Centrifugal Impellor in place of Axial Ducted Fan

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by Culleningus, Feb 4, 2010.

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  1. Feb 9, 2012 #61

    bob989

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    Hi Gordon,

    OK, I admit it. I cannot make the claim that a small engine could have just as good a thermal efficiency if I restrict my design to just a rescaling, even if I choose different scale factors for the different spatial directions. However, the direction parallel to the flow in a developing boundary layer is indeed special. If it were only a matter of having the same ratio of drag power loss to mass flow rate, then one would scale the parallel direction differently for a developing boundary layer. For a fully developed boundary layer, the scale factors would be the same. But there is also the requirement to preserve the pressure ratio across each compressor or turbine stage, and I don't know how to do that. So I'll have to accept your argument based on existing production models of compressors of various sizes. I don't have a design in my pocket that would contradict that.

    And because we are talking about an open Brayton cycle, the heating is isobaric and that makes it difficult to approach Carnot efficiency. Carnot efficiency would require isothermal, not isobaric, combustion. And the fact that it is an open cycle, taking in air at ambient pressure and returning it to ambient pressure, also makes it difficult to approach Carnot. The open Brayton cycle could only approach Carnot if the compressor and turbine were completely frictionless, which would permit a high pressure ratio "for free" (except that the combustion heat per unit mass flow goes to zero in that limit, so mass flow rate per unit engine power would have to go to infinity). The compressor and turbine drag, and the mathematics of the open Brayton cycle, force you into a box where the best efficiency you can achieve is uncomfortably sensitive to the isentropic efficiencies of the compressor and turbine components.

    It also occurred to me that if the use of a large number of small engines permits an increase in engine complexity, as we have been discussing for the problem of thermal efficiency, that observation also applies to the mechanical aspects of the design. In particular, we could start talking about gears. Pratt & Whitney seems to be engaged in a never-ending Battle of the Marketing MBAs to convince people that a gear is acceptable in a turbofan engine. It's another example of the collective paranoia surrounding the large-engine paradigm. A GEAR?!? Heaven forbid! It would be FAR TOO DANGEROUS!!!

    But if we don't put all of our eggs in one or two baskets...

    The small-engine paradigm opens up one further possibility. You mentioned that as the altitude increases the atmospheric temperature decreases, and thermal efficiency improves. I see that as a separate optimization problem. That is, I see two classes of engine, one optimized for takeoff conditions, the other for cruise conditions. The two classes would still be able to operate in each others' preferred conditions, just not optimally. Safety would not be compromised. The takeoff class would be mounted inboard, so that any failure during takeoff would introduce a smaller yaw moment. As you climb to cruise altitude, the control system would roll the thrust off of the takeoff class and on to the cruise class.

    -bob989
     
  2. Feb 10, 2012 #62

    gordonaut

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  3. Feb 10, 2012 #63

    gordonaut

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  4. Feb 10, 2012 #64

    bob989

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    Hi Gordon,

    We seem to be worshiping at two different churches.

    In my religion, complexity costs nothing because I assume an entirely robotic assembly line. The only reason to be careful about introducing thermal or mechanical complexity is that we do not want to compromise safety. My standard answer to the safety issue is to make the engines smaller and to have more of them on each aircraft.

    In your religion (I don't mean that to sound condescending), small engines imply recuperation. I see that as a design choice, not something that is dictated by the laws of physics. You take heat from the exhaust and use it to substitute for some of the heating that would otherwise be done by burning fuel. Fair enough, but it introduces a constraint, the constraint being that the temperature of the air coming out of the compressor is lower than the temperature of the air coming out of the turbine. That constrains the mathematics of the open Brayton cycle even further than it already is. OK, so if you adopt that constraint, then the optimization problem favours lower pressure ratios. In essence, you're gambling that drag in the heat exchanger is less of a problem than drag in the compressor and turbine.

    I agree that Wilson's approach is promising. If you think about it in terms of developing versus fully-developed boundary layers, chopping up the air with lots of blades creates leading edges and newborn boundary layers. And shock waves, as you mentioned. That's bad. If instead, you rely more on centrifugal compressor and turbine stages, there are fewer leading edges and boundary layers have more time to develop. You're doing Coriolis work against slippery walls. In the heat exchanger, the boundary layers are also fully developed, so drag is relatively low. It’s a good religion, I have to admit.

    In my religion, we worship Carnot. The way to build an efficient thermodynamic cycle is to start with a clean sheet of paper, draw a graph with a T on the vertical axis and an S on the horizontal axis, and then draw a perfect rectangle. Then we work to make our cycle as close to that perfect rectangle as possible. Each of the four sides of the rectangle brings its own challenges and opportunities. Is there room for precooling or intercooling to try to get closer to isothermal compression? Can I improve the compressor isentropic efficiency? Can I expand the working fluid while I'm heating it so that it more closely resembles isothermal heating? Can I improve the isentropic efficiency of the turbine? This does not result in an open Brayton cycle or a constrained open Brayton cycle. And, it very definitely increases complexity. But I don’t really care.

    Wilson says that he does not envision a large production run. Notice the box he puts himself in: small engines produced in small quantities. If that's where you are, then you can't justify fancy techniques. There isn't enough energy savings over the life cycle of all the engines you're going to produce to justify thinking so hard about efficiency.

    One more remark about robots. If the robotic assembly line drives the manufacturing costs way, way down, as I think it would, that would change the economics of engine maintenance. In the extreme limit, for example, let's assume that the engines are being given away in cereal boxes. If they cost nothing, then you could simply replace them every time you land. They're a commodity. Use once, recycle. Ask the obvious question: In a world where a good-quality digital camera or personal computer costs less than it costs to fill your fuel tanks, what should the engines really cost? An why would anyone open up an engine to do a hot-section inspection? What are you trying to save, a few pennies to replace the engine? Who cares? Grab a socket wrench, pop it out, plug in a new one, and you're good to go.

    Look again at your issue about fouling the little tubes inside your heat exchanger. Yeah, that's right, sooner or later they're going to accumulate dirt. So do styrofoam coffee cups. But who cares? We just throw them away. We don't treat it as an engineering problem to try to find ways to stop it from happening.

    Always interesting to read your posts, Gordon. I don’t accept the totality of your arguments, but I don’t think you’re too far off the mark, either.

    -bob989
     
  5. Feb 10, 2012 #65

    gordonaut

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  6. Feb 10, 2012 #66

    gordonaut

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  7. Feb 11, 2012 #67

    bob989

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    Hi Gordon,

    OK, maybe the comparisons to digital cameras, personal computers and styrofoam coffee cups are a bit strained, but I'm trying to push the debate into a mode where we don't consider the engine to be so precious that we start making economic arguments based on its supposedly astronomical cost and value. My take is that aircraft engines are expensive because they are produced in small quantities. There's no economy of scale. Production runs are in the hundreds, sometimes thousands, but that's the entire set of engines of that model ever produced in its entire history. The large engine paradigm says that you're only going to produce one or two engines per plane, plus a few spares and replacements. So, for example, the entire Boeing 747 series of aircraft, produced over four decades, numbers only about 1,400 planes. Therefore 4 times 1,400 would give you some idea of the entire engine production for forty years. It's not mass production. The engines are produced in small quantities. The Cessna 172 had 50,000 units altogether over its entire production history. By comparison, an automobile assembly plant produces 50,000 vehicles in 50 days. One thousand per day, not a few thousand over a few decades. So when people say that aircraft engines are expensive, they are really just saying that the small production numbers don't generate any significant economy of scale. The customer pays through the nose because it's a specialty product.

    Perhaps a better comparison would be automobile engines, which are produced on robotized assembly lines. But there are still workers on those lines, and workers cost money. The thing about a hard disk drive, for example, which is an electromechanical device having a motor and actuator, bearings, and tight tolerances, is that no human hands get anywhere near it during the manufacturing process. Humans build the robots, period. Robots build the disk drives. And they are dirt cheap. Now if you tell me that cannot be done for aircraft engines, I would really like to know why not. You'd have to admit that we could do at least as well as automobile engines, right? I think we could do even better.

    The Carnot cycle is a direction to go in, not an achievable goal. But the further you get away from it, the more you tie yourself in knots trying to recover and reroute and short-circuit the heat losses that are occurring because you abandoned the Path of the True Light. OK, so it's a religion.

    Google "isothermal combustion". It's not my idea; I just found it out there in the ether. But it doesn't seem crazy to me.

    Designing the best engine would involve choosing various efficiency enhancement techniques and you would have cost, weight, and volume to consider. I suggest that for cost, we simply take the increased cost of the engine, delivered and installed, and compare it to the cost of the fuel that would be saved over its expected service life. For weight, we take the extra weight and compare it to the weight of fuel that would be saved over a typical flight. And similarly for volume, we take the extra volume and compare it to the volume of fuel that would be saved over a typical flight. Once we have all three comparisons, then it's a matter of which church you go to.

    So for example, your heat exchanger... how does its volume compare to the volume of fuel saved? That is, if I build your engine into my wing, where it competes for space with the fuel tanks, do I win? Is the heat exchanger volume less than the volume of fuel that it would save?

    And do we really need light weight? That would depend on how much fuel we are going to save over a typical flight. Your engine can be heavier if it allows us to have smaller, lighter fuel tanks.

    -bob989
     
  8. Feb 12, 2012 #68

    gordonaut

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  9. Feb 13, 2012 #69

    bob989

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    Hi Gordon,

    Your argument about thrust to weight ratio works differently for the takeoff problem and the cruise problem. Takeoff is a low-altitude, low-speed, high-thrust problem. Cruise is a high-altitude, high-speed, low-thrust problem. People who believe in the large-engine paradigm try to solve both problems using the same engine. Oops!

    Example: the Eclipse taking forever to get off the ground. If we split the propulsion problem into two classes, the takeoff class and the cruise class, then we don't have to choose between good takeoff performance and good cruise performance. Consider, for instance, the relationship between airspeed and type of fan. Takeoff is a low-speed problem. But a turbofan engine is a way to get to high Mach number. The Mach number on the runway is never high, so why use a turbofan for takeoff? Answer: because people bow down and pray to the large-engine paradigm. In the large-engine paradigm, an Eclipse gets only two, count them, two (2), that is, 2 (two!), engines. And they're identical! No wonder it's crap.

    Since we're in the middle of a discussion thread on the subject of centrifugal versus axial ducted fans, perhaps it would be appropriate here to suggest that the takeoff problem would be more amenable to the centrifugal-fan approach. Once you're cruising, I'm not sure that the centrifugal fan would offer any net advantage. But that would depend on airspeed.

    I understand your enthusiasm for recuperation. It's not a bad approach. But designing a thermodynamic cycle is not a matter of choosing from a predefined menu of possibilities passed down from our esteemed ancestors. The only prophet you have to worship is Carnot, because that's physics. The other celebrities in the Thermodynamic Cycle Hall of Fame were not working in the year 2012. Today, we design the cycle. If you insist on accepting somebody else's preconceived design, then inevitably you end up making a contribution to their Memorial Fund. I have to pay the Carnot tax, because there's no way to get around that. But I don't have to pay the Brayton tax. Or the Stirling tax. Or the Rankine tax.

    When you say you get 30% thermal efficiency, part of me says, not bad. But another part of me says, huh? You want me to waste 70% of my fuel? As if we fly because we're trying to heat up the atmosphere? When the heat goes out the exhaust, it's gone forever, and I lose. I can't even use it to toast marshmallows. It's gone. I do not worship at the Church of ExxonMobil, but they get real money, my money, for that 70%. And then Breguet says that I have to pay even more, because the first few kilograms of fuel that I burn goes partly to accelerate and lift all the other kilograms of fuel, including the 70% that you keep telling me, over and over again, has to be wasted.

    Every time you make the case that aircraft engines have to waste fuel, you have to be careful not to base your argument on the existing large-engine paradigm. Since that is the paradigm that has reigned supreme over pretty much the entire history of aviation, naturally there is a whole boatload of engineering methodology and standard practices built around that paradigm. Lots of people worship at that church. And they really, really, really believe. But if you reject the large-engine paradigm, many of their arguments melt away like ice on a warm planet.

    The large-engine paradigm is insidious. Look at aerodynamic drag. When you design an airframe for high speed, you can't stick things out into the freestream. No stiffening elements, no struts or cables. Everything has to be pulled inside the smooth skin, because the faster you go, the more of a problem you have with drag. So you use ribs and stringers inside the wings and fuselage. Fine. Everybody knows this. But then why stick those big, clumsy engines out there in the freestream? Why is there one rule for the structure, another rule for the propulsion system? It's drag either way. But that's the large-engine paradigm at work. It makes things dumb.

    I want small, smart, inexpensive engines that treat fuel with the respect it deserves. I don't want big, dumb, expensive engines that treat fuel as something to be burned.

    If you think there's a hard and fast rule that says you always maximize the engine thrust-to-weight ratio, well, no, I disagree. You also have to take into account the weight of the fuel that you are wasting. Gravity works the same way on fuel as it does on engines. Or, as you might say, if you let go of it, it drops to the ground. Now it's probably true that some of the more elaborate efficiency schemes you find on ships or in electric-power plants would indeed turn out to be too costly/heavy/bulky if you did the math for any particular airplane. That is, some of those techniques would not pan out when you consider cost, weight and volume, even taking into account the fuel savings. But some of them would. Fuel is part of the propulsion system. The only reason we load the fuel onto the airplane is to power the engines. Inefficient engines waste money, they make the airplane heavier, and they cause the fuel tanks to take up more space inside the wing.

    The cost/weight/volume comparisons work differently for the two engine classes, because the amounts of fuel burned in takeoff (/climb) and (climb/) cruise are different and depend on the mission.

    I put climb in its own intermediate category because it has elements of both problems and I don't envision a separate engine class for climb. Climbing would involve smoothly transferring the thrust burden from the takeoff class to the cruise class. As the takeoff class powers down, the takeoff duct exit slot would have a door that would close to blend smoothly into the underside of the wing. The door might do double duty as the flap, but I'll have to think about that a bit more.

    Because cruise is a low-thrust problem, engine weight is already low. Efficiency enhancements would be easier to justify for the cruise class, even if they increase engine weight, volume and cost. Especially for long-range missions.

    -bob989
     
  10. Feb 14, 2012 #70

    gordonaut

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  11. Feb 16, 2012 #71

    bob989

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    Hi Gordon,

    That's interesting. Your reasoning suggests that it would be more efficient if we used a centrifugal approach at high speed and an axial approach at low speed. Up until I read your post, I would have said that for high speed, say, Mach 0.7, it wouldn't matter much, but at low speed, I might "get away with" a centrifugal approach. So I'll try to pick apart the reasons for and against the centrifugal approach, for both the takeoff problem and the cruise problem.

    First, I think it's useful to unravel the definitions of the nondimensional work and flow coefficients. These are nondimensionalized on the basis of an arbitrary velocity that just happens to be lying around, i.e. the rotor velocity (and its square, which is basically the mass-specific kinetic energy of the rotor). Rotor velocity and rotor kinetic energy are not things that directly impact efficiency; they impact efficiency only indirectly through, for example, the generation of shock waves. So when you say that work coefficient is high in the centrifugal case, you're saying that mass-specific enthalpy change is high relative to something that's irrelevant, i.e. mass-specific rotor kinetic energy. And rotor velocity varies more as a function of radial position in the centrifugal case than it does in the axial case, so you have to arbitrarily choose a radius to fix the rotor velocity. It's both arbitrary and irrelevant.

    But it's true that we can get a bigger enthalpy change, i.e. a bigger pressure ratio, across a centrifugal impeller stage. That's what interests me in the takeoff problem. I can use that high pressure ratio to create a high vacuum in front of the intake. If I use an axial ducted fan or a propeller, the pressure ratio is limited.

    The reason I want to create a high vacuum in front of the intake is that I get more air flow per unit area by doing that. You can calculate the optimum underpressure that gives you the maximum airflow per unit area arriving at the intake, starting from ambient atmospheric conditions.

    At the start of the takeoff roll, you really don't have much choice. The air isn't "coming at you". You have to reach out and pull it in. If you use an axial ducted fan or propeller, then you get a smaller airflow per unit area because you can only create a weak vacuum. (Unless you use multiple stages, which is a whole other discussion.)

    So my entire rationale for the centrifugal approach in the takeoff problem boils down to the small intake area. It makes better use of the limited real estate on the leading edge of the wing. Does it cost me propulsive efficiency? I think it probably does. So it's really a question of how much do I pay in propulsive inefficiency for the benefit of being able to tuck the propulsion system neatly into the wing. Integrating the propulsion system with the wing gets me aerodynamic efficiency because I'm not sticking the propulsion system out into the freestream. When I power down the takeoff engine class and close the back door on the ducts, the wing airfoils are smooth, as if the engines didn't exist. The dead intakes on the leading edge aren't an issue, because wing performance doesn't strongly depend on the shape of the leading edge.

    Now the problem of impeller design. It would be unreasonable to insist on either a purely radial flow or a purely axial flow. You can design the rotor to do a combination of both: a gentle push in the radial direction and a gentle push in the axial direction. Smooth, round channels with no sharp edges or corners. Sharp, streamlined trailing edges. Nothing that would risk separation.

    The parameters that go into the impeller design problem include the airspeed and the ambient atmospheric conditions. So it’s two problems, one for takeoff, and another for cruise. The airspeed tells you how much air is "coming at you" and how much more you might get by reaching out and pulling it in. The ambient atmospheric conditions would allow you to determine the optimum mix of radial and axial work.

    In the cruise problem, there's plenty of air coming at you. You just open up an intake and accept what you get. Mass flow rate = area times airspeed times density.

    What's interesting about the cruise problem, in light of your observation, is that it might be more efficient to replace the front and of a turbofan engine with a single, well-designed rotor. It would have a smooth outer surface, a surface of rotation similar to the outer surface of a nacelle. The channels would move the flow gently outward and gently aft, feeding a stationary duct that would taper down to an area maybe 15% smaller than the impeller intake area. From a propulsive efficiency point of view, that might do better than existing axial ducted fans. For one thing, I think you could avoid shock waves.

    But a solid impeller like than would be problematic from the structural rigidity and gyroscopic perspectives. So nix that idea, at least for the large-engine paradigm. In the small-engine paradigm, it’s a whole new ball game. The rigidity and gyroscopic issues would be much more manageable.

    So I've talked myself into at least a partially centrifugal approach for both the takeoff problem and the cruise problem.

    Regards,

    -bob989
     
  12. Feb 17, 2012 #72

    gordonaut

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  13. Feb 17, 2012 #73

    gordonaut

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  14. Feb 20, 2012 #74

    bob989

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    Hi Gordon,

    Your remarks are thought-provoking. It is of course difficult to prove that the combination of techniques I am considering, including the aerodynamic integration of the wing and propulsion system, small engines, separate engine classes, thermal efficiency improvements for the cruise class, partially centrifugal impellers at low speed, etc., would be more fuel-efficient than a well-designed large-engine system. The only way to prove it absolutely would be to design, build and test it. But it is also difficult to disprove it based on existing engineering knowledge and practices. And I believe that the small-engine paradigm is would be safer, even though it might turn out to be less fuel-efficient.

    Here are some responses to your particular concerns.

    We can certainly use the work and flow coefficients in making general arguments about turbomachinery, so long as we are careful not to over-generalize. In particular, the observation that the enthalpy increase across a centrifugal stage can be greater than the enthalpy increase across an axial stage seems to be consistent with your general comments about these coefficients. I agree with that, and I make beneficial use of it. I just don't want my argument to depend on the way those coefficients are nondimensionalized. Fluid mechanics has lots of dimensionless numbers flying around, and sometimes people fall into a mode where they give too much credit to a coefficient without thinking carefully about how it was defined. The use of the rotor velocity is arbitrary, because in the problem I'm considering, I really don't care about the rotor velocity per se, nor its square. So I'm just being careful about how the argument is constructed. I'm certainly not trying to dismiss all of humanity's accumulated wisdom on the subject of turbomachinery.

    Don't get me wrong. I'm a great fan of dimensional analysis, and it's breathtakingly efficient to construct an initial hypothesis in terms of commonly-defined dimensionless quantities. But I never grab somebody else's dimensionless number and start working with it without first checking if the way it's defined is useful for the problem I'm trying to solve.

    In the particular problem of minimizing the intake area, both the pressure difference and the mass flow rate enter the calculation. Thrust = pressure difference times area, but it's also mass flow rate times end-to-end velocity difference. The area in question is the combined effective area of the fan and the forward interior surface of the duct, i.e. in my case, the leading edge of the wing. To minimize that area, that is, to maximize thrust per unit area, I have to look at increasing the pressure difference across the impeller. But once I've got the pressure difference I need, the rest is mass flow rate and velocity speed up, and if I can't get the mass flow rate I want, I'll have to settle for a higher exit velocity by making the duct exit area smaller. This whole approach is directed toward the objective of making the takeoff-class propulsion system small enough to fit neatly into the wing. I'm only using the takeoff class to give a thrust boost during takeoff. During cruise, it's useless, so it has to be unobtrusive.

    I don't think of the integration of the wing and propulsion system as "taking air from one and giving it to the other" in the absence of design modifications. That is, I don't think that the wing thickness and chord would necessarily be unchanged. The combined system would split the air arriving at the leading edge into three parts, the air going over the top, the air going through, and the air going under. It's true, as you suggest, that in a sense the propulsion system would "steal" air from the wing, but the amount can be calculated and the wing dimensions adjusted accordingly. For the takeoff class, the high vacuum would steal more air at the beginning of the takeoff roll than at the end, because the amount stolen depends on airspeed. It's a happy accident that I don't need lift when I'm starting my takeoff roll, so I can steal all the air I want, and there's no problem. As I accelerate down the runway, the wing gets more and more air.

    I think of the combined system, during cruise, as having a more properly balanced mass-flow-rate partition between the lift function and the propulsion function. A "win-win" situation.

    The argument that the lift is decreased by stealing air at the leading edge depends on exactly where you take the air and what you do with it afterwards. If you look at the pressure distribution around an airfoil, the stagnation line at the leading edge has high pressure. But lift isn't being generated at that line. It's generated by the vertical component of the surface-normal pressure force integrated over the entire wing surface. If I take some air from near the stagnation line, I decrease the pressure there. Whether I decrease the top-to-bottom pressure difference at, say, the quarter-chord position isn't obvious. One would have to look at the pressure distribution around the surface of the integrated system. And of course, one would have to adjust the airfoil shape and size if that turned out to be necessary. Finally, the propulsion air coming out the back is also going to help generate lift, as is the case with other propulsion systems; everybody pitches the engines slightly upward. But you seem to be suggesting that I have to put the engines outside the airfoil for some very serious reason. I just don't see that.

    The structural argument is interesting. It's true that wing spars often have solid walls like I-beams, which would block air going through, and if I cut a big hole in an existing spar then I would be committing structural suicide by seriously compromising strength and stiffness. But of course, I would never do that. I would alter the structure. I don't think that is necessarily a bad thing from the perspective of structural efficiency. It's possible that a space frame composed of multiple struts would give better bending and torsional stiffness for the weight.

    Nobody designs an airframe without full knowledge of the propulsion system. Nobody takes an airplane, finds an engine, and bolts it on someplace. People solve the aerodynamic, structural and aeroelastic problems of the combined system. It's no different in the small-engine paradigm. We just have to do the homework. I'm not suggesting that we take somebody's airplane, cut off the engines with a hacksaw, and then attach a bunch of small engines with C-clamps and duct tape.

    If I don't tuck the takeoff-class engines into the wing, it's going to be difficult to make them disappear aerodynamically once I'm in the air. It's like retractable landing gear. It's too much drag to leave the gear sticking out into the freestream. I was once on a commercial flight where the landing gear had a problem, so I know firsthand that retractable landing gear has a cost: safety. The left indicator light, which tells the pilot that the gear is fully extended and locked into position, didn't go on. We were trying to land at Honolulu, and nobody knew whether the left gear was going to buckle under us when we hit the runway, because they couldn't tell if the gear was faulty or if the indicator light was faulty. The tower said the gear looked fine from the outside, but who knew? They decided not to foam the runway because that would have forced us to land on the belly of the fuselage. It makes you a bit philosophical when you look down and see the ambulances and fire trucks already out on the field, ready to scrape you off the pavement. We all braced for impact, and at that moment we would have traded in some aerodynamic efficiency if it bought us some safety.

    But even though we crashed and burned and everyone died and I'm posting this from the afterlife, still, we retract the gear and close the door when we're in the air. Otherwise there's just too much drag. It's the same for the takeoff-class engines. I need those engines to disappear into the wing. I don't see where else I could put them.

    The open-rotor calculations are a bit off the mark, because for both the takeoff class and the cruise class, the fans would operate in ducts. In the actuator disk theory, the thrust is considered to be generated by a pressure increase across the fan disk. In a duct, the thrust is produced by both the fan and the duct surface. Consider, for example, a duct in the form of a pipe closed at one end. Cut two holes in the round wall, diametrically opposite each other, near the blocked end, and fill them with two fans. The fans bring air in and pressurize it, but once inside, the air has no choice but to turn 90 degrees and accelerate toward the open end of the pipe. All of the thrust generated by the system is parallel to the pipe axis, but the forces acting on the fans are perpendicular. Therefore all of the thrust is generated by the duct, and none by the fans. In my problem, some of the thrust is generated by the fans, but some, perhaps most, is generated by the duct.

    As an aside, the actuator disk theory is somewhat suspicious anyway, because it defines a mathematically abstract disk and uses its area in two mutually exclusive ways. In a propeller or a windmill, the forces are generated on the surfaces of the blades, whereas the mass flow happens between the blades. If you say that the thrust and mass flow are happening over the same area, well, that's a bit of an oversimplification. It has the merit that the resulting equation agrees well with measured values of power and thrust for many rotors, but it's not a law of nature.

    What I'm trying to do is minimize the size of my intakes. I don't care all that much about the forces acting on the fans.

    The limits are imposed by what the outside atmosphere is willing to do for me in response to a localized vacuum, and how much I can reduce losses from shock waves that might form on the rotor. The atmosphere is going to do an isentropic expansion, including a density change and a temperature change (and therefore a local sound-speed reduction at the intake). This expansion process constrains mass-flow-rate per unit area, the limit being a choked nozzle. This is less severe than the constraint you mention resulting from velocity triangles. We broadly agree that we're talking about Mach numbers (relative to ambient sound-speed; always have to be careful using those dimensionless numbers!) of around 0.4 to 0.5. Fine. I'm happy.

    There seems to be an either-or logic in your discussion about axial versus centrifugal fans. I'm not really supposing that the impeller would direct the flow in a purely radial sense. I'm thinking that the optimum design is some combination of radial and axial. There isn't any rule that says it has to be purely one or the other. I would like both the radial push and the axial push to happen in the same channel, without any stator, but that's a subject for a detailed design study.

    The diffusing passage at the front of a turbofan pushes the flow radially, in addition to slowing it down. What's wrong with combining these two effects, plus the axial push from the fan, into a single rotor? I know people don't do it on existing engines, and I suspect that one reason is that the large fan is kept flat by centrifugal force. But in a small rotor, I can strengthen and stiffen the structure by adding thickness. We might get rid of shock waves at the blade tips if we redesign the rotor.

    The other alternative for the cruise class is a shared diffuser in the form of a linear entrance slot along the leading edge, a few inches tall, leading to a line of small fans. This is consistent with your comment about Mach 0.8. Once inside the slot, the air would expand vertically, but not horizontally. This area increase would serve the same purpose as the round diffuser on a large turbofan, i.e. slowing the air down before it hits the fans. The spaces between the fan disks would be filled by airfoil-shaped barriers to complete the pressure wall.

    For the takeoff class, the air that the outside atmosphere makes available at each intake is air that converges radially as well as axially in response to the localized vacuum. At zero airspeed, air converges spherically from all 4 pi steradians of solid angle, except from those directions that are blocked by something, such as the wing or the ground. My preference for the wing leading edge is partly because the airflow converging on the intakes is less constrained geometrically.

    As the example of the pipe indicates, there is no absolute rule that says the intake disk has to be perpendicular to the direction of flight. But as the airspeed increases from zero, the air arriving at the intake is coming more and more from the forward direction, and the other directions become irrelevant. Then the easiest way to suck in maximum air is to use intakes that face directly into the wind.

    Always interested in your comments, Gordon. You have an impressive command of the subject matter.

    -bob989
     
  15. Feb 23, 2012 #75

    gordonaut

    gordonaut

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  16. Feb 23, 2012 #76

    gordonaut

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  17. Feb 27, 2012 #77

    bob989

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    Hi Gordon,

    It was basically by considering low-speed aircraft that I was led to question propellers. In one of my earlier posts I posed that question. What exactly is it, as we increase the airspeed from zero, that causes us to change from ducted fans to propellers? I don't see where we run into difficulty with the ducted fan approach. The morphing of the duct into something wide and flat that blends with the wing doesn't seem to be a problem aerodynamically or propulsively. It's only a problem from the perspective of the large-engine paradigm. There isn't any room for a large engine. But there's room for small engines and fans.

    V/STOL aircraft have complications arising from the need for fast reaction time close to the ground. They use thrust for control. Placing the large engine in the fuselage decreases the roll moment of inertia relative to placing small engines in the wings.

    I'm mainly focused on high-endurance flight, either for long-range transport, or for loitering/hovering.

    I don't think of the duct as producing a high-speed exhaust relative to airspeed. I think of the duct as widening out toward the exit, so that the exit flow is relatively mild. The flow coming into the intakes on the leading edge, by contrast, would be more violent. So thrust augmentation, if applicable, would relate to the shape of the leading edge around the intake. On the trailing edge, I'm concerned about not generating a shear layer that would result in excess heat and turbulence in the wake.

    Regarding your discomfort with prospect of building everything into the wing, I recognize that that would raise a number of issues. But I don't see a show-stopper. For one thing, there's the matter of exactly what you mean by "the wing". If we take an existing airfoil and attach a wide, flat duct to the underside, and then build the whole propulsion system into the duct, aerodynamically we are substituting the exterior lower surface of the duct for an equivalent area that has been taken from the original "wing". But we can redefine the "wing" as being those new exterior surfaces.

    I don't think accessibility for maintenance is a problem. The whole engine and fan assembly could slide out through a rectangular hole in the leading edge. Pop in a new one, presto, done. The old one goes back for recycling/refurbishing, the new one automatically self-tests.

    What you seem to prefer (correct me if I'm wrong) is a more-or-less unaltered "wing" from the structural and aeroelastic perspectives, so that any new strip we attach to the lower surface has only propulsive implications. No altering of the wing structure, such as cutting holes through wing spars, and no risk of introducing flutter or control reversal. Your idea of the propulsion system is that it could be integrated aerodynamically, but should remain somewhat distinct structurally. It would be easier to design that way, because it's a perturbation on existing designs. I don't have any strong objection to that approach.

    There seems to be a struggle between the idea of a wing as something basically wide and flat and the idea of an engine as something basically cylindrical. Conceptually, one would like to slice open a large cylindrical engine, unroll it and flatten it out, and spread it out over the wing. But how could that be done without compromising what seems like the fundamentally rotary nature of the engine and fan?

    (Another way to flatten the engine would be to redesign it as a disk, together with the fan. There isn't any rule that says a turbine engine has to be cylindrical. The axis of the disk could be vertical. The airflow would be a bit more circuitous, perhaps travelling one full turn of a helix inside the duct.)

    The reason for spreading the propulsion system out over the wing is that we can combine the airflow from the fan and wing, so as to approximately nullify the lift-induced drag, and part of the skin-friction drag, during cruise. In the large-engine paradigm, it's not possible to locally nullify drag. The wing generates drag all along the span, but the propulsion system produces thrust only at one or two positions. That means that the wake contains extra kinetic energy, because there is always some horizontal velocity parallel to the direction of flight: backward behind the propeller or fan, and forward everywhere else. In a perfectly integrated small-engine system, taking the idealized case of a flying wing, the wake would contain only vertical velocity, i.e. the downwash associated with lift.

    But eliminating excess kinetic energy would only make the system more efficient if we could do it without dumping more heat into the wake. That's the question of propulsive efficiency of small fans and thermal efficiency of small engines. I see that as a collection of small design issues, and I see numerous ways to attack those problems. I understand your concern that in general, it's more difficult to achieve high efficiency in small engines/fans, but I don't accept a blanket statement that it's impossible.

    Your preference for a simple, large engine with recuperation might lead to (a) the excess kinetic energy described above, and (b) an over-optimization of the takeoff portion of the thrust. There is always going to be a difference between the thrust needed for cruise and the thrust needed for takeoff, especially from short runways. Your approach would add a heat exchanger to a large engine, but that's difficult to justify for both takeoff and cruise. Fuel efficiency is mainly for long-range and/or high-endurance missions; basically, it's cruise efficiency. Otherwise it's less interesting. An F-16, for example, is not a fuel-efficient cruising machine. It has plenty of thrust, enough to accelerate straight up, but it doesn't get it by sipping fuel. It gets it by burning fuel like there's no tomorrow. The takeoff problem is more like that, and less like the high-endurance cruise problem.

    If you size your large engines for cruise, you might not have enough takeoff acceleration. If you size the engine and heat exchanger for takeoff, the heat exchanger might be larger than necessary. You're only saving a small amount of fuel for that "extra" size.

    I don't have any problem with incorporating some thrust augmentation. My overriding concern is achieving the most efficient integration of the propulsion system and the airfoil. That would mean maximizing the pre-factor in the endurance equation, (L/D)/(g SFC), which I see as being equivalent to having a "clean" wake. It might turn out that having a plenum and multiple exit slots on the underside of the wing would do a better job of producing a clean airflow and wake. But if we introduce shear layers at trailing edges, for entrainment, then that shear is going to result in extra heat and turbulence.

    In general, I'm sceptical of using military research as a basis for a fuel-efficient, cost-effective airplane. They're just not in that business. Fuel efficiency doesn't matter to them because it doesn't win wars. Cost doesn't matter because it's not their own money they're spending; it's taxpayer money. When you're playing with taxpayer money, common sense has a funny habit of disappearing.

    So to summarize, I see a whole bunch of advantages for small engines, like ease of manufacturing, distribution and maintenance, and increased safety. I don't see any major problems, which of course is where we seem to differ. I know the idea of small engines goes against the grain when you consider that ever since the Wright brothers people have treated the airframe and propulsion system separately, and propulsion systems have almost always been built around large engines. But this is 2012. We have tricks up our sleeves that weren't available even a few years ago. We can choose to re-integrate the propulsion system and the airframe. The fact that the historical development of aviation focused mainly on large engines doesn’t impress me. It was always a choice, a habit of mind.

    The fanwing is an example of a system that spreads the propulsion out over the wing. It represents the third major way to orient the axis of rotation of the fan. It’s not incompatible with the small-engine paradigm, if the rotor is divided into sections that turn independently. I'm curious to know whether the fanwing approach could work efficiently for a large, high-speed aircraft. But I don't think so. I think it could work well only for low-speed loitering.

    The small-engine paradigm could also work for rotary-wing aircraft. A helicopter with small engines integrated into the rotor airfoil would not need a tail rotor (wasted kinetic energy again!), and it would be safer than having a single, large engine. An engine failure on a helicopter is a much more dangerous situation than on an airplane.

    -bob989
     
  18. Mar 1, 2012 #78

    gordonaut

    gordonaut

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  19. Mar 1, 2012 #79

    WonderousMountain

    WonderousMountain

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    Stop bickering and make a small jet of some type for under 5k dollars. Together.
     
  20. Mar 2, 2012 #80

    highspeed

    highspeed

    highspeed

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    Slight correction: Cdi=Cl^2/(Pi*AR*e)

    And e can be over unity for certain nonplanar configurations.
     

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