Solar chimeys - Feasible?

louis · 2018-12-21 19:26:31

OK - why don't we get specific?

How much energy would be required to tow say one ton of frozen CO2 from the polar region to the temperate zone (I am guessing that's about 3500kms, given Mars's extreme "wobble" factor. I think a robot Mars rover truck could cover 500kms per sol...so that would be 7 sols's worth of travel. At 50 kws constant that would be about 8.5 MwHs of energy used in towing one ton that distance. I don't know whether you could do it for less than 50 Kws constant over the 7 sols.

But anyway that is perhaps a starting point and one might ask how much energy one ton of solid CO2 might release when put into the right pressure chamber with a turbine attached....

JoshNH4H wrote:

Hey Louis,
I briefly discussed the possibility of bringing CO2 from the poles to the temperate equatorial regions as fuel in this post
I wrote:
It's certainly conceivable that mining dry ice at the poles could be economical, but it's hard (for me) to imagine that it would actually make sense unless the end user is actually at the poles.
You used coal as an analogy, and it's a pretty decent one. However, rather than showing the potential value of CO2 mining I believe it shows why it probably won't be worthwhile.
I believe the appropriate comparison is the system we were discussing before: a refrigeration system that uses energy to freeze CO2 out of the atmosphere. Here are the costs and benefits of such a system:
Costs:
Requires industrial equipment
Consumes energy
System has not been designed fully yet
Benefits:
Generates ~1 kg per kWh of inert gas (primarily Nitrogen and Argon)
Works equally well anywhere on Mars
Now, by comparison, here are the costs and benefits of pole-mining:
Costs:
Requires an ongoing supply of human labor (All mining does)
Consumes energy
Requires shipment over thousands of kilometers
Requires industrial equipment
System for mining a substance that sublimes at 195 K has never been built and would require some tweaks to existing techniques
Benefits:
Will produce water as a byproduct
In my view, the question is: Is more labor and thousands of km of shipping worth saving yourself 150 kJ/kg? In my opinion, it is not. It's good to compare this to coal: Coal on Earth has an energy content of 30 MJ/kg, 200 times greater than the energy you save. Because the energy content is so high, it really is worth pulling out out of the ground and shipping it to the point of use (or at least it was in times past). I question whether mining CO2 from the poles would save any energy at all.

SpaceNut · 2018-12-21 20:05:13

Well a prolonged stay waiting to fill up a carrier will take energy even doing nothing just to keep it possible to be in a useable. Then you need the energy for the equipment to carve it out of the solid ice dirt fields. The equipment to move it into the carrier and those equipment will also need heating to keep it useable.

https://news.yahoo.com/moody-photo-mars … 37923.html

https://www.engadget.com/2018/12/21/mar … ev-crater/

SpaceNut · 2018-12-21 21:40:44

998da01195006d6597e5ea9d4dfc3c3d

Mars Express satellite captured images of the 50-mile wide Korolev crater filled with ice. Which has remained even in summer.

Its most likely frost mixed water....

louis · 2018-12-22 05:21:08

I just checked on Wikipedia and find this crater has 2200 cubic kms of WATER ice! I make that to be about 2.2 trillion tonnes of water!!! No wonder it doesn't all evaporate in summer!

SpaceNut wrote:

https://s.yimg.com/ny/api/res/1.2/Eafvu … 9d4dfc3c3d
Mars Express satellite captured images of the 50-mile wide Korolev crater filled with ice. Which has remained even in summer.

At 73 degrees north, it's not as near the pole as I expected. It's probably about 2000 kms or so away from some of the best insolation on Mars at around 30 degrees north. I suspect we can find better water sources in terms of location but if worse came to worse you could definitely have a constant chain of water extraction robot rovers travelling to the crater and returning, each laden with a couple of tonnes of water.

JoshNH4H · 2018-12-27 10:55:43

louis wrote:

OK - why don't we get specific?
How much energy would be required to tow say one ton of frozen CO2 from the polar region to the temperate zone (I am guessing that's about 3500kms, given Mars's extreme "wobble" factor. I think a robot Mars rover truck could cover 500kms per sol...so that would be 7 sols's worth of travel. At 50 kws constant that would be about 8.5 MwHs of energy used in towing one ton that distance. I don't know whether you could do it for less than 50 Kws constant over the 7 sols.
But anyway that is perhaps a starting point and one might ask how much energy one ton of solid CO2 might release when put into the right pressure chamber with a turbine attached....

I can do my best, but any number I give will necessarily be a very rough estimate.

The physical minimum amount of energy required to transport something 3500 km is 0 J/kg (for an object moving on a perfectly level surface in a frictionless vacuum). No real world transportation system is that good, naturally, so that's not good enough. This means that we're really trying to get a handle on what we could expect technologically which is sort of a difficult question.

I think the closest analogy would be the energy use per mile of 18-wheeler trucks. Some factors suggest that the gas mileage will be higher (basically no drag, lower speeds, and lower gravity) while others suggest it might be higher (I don't think Martian roads will be anywhere near a US interstate in quality for a long while). Based on this website the average 18-wheeler gets 4.5 mpg (52.3 L/100 km) and according to this page they can haul up to 80,000 lb (36 tonnes).

Gasoline contains roughly 40 MJ/kg of energy (excluding Oxygen, naturally) and has a density of roughly 0.9 kg/L. This means that these 18-wheeler trucks use ~500 J/kg-km. Over 3500 km that works out to 1.75 MJ/kg (0.5 kWh/kg).

I have low confidence in this number, but it's a start. A reasonable range would be from, say, 300 kJ/kg to 10 MJ/kg (0.1 kWh/kg to 3 kWh/kg). It's worth noting that it would be much less if you use train transportation but it would be a major project to build a railroad through such wild countryside, comparable to the American Transcontinental Railroad. It's also worth noting that internal combustion engines are not very efficient so that you might expect to use 3 times less energy with a battery electric system, but also that a battery-electric system will have some sort of range limitation (necessitating charging stations every 100 or 200 km, which is not crazy at all along a major shipping route) or else will be basically 100% batteries.

My supposition is that you are going to be in favor of batteries, so I won't get into the various aspects of an internal combustion system. For the purposes of this thread I will use a figure of 100 kJ/kg-3.5 MJ/kg (0.03 kWh/kg to 1 kWh/kg). For reference, I estimated in this post that it would take 150 kJ/kg to freeze CO2 out of the atmosphere. The former number ignores the energy required to mine the dry ice, which will be substantial; the latter ignores the inefficiency of refrigeration (50-80%), which is also substantial, but at a first pass it's unlikely that trucking dry ice from the north pole will save any energy at all.

Now, the question of how much energy you can get out likewise is a difficult one. Unlike many chemical fuels, dry ice contains no inherent energy. The answer for how much energy you can get out really depends on what your heating source is. At various points in the steam powered rover thread, which I have linked to, I estimated: 41 kJ/kg, 80 kJ/kg, 166 kJ/kg, and 320 kJ/kg.

In short, having looked at the numbers, I believe that my initial feeling has been confirmed: Mining dry ice from a polar cap to use in an energy generator is a marginal activity in general, but is extremely unlikely to be worthwhile if you are not physically located near a polar cap.

SpaceNut · 2018-12-27 12:24:04

I would agree that local mining plus use is a must early on and that without nuclear power at the poles is a no go....

CharlesAnigh · 2019-04-01 16:51:07

Just wonder if any home owners have a solar panel setup to save money on electricity?

SpaceNut · 2021-02-09 18:21:29

Nuclear talk about molten salt, solar concentrating and such reminded me of this topic.

Which brings me to size matters in why KRUSTY make sense for mars use not to much mass, steady 10kw electrical, plus a plausible 30kw of IR heat make use of and its already a molten salt unit.
Use an up draft chimney to heat compress Mar's Co2 and create power from the updraft.

SpaceNut · 2021-10-24 20:26:57

Some links on solar chimneys....

Using a source of heat under the shape will accelerate the draw and updraft.

https://peer.asee.org/student-project-t … -power.pdf

https://en.wikipedia.org/wiki/Solar_chimney
https://en.wikipedia.org/wiki/Solar_updraft_tower
https://www.solaripedia.com/13/371/5041 … ssion.html
https://www.solaripedia.com/files/972.pdf
https://architecture.mit.edu/sites/arch … roject.pdf
https://en.wikipedia.org/wiki/Concentrated_solar_power

solar power towers on mars - km-high vertical wind tunnel turbo-elec
Solar chimeys - Feasible?
Solar thermal power - Fathers Day gift
An Empirical Model of Thermal Updrafts

https://www.briangwilliams.us/power-gen … power.html

https://www.researchgate.net/post/Hi_I_ … ns_of_this

https://www.solarpaces.org/how-csp-works/

Was thinking of how to combine the two things such that you end up with a sort of parabolic shape dish made of troughs that has the chimney as the receiving element of the concentrated sun light.

Calliban · 2023-11-17 14:44:56

A closed heat-pipe solar chimney could work. The Martian atmosphere has too low density for the Earth based solar chimney to work on Mars. But a closed pressurised tube could work.

We place solar panels at ground level. Pressurised carbon dioxide flows through these panels, heating it to 20°C. The tower consists of an outer steel tube, with an inner tube running within it. Hot CO2 rises up the inner tube by convection. It exits the top of the inner tube and then flows down the gap between the two tubes. As it does so, it loses heat to the skin of the outer tube, which in turn loses heat by radiation. A turbine is placed at the base of the inner tube. This captures kinetic energy from the rising CO2.

Something like this:

The vertical tube appears much shorter than in reality. It would be hundreds of metres tall to provide the highest thermal driving head possible. The mound of rock and soil would function as a thermal cold store. At night, heat would conduct out of the mound into the outer tube. The CO2 in the outer tube would rise by convection and would the tube would radiate heat into the Martian night.

Last edited by Calliban (2023-11-17 16:13:27)

SpaceNut · 2023-11-17 18:39:50

I have been reading the information for the tower normal earth tube if you make it shorter the amount of air flow drops but increase it and it rises. I believe it's due to shape of the chimney becoming wider at the top versus the base with colder air at the top.

On can also use a working fluid to do the conversion in a closed loop as well since that will act like a heat pump ac unit in reverse.

SpaceNut · 2023-11-18 18:59:40

Windmill blade technology applies to this topic to turn a rotor that connects to a shaft for a generator.

https://en.wikipedia.org/wiki/Wind-turbine_aerodynamics

Many of the equation answers are part of the updraft as well.

https://www.windpowerengineering.com/bl … art-of-ge/

https://www.nmmesa.org/wp-content/uploa … Blades.pdf

https://energy5.com/blade-dynamics-deco … ine-rotors

https://www.dnv.com/Images/Bladed-Techn … 149133.pdf

SpaceNut · 2023-12-16 14:12:50

A simple, clever twist in solar tower design produces power 24/7

Researchers from Qatar University and Jordan’s Hussein Technical University have found a way to double the power produced from a type of solar tower. The “twin technology solar system” they report in the journal Energy Reports can produce energy all day and all night.
Solar panels, which absorb light and turn it into electricity using photovoltaic materials, are a conventional, well-known technology to harvest the sun’s energy. The concept behind the new solar tower system is very different. It relies on the fact that hot air rises.
https://www.sciencedirect.com/science/a … 4723015512
Such solar updraft towers are typically made from glass or other greenhouse materials that trap heat. The air is heated at ground level and as it rises up the tall tower, it spins a turbine to produce electricity. But the idea remains experimental. Costs of building the large, tall glass towers remains prohibitive for mainstream use.
The new twin-technology tower could bring down cost by producing over twice as much power as previous designs, say the researchers. Their design entails building a secondary tower around the inner tower.
The second tower is a cooling tower, in which air would be sent downward to spin another turbine. To accomplish this, the researchers propose spraying a fine mist of water into the hot air that reaches the top of the tower, making it cooler and sending it downward.
https://www.anthropocenemagazine.org/co … rgy-tower/
In the paper, the researchers present details of a model tower structure that is 200 meters tall, with an inner updraft heating tower that is 10 meters in diameter. The outer downdraft cooling tower’s diameter is 13.6 meters. The gap between the towers is separated into 10 channels, each serving as a cooling tower, with water misting systems at the top and turbines at the bottom.
Using simulations of the tower combined with local weather data, the team estimated that it would generate a total of about 753 megawatt-hours of energy annually. That is about 2.14 times the power of a traditional solar updraft tower. The external cooling towers would produce about 400 megawatt-hours, and the inner heating tower working better during the day under the hot sun to generate around 350 MWh.
The researchers found that seasonal variations in temperature and humidity affected the external tower more, so its output power swung widely throughout the year. Its performance decreases significantly in high humidity, they say, so it is best used in areas with hot and dry weather. They tested their simulation in Riyadh City, which is a hot, dry desert climate, and the results show that the system could be beneficial to deploy there.
“However, the system has limitations, such as access to water for the operation of the downdraft system,” the team writes. They plan to work on a deep techno-economic analysis of the proposed system and a take a closer look at its scalability.

AA1lur4x.img?w=400&h=250&m=6

Calliban · 2023-12-18 05:35:51

The taller the chimney, the greater the power output. On Mars, we have a different situation. The air is a thin gas dominated by CO2, with a temperature far beneath its critical point. It takes very little mechanical work to compress the gas. If we compress it at the top of the tower, we have a dense gas which should fall down the tube. We can heat it with a low grade heat source at the bottom and expand it through a turbine.

The attached link shows the properties of CO2 at a temperature of -50°C, between the pressure of 0.1 and 1.0MPa, in increments of 0.01MPa.
https://webbook.nist.gov/cgi/fluid.cgi? … fState=DEF

If we inject CO2 at a pressure of 0.1MPa (1atm) at the top of the tower, static pressure will result in a pressure gradient between the top and bottom of the tower. The density of the gas increases roughly proportional to static pressure until the gas reaches a pressure of 0.68MPa, at which point it phase transitions into a liquid. If the tower is tall enough, CO2 will actually turn to liquid before reaching the bottom. The liquid CO2 can then be allowed to drain by gravity into a boiler, where solar, geothermal or nuclear heat convert it into a high pressure gas that exhausts through a gas turbine.

Static pressure increases with the density of the gas above that point and density is a function of pressure. I used a spreadsheet to work out how tall the tower would need to be to reach a pressure sufficient to liquefy the CO2 for various injection pressures at the top. For an injection pressure of 0.1MPa, this works out to be 20.85km. If injection pressure is 0.2MPa, this declines to 13.16km. If injection pressure is 0.5MPa, minimum h is 3.24km. The density of liquid CO2 is 1155kg/m3. So every 10m of tower height beneath the liquidus point, increases pressure at the base by 43KPa.

The significance of this finding is that a nuclear reactor built on Mars, will not need a large radiator panel. We use the nuclear heat to boil the liquid CO2, expand it through a gas turbine and let the expanded gas carry away the waste heat as it exhausts into the atmosphere. We could even build reactors that pass the CO2 directly through the core, obviating the need for heat exchangers. The liquid CO2 in the tower will exert its own static pressure, also avoiding the need for feed pumps. However, the CO2 condensation tower is obviously not free. It would be cheaper to build if we could use a convenient mountain to provide the required elevation for the compressor. That way, instead of building a tower, we build a steel pipe running down the mountain. If we add an additional pipe length beneath the liquidus point, then the pressure at the bottom of the pipe can be tailored to provide any desired pressure input for tge reactor without need for an injection pump.

Last edited by Calliban (2023-12-18 07:15:03)

tahanson43206 · 2023-12-18 07:14:46

For Calliban ....
Re your reply in the Van Allen Belt topic ... thank you for finding a use for that otherwise mostly annoying natural phenomenon!

Regarding Post #39....

Picking up on your observation about possible value as a way to generate power from otherwise wasted low grade heat...

1) Can this concept be scaled down, or is there a minimal size below which it is less attractive?
2) Would this concept work with NASA's Krusty at only 10 KW?
3) Would this concept work on Earth?

Follow up question about the Van Allen Belt .... is there a way to capture some of that energy from the ions in the Van Allen Belt? You have shown that the ions there might contribute to slowing a space craft despite their small mass. I was surprised to learn that the total mass of the entire Belt is estimated to be so much less than a kilogram.

(th)

Calliban · 2023-12-18 07:45:52

TH, If we inject CO2 into the tower at its liquefaction pressure of 0.683MPa, then the tower can be scaled down. It all depends upon what pressure we want to inject CO2 into the boiler. The higher that pressure is, the higher the thermal efficiency of the plant and the more compact the turbine can be. Both are important economic drivers.

On Earth, liquid air energy storage is being developed as a grid energy storage system. If we build the liquid air tank on top of a mountain, then the energy recovery plant can be located at the bottom of the mountain and can benefit from the gravitational potential energy of the liquid column. The downside is that the compressor plant is starting with air at a lower pressure due to the height. However, air temperature also falls as height increases, which makes compression more efficient. Maybe the two effects will balance out, leaving us with a net benefit.

Another possibility occurs to me as an application on Mars. What if we drill a deep well instead of building a tower? Liquid CO2 injection could be an interesting way of harvesting geothermal heat to produce power. The CO2 can turn back into gas at temperatures beneath 0°C. So we don't neccesarily need a lot of heat to make this work on Mars. At 0°C, CO2 saturation pressure is 35bar.
https://www.engineeringtoolbox.com/CO2- … _2017.html

So geothermal resources on Mars won't necessarily need to be hot in the way we tend to think of geothermal heat. Which is convenient given that the Martian geothermal gradient is much shallower than Earth.

Last edited by Calliban (2023-12-18 07:57:07)

tahanson43206 · 2023-12-18 08:00:13

For Calliban re #41

Thanks for taking up the question of use of your idea for a KRUSTY plant ....

It seems to me it ** might ** be possible to estimate the tradeoffs at work in this situation .... We are investing energy from our primary resource (fission) to try to recover energy from otherwise wasted low grade heat. What I cannot determine, but which might be something you can work out, is whether there is a net benefit to making the investment?

If it takes more of our primary energy than we can recover from our secondary process, then it is not worth while.

Is this something you can work out?

The KRUSTY is likely to take up residence on Mars in the next few decades.

Certainly a Chinese version of a low power reactor is likely to show up on Mars.

NASA is restricted in funding by US Congressional needs and conflicts, but a Chinese success might provide incentive to place KRUSTY on site sooner than would otherwise be the case.

What material might be used to make that long pipe?

What investment of energy is likely to be needed to make that pipe?

A lot of low grade heat is wasted on Earth because recovery just isn't worth the trouble.

That rule-of-thumb may apply on Mars as well.

(th)

Calliban · 2023-12-18 08:07:56

Looking at the geothermal case, Martian geothermal gradient is estimated to be one third of Earth's average, which is 25K/km. So that is 8.33K/km. The average surface temperature of Mars is -55°C. So to harvest heat at 0°C, we would need to drill down 6.6km, or about 21,500'. That is a non-trivial depth, even on Earth. It suggests to me that it is important to locate our base in an area with a locally high geothermal gradient.

However, one thing this estimate doesn't account for is the porosity of the Martian surface. The outer regolith is a loose layer and under the vacuum conditions on the surface of Mars, it provides about the same insulation value as rockwool. So temperature could increase more rapidly than 8.33K/km in the upper layers.

As to what we would make the tube out of, it would depend upon ground conditions. If the well is completely dry, then I would suggest low carbon steel. But it is entirely possible that we would encounter groundwater on Mars at that depth. If so, then plain carbon steel would suffer corrosion issues. Stainless is probably too expensive. We could try a segmented pipe made from drip galvanised steel or even cast basalt.

Last edited by Calliban (2023-12-18 08:16:05)

Calliban · 2023-12-18 08:34:07

On Earth, we would build a LAES plant wherever we happen to have a convenient source of low grade heat. Such a heat source greatly increases the efficiency of the expansion process. One resource that we could use is waste heat from thermal powerplants. A low pressure turbine typically exhausts steam at a pressure of 70mbar. This equates to a condenser temperature of 30°C. We could store this heat in a pond or within a rock mass, through which air evaporation pipework also runs.

There are two options. We can run the energy recovery plant and steam plant continuously, in which case we don't really need to store very much heat as we are using it immiediately. The air liquefaction plant would run intermittently when grid power was in excess. The second option is to store the heat in a thermal mass and only run the energy recovery plant intermittently. The first option eliminates the need for a large heat reservoir. But the reservoir is really just a pond or mass of rock. The second option requires a somewhat smaller liquid air tank. Without a proper engineering study I don't know which is the best option. But both would work.

On Mars, we could actually do something similar, but using L-CO2 instead of L-Air. The tower used to store the L-CO2, could be made from steel. It could also be made from a ceramic like brick or concrete. Although the CO2 is pressurised, the weight of the tower would result in compressive forces which would allow a concrete tower to resist the outward pressure exerted by the liquid CO2. This is how compressive concrete water towers work here on Earth. They don't explode because the net forces on each element remain compressive. It is also how we are able to build dams out of stabilised earth, even though it has pitiful tensile strength. So we could build towers out of materials like adobe or bonded stone, provided there were a leak resistant lining and enough loading to keep net forces compressive. Building the liquefaction plant on top of the tower provides some of the weight loading needed to resist the internal pressure.

Last edited by Calliban (2023-12-18 08:59:02)

tahanson43206 · 2023-12-18 08:51:21

For Calliban ... at the risk of taking this topic wildly off course, I'm following up on what I understand to be the general flow of your presentations on capture of useful energy from low grade heat .... The Earth provides substantial quantities of low grade heat at thermal vents in the deep ocean.

A problem humans face is heating of the oceans.

If I understand the process you are describing correctly, low grade thermal energy could be removed from the ocean, if a plant were deployed at a location where that makes sense.

If we need a new topic to consider this question, please create one.

(th)

SpaceNut · 2023-12-18 10:09:24

Most of the experimental towers have greenhouses under the canopy of water as well as possibly sand but the issue here is we are not controlling the input of air to the rise of the thermal change only the amount of heat reflection or absorption to cause the lift effect to happen.

Those were greeat numbers for a mar's version Calliban and using the KRSTY reactors surplus heat as the means to generate lift is of course something that I did suggest as well. for power and collecting of co2,

SpaceNut · 2024-05-26 10:13:47

Even a small solar chimney can be used to create cooling for a building occupant.

rPSIscAoNLoALG-ZMdu8SGctHj5_bt0sQMkYRlCtSQvv0e2zaLPJfdMgaI2cuxre5Bqq3_DUzgWBpyeBg7mIaB2eH9JCuoBJY1z1evowlmQO0ubemCFxL-A5zopLjO9WSqIHX8FMonYRQAD9dA

https://theconstructor.org/building/sol … rk/564685/

https://www.pinterest.com/pin/726698089842292947/

SpaceNut · 2025-08-24 13:38:08

updraft thermal home size chimney

AI Overview Designing a thermal updraft, or solar chimney, for a home requires custom calculations rather than using standard chimney sizing for a fireplace. While a standard fireplace chimney is sized for hot, fast-moving exhaust, a solar chimney is designed for much slower, cooler air movement and is influenced by external factors. Residential versions are often used for passive cooling or ventilation, and achieving a useful updraft may require a significantly taller chimney than is typical for combustion.
Key principles of residential thermal updraft Solar chimney function: The chimney creates an updraft by heating the air inside it to a higher temperature than the air outside. The rising, buoyant warm air then draws in cooler air from within the house.Optimal placement: To maximize heating, the chimney should be installed on an exterior wall with the most sun exposure, preferably a southern wall in the Northern Hemisphere. For best performance, it should also be integrated into the main structure, with as little exposure to outside temperatures as possible.Passive cooling and heating:
Passive cooling: When used for passive cooling, a solar chimney draws hot air out of the home, pulling in cooler air from a lower intake point. Dark-colored or ceramic materials at the top of the chimney can help increase heating to enhance this effect.Passive heating: When combined with a heat source like a Trombe wall, a solar chimney can pull heated air back into the house. Sizing and calculation considerations Standard chimney-sizing rules, such as the 3-2-10 rule for safety and drafting, are primarily for combustion appliances and do not apply to a passive thermal chimney. For a residential-scale thermal updraft, consider these factors:
Chimney dimensions Height: A taller chimney creates a stronger draft because of the greater pressure differential between the top and bottom. Residential solar chimney concepts often recommend heights of 20 meters (about 65 feet) or more to function optimally.
Cross-sectional area: The area must be large enough to allow for good airflow, but if it is too large, the air will lose heat too quickly, weakening the draft. For passive ventilation, the air velocity will be much slower than in a combustion flue.Ratio of area to height: The ideal sizing depends on a complex interplay of the cross-sectional area and height.
As an example, one engineering calculation for natural draft uses the formula for airflow rate (\(Q\)), which depends on the chimney height (\(H\)), cross-sectional area (\(A\)), and the temperature difference between the inside (\(T_{i}\)) and outside (\(T_{o}\)) air.\(Q=A\times \sqrt{2\times g\times H\times \frac{T_{i}-T_{o}}{T_{o}}}\)
Example calculation for natural draft ventilation To calculate the airflow rate (\(Q\)) for a simple, two-story house with an 8-meter high chimney (from ground floor to top duct) in a climate where the inside temperature (\(T_{i}\)) is 20°C and the outside temperature (\(T_{o}\)) is -10°C:
Step 1: Convert temperatures to Kelvin \(T_{o}=-10\degree C+273.15=263.15K\)\(T_{i}=20\degree C+273.15=293.15K\)
Step 2: Define variables \(H\) (chimney height) = 8 m\(g\) (gravitational acceleration) = 9.81 m/s²
Step 3: Calculate the density of the air Outside air density (\(\rho _{o}\)):\(\rho _{o}=\rho _{standard}\times \frac{T_{standard}}{T_{o}}=1.293\frac{kg}{m^{3}}\times \frac{273.15K}{263.15K}\approx 1.342\frac{kg}{m^{3}}\)Inside air density (\(\rho _{i}\)):\(\rho _{i}=\rho _{standard}\times \frac{T_{standard}}{T_{i}}=1.293\frac{kg}{m^{3}}\times \frac{273.15K}{293.15K}\approx 1.205\frac{kg}{m^{3}}\)
Step 4: Calculate the velocity and flow rate (simplified) A simplified formula for velocity (\(v\)) shows that it is driven by the pressure difference created by the height and temperature differential. The airflow rate is then calculated based on this velocity and the cross-sectional area of the chimney.The final calculation for a 0.2m (approx. 8 inches) diameter duct in the example yields an airflow of 0.12 m³/s. Practical design considerations
Insulation: Insulating the chimney is crucial to maintain high internal temperatures and a strong draft. Placing the chimney within the house's warm envelope is more effective than placing it on an exterior wall.Location: The optimal location depends on the purpose. For passive heating, a central location might be effective, while for ventilation, a location that draws air effectively from the living space is best.Professional consultation: Due to the complexity and reliance on external factors, consulting with an engineer or experienced chimney professional is recommended for a residential-scale updraft thermal system.

https://www.rumford.com/draft.html

Buckley Rumford Fireplaces
Chimney Draft

11/5/23
Chimney draft can be complicated but the principles are well known. If we consider three factors that affect draft separately, we can build chimneys to vent fireplaces that will work. The three factors are:
1) Pressure differential - the basic mechanism of draft.
2) Flow capacity or rate - getting enough draft.
3) The chimney in relationship to the house.

1) Pressure differential - the basic mechanism of draft.
The combustion flue gases inside chimneys are hotter than the ambient outside air and therefore less dense and lighter than the ambient air. The column of warm air inside the chimney, being more buoyant, rises in the chimney, reducing the pressure at the bottom of the chimney so that ambient air flows into the combustion zone and moves the flue gases up and out of the chimney. That movement or flow of combustion air and flue gas is called "natural draught", "natural ventilation", "chimney effect", or "stack effect". The taller the stack, the more draught is created. The equation below provides an approximation of the pressure difference, ΔP, (between the bottom and the top of the flue gas stack) that is created by the draught:

where:
ΔP = available pressure difference, in Pa
C = 0.0342
a = atmospheric pressure, in Pa
h = height of the chimney, in m
To = absolute outside air temperature, in K
Ti = absolute average temperature of the flue gas, in K
The above equation is an approximation because it assumes that the molar mass of the flue gas and the outside air are equal and that the pressure drop through the flue gas stack is quite small. Both assumptions are fairly good but not exactly accurate.
The important thing for us is to note that draft is directly proportional to the height of the chimney, the temperature of the flue gasses and the atmospheric pressure. A twenty foot tall chimney creates a pressure differential twice as great as a ten foot chimney. A chimney at sea level where a = 14.7 pounds per sq.ft. has almost one and a half times the pressure differential as an equal chimney at 10,000 feet in elevation where a - 10 pounds per sq.ft.
The pressure differential is only part of the question. Notice that flue size doesn't matter at all.
2) Flow capacity or rate - getting enough draft.
How much air flows into the bottom of the chimney is estimated by the formula below.

where:
Q = flue gas flow rate, m³/s
A = cross-sectional area of chimney, m²
C = discharge coefficient (usually from 0.65 to 0.70)
g = gravitational acceleration at sea level, 9.807 m/s²
H = height of chimney, m
Ti = absolute average temperature of the flue gas in the stack, K
To = absolute outside air temperature, K
Again, without getting too concerned about the math or the units, the important thing for us is to note that the flow is directly proportional to the cross-sectional area of chimney and to the square root of the height of the chimney and the temperature differential multiplied by a big number. In other words the height of the chimney and the temperature of the flue gasses, while directly proportional to the pressure differential in the static case above are a little less important due to friction or drag and energy it takes to accelerate the gasses.
3) The chimney in relationship to the house.
That's all great if the chimney were standing out in the middle of a field. But most fireplaces are inside houses. Houses are filled with warm air relative to ambient air in the heating season and, like in a chimney, the warm air in a house is less dense than the ambient cooler air and tends to rise. In other words the house itself can act as a chimney. If you open an upstairs window the warm air in the house would rise and flow out of the window while creating negative pressure downstairs that would cause air to flow in an open downstairs window. Complicate this situation with various fans and other appliances that draw air out of the house.
In a house what matters is the pressure differential between the air in the bottom of the chimney compared with the pressure at the same level inside the house. If the house is taller than the chimney the house could draft better than the chimney and outside air will flow down the chimney into the house. If an appliance, like a kitchen fan, is turned on that could reduce the indoor air pressure and cause a downdraft even if the chimney is tall enough.
Flow matters too. In a tightly sealed up house with no fans on and no leaks or open windows there may not be an excessively negative indoor air pressure but there also needs to be enough flow rate (Q) for combustion and to carry away the smoke in the fireplace.
Effects of Altitude
Altitude affects the pressure differential probably because pressure vs altitude is logarithmic rather than lineal. A 30 foot tall chimney at sea level spans a greater pressure differential than it does at 10,000 feet.
Altitude has no effect on flow rate, but flue size does.
The rule-of-thumb advice is usually to increase the flue area at high altitudes but, if you want to compensate for a decreased pressure differential, the chimney height should be increased.
In our smoky fireplace recommendations we recommend under normal living conditions (furnace, bath and kitchen fans on or off windows open or closed, etc.) there should be an updraft in a cold chimney with no fire in the fireplace. This is the pressure differential test.
We also recommend that adequate outside air be ducted into the house to make up for all the air being leaked out or exhausted by all the appliances and fans likely to be on - and enough extra for the fireplace - at least one cubic foot per minute (CFM) for every square inch of flue area. This is to test for adequate flow.
As a practical matter we recommend that no altitude adjustment is needed because what really matters is chimney draft compared with indoor air pressure. Just like at sea level, if the chimney draws when cold while simulating the one CFM per sq.in. of flue area with a fan, the fireplace will work fine at any altitude. But at altitude if you have trouble getting a pressure differential (updraft) you can increase the height of the chimney and if you can't get enough flow you can use a larger flue size.

SpaceNut · 2025-08-24 14:58:36

I thinks of the issues is looking at this from a high speed windmill rather than a forse to move the generator.

AI Overview

+11
The fundamental equation for wind power generation is P = 0.5 * ρ * A * v³, where P is the power generated, ρ (rho) is the air density, A is the swept area of the turbine blades, and v is the wind velocity cubed. To calculate the power derived from a wind turbine, you multiply these variables, and for a more practical application, you also multiply by the turbine's efficiency factor, or power coefficient (Cp), to get P = 0.5 * Cp * ρ * A * v³.
Understanding the Variables
P (Power): The power of the wind in Watts.
Cp (Coefficient of Performance): A non-dimensional factor representing the turbine's efficiency, or how much of the wind's kinetic energy it can convert to mechanical energy.
ρ (Rho): The density of the air in kilograms per cubic meter (kg/m³). This value can be around 1.225 kg/m³ at standard conditions.
A (Swept Area): The circular area covered by the rotating turbine blades. It is calculated using A = πr², where 'r' is the length of the blade or the radius of the rotor.
v (Velocity): The speed of the wind in meters per second (m/s).
Why the Cube of Velocity Matters
The most critical factor in the equation is the wind velocity (v), which is raised to the power of three (v³). This means that a small change in wind speed has a large impact on the power output. For example:
If the wind speed doubles, the power output increases by a factor of eight (2³ = 8).
If the wind speed halves, the power output decreases to one-eighth (0.5³ = 0.125) of its original value.
Factors Affecting Actual Power Generation
Turbine Design and Blade Length:
.
The swept area (A) is directly proportional to the square of the blade length.
Air Density:
.
Air density varies with temperature and altitude, impacting available power.
Efficiency:
.
The power coefficient (Cp) and generator efficiency (Ng) reduce the theoretically available power to the actual output.
Location and Wind Conditions:
.
The amount of power generated depends on the wind speed frequency distribution and how often the wind blows at certain speeds.

SpaceNut · 2025-08-24 15:04:42

https://home.uni-leipzig.de/energy/ener … als/15.htm

Physics of Wind Turbines
Over a thousand years ago, windmills were in operation in Persia and China, see TelosNet and Wikipedia. Post mills appeared in Europe in the twelfth century, and by the end of the thirteenth century the tower mill, on which only the timber cap rotated rather than the whole body of the mill, had been introduced. In the United States, the development of the water-pumping windmill was a major factor in allowing farming and ranching across vast areas in the mid-nineteenth century. These windpumps (sometimes called Western mills) are still common in America and Australia. They have a rotor with about 30 vanes (or blades) and the ability to turn themselves slowly. Of the 200,000 windmills existing in Europe in the mid-nineteenth century, only one in ten remained a century later. The old windmills have since been replaced by steam and internal combustion engines. However, since the end of the last century the number of wind turbines is growing steadily, and they are beginning to take an important role in power generation in many countries.
We first show that for all wind turbines, wind power is proportional to wind speed cubed. Wind energy is the kinetic energy of the moving air. The kinetic energy of a mass m with the velocity v is

The air mass m can be determined from the air density ρ and the air volume V according to

Then,

Power is energy divided by time. We consider a small time, Δt, in which the air particles travel a distance s = v Δt to flow through. We multiply the distance with the rotor area of the wind turbine, A, resulting in a volume of

which drives the wind turbine for the small period of time. Then the wind power is given as

The wind power increases with the cube of the wind speed. In other words: doubling the wind speed gives eight times the wind power. Therefore, the selection of a "windy" location is very important for a wind turbine.
The effective usable wind power is less than indicated by the above equation. The wind speed behind the wind turbine can not be zero, since no air could follow. Therefore, only a part of the kinetic energy can be extracted. Consider the following picture:

The wind speed before the wind turbine is larger than after. Because the mass flow must be continuous, A v = constant, the area A2 after the wind turbine is bigger than the area A1 before. The effective power is the difference between the two wind powers:

If the difference of both speeds is zero, we have no net efficiency. If the difference is too big, the air flow through the rotor is hindered too much. The power coefficient cp characterizes the relative drawing power:

To derive the above equation, the following was assumed: A1v1 = A2v2 = A (v1+v2) / 2. We designate the ratio v2/v1 on the right side of the equation with x. To find the value of x that gives the maximum value of CP, we take the derivative with respect to x and set it to zero. This gives a maximum when x = 1/3. Maximum drawing power is then obtained for v2 = v1 / 3, and the ideal power coefficient is given by

Another wind turbine located too close behind would be driven only by slower air. Therefore, wind farms in the prevailing wind direction need a minimum distance of eight times the rotor diameter. The usual diameter of new wind turbines is 140 m with an installed capacity of 5 MW onshore. 200 m diameter and 10 MW will come soon offshore.
The installed capacity or rated power of a wind turbine corresponds to an electrical power output of a speed between 12 and 16 m/s, with optimal wind conditions. For safety reasons, the plant does not produce greater power at the high wind conditions than those for which it is designed. During storms, the plant is switched off. Throughout the year, a workload of 23% can be reached inland. This increases to 28% on the coast and 43% offshore.
More details can be found in the Internet pages wind-works.org and in the pages of the American Clean Power Association (ACP).
For 2023, IRENA reports an installed wind power capacity of 1017 GW worldwide and 148 GW in the United States. The Alta Wind Energy Center in California has been the largest wind farm in the United States since 2013, with a capacity of 1.6 GW. The electricity produced from wind power in the United States amounts about 10% of all generated electrical energy. Detailed information about the present state in the US can be found in Wikipedia and in a 2024 PNNL report.
A crucial point about wind power is that the times of peak electricity demand and the times of optimal wind conditions rarely coincide. Thus, other electric power producers with short lead times and a well developed electricity distribution system are necessary to supplement wind power generation.
Why have the wind turbines of today lost one blade in comparison to the old four-blade windmills?
The rotor power Pmech = 2π M n is proportional to the torque M acting on the shaft and the rotation frequency n. The latter is influenced by the tip speed ratio λ, which is calculated according to λ = vu / v1 from the ratio of peripheral speed (tip speed) vu of the rotor and the wind speed v1. The torque M increases with the number of blades. It is therefore largest for the many-vaned Western mills, smaller for wind mills with four blades, and smallest for today’s wind turbines with 3 blades. However, every blade, as it rotates, reduces the wind speed for the following blades. This "wind shadow" effect increases with the number of blades. The optimal tip speed ratio is about one for the Western mill, barely over 2 for the four-bladed type, and 7−8 for the three-bladed rotors. At their optimal tip speed ratio, three-bladed rotors achieve a cp value of 48% and come closer to the ideal value of 59% than wind turbines with 4 blades. For wind turbines with two blades or weight-balanced one-bladed rotor configurations, the yield is smaller in spite of a higher tip speed ratio, because of the smaller torque M. Therefore, wind turbines today have three blades.

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