Martian Hydroelectric Concept

[sethoflagos]

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. 

[Tom Booth]

5 hours ago, sethoflagos said:

If only for an hour or so a day. 

Why for only an hour a day?

Space several turbines at different locations along the pipeline and generate power all day and night somewhere on the planet.

[exchemist]

6 hours ago, sethoflagos said:

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. 

I don't think there will be a sharp ice/water interface, hurtling round the planet. There will just be a progressive wave of melting and thawing.

I'm not sure I follow why the water has to move at all. Won't it just gently expand and contract in situ?

Just as any other wave does not involve net physical motion in the direction of travel of the wave. 

 

 

 

[swansont]

7 hours ago, sethoflagos said:

extracting just 1 MPa of this in a water turbine could yield maybe 16 MW per m^2 pipe x-section

How do you calculate this result?

[studiot]

7 hours ago, sethoflagos said:

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. 

After checking a few figures, I agree with your starting point about the length and rotational velocity of the pipeline in rounded numbers.

But exchemist has a more supportable view of the rotational velocity of the interfaces.

Have you thought about how long it takes for the thawing to occur ?
 

Here is a table of measurements from Wikipedia.

Note that at this site the temperature does not rise above the freezing point of water at any time of day or night from November to May

Edited May 11, 2021 by studiot

[sethoflagos]

5 hours ago, Tom Booth said:

Why for only an hour a day?

Space several turbines at different locations along the pipeline and generate power all day and night somewhere on the planet.

Yes. That makes sense.

5 hours ago, exchemist said:

I don't think there will be a sharp ice/water interface, hurtling round the planet. There will just be a progressive wave of melting and thawing.

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. 

5 hours ago, exchemist said:

I'm not sure I follow why the water has to move at all. Won't it just gently expand and contract in situ?

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.

5 hours ago, swansont said:

How do you calculate this result?

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

5 hours ago, studiot said:

Have you thought about how long it takes for the thawing to occur ?

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.

 

[Tom Booth]

Pipe rupture due to water expansion pressure rather than displacement?

In a completely rigid pipe, the water sealed between ice dams,... Lots of potential expansion and contraction issues, maybe?

If the pipe is elastic to avoid rupture, that reduces horizontal displacement leaving a long pipe that just kind of throbs around, possibly rupturing and ripping itself from its mores like a loose firehouse.

But that's just one of those practical challenges.

I had a picture flash in my mind of a Nitinol engine. The kind where a loop of Nitinol wire revolves around some wheels.

In this case, the Nitinol pipe circling the planet.

Eliminate any possibility of rupture, and enhance the displacement effect, by "training" the metal to...

Not sure what, but the super-elasticity might be of some advantage.

 

[swansont]

1 hour ago, sethoflagos said:

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

Thanks

Why do you think the water will flow, when it’s in a closed loop blocked at both ends? 

 

[sethoflagos]

21 minutes ago, swansont said:

Thanks

Why do you think the water will flow, when it’s in a closed loop blocked at both ends? 

 

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. 

[studiot]

3 minutes ago, sethoflagos said:

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. 

 

Well perhaps you are not the only one being unclear since this post of yours describes exactly what is worrying me and I thought I had stated in my last post. Someone seems to have perhaps understood it, although your answer suggested that you did not catch it.

Do you think that either Martian conditions allow either freezing or thawing at 18m/s  ?  That is driving along at 40mph.
What sort of heat transfer coefficients are you envisaging for the pipline and what about the energy flows to accomplish this ?

[sethoflagos]

6 minutes ago, studiot said:

Do you think that either Martian conditions allow either freezing or thawing at 18m/s  ?  That is driving along at 40mph.
What sort of heat transfer coefficients are you envisaging for the pipline and what about the energy flows to accomplish this ?

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.

 

[studiot]

1 hour ago, sethoflagos said:

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.

 

Sadly you are still not answering my question(s)

[sethoflagos]

2 hours ago, Tom Booth said:

Pipe rupture due to water expansion pressure rather than displacement?

In a completely rigid pipe, the water sealed between ice dams,... Lots of potential expansion and contraction issues, maybe?

If the pipe is elastic to avoid rupture, that reduces horizontal displacement leaving a long pipe that just kind of throbs around, possibly rupturing and ripping itself from its mores like a loose firehouse.

But that's just one of those practical challenges.

I had a picture flash in my mind of a Nitinol engine. The kind where a loop of Nitinol wire revolves around some wheels.

In this case, the Nitinol pipe circling the planet.

Eliminate any possibility of rupture, and enhance the displacement effect, by "training" the metal to...

Not sure what, but the super-elasticity might be of some advantage.

 

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. 

[sethoflagos]

1 hour ago, studiot said:

Sadly you are still not answering my question(s)

Let me check back and see what I overlooked:

3 hours ago, studiot said:

Well perhaps you are not the only one being unclear since this post of yours describes exactly what is worrying me and I thought I had stated in my last post. Someone seems to have perhaps understood it, although your answer suggested that you did not catch it.

Is this a question? 

If it is then I've frankly no idea what you're alluding to. 

3 hours ago, studiot said:

What sort of heat transfer coefficients are you envisaging for the pipline and what about the energy flows to accomplish this ?

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.  

 

  

Edited May 11, 2021 by sethoflagos

[Tom Booth]

I'm wondering, why not build a small model, a loop of pipe, a heat lamp in a cold room, some flow meters in the pipeline, a stepper motor to keep it revolving.

Like a planetary mobile, to provide a sense of realism.

A relatively inexpensive setup I think. Hardly complicated at all.

If some actual flow potential is indicated, maybe even spring for some miniature turbines. Someone could probably even 3D print the things on the cheap. Maybe get some actual power output measurements going.

And, might this not actually work, (if it works at all that is), on a mid-scale, say for instance circling a mountain or building somewhere near the poles. In Alaska perhaps, where the sun never sets.?

 

[sethoflagos]

16 minutes ago, Tom Booth said:

I'm wondering, why not build a small model, a loop of pipe, a heat lamp in a cold room, some flow meters in the pipeline, a stepper motor to keep it revolving.

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

[swansont]

4 hours ago, sethoflagos said:

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.

No, this does not follow.  Why wouldn’t the pressure just go up? (also you seen to assume instantaneous freezing and melting, and that it would happen along the direction of the pipe, and not in the radial direction, from outside in.

The thing is, some distance away, you are melting ice and having a corresponding collapse of 240 m of ice into 222 m of liquid water, which means there could just be a certain pressure increase, which remains static, and the system is in steady-state. No motion relative to the ground. I’m not seeing a net impulse exerted to the water.

[sethoflagos]

2 minutes ago, swansont said:

No, this does not follow.  Why wouldn’t the pressure just go up?

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.

7 minutes ago, swansont said:

Also you seem to assume instantaneous freezing and melting, and that it would happen along the direction of the pipe, and not in the radial direction, from outside in.

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.

24 minutes ago, swansont said:

The thing is, some distance away, you are melting ice and having a corresponding collapse of 240 m of ice into 222 m of liquid water, which means there could just be a certain pressure increase, which remains static. No motion relative to the ground. I’m not seeing a net impulse exerted to the water.

 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.

[Endy0816]

What is the plan for sublimation?

[sethoflagos]

1 minute ago, Endy0816 said:

What is the plan for sublimation?

That would be Revision 2, the CO2 version,

[Endy0816]

1 minute ago, sethoflagos said:

That would be Revision 2, the CO2 version,

I mean water will also sublimate on Mars at Martian atmospheric pressure, depending on temperature.

 

[sethoflagos]

2 minutes ago, Endy0816 said:

I mean water will also sublimate on Mars at Martian atmospheric pressure, depending on temperature.

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

[Tom Booth]

57 minutes ago, sethoflagos said:

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 wouldn't go so far as to day "nobody".

I may not be 100+1% convinced, but neither are you, right? Or why ask if others here think it's viable or not.

I was all geared up to get ready to help build a prototype.

I mean, as much as I might play up my "ice bomb" engine from a purely theoretical standpoint, even I have my doubts it would actually work in practice.

I'm much more an experimentalist than a theorist. I'm skeptical that I've actually been posting messages on the internet all these years. I might just wake up someday and find out it was all a crazy dream and have to go back to using the telephone. The internet is fantastic, but still seems a bit unreal to me.

If I build something and see it actually work, or do an experiment and see a positive outcome, I still want some independent confirmation, peer review, replication, and probably still wouldn't fully "buy into it" 

The theoretical foundation for why it worked could still be complete hogwash, which is why I don't "believe" established science.

It isn't that I don't believe established science. I just live in a perpetual state of suspended judgement, silently watching the world go round.

 

Edited May 11, 2021 by Tom Booth

[swansont]

59 minutes ago, sethoflagos said:

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.

And why won’t the pressure just equalize?

 

Quote

 

 Well if you see a pressure gradient along the water column then we're more than half way there.

Once it has propagated, the whole tube is at pressure. You’re all done. 

How big of a gradient are you expecting?

 

Quote

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.

How fast does the pressure differential propagate? 

 

 

[studiot]

3 hours ago, sethoflagos said:

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.  

 

  

As an obviously competent engineer I am disappointed with the obviously politician's brush off when pressed for hard detail, more especially as you invited comment.

Here is the problem I am trying to reconcile.

 

You have mentioned several different pipe sizes, and somewhere a square metre of cross section.

So let us consider 1 m² section of pipe 1 metre long, at the frozen stage.

This has a volume of 1 cubic metre.

Ignoring, for the moment,  the small difference in density between ice and water, this has a mass of 10³ kg

So to calculate the approximate energy reuqirement to raise this from ice at -4 C to water at  +1 C  ie to melt it we require

10³(4*2050 + 334000 + 4200)  = 3.464 10⁵ x 10³ Joules per m³

Now the rate of insolation on the mars is 590 w/m²

or 5.9 x 10² J/m² per second

So it requires ( 3.464 x 10⁸ ) / (5.9 x 10² ) = 6 x 10⁵ square metres of martian surface to receive this energy every second multiplied by the rate of movement of the ice/water interface  as this was calculated on a 1m/s basis and assuming perfect energy conversion.

 

Edited May 11, 2021 by studiot