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=== Introduction === | === Introduction === | ||
| − | This page is about | + | This page is about using math to predict how combustions inside furnaces behave. It's not about engineering or design. |
| − | The furnace is one of the most important objects in the entire game, but it | + | The furnace is one of the most important objects in the entire game, but it's also complicated and hard to use, especially when making alloys and super-alloys. As of writing, there are several loop holes that makes a furnace easier to control (insulating a furnace inside a fully welded frame, or keeping a furnace in a sealed room with vaccum, or surrounding a furnace with an atmosphere with the same temperature as the gas inside of the furnace; it's also possible to manipulate the Air Conditioner into superheating gas to avoid using fuel, which is aided by the fact that insulated pipes and tanks never loose temperature). Should the game suddenly patch any of these things, this page could be helpful, but right now there is abosolutely no need to know any of this. |
| − | There are two MIPS | + | There are two MIPS programs included (click the links to expand/collpase the code), that can do the math on this page inside the game. The first script predicts what temperature and pressure a furnace will reach when it's ignited, based on the gas currently inside of it. The second script is used to predict how much perfect fuel (33.3 oxygen and 66.7% volatiles) and how much other gas (not fuel) that needs to be combined in a furnace to reach a desired temperature and pressure on ignition (comment: Waspalloy is a tricky one however, since the gas mix calculated is too diluted to ignite, more bout that in the last section of this page). |
<div class="mw-collapsible mw-collapsed" data-expandtext="{{int:EXPAND - a MIPS script that predicts the ignition temperature and pressure of a furnace based on the gases inside of it}}" data-collapsetext="{{int:COLLAPSE - a MIPS script that predicts the ignition temperature and pressure of a furnace based on the gases inside of it}}"> | <div class="mw-collapsible mw-collapsed" data-expandtext="{{int:EXPAND - a MIPS script that predicts the ignition temperature and pressure of a furnace based on the gases inside of it}}" data-collapsetext="{{int:COLLAPSE - a MIPS script that predicts the ignition temperature and pressure of a furnace based on the gases inside of it}}"> | ||
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blt ratioOx 0.05 noCombustion | blt ratioOx 0.05 noCombustion | ||
blt ratioVol 0.05 noCombustion | blt ratioVol 0.05 noCombustion | ||
| − | |||
| − | |||
j displayResults | j displayResults | ||
noCombustion: | noCombustion: | ||
| − | |||
| − | |||
move temp r0 | move temp r0 | ||
move pres r1 | move pres r1 | ||
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<br> | <br> | ||
| − | <div class="mw-collapsible mw-collapsed" data-expandtext="{{int:EXPAND - a MIPS script that calculates how to mix fuel and diluting gas | + | <div class="mw-collapsible mw-collapsed" data-expandtext="{{int:EXPAND - a MIPS script that calculates how to mix fuel and a diluting gas to reach a desired temperature and pressure}}" data-collapsetext="{{int:COLLAPSE - a MIPS script that calculates how to mix fuel and a diluting gas to reach a desired temperature and pressure}}"> |
<pre> | <pre> | ||
| − | #A script for calculating how to dilute fuel.. | + | #A script for calculating how to dilute fuel inside a.. |
| − | #.. | + | #..furnace to reach a desired temperature and pressure |
| − | |||
| − | # This script requires perfect fuel (O2 + 2 H2) | + | # OBS! This script requires perfect fuel (O2 + 2 H2) |
# The diluting gas can be anything, even a mix | # The diluting gas can be anything, even a mix | ||
# Temperature of fuel and dilutant can be different | # Temperature of fuel and dilutant can be different | ||
| − | |||
| − | |||
#Inputs are desired temperature (K) and pressure (kPa) | #Inputs are desired temperature (K) and pressure (kPa) | ||
| − | #Outputs are the pressure of fuel (kPa) and | + | #Outputs are the pressure of fuel (kPa) and.. |
| − | #..total pressure (kPa) after adding | + | #..the total pressure (kPa) after adding dilutant |
alias inputTemp d0 #logic memory | alias inputTemp d0 #logic memory | ||
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alias dilutantSpecificHeat r13 | alias dilutantSpecificHeat r13 | ||
alias ratioFuel r14 | alias ratioFuel r14 | ||
| − | alias | + | alias pressureBefore r15 |
| − | |||
main: | main: | ||
yield | yield | ||
| − | |||
#calculate specific heat values | #calculate specific heat values | ||
div r0 61.9 3 | div r0 61.9 3 | ||
move fuelSpecificHeat r0 | move fuelSpecificHeat r0 | ||
| + | move r3 13 | ||
| + | move r4 5 | ||
jal specficHeatCalculation | jal specficHeatCalculation | ||
| + | |||
#calculate how to reach input values | #calculate how to reach input values | ||
| − | l r5 fuelAnalyzer Temperature | + | l r5 fuelAnalyzer Temperature |
l r6 inputTemp Setting | l r6 inputTemp Setting | ||
l r7 dilutantAnalyzer Temperature | l r7 dilutantAnalyzer Temperature | ||
move oldTmix r5 | move oldTmix r5 | ||
| − | |||
iterate: | iterate: | ||
jal fuelRatioCalculation | jal fuelRatioCalculation | ||
jal temperatureMixCalculation | jal temperatureMixCalculation | ||
| − | sub | + | sub r0 Tmix oldTmix |
| + | abs r0 r0 | ||
move oldTmix Tmix | move oldTmix Tmix | ||
| − | + | bgt r0 1 iterate | |
| + | blt ratioFuel 0.15 noCombustion | ||
| + | |||
#calculate total fuel+dilutant pressure | #calculate total fuel+dilutant pressure | ||
l r8 inputPres Setting | l r8 inputPres Setting | ||
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mul r1 r1 r6 | mul r1 r1 r6 | ||
mul r0 r8 Tmix | mul r0 r8 Tmix | ||
| − | div | + | div pressureBefore r0 r1 |
| + | |||
#calculate fuel pressure | #calculate fuel pressure | ||
| − | mul r0 r5 | + | mul r0 pressureBefore r5 |
mul r0 ratioFuel r0 | mul r0 ratioFuel r0 | ||
div r0 r0 Tmix | div r0 r0 Tmix | ||
| − | + | ||
| − | |||
| − | |||
| − | |||
| − | |||
#check for too high input temperature | #check for too high input temperature | ||
| − | + | bgt r0 pressureBefore noCombustion | |
| − | #display | + | |
| − | + | #display | |
| − | |||
s outputFuel Setting r0 | s outputFuel Setting r0 | ||
| − | s outputTotal Setting | + | s outputTotal Setting pressureBefore |
j main | j main | ||
| + | |||
noCombustion: | noCombustion: | ||
s outputFuel Setting -1 | s outputFuel Setting -1 | ||
s outputTotal Setting -1 | s outputTotal Setting -1 | ||
j main | j main | ||
| − | |||
| − | |||
| − | |||
fuelRatioCalculation: | fuelRatioCalculation: | ||
div r0 563452 3 | div r0 563452 3 | ||
sub r4 fuelSpecificHeat dilutantSpecificHeat | sub r4 fuelSpecificHeat dilutantSpecificHeat | ||
| − | mul r1 | + | mul r1 r5 r4 |
add r0 r0 r1 | add r0 r0 r1 | ||
mul r1 r6 r4 | mul r1 r6 r4 | ||
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mul r1 r6 r1 | mul r1 r6 r1 | ||
sub r0 r0 r1 | sub r0 r0 r1 | ||
| − | sub r1 r6 | + | sub r1 r6 r5 |
mul r1 r1 dilutantSpecificHeat | mul r1 r1 dilutantSpecificHeat | ||
div ratioFuel r1 r0 | div ratioFuel r1 r0 | ||
j ra | j ra | ||
| + | |||
temperatureMixCalculation: | temperatureMixCalculation: | ||
| − | sub r4 1 ratioFuel | + | sub r4 1 ratioFuel |
mul r0 dilutantSpecificHeat r4 | mul r0 dilutantSpecificHeat r4 | ||
mul r1 ratioFuel fuelSpecificHeat | mul r1 ratioFuel fuelSpecificHeat | ||
add r3 r0 r1 | add r3 r0 r1 | ||
mul r0 r7 r4 | mul r0 r7 r4 | ||
| − | mul r0 r0 dilutantSpecificHeat | + | mul r0 r0 dilutantSpecificHeat |
mul r1 r5 ratioFuel | mul r1 r5 ratioFuel | ||
mul r1 r1 fuelSpecificHeat | mul r1 r1 fuelSpecificHeat | ||
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div Tmix r0 r3 | div Tmix r0 r3 | ||
j ra | j ra | ||
| + | |||
specficHeatCalculation: | specficHeatCalculation: | ||
| − | l r5 | + | l r5 dr4 RatioOxygen |
| − | l r6 | + | l r6 dr4 RatioVolatiles |
| − | l r7 | + | l r7 dr4 RatioCarbonDioxide |
| − | l r8 | + | l r8 dr4 RatioPollutant |
| − | l r9 | + | l r9 dr4 RatioNitrogen |
| − | l r10 | + | l r10 dr4 RatioNitrousOxide |
| − | |||
mul r0 r5 21.1 | mul r0 r5 21.1 | ||
mul r1 r6 20.4 | mul r1 r6 20.4 | ||
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add r0 r0 r1 | add r0 r0 r1 | ||
mul r1 r10 23 | mul r1 r10 23 | ||
| − | add | + | add rr3 r0 r1 |
j ra | j ra | ||
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*Combustion reaction formula: 1 O2 + 2 H2 -> 6 CO2 + 3 X + 593 107.3684 J ''(this energy value is an approximation, see discussions for details)'' | *Combustion reaction formula: 1 O2 + 2 H2 -> 6 CO2 + 3 X + 593 107.3684 J ''(this energy value is an approximation, see discussions for details)'' | ||
*Each press of ignite adds 5 J of energy to the furnace (only the advanced furnace was tested) ''(see discussions)'' | *Each press of ignite adds 5 J of energy to the furnace (only the advanced furnace was tested) ''(see discussions)'' | ||
| − | *A furnace | + | *A furnace built in a sealed room with vacuum will not loose temperature (this is seen during the furnace tutorial), nor will a furnace built partially/completely inside a fully welded frame. |
*Ores placed in a furnace will release gases, this reduces the temperature and increases the mols of gas. | *Ores placed in a furnace will release gases, this reduces the temperature and increases the mols of gas. | ||
*Ingots placed in a furnace will reduce the temperature (~half compared to the ore, only copper tested) without releasing gas. | *Ingots placed in a furnace will reduce the temperature (~half compared to the ore, only copper tested) without releasing gas. | ||
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*The outlet pipe is the only place where gas can exit the furnace. It has a built in volume pump. | *The outlet pipe is the only place where gas can exit the furnace. It has a built in volume pump. | ||
*Unlike the regular furnace, the advanced one always have a volume of 1000 L, regardless of how many pipes are attached to it. This saves a little bit of fuel. | *Unlike the regular furnace, the advanced one always have a volume of 1000 L, regardless of how many pipes are attached to it. This saves a little bit of fuel. | ||
| + | |||
=== Known errors of the math formulas === | === Known errors of the math formulas === | ||
| − | The formulas were created by hand, no data mining or peeking into the game code. | + | The following formulas were created by hand, no data mining or peeking into the game code. They have a tiny unexplained error that can appear in the 6th digit and it's most noticeable at very low fuel pressures. |
| − | |||
| − | |||
=== Using perfect O2 + 2 H2 fuel === | === Using perfect O2 + 2 H2 fuel === | ||
| − | |||
'''Temperature peak''' | '''Temperature peak''' | ||
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**61.9 is the heat capacity for 1 mol O2 and 2 mol H2, the sum of their specific heat values, the mol amounts comes from the reaction formula | **61.9 is the heat capacity for 1 mol O2 and 2 mol H2, the sum of their specific heat values, the mol amounts comes from the reaction formula | ||
**234.515 is the heat capacity for the gas obtained when 1 mol O2 and 2 mol H2 combusts with 95% efficiency (243.6 * 0.95 + 61.9 * 0.05) | **234.515 is the heat capacity for the gas obtained when 1 mol O2 and 2 mol H2 combusts with 95% efficiency (243.6 * 0.95 + 61.9 * 0.05) | ||
| + | *The number of mol combusted doesn't actually matter for the temperature, it will always reach the same value. More fuel will however release more total energy which means it takes longer for the furnace to cool down. | ||
*The equation can be arrived at by using the released energy per mol and the specific heat per mol of the mixture before and after combustion, also account for the 95% combustion efficiency. | *The equation can be arrived at by using the released energy per mol and the specific heat per mol of the mixture before and after combustion, also account for the 95% combustion efficiency. | ||
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=== Using diluted fuel === | === 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. | |
'''Temperature peak''' | '''Temperature peak''' | ||
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**The equation comes from calculating the Thermal Energy (temperature*specific heat per mol) before combustion, add the released energy calculated from the ratio of O2, then divide with the ''specific heat per mol'' of the gas obtained after combustion, which is known thanks to the reaction formula, all of this becomes the temperature on ignition | **The equation comes from calculating the Thermal Energy (temperature*specific heat per mol) before combustion, add the released energy calculated from the ratio of O2, then divide with the ''specific heat per mol'' of the gas obtained after combustion, which is known thanks to the reaction formula, all of this becomes the temperature on ignition | ||
| − | same thing but | + | same thing but easier to read |
*T(after) = ( T(before) * specificHeat(before) + fuel * 563452 ) / ( specificHeat(before) + fuel * 172.615) | *T(after) = ( T(before) * specificHeat(before) + fuel * 563452 ) / ( specificHeat(before) + fuel * 172.615) | ||
**specificHeat(before) = RatioOxygen*21.1 + RatioVolatile*20.4 + RatioCarbonDioxide*28.2 + RatioPollutant*24.8 + RatioNitrogen*20.6 + RatioNitrousOxide*23 | **specificHeat(before) = RatioOxygen*21.1 + RatioVolatile*20.4 + RatioCarbonDioxide*28.2 + RatioPollutant*24.8 + RatioNitrogen*20.6 + RatioNitrousOxide*23 | ||
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*P(after) = P(before) * T(after) * ( 1 + 5.7*min(ratio(O2), ratio(H2)*0.5) ) / T(before) | *P(after) = P(before) * T(after) * ( 1 + 5.7*min(ratio(O2), ratio(H2)*0.5) ) / T(before) | ||
**this expression comes from two sets of PV=nRT, one after and one before combustion. The reaction formula say that for each mol consumed O2 we gain 6 mol gas (9-3), this creates a link between the equations, n(after) = n(before)*(1+min(ratio(O2), ratio(H2)*0.5)*6), then include the 0.95 efficiency as well | **this expression comes from two sets of PV=nRT, one after and one before combustion. The reaction formula say that for each mol consumed O2 we gain 6 mol gas (9-3), this creates a link between the equations, n(after) = n(before)*(1+min(ratio(O2), ratio(H2)*0.5)*6), then include the 0.95 efficiency as well | ||
| + | |||
=== Using Ice(Oxite) and Ice(Volatiles) === | === Using Ice(Oxite) and Ice(Volatiles) === | ||
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Observations | Observations | ||
| − | *the rate of cooling is temperature dependent, hotter cools faster | + | *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 time dependent (game tick speed is once per 0.5 seconds) | ||
*the rate of cooling is mol dependent (small amounts cool faster) | *the rate of cooling is mol dependent (small amounts cool faster) | ||
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*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. | *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 | *Remember to record the ''total amount of moles'' as well | ||
| + | |||
=== Calculating how to reach a desired Temperature and Pressure on ignition === | === Calculating how to reach a desired Temperature and Pressure on ignition === | ||
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†It's helpful to separate out the fuel part like this since everyone should be using pre-mixed fuel, it makes the diluting easier and has a lower risk to cause confusion when using either O2 or H2 to be the dilutant gas | †It's helpful to separate out the fuel part like this since everyone should be using pre-mixed fuel, it makes the diluting easier and has a lower risk to cause confusion when using either O2 or H2 to be the dilutant gas | ||
| − | To freely control the temperature and pressure, the fuel must be diluted with a non- | + | 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, doing so after ignition is more of an art than a science (it depends on how the furnace is built and how fast the operator can work). The method prefered here is to add the non-combustable gas before ignition. |
Diluting the fuel can be done in the furnace directly or in pipes outside of it. There are good and bad points with both ways. Diluting outside fits the advanced furnace best (the built-in volume pump can easily move all of the prepared gas inside), diluting inside fits the regular furnace best (the exhaust outlet can be used as an inlet but it's a little bit quirky, and diluting in pipes outside means not all of the prepared gas can be moved into the furnace (the pipe directly on the furnace inlet will hold on to some of the diluted fuel) so extra gas must always be prepared). | Diluting the fuel can be done in the furnace directly or in pipes outside of it. There are good and bad points with both ways. Diluting outside fits the advanced furnace best (the built-in volume pump can easily move all of the prepared gas inside), diluting inside fits the regular furnace best (the exhaust outlet can be used as an inlet but it's a little bit quirky, and diluting in pipes outside means not all of the prepared gas can be moved into the furnace (the pipe directly on the furnace inlet will hold on to some of the diluted fuel) so extra gas must always be prepared). | ||
| − | It is worth noting that for some temperatures and pressures suitable for advanced alloys, the calculation can suggest a fuel ratio below 0.15. This will not work however, since it means having less than 5% oxygen, that mix will not combust (unless the dilutant contains extra oxygen). This is a particular problem with | + | It is worth noting that for some temperatures and pressures suitable for advanced alloys, the calculation can suggest a fuel ratio below 0.15. This will not work however, since it means having less than 5% oxygen, that mix will not combust (unless the dilutant contains extra oxygen). This is a particular problem with Waspalloy (400-800K, 50+MPa), that can be solved by having oxygen in the diluting gas, or by igniting the furnace prematurely before all the dilutant has been added. |
| − | The dilution can | + | The dilution can be double checked by using the tablet and looking at the mol% values for the fuel mix. If the outlet on the regular furnace was used as an inlet, the first gas that entered there will have been mostly pushed back into the furnace, making the mol% values diffrent but the total number of mol are still the same. |
'''Calculating the fuel ratio''' | '''Calculating the fuel ratio''' | ||
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***example: 15% N2 and 85% CO2 as dilutant -> specific heat = 0.15*20.6 + 0.85*28.2 = 27.06 | ***example: 15% N2 and 85% CO2 as dilutant -> specific heat = 0.15*20.6 + 0.85*28.2 = 27.06 | ||
*This equation comes from the equation under ''Using diluted fuel'', it was arrived at by doing the following things | *This equation comes from the equation under ''Using diluted fuel'', it was arrived at by doing the following things | ||
| − | **ratio(fuel) was introduced (which is 3 times higher than min(ratio(O2),ratio(H2)*0.5), everyone should be using pre-mixed fuel so this should make things simpler, having 1 represent 100% fuel is also more | + | **ratio(fuel) was introduced (which is 3 times higher than min(ratio(O2),ratio(H2)*0.5), everyone should be using pre-mixed fuel so this should make things simpler, having 1 represent 100% fuel is also more intutive than having 0.333 mean 100% fuel |
**everything is calculated per 1 mol fuel here, the original one uses per 3 mol fuel (1 mol O2 + 2 mol H2), so several values must be divided by 3 | **everything is calculated per 1 mol fuel here, the original one uses per 3 mol fuel (1 mol O2 + 2 mol H2), so several values must be divided by 3 | ||
**the dilutant (even a mix) can be treated as a single gas, which turns ''sum(specific heat * mol of gas (before))'' into ''ratio(fuel)*(specific heat(O2)+2*specific heat(H2) )/3 + (1-ratio(fuel))*specific heat(dilutant)'' | **the dilutant (even a mix) can be treated as a single gas, which turns ''sum(specific heat * mol of gas (before))'' into ''ratio(fuel)*(specific heat(O2)+2*specific heat(H2) )/3 + (1-ratio(fuel))*specific heat(dilutant)'' | ||
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'''Diluting fuel''' | '''Diluting fuel''' | ||
| − | Mixing gas is temperature sensitive. This is because pressure is used as an indirect measure of the amount of mol (n=PV/(RT)) being | + | Mixing gas is temperature sensitive. This is because pressure is used as an indirect measure of the amount of mol (n=PV/(RT)) being transfered, and pressure is also dependent on temperature. It is however possible to get around this issue with a bit of math. |
'''A)''' When fuel and dilutant have the same temperature | '''A)''' When fuel and dilutant have the same temperature | ||
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**ratio(H2) = 0.28237 * 2/3 = 0.188 = 19% | **ratio(H2) = 0.28237 * 2/3 = 0.188 = 19% | ||
| − | This was tested in practice. After adding fuel and dilutant the game was saved, then the furnace was ignited. Adding the ores reduced the temperature and increased the pressure a bit, which pushed the pressure up above 20MPa and out of the needed range. After waiting for the pressure to drop back down, the temperature was still high enough to make the desired alloy with several seconds to spare. In hindsight, 20MPa was a bit too high and 1500K a bit too low, better values could | + | This was tested in practice. After adding fuel and dilutant the game was saved, then the furnace was ignited. Adding the ores reduced the temperature and increased the pressure a bit, which pushed the pressure up above 20MPa and out of the needed range. After waiting for the pressure to drop back down, the temperature was still high enough to make the desired alloy with several seconds to spare. In hindsight, 20MPa was a bit too high and 1500K a bit too low, better values could definately have been chosen. |
Reloading the save and placing the furnace inside a welded frame to insulate it (no loss of temperature or pressure) showed the following. The furnace reached 1477K and 19.90MPa after ignition. The fuel was added with a regulator (the furnace showed: 325kPa, 133K), the fuel mix was decent but not a perfect 1:2. Then the diluting O2 was added, it was slightly too cold (the furnace now showed: 1.16MPa, 130K), so a bit too much dilutant was added to the furnace (since cold gas has a lower pressure). The dilutant was inserted via the furnace outlet, checking the mol% with the tablet showed 3% H2 in the outlet pipe and 20% inside the furnace instead of 19% in both, the total number of H2 mol was unchanged. The temperature and pressure was really close to the calculated ones, even though the execution was a bit sloppy. The observed loss of temperature could be explained by using too much dilutant, using a lower starting temperature and a flawed fuel mix. The lower pressure is related to the temperature, going from 1500K to 1477K should mean -1.5% reduction in pressure, but the change was just -0.5%, an indication that too much dilutant had been added. | Reloading the save and placing the furnace inside a welded frame to insulate it (no loss of temperature or pressure) showed the following. The furnace reached 1477K and 19.90MPa after ignition. The fuel was added with a regulator (the furnace showed: 325kPa, 133K), the fuel mix was decent but not a perfect 1:2. Then the diluting O2 was added, it was slightly too cold (the furnace now showed: 1.16MPa, 130K), so a bit too much dilutant was added to the furnace (since cold gas has a lower pressure). The dilutant was inserted via the furnace outlet, checking the mol% with the tablet showed 3% H2 in the outlet pipe and 20% inside the furnace instead of 19% in both, the total number of H2 mol was unchanged. The temperature and pressure was really close to the calculated ones, even though the execution was a bit sloppy. The observed loss of temperature could be explained by using too much dilutant, using a lower starting temperature and a flawed fuel mix. The lower pressure is related to the temperature, going from 1500K to 1477K should mean -1.5% reduction in pressure, but the change was just -0.5%, an indication that too much dilutant had been added. | ||
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