. The starting temperature of the fuel and the atmosphere are both at -140°C.

• ratio(fuel) = s*(T(after) - T(before)) / ( T(before)*(61.9/3-s) + (0.95*595000/3) - T(after)*(61.9-s) - T(after)*(0.95*181.7/3) )
  • s = specific heat of the dilutant = 21.1
  • T(after) = 1500K (this is the chosen value)
  • T(before) = -140C = 133K (temperature inside the furnace before ignition)
• ratio(fuel) = 0.281

Since O2 is also the dilutant here, the ratio of H2 will be the limiting value for the fuel, knowing this value will help when diluting it

ratio(H2) = 0.281 * 2/3 = 0.187

The fuel mix should have 18.7% moles of H2, the rest of it will be O2

The necessary pressure of the pre-ignition fuel mix inside the furnace will be

• P(before) = P(after)*R*T(before) / ( R*T(after) * (1 + ratio(fuel)*2*0.95) )
  • ratio(fuel) = 0.281
  • P(after) = 20MPa (this is the chosen value)
  • T(before) = -140C = 133K
  • T(after) = 1500K (this is the chosen value used in the temperature calculation)
• P(before) = 1156.5kPa

The furnace will first be fed 0.281 * 1156.5kPa = 325kPa of fuel. Then pure O2 is added via the exhaust pipe until the total pressure reaches 1.16MPa. Inside the furnace is 19% H2 and 81% O2. On ignition this will produce the desired 1500K and 20MPa.

Making 100g of invar this way is possible, but the ores chilling effect on the temperature and the increase in pressure is definately noticeable. One has to wait for a few seconds to let the pressure drop down below 20MPa after adding the ore, when this happens the temperature is still a bit over 1200K, leaving a big enough time window to easily get the ingot out. Choosing less than 20MPa as the desired ignition pressure might have been better, but the tradeoff is that the furnace cools faster.

Experiment used to determine the amount of released energy from combustion (so it can be verified)

1. Place a frame, build a furnace partially inside the frame, complete the frame. The furnace is now perfectly insulated and will no longer loose temperature (unless ore is added) nor explode from high pressure
2. Add fuel (2:1 not required) via a pipe, use over 1000 mol of O2, remove the pipe attached to the furnace
3. Record all mol amounts and temp with a tablet (atmos cartridge), convert temp to K (add +273)
4. Ignite furnace, record all mol amounts and temp with tablet, convert temp to K
5. Calculate moles of combusted O2 (= moles before - moles after)
6. Calculate the Thermal energy in the gas, before and after (Thermal energy = Temp * sum(mol of each gas * specific heat)
7. Calculate energy released per mol of combusted O2 (= TE.after - TE.before) / moles of combusted O2)
8. Deconstruct the furnace completely to disarm it safely, or connect a single pipe so it can burst and act as a vent
9. Alternatively: A circuit can probably also be used to capture the temperature and pressure at the point of ignition