Thermodynamic cycle that can reuse latent heat of condensation 8

[haruosan]

I'm developing a thermodynamic cycle that transfers existing heat to generate steam. The heat transfer includes reusing the latent heat of condensation harvested at the condenser to heat the working fluid. Normally, this is not possible because the condenser is not the hottest point in the cycle and therefore any heat harvested cannot be transferred back into the working fluid which is hotter at any point in the cycle before the condenser. This limitation does not exist in the cycle I'm developing. Unlike a Rankine Cycle which generates high temperature heat for the generation of superheated steam, this cycle uses and re uses low temperature heat for the production of steam.

I'm looking for a mechanical engineer who'd like to be a cofounder for a green tech company based on this cycle. Preferably you live in CA or would be willing to move to CA at some point after funding is achieved and you are receiving a salary. The skills needed to prove the viability of the cycle and develop it are:

CFD
Heat Balance
MATLAB
Simulink
CAD
Turbomachinery
Electrical Engineering knowledge is a plus

I am familiar with OpenFOAM, Fusion360, MATLAB and other tools.

Please respond only if you are interested, have the skills, and are willing to become a cofounder.

 

[haruosan]

GBTorpenhow (Mechanical)16 Jan 24 20:15
Are these pressures absolute or gauge? If absolute, then how does the condensate exist as liquid at 0 abs pressure and 373K? If gauge, temps are way off (1.659 m3/kg @ 101.325 kPag is 730K).

What causes the pressure change between 2 and 3? 4 and 5?

How does the turbine spin if there is no pressure differential across it?

Do you think it is realistic to have vapor at the turbine inlet with a fluid velocity of 8,851 m/s? What is the speed of sound for this fluid at those conditions?

The pressures are absolute. The condensate expands in an adiabatic process as the pressure is reduced and reaches 0 Pa. The process occurs in 200 μs. My goal was to represent this expansion from liquid @ .001 m^3 to vapor @1.24 m^3 (state point 2) then further expand to 1.69 m^3 as it is heated to 373 K.

What causes the pressure change between 2 and 3? 4 and 5?
I do not know what pressure will be achieved within the boundary layer turbine as the vapor enters it or after heat is applied. So, to get a ball park idea of the potential work achievable, I modeled the expansion in a hypothetical isobaric process as heat is added to calculate the specific volume expansion. Will this result in that much work through a boundary layer turbine? I don't know.

How does the turbine spin if there is no pressure differential across it?
In a real scenario there will be a pressure differential, but at this time, I do not know what this pressure differential is. Research does show there is an increase in pressure within the boundary turbine and a decrease in pressure of the fluid upon exit from the turbine, but exact pressure in this scenario are not yet known. I used an isobaric process with heat added to illustrate how the vapor expands in specific volume as a prediction of the work possible.

Do you think it is realistic to have vapor at the turbine inlet with a fluid velocity of 8,851 m/s? What is the speed of sound for this fluid at those conditions?
I do think this value is high and, actually, my calculation is incorrect due to the wrong area. The diameter of the exit for a 1 l/s flow rate is 25 mm, not 12 mm so the area of the exit should be .0004908. 1/.0004908 = 2,037 m/s. Also, the liquid flow at the inlet of the Venturi is 3 m/s and accelerates to 35.67 m/s through the throat.

 

[3DDave]

.0002 secs, a delta V of 30 m/sec, a mass of 1 kg/sec.

Force = m dv/dt = 1kg * 30m/s /.0002 s => 150 kNewtons (33,000 lbf) of thrust.

Seems like a waste of energy to convert the pressurized liquid to a gas rather than driving whatever the boundary layer turbine (I assume that's the actual device) is supposed to be driving. There isn't energy being added to the working fluid ahead of the turbine so the flash reactor and turbine are just energy wasting components.

 

[haruosan]

3DDave (Aerospace)16 Jan 24 22:00
.0002 secs, a delta V of 30 m/sec, a mass of 1 kg/sec.

Force = m dv/dt = 1kg * 30m/s /.0002 s => 150 kNewtons (33,000 lbf) of thrust.

Seems like a waste of energy to convert the pressurized liquid to a gas rather than driving whatever the boundary layer turbine (I assume that's the actual device) is supposed to be driving. There isn't energy being added to the working fluid ahead of the turbine so the flash reactor and turbine are just energy wasting components.

3DDave,

Not sure I follow, but I think you're saying the force is reduced by the phase change from water into steam. Liquid water, in this case, is more effective at providing kinetic energy to the turbine.

Shouldn't the thrust of the steam be greater than the liquid - up to 1600 times more, or at least something on the way to 1600X more. If the velocity of the exiting steam is 2037 m/s:

Force = m dv/dt = 1kg * 2037m/s /.0002 s => 10.185 MNewtons (2,289,679 lbf) of thrust.

 

[3DDave]

I'm saying the pump is adding putting energy into water. Then you are wasting that energy. The steam is not going Mach 75.

 

[haruosan]

I'm saying the pump is adding putting energy into water. Then you are wasting that energy. The steam is not going Mach 75.

The pump does add energy to the water which increases it's velocity through the Venturi. This reduces the pressure of the water to below its saturated vapor pressure. This drop in pressure imposes a metastable state that directs the sensible heat to latent heat. If the velocity of the water is 35 m/s and it changes phase into vapor, the velocity of the resulting vapor should be greater than the velocity of the liquid.

The energy isn't wasted, it facilitates a change in phase and the expansion creates work.

For the Bernoulli calculations from the spreadsheet above. The inlet and outlet of the Venturi is 25mm, r=12.5mm

3.14·12.5^2 = 490.625 mm² 0.0004906 m²

If the steam flow is 1kg/s
1/.0004906 = 2,038 m/s

I don't think the steam reaches this velocity because there are other factors such as friction, pressure, etc, but it's somewhere between 35m/s and 2037m/s

 

[3DDave]

You have a mechanical input to drive a mechanical output with energy wasted in between for no reason, using complicated and impractical intermediate steps.

You only can have that expansion if there is a downstream vacuum, but there isn't a means to maintain a vacuum in your system.

Best of luck that you limit the money and time wasted on this project.

 

[haruosan]

You have a mechanical input to drive a mechanical output with energy wasted in between for no reason, using complicated and impractical intermediate steps.

You only can have that expansion if there is a downstream vacuum, but there isn't a means to maintain a vacuum in your system.

Best of luck that you limit the money and time wasted on this project.

When water becomes vapor, it won't condense unless it comes in contact with a surface that is cooler than the vapor itself. The Venturi creates a zone of low pressure at the throat, this is where the water changes phase. Studies have shown that the length of the throat does not affect the pressure of the throat so if you make the throat long enough to accommodate the fluid for at least 200μs you have a chance to vaporize it before it exits the zone of low pressure. This process is already being used in geothermal power plants where hot water is forced through an expansion valve to create a two-phase flow without a flash chamber and only the expansion valve. I'm proposing to engineer a way to add heat through steam entrainment to create saturated steam or accept the two phase flow into a turbine that can handle two phase flow. Whether or not a saturated or two-phase flow is created, additional heat can be added to the turbine to further heat the vapor, vaporize any remaining water, or prevent any of the vapor from condensing. Then, heat the working fluid when it's a gas and it's specific heat is 1996 J/kg/K instead of heating it when it is liquid with a specific heat that is more than twice that at 4186 J/kg/K.

The single flash cycle contains only one throttling valve (expansion valve)
through which the geothermal fluid is expanded, and one separator to separate
the vapor from the liquid after the expansion process in the expansion valve.

The two-phase geothermal fluid is separated into steam and liquid brine in a
separator vessel at a pressure higher than atmospheric pressure.

 

[GBTorpenhow]

Any prospective employee worth their salt will likely see the following as red flags:
- A power cycle with an expansion valve immediately after a pump
- A power cycle where the only external heat input is applied after the work extracting device
- A work extracting device that is claimed to heat up the fluid stream
- Straight faced references to negative absolute pressures
- Liquid being conveyed to the inlet of a pump at 0 Pa absolute and 100C
- Vapor velocities 3-4x sonic velocities

Practical/technical issues aside, the fundamental conceit of your idea - that instead of rejecting condenser heat to atmosphere it can be used elsewhere in the cycle - is a violation of the laws of thermodynamics.

"It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the production of work and cooling of a heat reservoir." (Planck)

 

[SwinnyGG]

I mean from first principles.. you're saying you can input 350kW and get out 620kW?

You don't see an issue there?

 

[haruosan]

Any prospective employee worth their salt will likely see the following as red flags:
- A power cycle with an expansion valve immediately after a pump
- A power cycle where the only external heat input is applied after the work extracting device
- A work extracting device that is claimed to heat up the fluid stream
- Straight faced references to negative absolute pressures
- Liquid being conveyed to the inlet of a pump at 0 Pa absolute and 100C
- Vapor velocities 3-4x sonic velocities

Practical/technical issues aside, the fundamental conceit of your idea - that instead of rejecting condenser heat to atmosphere it can be used elsewhere in the cycle - is a violation of the laws of thermodynamics.

"It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the production of work and cooling of a heat reservoir." (Planck)

Any prospective employee worth their salt will likely see the following as red flags:
- A power cycle with an expansion valve immediately after a pump

Geothermal power plants use the natural pressure of geothermal steam to force hot water through an expansion valve. Natural pressure or a pump, there really isn't a difference except you have to ensure you have the correct head for the pump inlet so cavitation doesn't occur through the pump. 

- A power cycle where the only external heat input is applied after the work extracting device

The heat input is applied at the work extracting device (or series of extracting devices). When heat is applied to a gas cycling through a boundary layer turbine it expands and forces the turbine to spin faster as well as adds torque. 

- A work extracting device that is claimed to heat up the fluid stream

The work extracting device itself doesn't heat up the fluid stream, but instead heat is applied to the work extracting device which, in turn, heats the working fluid.

- Straight faced references to negative absolute pressures

What's wrong with negative pressure? Do you still believe that negative pressure in fluids do not exist? 

Thermodynamics of  Negative  Pressures  in  Liquids

https://www.degruyter.com/document/doi/10.1515/jnet.1998.23.4.351/pdf

Exploring water and other liquids at negative pressure

https://insu.hal.science/insu-00726437/document

The Physics of Negative Pressure

https://www.discovermagazine.com/the-sciences/the-physics-of-negative-pressure

I believe it's related to molecular bond forces such as hydrogen bonds in water. Even when pressure and temperature are 0 there's no longer any heat to break hydrogen bonds and the only force left to counteract the molecular forces is stretching or negative pressure. However, it's difficult to study since it forces liquids into a metastable state which is forced to equilibrium. 

- Liquid being conveyed to the inlet of a pump at 0 Pa absolute and 100C

With the right head, it's possible

- Vapor velocities 3-4x sonic velocities

I don't believe the vapor reaches these speeds, for various reasons but, as many papers describe there is a shockwave force when water flashes into steam. the force created high velocity. How high, I don't yet know. 

Practical/technical issues aside, the fundamental conceit of your idea - that instead of rejecting condenser heat to atmosphere it can be used elsewhere in the cycle - is a violation of the laws of thermodynamics.

I don't believe it is a violation of the laws of thermodynamics. Take for example, condensate reuse. How is heat from a previous cycle reused in the next cycle? How about we use the latent heat of condensation to heat water. Are you suggesting that the heated water could never be reused in the same cycle the heat came from?How about we use the latent heat of condensation to heat steam. Are you suggesting that the heated steam could never be reused in the same cycle the heat came from to heat the boiler feed water?Heat transfers from hotter to colder - it doesn't matter where the hot or cold is. 

"It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the production of work and cooling of a heat reservoir." (Planck)

The important part of Planck's statement above is the suggestion that heat must be shed to a cold reservoir. The heat has to transfer from hot to cold in order to create work. Heat transfers from hot to cold, it doesn't matter where the heat or the cold is. 

 

[haruosan]

I mean from first principles.. you're saying you can input 350kW and get out 620kW?

You don't see an issue there?

My intention is to increase the efficiency of steam power cycles by rethinking how they're done. Efficiency improvements of 10%, 20% would be great and products can be created to accomplish these improvements.

Creating more power from less power violates the second law of thermodynamics and is a problem - it's impossible. But I also know that a heat pump that transfers more heat than its power input could generate, also seems to violate this law. But, of course, it doesn't. Instead, it moves heat rather than generate the heat so it can have a COP of 1 or higher. Even as high as 8. A heat pump using 1 kilowatt can transfer 8 kilowatts of heat.

I don't know if it can be achieved, but I'll certainly investigate the ability to move heat for the phase change of water. If a system is moving heat like a heat pump and using it for phase change, it may be able to achieve a COP value greater than 1.

 

[SwinnyGG]

If a system is moving heat like a heat pump and using it for phase change, it may be able to achieve a COP value greater than 1

Except in your system, the heat being 'pumped' is heat that was generated by the system itself. This is perpetual motion.

Actual heat pumps move heat between infinite reservoirs.

 

[GBTorpenhow]

The important part of Planck's statement above is the suggestion that heat must be shed to a cold reservoir.

Yes.

Heat transfers from hot to cold, it doesn't matter where the heat or the cold is.

No, it does matter (a lot) if the source/sink is internal to the heat engine or external to the heat engine. "Hot reservoir" and "cold reservoir" must be (and are by definition) external to the heat engine.

The first thing any competent engineer will do is draw a box around your heat engine separating internal and external components and label all the flows of heat and work crossing the box.
If the energy flows don't sum to zero, something is wrong.
If the net work out per heat in is more than the Carnot efficiency allows, then something is wrong.
If there is no heat transfer leaving the box, something is wrong.

I see a heater (Q_in), a pump (W_in), and a turbine (W_out). No Q_out which means you have violated the law and Officer Planck is en route with an arrest warrant.

 

[GBTorpenhow]

But I also know that a heat pump that transfers more heat than its power input could generate, also seems to violate this law.

No, heat pumps don't violate or seem to violate anything. Heat pumps move heat from cold to hot reservoirs, with work input required. Perfectly fine to get more heat transfer than work in.

Just a reminder, OP, you are proposing a heat engine, not a heat pump, and as such you are limited to the Carnot efficiency.

 

[haruosan]

Quote (haruosan)
If a system is moving heat like a heat pump and using it for phase change, it may be able to achieve a COP value greater than 1

Except in your system, the heat being 'pumped' is heat that was generated by the system itself. This is perpetual motion.

Actual heat pumps move heat between infinite reservoirs.

No, it's not perpetual motion. It's heat being added from a hot source to a cooler source.

I guess you didn't read my other comment about condensate reuse.

Condensate reuse is when steam from the cycle is condensed and the hot water (which, by the way, contains heat from the original cycle) is reused in the cycle itself. Is this a violation of any law of thermodynamics? No, it's not.

Is the heat from a cycle somehow marked with an identifier that says this heat came from cycle X therefore it can't flow from hot to cold in cycle X???? Really. Do you really believe that? If that's the case, condensate that was heated in cycle x could never be reused in cycle X.

 

[3DDave]

Since no work is extracted from the turbine, you can eliminate the turbine. With it gone you can eliminate the heater, the heat pipe, the pump, the flash reactor, and the condensor. Keep the water bucket. You might need water.

The flash jet expansion cycle doesn't show the energy state. Trust me, no one cares about changing the density of water from liquid to vapor if it is just in a closed system that does no useful work.

 

[haruosan]

Quote (OP)
The important part of Planck's statement above is the suggestion that heat must be shed to a cold reservoir.

Yes.

Quote (OP)
Heat transfers from hot to cold, it doesn't matter where the heat or the cold is.

No, it does matter (a lot) if the source/sink is internal to the heat engine or external to the heat engine. "Hot reservoir" and "cold reservoir" must be (and are by definition) external to the heat engine.

The first thing any competent engineer will do is draw a box around your heat engine separating internal and external components and label all the flows of heat and work crossing the box.
If the energy flows don't sum to zero, something is wrong.
If the net work out per heat in is more than the Carnot efficiency allows, then something is wrong.
If there is no heat transfer leaving the box, something is wrong.

I see a heater (Q_in), a pump (W_in), and a turbine (W_out). No Q_out which means you have violated the law and Officer Planck is en route with an arrest warrant.

Really?? Think about it. Think about it long and hard.

Your claim is that heat knows where it came from. Hypothetically, let's say 1 kg of steam at 1000C is condensed to create 1 liter of condensate at ~95C. The heat released from the condensation process is 1996 x 900 = 1,796 kJ + 2,256 (latent heat) = 4,052 kJ @ roughly 1000C. Are you saying this heat could be used to heat water, but that water could never be used as condensate for the next cycle. ??

Or, hypothetically, a geothermal power plant creates steam using an expansion valve and the steam exits at 100C. A pre heater heats the steam to 500 C before it enters a turbine. The steam upon exit from the turbine is 150 C. All of the thermal energy is transferred to a thermal block for storage. Are you saying that this 150C thermal storage block could not heat the steam that exits the expansion valve at 100 C. Is there some force stopping the 150C temperature from transferring to the 100C steam because the heat originally came from that cycle?

The cold reservoir needs to be present in order to shed heat, but that heat could always be used back into the same cycle as long as you can transfer the heat to a cooler area.

It is really quite simple. Don't overthink it.

 

[haruosan]

Here's an example of latent heat reuse from a cycle to heat the working fluid of the same cycle:

The Principle Behind the Regenerative Rankine Cycle

Relatively more specific, the Regenerative Rankine Cycle deviates from a simple Rankine Cycle by using feedwater heaters. These heaters recover energy from the steam exiting the turbines. This process, known as 'regeneration', is the reason for the cycle's name as it regenerates heat internally, hence bettering the efficiency of the cycle and generating more power with the same amount of input.

1. Introduction
Regeneration is a widely implemented method for increasing the thermal efficiency of a Rankine cycle. In this method, extracted steam from steam turbine is used to increase feed water temperature before feed water enters boiler.

https://www.sciencedirect.com/science/article/pii/S2214157X21006390

https://www.researchgate.net/figure...-open-feedwater-heater-process_fig2_266870678

The regenerative Rankine Cycle reuses heat by using the steam to heat the next cycle instead of losing the heat to the environment. Anytime heat can be reused, a cycle will become more efficient. I am only pushing that idea further than it has been before which equals more efficiency. Simple.

 

[GBTorpenhow]

Nobody is saying you can't use a hot stream from one spot in a cycle to heat another spot. Regenerative Rankine is a fine example of that. What Officer Planck is saying is that you can't use all of it.

Are you saying this heat could be used to heat water, but that water could never be used as condensate for the next cycle. ??

I don't know what "the next cycle" means in relation to a steady state closed loop, but yes, in Rankine cycle terms, hot turbine exhaust absolutely cannot entirely transfer its heat back into the boiler feedwater because it isn't possible for a process stream to cool itself.

Or, hypothetically, a geothermal power plant creates steam using an expansion valve and the steam exits at 100C. A pre heater heats the steam to 500 C before it enters a turbine.

This example demonstrates one of the mistakes you have made in your cycle design. Steam coming out of a flash drum as saturated vapor at 100C (P_sat = 101.42 kPa), then heated to 500C (still at 101.42 kPa) can't realistically power a turbine at all because even though it is appreciably superheated it is at essentially atmospheric pressure. Turbines run on pressure differential, not inlet temperature. This is why pump then heat then flash (similar to a geothermal flash cycle) makes sense, whereas pump then flash then heat does not.


This is all very droll, but you can prove that you aren't running afoul of Sergeant Carnot and Officer Planck very easily with a simple control volume analysis - just draw a box around your heat engine separating internal and external components and label (and quantify) all the flows of heat and work crossing the box.

 

[SwinnyGG]

Is the heat from a cycle somehow marked with an identifier that says this heat came from cycle X therefore it can't flow from hot to cold in cycle X????

Your claim is that heat knows where it came from.

No one is saying that. You're missing the point. By engaging in all these arguments about what things are what temperatures at what locations, you're skipping like 9 steps in the process of trying to come up with a cycle description that makes any sense at all, let alone one that might function in the real world.

So, back to basics. A couple of very simple, as-yet-unexplained first principles problems with the cycle you have put on display thus far:

1) As drawn, your cycle utilizes what you are calling a 'turbine' which increases the enthalpy of the working fluid between inlet and outlet. This means your 'turbine' is applying work to the system, not extracting work from the system. When challenged on this thus far, you hand wave it away by saying 'the working fluid is heated in the turbine'. Physical realities of connecting a giant heat pipe to a moving turbine surface aside, in schematic terms you can't do that. Turbines extract energy from the system as useful work, they don't add energy in. Showing two separate processes (expanding the working gas to extract work, adding heat to the working gas to increase enthalpy) as a single schematic item is a very confusing practice, and as a result is not how it's done.

2) As drawn, there is no waste heat lost from your system, anywhere. You show three power inputs ('heater', 'pump', 'turbine') and no losses. Your cycle as drawn just heats the working fluid to higher and higher enthalpy, forever, with no losses and no extracted useful work.

3)There appear to be a lot of mathematical errors in your state equations- ie you show 'vapor' at some pressure and temperature that aren't correlated correctly. How exactly are you calculating each state point? I suspect you might be using ideal gas law for steam. If that's the case, steam cannot be modeled as an ideal gas - this is why steam tables exist. If that's what you're doing, you're introducing a lot of error via calculations using incorrect values.

4) Based on what you've posted thus far, it doesn't seem like you understand P/V or T/S diagrams. Not trying to offend you, but the giveaway here is that you keep posting P/V diagrams for a cycle you claim is closed, that isn't closed according to the PV diagrams you're providing. If you're serious about this, it's going to be way easier to iterate some version of the cycle you want and also to communicate to an engineer how you think it should work with a correct PV diagram than it's going to be with a process layout. In system design the PV or TS diagram informs the process layout - not the other way around.

Laying out a P/V or T/S diagram is actually very easy - you'll get better results by hand than with excel. Calculate and plot values (or in the case of steam, just look them up) for each state point, connect the lines at the slope dictated by the type of process taking place between each state point. A competent engineer is going to understand this in about 2 seconds. The fact that you either can't or just have not provided a closed PV diagram up to this point in the thread is why no one believes you. This is the most basic tool for theoretical analysis of a thermodynamic cycle, and the easiest one to understand. Not having this basic piece of information is a red flag for all of us.