A new calculation model for thermal management

[jamesruan]

The current calculation is some what unreal and cause many naughty problems such as https://github.com/FractalUK/KSPInterstellar/issues/60 .

Here I present a more realistic model for heat and radiation calculation.

The primary energy source (reactors) just produce energy. The core temperature of a reactor and it's power output is internal relative by an arbitrary function.

The use of it's output energy power is then divided into two part: the Power to do Work, and the Power to heat up the body.

A generator is able to convert the power into Mega-joules that can further be stored in batteries and Waste heat that heat up the body. A thermal power based engine is able to convert the power into Thermal Energy that can only be stored as waste heat or used immediately as driving energy.

When the waste heat accumulates that heat the radiator beyond its highest functional rate, The energy source must be shutdown or the vessel will eventually explode.

[jamesruan]

Above is the big picture of the model. And here comes the detail.

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Reactor

A reactor produce Thermal Power quantified by MW. A reactor has a core temperature related to it power output (Thermal Power). The relationship is calculated based on thermal conductance and thermal capacity.

Generator

A generator convert part of Thermal Power * time into electric energy stored in batteries, quantified by MegaJoules. 1MJ = 1MW * 1s A generator convert part of Thermal Power * time into waste heat that heat up the body (radiator), quantified by Waste-heat. 1WH = 1MJ = 1MW * 1s The converting efficiency depends on the delta-T (short for temperature) between the hottest part of the vessel (usually the reactor) and the coolest part the the vessel (the reactor).

Thermal powered engines

Thermal powered engines use all the thermal power that the energy source can provide.

Radiator

Radiators dissipate the waste heat by thermal radiation. The radiation power is confined to Boltzmann Law.

Microwave Receiver

Act like a generator, but it is a converting MegaJoules measured electrical energy into MJ and Thermal Power with an efficiency. At the same time, it act as a thermal source. That Thermal power can further be used as input of generators or just turn into WH and dissipates by radiators.

Thermal Receiver

Act as a Microwave Receiver with the internal MJ generator shut down (i.e. electrical energy converting efficiency is 0). All received power is Thermal Power and of course act as a thermal source. This power can further be used by a generator or thermal powered engines or just turn into WH and dissipates by radiators.

The calculation model

The calculation model is slightly different from original model by delay the WH calculation into radiators.

1. Many parts are now themselves radiators, with a quite little radiation surface compared to dedicated radiators.
2. Thermal Power is first used converting into electrical energy (MJ), then look for other attached thermal sinks (Mircowave transreceivers in relay/transmitting mode, thermal powered engines), and then reach the WH converter (is a module within the thermal source) and heat up the body. If radiator is attached, it will be the coolest part of the vessel so it got its temperature by the WH converter.

I believe the most words above is just the author wants in the very first. So here I point out the most prominent part to define NEW:

1. Mircowave Receiver or Transreceiver in receiving mode is now a thermal source and provides source power.
2. Thermal Power is first used by MJ converters ( e.g. generators ) them Thermal power sinks ( e.g. thermal powered engines), then WH converter.
3. Every thermal source is a WH converter that has a temperature after converting process. So each has a core temperature before any Thermal Power converted. 4.Vessel have a dissipating temperature that is calculated as a balance temperature where the radiator's dissipating power (MW) * time(1s) equals the WH (MJ). All radiator holds this temperature,
4. Many parts is themselves radiators and can store some WH (the store value is related to its thermal capacity measured in MJ/K).

[jamesruan]

The core/dissipating temperature and power output are calculated as described below:

• When thermal sink is active and demanding:
  • Thermal sources increase their power output to Ps_i, and have core temperatures Tc_i.
  • Thermal sinks must have temperatures Ts_i higher than radiators' Tr.
  • The thermal power used by thermal sinks is Pu_i.
  • The thermal power not used by all is then Pr = sum( Ps_i) - Sum( Pu_i ) and converted to waste heat.
  • ( Tc_i - Ts_i ) * k_i * e_i = Pu_i, where k_i is thermal conductance of the ith source/sink interface and the e_i the efficiency of the ith thermal sink.
  • Pr = ( sum(Ts_i) - Tr ) * kr, where kr the thermal conductance summed of all radiators. Pr and Tr in this equation also constraint to Boltzmann Law, which finally constrain the Ps_i and Tc_i.
  • The kr, k_i, e_i are relatively constant.
  • The thermal power output continues to increase until:
  • Radiators dissipating temperature Tr reached it's maximum.
  • Core temperature of ALL thermal source reached it's maximum.
• When thermal sink is not demanding or even not active at all:
  • Thermal source decrease its output and all equations are same.
  • Thermal power output continues to decrease until:
  • Thermal source core temperature reached it's minimun (which is ambient temperature Ta by default and a fixed value for reactors).

[jamesruan]

Giving a reactor with minimal output temperature 1500K and unlimited power output, and a generator connected to it with k_i = 1MW/K and efficiency 30%, 4 radiators with maximum temperature 3500K. Each radiator has a kr_i of 0.05MW/K and surface area of 5m^2.

When generator (the thermal sink) is demanding and a battery charging the maximum output Ps is reached.

Solving it by using the Boltzmann Law, a radiator at its maximum dissipating power is to have a temperature of 3500K and dissipating at 7682449 W/m^2 * 5m^2 = 39MW. Total dissipating power is 39 * 4 = 156MW. The total thermal conductance power is (3500K-0K) * 0.5MW/K *4 = 700MW which is enough to dissipating 156MW. The Ts is then 156MW/4/0.5MW/K + 3500K = 3578K. So we know the generator is using 156MW/70% = 223MW total, and converting 223MW - 156MW = 67MW into electric power. So the core temperature of reactor is then 223MW / 1MW/K + 3578K = 3851K. All unknown variable is now known. Tc = 3851K Ts = 3578K Tr = 3500K Ps = 223MW Pu = 67MW Pr = 156MW

Similarly, the minimal demanding condition can also be calculated: Tc = 1500K Ts = 1494.8K Tr = 1492.2K Ps = 5.19MW Pu = 0MW Pr = 5.19MW