03 November 2006
Metastatic Systems: Thermodynamic Economies Follow-on.
A better name for this post would probably be ‘homeostatic systems.’ The only problem is that you can’t associate the word ‘homo’ or any of its derivatives with airplanes. Really. It’s a pilot thing. We’re juvenile, I know. I plan on growing up after I’m senile. That way, I’ll keep forgetting that I was supposed to grow up at some point, and I‘ll never have to. Anyways, here’s the post. Its boring… consider yourself warned.
This is a continuation of the Thermodynamic Economies post, in a series of three posts. They work from theoretical to practical, beginning with systems engineering methodologies and ending with a single-fluid aircraft. One of the implications of the first post was that passive energy reclamation would create a more efficient overall system. Building reclamation systems as a finishing touch on an extant design would result in some savings, but tying together multiple systems from the outset would yield a far more efficient overall result. Fusing systems ensures that the summed absolute sub-system heat flow is closer to net thermodynamic flows, hence the system as a whole would be more elegant and economical. In order to do so, the now-fused systems would need some means of regulating themselves to an equilibrium. Let’s steal a page from God (and biology.)
Stealing From Biology. It’s cold outside. You start shivering. Your body burns energy to produce heat, bringing your core temperature back up to where it’s supposed to be. It’s hot outside. You start sweating. Your body burns energy to dissipate heat, bringing your core temperature back down to where it’s supposed to be. Both of these are active heat pumping systems, something along the lines of the Carnot cycle. Nothing cosmic here. We do this in human engineered systems all the time. The oil temperature is high, so the oil cooler flaps open wider, increasing drag. We burn energy to pump out heat. We need anti-ice on the leading edges of the wings, so we steal late stage compressor bleed air to heat it. We burn energy to make heat. We shiver and we sweat. At the same time. And here is the problem.
Bodies generally don’t shiver and sweat at the same time (unless you‘re snowboarding.) In fact, most of the time bodies are neither shivering nor sweating. Usually, our bodies are well able to keep core temperature near nominals merely by varying the rate at which the heat produced through normal processes is lost to the environment. We open or close pores, allowing more or less heat to escape into the environment. There will be times where energy production is too high or the environment is either too hot to allow heat to escape or too cold to allow heat to be effectively retained. We’ll call this surge capacity. During surge states, the body must resort to active means of pumping heat. This active pumping only serves to pick up the slack that the passive systems are unable to provide. This results in a much more efficient system that is still able to deal with a variety of environments.
System Basics. In order to appropriate this design, we must understand two things: energy flows and system architecture. Energy flows will allow the system to interact with the outside world; System architecture will allow the system to interact with itself. So quick thermo lesson. Exothermic systems give off heat to their environment. Endothermic systems take in heat from their environment. Set a fire, it’s exothermic (once you get past the activation energy thing.) Melt an ice cube, its endothermic. Because I’m lazy and I don’t feel like using the ‘cut and paste’ function of my word processor, I’ll call these ‘down’ and ‘up’ respectively. A ‘down’ transfer will reduce system temperature by moving heat to the outside. (We’re assuming the outside world is a giant heat sink.) A ‘up’ transfer will do the same. No, just kidding. It will do the opposite, of course.
So the basics of our system. In the course of normal ops, our system creates a degree of heat. In burning food, the body’s core temperature goes pretty high. In burning gas, an engine’s core temperature gets pretty hot. Same deal. At thirty grand, the air is pretty cold, and so is an aircraft’s skin. In normal weather, skin is touching air much cooler than 98.6, hence the skin is going to be the coolest part of the body. All the stuff in between is going to be somewhere between the core temperature and the skin temperature.
Energy Flows. The core of our system is the passive up and down transfer mechanisms. Assuming that during normal ops, heat is being created by the system, we can passively regulate the temperature of the system by changing how much of that heat is dissipated by the system. Using our biological example, closing pores is a passive up, opening them is a passive down. We can also increase or decrease how much of the ’normal ops’ heat is incorporated into the system, regulating both the inflow and the outflow of heat. For example, if we put a heat exchanger next to a propulsion system to capture additional heat, as well as an outflow heat exchanger open to the outside world, we could regulate how much fluid went through those heat exchangers and hence control system temperature using only ambient energy.
Such a system would rely on a large number of bypasses to increase or decrease fluid flow through the heat exchanger. In fact, these bypasses could turn many things into heat exchangers, for instance an aircraft’s wing. Run a bunch of lines in parallel across the wing’s surface area, starting at the leading edge and moving back. When you need more cooling, open up more lines. This increases the volume of the fluid required in the system, requiring either surplus capacity on the primary fluid pump or reserve fluid in a variable-sized accumulator (or both.) This parallel construction would allow an inherent anti-hemorrhage capability. If the bypass valve detected a massive uncommanded pressure drop in the line, it would close itself (and the other valve connected to the parallel circuit,) hence isolating the leak. The system would then automatically reroute itself through the remaining lines due to pressure gradients.
For surge capacity, such as running for a person or takeoff for an aircraft, we will need to augment our passive systems with active heat pumps. Most likely, we will need an active up and an active down. For the person, the active up is shivering, while the active down is sweating. For our system, some sort of a heater would be our active up, and some sort of refrigerator would be our active down. These supplemental systems sustain us until we can get back into normal ops conditions.
It is critical to understand that surge systems are for transient conditions. During takeoff, the ambient air temperature is not low enough to be an effective heat sink, and the engines are at max power. While running outside in 100 degree weather, ambient air which would normally be a heat sink actually begins to transfer heat into the body. Surge capacity is for times like this. If you need more cooling or heating during normal ops, you should increase the size of the passive system, rather then relying on the active system. Similarly, it is inefficient to design a passive system to accommodate transient conditions: you will have a lot of extra weight for capacity that you’re not going to use much. The active system will typically cost far more energy to move heat, although it will have a much higher capacity. This is similar to an afterburner, but remember that you don’t use ‘speed of heat’ for stable conditions (or you‘d be bingo fuel in 10 minutes.)
For an overall view, imagine a line. Here, Ill draw one.
---------------------------------------------------------------------------------------------------------------------
Unsustainable | Lo Surge Rng| Normal Governing Range |Hi Surge Rng| Unsustainable
----(Active up engaged)---- -----(Passive transfers only)----- ----(Active down engaged)----
[Sorry... looks better on Microsoft Word.]
System Architecture. Energy flows give us the means by which our system can seek an equilibrium with the outside world. External flows are only one half of the puzzle: we also need to figure out internal thermodynamic flows. We have to tie our system together thermodynamically. In order to do this, we need an internal heat transfer mechanism, and a partitioning of internal temperature zones.
Thermo gives us three options for heat transfer: conduction, convection and radiation. Conduction moves heat the fastest, and generally involves the least amount of losses. Guess what… we’re going to plagiarize God again here. Blood. The human body’s primary internal heat sink is blood. Blood moves heat from the core to the extremities, and ties the body together as one thermodynamic entity. So we’ll use fluid as our primary internal thermodynamic medium. Blood doesn’t just sit there and wait for conduction to take its course, it speeds up the process by being pumped through the body. The blood that was just next to the bodies core is taking that heat to the body’s extremities due to its motion from the heart. So our fluid must also be pumped. Accordingly, as a heat sink, we will use a relatively high volume of low pressure fluid. This will also make our design more survivable and maintainable.
The core temperature will always be higher than the temperature of the extremities, even if we increase the amount of fluid and the flow rate. Our design must reflect this. Now that we have tied the system together, we must decide how to partition the internal thermodynamic zones of the system. There are two basic options: continuous or discrete. Continuous designs, where temperatures move gradually down as you move away from the core, are very efficient and elegant, but they require very advanced adaptive processes, such as those found in biology or Nanotechnology (which are really the same thing.) So since we’re not cool enough to make a continuous system, we’re stuck with a discrete system with a number of zones of set temperature.
Two is the minimum number of zones for our discrete system: one hot and one cold. Three is a better design, though. You have one hot zone, which is the exothermic reservoir or ‘hot sink’ for the system. This hot zone can increase its temperature through passive means, capturing more of the heat from the core area, or through active means with an incorporated heat pump. It decreases its temperature by transferring fluid to the cold zone. The cold zone, the endothermic reservoir or ‘cold sink’ of the system, does the opposite. It decreases its temperature passively by opening more of itself to the outside and hence dumping heat, or actively through an incorporated heat pump. (You could make both heat pumps the same pump if you were really slick. I don’t know how to do that, so I won’t try.) It increases its heat by siphoning off more fluid from the hot zone. The mixed zone regulates its temperature with fluid from the hot and the cold zones, and completes the circuit by sending back the now warm fluid to the two zones in the proportion it came in at, thereby maintaining constant system pressure. Just as in the passive transfer systems, we rely on bypasses to regulate temperature.
We can increase the number of zones if we require different temperatures in different places (avionics at one temperature, passengers at another, etc.) Note, though, as we increase the number of zones past a certain point, we need to be more creative with the routing. It starts to look more like a continuous system. Note also that the fused system actually simplifies our design process. Instead of thermodynamically engineering every single subsystem, we only measure that subsystem’s thermodynamic impact on the total system during different phases of flight. We then adjust pump flow rate, total fluid capacity, passive transfer and active transfer capacity accordingly (and zoning if required.)
Example: ExecJet. This is what the whole thing was really about, in case you haven’t guessed it. Airplanes. Tragically, not Herks. ExecJets typically have more than enough runway, so takeoff performance is not quite as critical as with other aircraft. Also, they typically cruise straight and level at thirty grand, where the air is cold (and a great heat sink.) They don’t do anything really cool or exciting (sorry C-21 guys,) so they make a pretty good test case.
We’ll start with system architecture. We’ll fuse the endothermic leading edge anti-ice system, the exothermic engine oil system, and the variable environmental control system (excluding the pressurization function.) We’ll use oil as a medium, as we require the viscosity in order for it to work in the engine, and oil works as an effective heat sink. Neither of the other two systems have any viscosity requirements, only heat capacity requirements. We’ll run the fluid through a high-capacity, low-pressure pump attached to the engine shaft. (Next post, we’ll describe the specifics of that pump along with many other things.)
Now that we have a means of fusing the system, let’s define discrete thermal zones. There will be three: engine section, wing section and cabin section. The engine section will incorporate the active and passive up systems, and will also lubricate the engine. This lubrication process generates a significant amount of heat, and forms our core section of our system. This system will be regulated to 200 deg F (subject to change.) The wing section will incorporate the active and passive down systems. The leading edge needs to be heated to at least 32 deg F, so this system will be regulated to 50 deg F. The cabin section is built to meet the passenger’s comfort needs, and is regulated to approx. 70 deg F (variable.) This zoning follows the three zone discrete architecture previously discussed.
The passive down system incorporated into the wing system is composed of multiple fluid lines running in parallel from the leading edge, working back along the wing lengthwise. Bypasses govern the amount of fluid flowing through the virtual heat exchanger. The active down is a traditional ram-air oil cooler, possibly augmented by Venturis (an air conditioner run off the engine would supplement cooling requirements during ground ops.) The passive up system incorporated into the engine system is comprised of multiple parallel coils running around the turbine’s exhaust. If inadequate heat is being drawn from the lubrication process, oil will be routed through these tubes, costing some power but far less than bleed air currently does. The active up system is an electrical resistance heater.
Concept of operations is that the air conditioner runs during hot temperature ground ops. The cooling system is at surge capacity during takeoff, until the aircraft gets to altitude, and active systems are no longer required. The aircraft cruises at altitude, using ambient air and engine heat to regulate its temperature. Then the aircraft returns for landing, retaining surge capacity for a go-around.
Next time, we’ll go all the way with our plagiarism of the circulatory system. We’ll try to get rid of the pesky bleed air system, and create a more efficient, more survivable, and simpler aircraft: a single-fluid system. (Well, sort of two-fluid system. We’d have to use organic chemistry to get to a true single-fluid system. I’m not smart enough for that.) The more we look like nature, the better off we are. After all, if we could design an aircraft to the specs of a cockroach, that thing would never die (of course, the passengers and crew might turn to mush well beforehand. So you still can‘t crash unless you can undo the laws of deceleration. You need a pretty big crumple zone for 500 knots.) Anyways, see ya next time.
23:17 Posted in Boring Theories (Engineering) | Permalink | Comments (0) | Trackbacks (0) | Email this
12 September 2006
The Drive to Suburbia.
So the title is kind of a pun. The problem is that I hate puns. Oh well. So I have this other problem. When I write down theories, I generally end up coming up with new ideas. I keep hoping to reach the end of my ‘theories to write’ list, but the list keeps getting longer. Kind of like manna from the sky, but manna tastes good. So not that much like manna. I figured I wrote enough emotional stuff recently, so Ill write some uninteresting stuff for a while. This is the beginning on a three post series (I like threes and sevens..) on future economic frontiers in transportation. Boring, huh? Then don’t read it. Hahaha. (I get to be eccentric. It’s my blog.)
About two years ago, I’m on this ten hour drive with some friends, coming back from a resort in the mountains. I get totally restless on a drive that long, so I start thinking. This thing totally occurs to me about opportunity cost. A ten hour journey is prohibitive for routine purposes. But the same journey is still about 8 hours door-to-door if you were to fly on a major commercial carrier. A charter Cessna is prohibitively expensive, even though the journey would probably only be 3 hours door-to-door with a light aircraft. So the transportation cost is an amalgam of the time and the monetary expenses involved. Both of these factors are a function of available technology.
All of this is basic econ. Here’s the crazy part: it has something to do with how we live. So back in the day, back when it was hard, when we had to walk uphill both ways because we were hard-core like that, we lived in hunter-gatherer societies. Eventually, we got bored of that and decided that we want to live in one place. So we built nice Ziggurats and the like and start growing crops. In the process, we invent real estate. Yuck. Everything is cool, though, because as farmers, we live the same place we work. Not much in the way of transportation costs. That is, until we start doing crazy things like making things we can’t eat. So we go to factories to make widgets that can be sold for money which can be used to buy food. The problem is that we can’t all live at the factory. We start needing transportation. So this real estate equation gets more complicated. Let’s do some math. Cause math is fun. Sort of.
Equation #1: (Total Real Estate Cost) = (Property Cost) + (Transportation Costs)
Equation #2: (Property Cost) decreases as a function of the square of distance (from pop. center)
Note: Past a certain point, the curve becomes convex to the origin and starts to level out. The unit is cost per unit quantity.
Equation #3: (Transportation Costs) increase as a linear function of distance (from pop. center)
Note: This will vary for different modes of transportation. Each will have their own curve for cost per unit distance.
Equation #4: (Total Real Estate Utility) = (Property Utility) - (Transportation Utility Cost)
Equation #5: (Transportation Utility Cost) is an exponential function of distance, as it is a function of time. Its slope varies with different modes of transportation.
What does this mean? Two major things: first, changing modes of transportation greatly affect possibilities frontiers. If there are new transportation options, previously practically inaccessible real estate becomes available. Second, and as a function of this, the ‘carrying capacity’ of an area is determined by transportation technologies. As an area approaches its carrying capacity, real estate becomes prohibitively expensive, and leasing becomes more and more the only possible option. This has implications for class structures, as we will see later.
Let’s see this played out in history. Jump back to the industrial society. Now that people no longer live where they work, they have to live somewhere. This is a function of transportation. Public transportation systems are developed. They are efficient given the population densities of the time. (Note that public transportation ceases to be practical or efficient below a certain population density.) So tenement dwellings are constructed for the urban workers. Admittedly, this is a great oversimplification, but play along for a while. So the cities hit their carrying capacity, and those who already own land are the ones who make the profits off the rent. Stratification is strong, social mobility relatively low.
After a while cars roll around. There is now a means for people to live much farther from their work. So people who could not previously own land are able to purchase houses. Suburbia follows. People begin the individual commute, roads become the primary means of transportation. (This was greatly facilitated in the United States by the development of the interstate system.) Transportation costs go up, but housing costs go much farther down.
The rise of suburbia has some unique and undeniably middle class effects. With the ability to practically own land, social stratification is lessened. (Admittedly, this affects different groups differently due to inequities in the system. I’m speaking in broad generalities.) Consider Britain vs. America. In Britain, all the land has been owned for a long time. In order to ‘buy in’ to the property holding class, your family has to play good hands for good while. Because of this, the social stratification is stronger. For the American suburbanite, the buy-in cost is very low, easily achievable within a generation. Owning a token amount of land creates a middle-class consciousness, rather the total lack of a class consciousness. 95% of Americans self-identify as middle class. Perhaps this explains why (after the fizzling of the IWW ‘Wobblies’) Marxism never really caught on in mainstream America. Marxism points to the dialectic between those who own capital and those who provide labor. This assumes that these are separate groups. The paradox of the middle class is that they are capital-owning laborers. This is epitomized in the small businessman. Note that the only places where Marxism ever really caught on were the campuses of elite colleges, often occupied by the children of the wealthy. They would be some of the few who would really have any sort of non-middle class consciousness. This has sociological effects, to be certain. Some of the most interesting being the anti-gentrification of San Antonio by means of the suburbs. It is hard to segregate when people are simply buying where property values are the best. The suburbs serve as a means of melding cultures in SA. Gentrification seems to be most common in urban areas where all the property has basically static ownership. Tenancy, rather than ownership, seems to be the progenitor to ’white flight.’ This is a topic for another time, but it is ironic that intellectuals who hate suburbs on general principle are generally those who most actively participate in gentrification, which they claim to oppose. As another interesting note, as a child of a very proletarian family (son of a cop and a nurse,) I was very privileged to have trees and a back yard while growing up. I was also privileged to live in a very diverse neighborhood. As popular as it is to hate suburbia, because of suburbia I had opportunities I would never have had otherwise. A hundred years ago, my family would have been in a tenement paying rent to a landlord.
Anyways, my point before I started blathering on about sociology was that suburbs are currently approaching carrying capacity. In California and on the East Coast, property values within reasonable commuting range are becoming prohibitive. This is causing a drive toward the mid-west, but certain jobs are still centered on certain cities. There is pressure building toward the next transportation revolution, the next big thing to increase the carrying capacity of population centers. The creation of super-suburbia, a world where an average family will be able to have a weekend home with land, where affordable housing will not become an elusive dream. Where will this revolution be? In the air (of course.)
The next big thing. Flying. Come on, all the cool kids are doing it. But really, the point where individual/family aircraft replace cars as our primary means of commuter transportation is the point where we hit our next revolution. With affordable aircraft, the time and cost per unit distance decreases drastically. What once took 10 hours takes two, so the house that was 4 hours drive and hence inaccessible is now a 30 minute commute. There’s always more sky, so there would not be the same rush hour problems. And you could fly straight there, so you would save time and fuel. Alarm bells. Lots of big problems. First, aren’t airports generally pretty far away? Doesn’t it take a long time to get to one? Yes, if you’re flying a 747. When I first started flying I was astonished at how many little airfields there are scattered around. Many are WWII fields that have been abandoned, but if you count all the repairable fields, I would be surprised if 50% of American homes weren’t within a 15 minute drive of a small airport. That’s a total WAG, though. I grew up around a lot of farmland, and there were two active airparks within 15 minutes. Second big problem, gas costs. If cars are expensive, wouldn’t planes be more so? There are a few factors that mitigate this. Fuel efficiency for a light aircraft is generally not very bad. Most light aircraft use piston engines, just like a car. Instead of pushing against road friction, they are pushing against wind resistance and gravity. You can also fly straight and not idle in traffic, both of which offset fuel costs somewhat. I admit, though, this is a weak point of the model. We must predicate the model upon advances in piston-driven efficiency, or availability of new propulsion technologies. Third big problem, isn’t flying dangerous? Don’t you have to get a lot of training to fly? That’s a longer question to answer.
Bert Rutan (who is awesome) said something once to the effect of personal commuter aviation will never be practical until you can make an airplane which will take home a person stumbling drunk out of a bar. The weakest link is the human element. This is also true on the road, although aviation certainly involves more variables. The human factor problem is complicated by the inaccessibility of aviation. There is a cycle: aircraft are expensive, so few people learn to fly them, so they aren’t mass produced, so they’re expensive. We can adjust this cycle in two places. First, if learning to fly them for commuter purposes was not as demanding, then it would be more practical to learn to fly, which would allow mass production, which would make airplanes cheaper, and even more people would learn to fly. If we made just one Honda Civic, it would be very expensive. Especially if you put in electronics. But if you make a zillion Honda Civics, they’re pretty cheap. (Especially with electronics, which have huge economies of scale.)
Flight safety warning horn! If learning to fly was not as demanding, we would have a zillion unsafe wanna-be pilots trying to pull Kennedies all over the place. The current leading cause of aviation mishaps is pilot error. This has been true for some time, and will almost certainly remain true as materials technology continues to improve. So you engineer the human element to a minimum. The human becomes the safety observer, where he is only flying in emergency circumstances. To teach safety observer skills for a highly automated platform would take, perhaps 10 hours. This basic course would give the commuter the ability to program the navigation system, to recognize problems with automated systems checks, and to fly and land the aircraft given very specific instructions. The aircraft would have graceful failure modes (to be discussed in the aircraft design section,) and only in the most dire of circumstances would the commuter actually have to fly. In fact, disengaging the FCS would be an override that the commuter would later have to explain to the FAA, as emergencies currently are (of course, manual override would always remain an option.) An Iridium-style self contained satellite communications system would allow the commuter to connect to a very directive controller in the event of total systems failure. The controller would set him or her up on a very long final, monitor the approach from GPS fixes in the radio, and direct a go-around if necessary. Second flight safety thing. We all know how many beater cars are out there driving. If your engine dies while driving, you pull over. Obviously, you can’t pull over the aircraft. Two fixes. First, maintenance. In order to fly, you would have to have routine inspections performed by qualified maintainers. Second, controlled landings. More ambitious solution, allow the flight control system to reference a database of suitable landing or ditching sites, and allow the commuter to select one (free of obstructions,) and allow the aircraft to land itself there. Less ambitious is the equip aircraft with parachutes (as has been recently been suggested in several flight journals.)
Should this light aircraft revolution occur at some point, there would be systemic effects. First, our Air Traffic Control system would have to drastically change. One option may be to keep the current Class A airspace for the traditional ATC functions, and primarily communicate with individual commuter aircraft (and their flight control systems) through data-link (mostly transparent to the commuters.) Back-up would be voice comms. Separate emergency channels would be reserved for emergency controllers for aircraft using Iridium comms due to total electrical failure. Many functions would have to be automated, but this would be facilitated by the establishment of a GPS-based airways system (to replace our old VOR system that concentrates aircraft into small channels.) Maintenance markets would come about to do preflight and routine inspections (which would be simplified by BIT (built in test) functions of the aircraft.) Arrival taxi services (vans that went from the small airports to the workplace or the home) would become profitable, and provide an option other than driving. So of course things would change, just as they changed when we had cars (stoplights and the like.)
One could make an analogy to steam engines ending up at cars. The first few non-organic earth-bound conveyances were merely a novelty. At some point the steam engine gets harnessed for mass transport, though. The railway system comes about, where full-time conductors and manually operated switches keep everything safe. Then, there is a revolution in propulsion systems in the piston engine, and you get generally practical and affordable individual means of transportation. You do not need a full time conductor to run the car, nor do you need individuals to manually turn on or off lights to direct the car. We are at locomotives with modern aviation. Trained and experienced professional pilots follow individually issued instructions for safety’s sake. And rightfully so. At some point, though, the locomotive gives way to the car (even though trains remain even today.)
What will this mean economically and socially? Like the car, the ICA (individual commuter aircraft) will start with the well off, who will cause the initial rudimentary infrastructure to be built. This will make the prospect of a rural weekend home or ranch a possibility for the urban working rich or the upper middle class. At some point, as R&D costs decrease, the ICA comes down to price. Then the prospect of super-suburbs becomes a possibility, where ICAs fill the role cars currently occupy in our extant suburbs. As ICAs grow more prevalent, urban spheres of influence expand, which will result in the megalopolis (already starting in Cali and on the US East Coast.) As opposed to the Japanese megalopolis, though, housing will be affordable. And kids still get to grow up with trees in their backyards.
So next time, we get to design this mythical ICA. (To be continued in The Airplane for the Masses.)
23:55 Posted in Boring Theories (Engineering) | Permalink | Comments (0) | Trackbacks (0) | Email this
17 August 2006
[Warning: Boring Theory] Thermodynamic Economies
A note of introduction. Given that I have put ‘boring theory’ stamps all over this, I feel no obligation to be zany or witty or anything of the sort. So I’m shooting for dry and boring. I did, however, want to point out why I like the whole fusing multiple field type theories. If one Author made everything up, it makes sense that His fingerprints are all over everything. And if you’re listening to one band, you hear the same guitar rifs multiple times. In fact, the better you know one song, the better you can recognize their artistry in another song. We draw a lot of false dichotomies between fields of study. Consider Aerobic Respiration. You can tie in Chemical Engineering, Thermodynamics, Structures, Statics, Dynamics, Electrical Engineering, Mechanical Engineering, and, of course, Biology in the way it works. We would never make a system with such efficient Systems Engineering, because we believe that EE has very little to do with Chemical Engineering. But, really, an electron in a covalent bond isn’t really that different from an electron excited up a few quanta. It’s all the same stuff, and truly elegant solutions break down a lot of these pre-existing boundaries that tell us what we can and can‘t do with the same stuff. Kind of like Unified Field Theory. But more a Unified Engineering Theory. So what the following theory is good for is to make a Figure of Merit for energy economy in a system that incorporates several sub-systems (or at least sub-functions.)
System Boundaries and Interactions. Thermodynamics, in its most direct form, is well adapted to dealing with one-dimensional energy systems, such as a Carnot cycle or a heat pump. Generally, though, large advanced systems incorporate many such systems, which may be pumping energy different directions through different media within the larger thermodynamic boundaries of the entire system. While not particularly useful for analyzing, say, a HVAC system, it would be tremendously useful to have a figure of merit on these internal energy flows for say, a urban area, or for an aircraft (which is, of course, why I care. Airplanes are cool. People who fly them are cool. And humble.)
Let’s boil this down by using an example. Take, for example, hmm… I know… the mighty Herk (C-130 to the uninitiated.) Which is awesome, but not exactly an example of thermodynamic elegance. So the Herk has this cool little thing called an Oil-to-Fuel heater. Hot oil, coming off the engine, goes through a heat exchanger, and heats the fuel before it goes into the engine. This does a couple of things, most importantly, keeping the fuel warm enough so there won’t be any problems with ice in the gas. From a thermodynamic viewpoint, though, it incorporates a degree of elegance. Waste heat that you’re trying to dump overboard is reincorporated to pre-heat (to a very small degree) the fuel, which allows a bit of thermodynamic recapture. You take something you’re going to throw out anyways and put it somewhere useful. There is a degree of stinginess in this, which to some degree reflects (to a very small degree) the high degree of thermodynamic recapture in natural designs. Despite multiple subsystems, most natural systems don’t throw overboard energy that would be useful somewhere else. That said, there is a cost on energy recapture. For the oil-to-fuel heater, there had to be a heat exchanger built into the engine, and more piping run. It was pretty low cost, because everything was there anyways, but that cost has to be subtracted from the benefit of the recaptured energy in order to find the energy ’profit’ from the recapture. Given the simplicity of the oil-to-fuel heater, and the high degree of usefulness, it is pretty safe to say that was a good idea. How, though, would we make a figure of merit to tell us if it would be worth doing thermodynamic recapture somewhere else, and where?
Let’s look at a bit more complex problem. The engine oil system takes hot oil from the engine and runs it through a ram air cooler to bring it back to a more manageable temperature. The thing is that the cooler increases drag, which means you have to kick up the power to maintain the same airspeed, which means you’re burning more gas. So you’re incurring an energy loss to throw heat overboard. Consider, now, the anti-icing system. This system uses hot air off of the engine, (bleed air) routes it through the leading edge of the wing to heat up the wing so ice can’t form. But, in drawing bleed air off the engine, you’re reducing engine power (ceteris parabus.) The actual thermodynamic flow is you’re drawing power off the turbine from the compressor, which comes from combustion, going back to costing you more gas. So you’re spending energy to make heat. Both of these systems could be on at the same time. Which then begs the question, why are we spending energy to both make and dump heat at the same time? Here’s the thing, though. There are two different fluids involved here (engine oil and air,) and there are going to be some losses associated with the energy transfer between two media. Also, you will have to add complexity and systems to the aircraft to do the heat exchange, which will add weight (losses) and lifecycle costs. This is not that different from a market, though. You make flour into bread. People will pay a certain amount for that bread. But, in order to sell them the bread, you have to pay for a store. And you have to work at that store. So you need to at least cover your costs (including overhead… fixed and variable) if its worth making your bread store. This is the same thing. But you have to have a means by which you can measure whether its worth building your energy store if you’re going to make your system energy stingy. Economics tells us when its worth running a market interaction. Thermodynamics tells us how energy works. Let’s put them together.
Thermodynamics in Economics Language. So there are two laws of Thermo (really three, but the third is not useful to us here, so we’ll skip it.) In simple language, the first law, enthalpy, says that you can’t make or destroy energy (counting matter.) You end up with the energy you started with, you can just re-arrange it. The second law, entropy, tells you that energy tends to progress from more useful, or accessible, forms to less useful forms. Most people focus on the progression from order to disorder, but the useful part to us is the idea of inaccessible energy. The third law is boring and I already talked about it in the theory about quantum-level voltage and superconductors.
First law. So rocking the economics party on the first law, think back to the gold standard. When currency was tied to precious metals, there was always a finite amount of money in the economy. (Banks still multiplied it and all, but imagine that there are no banks. Like Old West style. Or Hazzard county.) Unless you were to dig up some more gold, you couldn’t really make more money. But you could use that money to do more or less useful things. You could gamble it all away, or you could build a store with it and take other people‘s money. In the same way, you can release about the same amount of energy and propel a car for a good ways or blow up your sister’s toys with M80s. The amount of energy didn’t change, but the usefulness of it did. (This is getting into the second law somewhat.) The important thing is that the amount of money out there is set, but that fixed amount of money doesn’t imply a fixed amount of utility.
Second law. Even if there’s set amount of energy out there, not all of it is as accessible. Say you’re a bank robber. You have a six-shooter. Say there’s some money just laying out on the ground. That money is easily accessible. The costs to pick up that money are very low, far below the revenue involved. So revenue minus costs equals profit. So now say there’s some money in a vault guarded by really mean dogs, the Terminator (from the first movie) and Vasquez from Aliens with that awesome Smart-Gun. Probably, the costs involved in getting that money are going to outweigh the money itself. The costs are more than the revenue, and you would make a loss. So probably you won’t try to get the money. That money is inaccessible, not because there’s no way to get to it, or because its not there, but because it would take more money to get that money than you would make from it. If it costs you a zillion dollars to make a widget, and you make a dollar from it, its not like there’s not still revenue. Its just not worth getting. That’s entropy. If you’re really cold, it doesn’t do you a whole lot of good that the planet Mercury is hot. It would take more energy to go to Mercury to get that heat than the energy you would get from that heat. That’s inaccessible energy: energy that costs you more to get than you get from it. So that’s thermo. Lets do econ now.
Economics in Thermodynamics Language. So the important thing from Econ are the supply and demand curves. (micro, at least. Hescher-Ohlin is cool and all, but not really helpful here. But, look at me, I’m smart because I mentioned it. Really. I can also say ’problematic’ and ’paradigm.’ That‘s what I learned with my vastly overpriced degree.) I’m going to use the single-firm startup/shutdown ATC/ATR/MR curves here.
Marginal Revenue, Average Total Revenue Curves. On our graph, the marginal revenue. This curve is the derivative of the total revenue curve, and basically tells you how much more money you can get for making one more thing. Put in energy terms, potential revenue is available energy. This curve is how much energy could be harvested per unit capacity (regardless of cost.) Imagine increasing a heat exchanger’s capacity between two systems, and seeing how much more energy you could reclaim. Hence, this curve is closest to enthalpy. This curve is also related to the Average Total Revenue curve, which is revenue divided by quantity. If you multiply the ATR curve by quantity, you get the total amount of revenue. Revenue is energy. So the one unit increase in capacity increases energy by MR there, but total energy reclaimed is the square carved out by ATR and Q (which is the same as the area under the MR curve.)
Average Total Cost, Marginal Cost Curves. All attempts to claim either revenue or energy inherently incur costs. The added energy gained from a compressor requires a turbine, which gives you a good return on investment, but it is an investment nonetheless. The additional costs incurred per unit capacity can be described as marginal cost, and the costs spread out through the capacity can be described as average total cost. Multiply that by capacity, and you get total cost. Cost has two big pieces: Variable and Fixed. Fixed is the easier of the two for us to describe. It is the overhead, the equipment costs. Whether or not your heat exchanger is exchanging heat, it is weighing something. It cost something to build. And it costs something to maintain. Variable Costs increase with the capacity on the heat exchanger. For our purposes, we will describe two different types of variable costs. The first, static variable costs, are increasing costs as the size of the heat exchanger increases. These are obviously fixed with the complete design, but they are variable during the design process, which will allow us to optimize the size of the heat exchanger. The second, dynamic variable costs, describe the losses inherent in a heat exchanger. In the transfer process, a good deal of the energy is lost. Dynamic variable costs, (like induced drag) are a function of energy reclamation. Dynamic variable costs must both be considered during the design process and be considered in subsequent analyses of the system. In this curve, we start to get at entropy, for an exchange for which cost exceeds revenue is an exchange with inaccessible revenue.
Profit. The area between the average total cost square and the average total revenue square is the profit. In energy terms, this is the reclaimed energy. An efficient heat exchanger maximizes this area. If there is no area to maximize (maximum profit is less than zero,) then there is no use in putting a heat exchanger between those two systems. And in this, we see entropy. This energy is inaccessible. Energy profit is the same as reclaimed losses.
Terms.
Reclaimable Energy is the sum total of energy that could theoretically be reclaimed between sub-systems. This term takes no account of recovery costs. Reclaimable energy is found by taking the sum of the absolute values of the sub-system energy flows (into and out of the total system, not counting internal transitions) and subtracting the sum of the sub-system energy flows. A loss-less system, which is impossible due to entropy, would have absolutely no difference between the sum and the absolute sum, as there would be total synchronization between the subsystems and the total system. Such a system would have no reclaimable energy.
Reclamation Cost is the cost to reclaim a given amount of energy. It is the total of fixed and variable costs for a given capacity heat transfer mechanism. It includes lifecycle costs, such as construction and maintenance, operations costs, such as weight, and thermodynamic costs, such as heat transfer losses.
Enthalpic Losses are lost energy that we can effectively reclaim with a heat exchanger. A first-order efficient system eliminates enthalpic losses, optimizing an existing design. The total amount of reclaimable energy minus recovery cost in all simultaneously possible profitable exchanges is the total amount of enthalpy losses. Specific enthalpic losses (referenced against total energy flow) is an overall figure of merit for first-order efficiency.
Entropic Losses are lost energy which would cost more to reclaim than the energy that would be gained. This energy, within a static design, is lost. But in a second-order efficient system, one that rethought its systems from the outset for thermodynamic efficiency. The difference between enthalpy losses and reclaimable energy is entropic losses. Specific entropic losses is a measure of second-order efficiency.
Recovered Energy is the difference between the reclaimable energy and the reclamation costs for a given combination of systems. This can be optimized by choosing the best combination of exchangers to maximize this term.
Reclaimable Energy Curve (Revenue.) We can construct a reclaimable energy curve for a given system by first deciding which two systems we are looking at. It makes sense, of course, to choose two systems with complimentary energy flows (one dumping, one creating heat.) Then, build the curve by determining how much energy will be transferred in a given set of conditions for a certain capacity system. Capacity is our independent variable, and energy is our dependent variable. Given that this curve is only for one possible interaction, it would do some good as an analytical tool to find the optimal points on a number of these curves and place them of a traditional supply/demand graph. This will allow the linkages between compliments and substitutes (substitutes would be multiple systems with complimentary flows. If waste heat has is reclaimed somewhere, it cannot be reclaimed somewhere else.) These can then be evaluated, and all the different individual graphs tied together to find a single optimized solution between all systems.
Reclamation Cost Curve (Costs.) There are three parts of reclamation costs. We can plot these on a traditional graph as Fixed costs and Variable Costs. Lifecycle costs and part of operational costs are fixed costs. Lifecycle costs include the cost of production, the purchase price, and the maintenance costs over the life of the unit. Fixed operational costs are the added weight and complexity that exists regardless of capacity, such as extra tubing and set parts of the heat exchanger. Variable costs include the remainder of operational costs, such as size of the heat exchanger, and the thermodynamic transfer losses.
Possible heat exchange mechanisms include:
Fluid <-> Fluid (Traditional Heat Exchanger)
Fluid <-> Electrical (Turbine/Fan)
Possible Pressure Differential Systems
Design Cycle. Once cost and revenue curves have been constructed, the designer can experiment with different combinations of individual transitions. With a bit of ingenuity, you can get a pretty good idea of where your energy is hiding and what you can get back. There is a mathematical way to do this, though, with Lagrangians, and using Supply/Demand graphs to plot out the possible interactions. If you can construct a web of total available energy, you can determine minimum reclamation cost, and then maximize total profit. The systems engineer should analyze these under different given conditions, for the different environments of the system (for an aircraft, ground, takeoff, cruise, landing. Or whatever.) You should give mind to surge capacity and emergency conditions. Note that this is a Systems Engineering methodology best applied as a finishing touch on an already nearly completed design. This methodology would do much to reduce enthalpy losses, but can do little to reduce entropic losses. This is first-order optimization, and achieves static efficiency for a design.
Second-order optimization, dynamic optimization, requires consideration of thermodynamic economies from the outset. This can modify the factors of production of the cost curve. By reducing the numbers of media used, or redesigning the system to be more unitary from the outset, much more energy can be reclaimed. A more unitary system reduces the number of necessary transitions, reducing losses from the outset. Reducing the number or types of media reduces the transition costs. Therefore, the tendency as systems become more and more thermodynamically efficient is for the systems to become more and more elegant, with less systems accomplishing more things synergistically. Sorry about the MBA word. One further offshoot of this is moving away from a large number of active pumps to more passive systems which regulate themselves by bypasses of available energy. These meta-stable systems, and their dynamic equilibria, more and more closely approximate biological designs. Which, of course, makes sense. About the best you can do is plagiarize God.
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