Last month I complained that the Hyperloop-alpha proposal has a heat balance problem. Here is the fix for that problem, as promised. I’ve broken up my changes to the design in a series of steps, to make it easier to see that each step is individually beneficial.
Step 1: Hyperloop + 3 MPa steam heat dump
My numbers don’t exactly match Mr. Musk’s. It seems we have slightly different specific heats for low pressure air, among other things. This diagram should serve as a base case which can be compared directly to the diagram from the Hyperloop-alpha proposal (check the last blog post).
I’ve detailed the steam heat dump system to run up to 3 MPa. Water is sourced from a small tank and steam is dumped into a much larger tank. The tanks are connected, so that as the steam pressure rises so too does the water pressure, which should reduce pumping losses. Eventually even the small tank is completely filled with steam. I've accounted for the two tanks as a single tank here, as the wall-in-the-middle detail should not affect the mass budget at all.
As I predicted in my last post, the heat dump tank is far too big... at least 12 meters long. The tube taking bypass air to the rear nozzle is also far too big, and will interfere with the passenger compartment. Finally, the battery to run the turbines is gigantic.
Step 2: ... + bypass intercooler
By picking off the air output from before rather than after the first intercooler, the heat load is radically reduced to practical dimensions. The heat going through the first intercooler is not a typo... it's really been reduced to 10% of the prior value. Part of this reduction comes from balancing the pressure ratios across the two compressors. Unfortunately, the bypass tube is now even larger and less practical.
Step 3: ... + Reduced Tube Pressure
Reducing the pressure in the transport tube to 25 Pascals decreases the compressor power, but oddly increases the amount of cooling required. That's because we're still cooling the same mass flow of air, but compressing that air more.
The cooling tank gets larger, but note that the battery gets cut in half, for significant savings in mass and cost. The bypass tube is smaller but still too large.
Reducing tube pressure should not cause problems with the vacuum pumps. 25 Pa is considered a "rough" vacuum, and corresponds to an altitude of 59 km, where helium balloons operate. The mean free path in this gas is around 0.3 mm, which is small enough relative to vacuum pump turbine blades that the gas still acts like a gas. Ordinary vacuum pumps will work fine.
Turbomolecular pumps, which use different aerodynamics than regular vacuum pumps, generally start operating at 10 Pa or less. I am not suggesting we drop into that range.
Step 4: ... + Cryogenic Heat Dump + Intake Intercooler
The intercoolers above are removing nearly all the energy added by the turbines. We can avoid adding so much energy in the first place if the turbines operate on cryogenically cold air. This is a big step, but it's necessary because the capsule design in Step 3 is too bulky.
To do it, we swap the water/steam heat dump for a more compact but substantially heavier liquid air heat dump. Boiling liquid air does not absorb as much heat as boiling water, but it also does not expand as much. For the same heat absorbed, the tank weighs less but the fluid weighs far more.
The real magic, however, is that the heat is absorbed at a much lower temperature. The intercooler output will now approach the cold sink temperature of 75 Kelvin. Once again, the battery loses more weight than we add to the heat dump, for a net savings of cost and mass.
The high speed, low density intake intercooler here is similar to but much less extreme than the one proposed for the Skylon spaceplane. It is not completely settled technology but much of the R&D has already been done. In particular, one of the issues would be clogging from frozen water and CO2 ice. In an operating system, the tube air would be dried by prior passages of capsules. So clogging would mainly be an issue when restarting.
The heat dump can also be used as a source of air. For instance, at low speeds the bow intake compressor may not supply enough air for the air bearings. Make-up air can be taken from the heat dump. In an emergency, while waiting for the tube to repressurize, air from the heat dump tank could be used to supply 20 occupants with breathing air for 20 hours.
I think this design largely achieves what Mr. Musk was attempting to accomplish.