sethoflagos

Because the imbalance is being generated continuously by expansion at one end and contraction at the other. The pressure gradient across any given pipeline section is (in the absence of fluid acceleration) balanced and preserved by the nett hydraulic shear forces due to fluid flow in that section. It's under operator control. If you fully throttle fluid flow by shutting an inline valve, the ice does not have the 8% space it needs to expand freely generating a theoretical pressure spike ~ 8% of its bulk modulus (8.4 GPa) = 672 MPa. It would never actually get that high due to spontaneous disassembly of its containment. Desirable operating pressures are set by dialling in the appropriate resistance to flow. Depends on context. Disturbances to steady state would propagate at sonic velocity (~1,400 m/s at 0 C) You got ahead of me. Though I have no intention whatsoever of detailing this idea out (other than the highly unlikely event I was paid union rates for it!) What's the area of a 5,000 km strip 100 m wide? 5 x 10^8 m. A bit generous for a pipeline RoW, but it isn't as if we were displacing indigenous residents.

It's in a pressurised, fully contained system. There should be no physical contact with the martian atmosphere.

That would be Revision 2, the CO2 version,

But the pressure does go up in the zone where ice expansion is displacing the incoming water, just as it drops where melting contraction creates space for water to flow into. No, I don't assume that at all. Quite clearly freezing (and thawing too) progress from the pipewall to the centre over a significant period. I think I said in an earlier post that I envisioned the interface to be a deep taper, (probably thousands of kilometres long). Note that as the taper narrows, the expanding ice will squeeze that 8% excess volume of water back the way it came just like a tube of toothpaste. Well if you see a pressure gradient along the water column then we're more than half way there. All that remains is to be able to visualise the contraction of ice to meltwater as continuously creating a space for water to flow into. The impulse exerted on the water is purely and simply the pressure gradient: the continuous creation of upstream space (and corresponding continuous denial of space downstream) then yields all that is necessary to establish bulk water flow towards the thawing zone. I do appreciate that dynamic systems in peculiar coordinate systems like this can be hard to visualise with clarity. Especially if you're not particularly predisposed to accept a particular person's viewpoint. So while I note that no one has actually stepped forward to say that they've bought into this picture, that's really not an issue. Sometimes that's just the way things are. Thanks to all who contributed for your assistance.

I guess I've got too used to having my designs constructed to a scale of 1:1.

Why do you say this? Partial condensation within a turboexpander reduces its performance. The phase change does not produce work, it renders some of the potential work output unavailable. It is therefore undesirable, though often unavoidable in some typical applications (eg chilling and depressuring the inlet stream to a demethaniser). You do not strengthen your posts by pretending expertise in fields where you have limited insight.

I've been doing business with them for 40 years, and have no such hesitation. And not behind their backs either.

Let me check back and see what I overlooked: Is this a question? If it is then I've frankly no idea what you're alluding to. Again, more detailed engineering design issues than challenges to the underlying physics. It would be a complete waste of time to evaluate individual heat transfer coefficients at this stage of the process, but in general the external coefficients would be derived from the Stefan-Boltzmann Law, while the convective heat transfer coefficient for water would be estimated via the Sieder-Tate correlation. The simple conductive heat transfer coefficients would come from direct integration of Fourier's Law. The overall heat flow in the preliminary line size I picked (48" ND 2" wall) was around 72 GW (oto half the thermal load for all installed electrical generating capacity in the UK) so not unreasonable for a planet-wide system. A back of envelope calculation indicates that this line size would shed only around 12 GW at night-time, so a practical system would have to have considerably more surface area for the same volume. 16 x 8" ND pipes in parallel may do the trick.

Again, these are detailed engineering design challenges rather than issues with the underlying physics. Most of the concerns you raise are grist to the mill for a competant pipeline design engineer.

Delete 'remarkably', replace with 'deceitfully'. Any fool can convert work to heat with 100% efficiency. Only a fool thinks you can do the reverse. Until you grasp this fundamental difference between work (shaft energy, electricity, potential energy, elastic energy etc) and heat, thermodynamics will remain a complete mystery to you. Currently, you are treating the two concepts as equivalent in all your postings.

The freeze thaw interfaces actually travel at 240 m/s relative to the pipeline. Like I said in the OP, there are many practical challenges. Actually I don't see the phase change velocity as an issue: it's like a cloud's shadow passing over the landscape; the cold chill spreads very quickly across the land, but nothing material on the land's surface is truly moving at that velocity.

Okay, I seem not to have been explaining this clearly enough. In one second 240 m of pipeline containing liquid water enters the freezing zone on the dusk horizon. On freezing, it becomes 240 m of pipeline containing ice. But this has consumed only 222 m of water. Therefore the water velocity entering the freezing zone must have a velocity of 222 m/s. Therefore the water velocity relative to the pipeline must be 18 m/s away from the freezing zone. On the dawn horizon, 240 m of ice-packed pipeline enters the zone per second generating just 222 m of liquid filled pipe. Filling the remainder of the pipe requires an inflow of 18 m/s relative to the pipeline towards the melting zone. It's really just a solution of the continuity equation in one dimension: if the time derivative of density is non-zero, then the divergence of velocity must be non-zero also.

Yes. That makes sense. Doesn't this depend on pipe diameter? Given typical martian night temperatures, a small bore pipe will definitely freeze solid, so there would be an interface somewhere. Since freezing would start at the inner wall and progress toward the centre the interface profile would be deeply tapered. Too large a pipe diameter would have insufficient surface area per volume and freezing would not complete before the thawing cycle began. Imagine a stationary pipe, frozen solid to the left hand side, with freezing progressing left to right. For every 222 m^3 of water that freezes. 240 m^3 of ice is created. which must displace 18 m^3 in some direction. It cannot flow to the left, because that direction is blocked solid. So it must flow to the right ahead of the freezing zone. This displaces 18 m^3 from the next pipeline section and so on, until an 18 m^3 'space' opens up at the melting zone. Modern large water turbines have around 90% hydraulic efficiency. So for a flowrate of 18 m^3/s and 1 MPa pressure drop Power = Eff x V x dP ~ 0.9 x 18 x 1 = 16 MW Noon temperatures at the equator seem to regularly exceed 0 C except maybe during winter (Viking Orbiter, Spirit Rover data) Where I said 'it's equipped with sunlight collectors', I envisaged parabolic mirrors or suchlike to concentrate the incoming feeble rays up to whatever was necessary to do the job. I'm well aware that collecting about 75 GW of solar power to generate 16 MW of electricity isn't terribly efficient. But that isn't really the point. I was simply interested in whether it was possible in principle to extract a significant power output from a solar freeze-thaw cycle. I think it may well be.

Into the suction port of your compressor where you heat it up with your costly electricity.

Yes I've only designed refrigeration cycles down to 80 K, not the deep cryogenic stuff. Yes, so the refrigerant can be condensed upstream of the expansion valve. You're not recovering the heat from the cooling stage here, you're recovering excess heat produced by a low efficiency cheap domestic compressor. It is still waste heat.

The heat content of low pressure gaseous refrigerant is just waste heat. Only the Work term counts.

Leaving aside the practical challenges, of which there are many. I'd appreciate members' views on whether the basic physics of this concept holds water. Imagine a 20,000 km pipeline encircling Mars' equator. It's equipped with sunlight collectors and so forth sufficient to ensure that the daylit half contains water which freezes at dusk and remelts at dawn. Hence within the pipeline, we have two ice/water interfaces circling the planet at ~240 m/s, the equatorial rotational velocity. Due to the 8% expansion on freezing, 240 m of melting ice produces only 222 m of water, and on the other side of the planet, 222 m of water freezes into 240 m of ice each second. So while the ice and pipeline rotate in step with the planet, the water is forced 'backwards' at around 18 m/s (40 mph). Running the high pressure (freezing) interface at say 8.4 MPa (0.1% bulk modulus) should not significantly impact the above figures, and extracting just 1 MPa of this in a water turbine could yield maybe 16 MW per m^2 pipe x-section. If only for an hour or so a day. Not a serious proposal by any means, but the principle interests me.

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What seems unlikely is you managing to break the 2nd Law of Thermodynamics. You are missing something. Improved air circulation around the chamber baseplate, for example?

Correct. But relative to it's non-local origin... ?

Stirling Engines don't run without a heat sink. Whatever you did to it, you improved the heat sink.

Including a particle that has receded beyond the Hubble horizon?

You may be correct. I don't know. Hence the question marks in my post. No he didn't. But the temperature JC quoted exceeded the minimum necessary to initiate fusion reactions. Please explain why not.

It's not clear. joigus' interpretation is entirely valid in one sense. However, the only thing leaving a black hole at light speed is what? .... Hawking radiation? Similarly, John Cuthber's plasma fusion reactor is also quite valid. Though again, it isn't exactly going to be 'air' leaving that scenario at light speed. My own post simply suggested a point of view which resulted in air molecules travelling at, and indeed exceeding, c. Maybe not the most interesting point of view to some, but a view nonetheless. wrt your last point, if the air can't escape it's own self-gravitation, it isn't going anywhere fast. Is it?

I'm assuming the process occurs in deep extragalactic space. My understanding is that providing some divergent velocity is maintained, eventually there will be sufficient distance between particles for differential Hubble expansion to drive relative velocities to c and beyond.