1 Excerpt: Principles of Fast and Efficient Electric Flight J. Philip Barnes Senior Technical Fellow, Pelican Aero Group, San Pedro, CA 14 October, 2016 Abstract Here we excerpt from Phil’s technical paper, AIAA 2016-4711 “Principles...Part 1” and we preview its 2017 follow-on “Principles...Part 2.” Free EXCEL “beta” software for each part is embedded in the free PowerPoint presentations at Phil’s website: www.HowFliesTheAlbatross.com Part 1 focuses on the performance and system optimization of motor-generator, battery, and power conditioning. We reveal severe losses of the popular main-current “pulse-width modulation” method of cruise power conditioning, and then introduce the far-more efficient alternative of DC-DC conversion, with which we can double or triple cruise range. Part 2 reviews and renews propeller, windprop, and propfan aerodynamic design and performance, hybridizing a numerical lifting line with core features of Hermann Glauert’s Blade Element Method to model rotor aerodynamics at low speed and swept-blade aerodynamics at high speed, in all cases numerically integrating the helical wake-induced velocities and taking most aerodynamic parameters normal to the local lifting line of the blade. Introduction The regenerative-electric aircraft (Figure 1) is one of myriad applications of the “permanent-magnet” (P-M) motor generator. Part 1 herein illustrates high-efficiency integration of one or more such machines with either a battery or fixed- voltage supply, with particular focus on efficient electric flight in all regimes including climb, cruise, and “regen.” In Part 2, we’ll study propeller, windprop, or propfan aerodynamics. The “regen” shown below uses its “windprops” as propellers for climb or cruise, and as airborne wind turbines to recharge the battery in ridge lift, thermals, or descent. Part 1 -generator, battery, & power conditioning : Motor The permanent-magnet brushed or brushless machine, whether motoring or generating, develops a battery-opposing electro- motive force (EMF, ε), or Voltage, proportional by a constant (k) to the rotational speed (ω). Here, we shouldn’t confuse the EMF constant (k≡ε/ω), having units of N-m/Amp, with the Voltage constant (K v ), of units RPM per Volt. Arcing and other limitations of the brushed machine have favored brushless machines for a vast array of applications, including propulsion of ground and flight electric vehicles. Figure 1. “Regen” regenerating in ridge lift 3D math modeled with Python script and rendered with free www.Blender.org graphics
Transcript
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Excerpt: Principles of Fast and Efficient Electric Flight
J. Philip Barnes Senior Technical Fellow, Pelican Aero Group, San Pedro, CA 14 October, 2016
Abstract Here we excerpt from Phil’s technical paper, AIAA 2016-4711 “Principles...Part 1” and we preview its 2017 follow-on “Principles...Part 2.” Free EXCEL “beta” software for each part is embedded in the free PowerPoint presentations at Phil’s website: www.HowFliesTheAlbatross.com Part 1 focuses on the performance and system optimization of motor-generator, battery, and power conditioning. We reveal severe losses of the popular main-current “pulse-width modulation” method of cruise power conditioning, and then introduce the far-more efficient alternative of DC-DC conversion, with which we can double or triple cruise range. Part 2 reviews and renews propeller, windprop, and propfan aerodynamic design and performance, hybridizing a numerical lifting line with core features of Hermann Glauert’s Blade Element Method to model rotor aerodynamics at low speed and swept-blade aerodynamics at high speed, in all cases numerically integrating the helical wake-induced velocities and taking most aerodynamic parameters normal to the local lifting line of the blade.
Introduction The regenerative-electric aircraft (Figure 1) is one of myriad applications of the “permanent-magnet” (P-M) motor generator. Part 1 herein illustrates high-efficiency integration of one or more such machines with either a battery or fixed-voltage supply, with particular focus on efficient electric flight in all regimes including climb, cruise, and “regen.” In Part 2, we’ll study propeller, windprop, or propfan aerodynamics. The “regen” shown below uses its “windprops” as propellers for climb or cruise, and as airborne wind turbines to recharge the battery in ridge lift, thermals, or descent. Part 1 -generator, battery, & power conditioning : MotorThe permanent-magnet brushed or brushless machine, whether motoring or generating, develops a battery-opposing electro-motive force (EMF, ε), or Voltage, proportional by a constant (k) to the rotational speed (ω). Here, we shouldn’t confuse the EMF constant (k≡ε/ω), having units of N-m/Amp, with the Voltage constant (Kv), of units RPM per Volt. Arcing and other limitations of the brushed machine have favored brushless machines for a vast array of applications, including propulsion of ground and flight electric vehicles.
Figure 1. “Regen” regenerating in ridge lift 3D math modeled with Python script and rendered with free www.Blender.org graphics
The brushless machine is electronically commutated by an inverter which as a byproduct also provides rectification to enable regeneration. The brushless M-G as a system with its inverter-rectifier (Figure 2) has the same two-wire battery interface and the same voltage-speed and torque-current proportionality of a brushed machine. Thus, we can model the system with two batteries, one “fixed” and the other variable, “competing” to set the direction and quantity of current (i) through a combined resistance (R). If a “power supply” (fixed Voltage source) is used, “battery EMF” is the source voltage, and “battery resistance” becomes zero.
Figure 2. Brushless motor-generator system
With or without losses, motoring efficiency is given by the ratio of shaft power (τω) to battery electrical power (εbi) taken “upstream” of the loss due to battery internal resistance (Rb). Given P-M machine behavior, we are led to an “EMF ratio” (kω/εb) which is also a “speed ratio” or non-dimensional speed [ω/(εb/k)=RPM/(Kvεb)]. We designate this fundamental parameter (ν), noting that when it is unity, the EMF of the motor-gen matches that of the battery, with current at zero and torque near zero. We further discover non-dimensional groups representing current [iR/εb = 1-ν], torque [τR/(kεb) = 1-ν-ψ] and torque loss ψ ≡ [λR/(kεb)], taking the torque (τ) and torque loss (λ) each as a ratio with ideal stall torque (kεb/R) where (ω=0). The non-dimensional torque loss (ψ) typically ranges from around 0.020 at model scale to 0.005 at “sport flyer” scale, depending also on design. These non-dimensional parameters are related as in Figure 3, representing data for a range of power-supply voltages, for a typical model-scale brushless outrunner.
Figure 3. Mfly motor non-dimensional characterization
Although the test data for Mfly motoring system efficiency validates the theoretical linearity with speed over most of the speed range, the efficiency peaks near 85% of base speed and falls to zero at 100% thereof. In those regions, parasitic losses render the theoretical ideal motor-generator model unusable. However, knowing the relationships of the non-dimensional parameters, we can predict peak efficiency, the rotational speed for such, and the optimum battery EMF (see full paper). But given optimality at full power, what becomes the system efficiency at cruise, requiring only about 20% of full power? Power Conditioning: Big Losses, Main-current PWM In the popular method of reducing power for cruise, the electronic speed control (ESC) superimposes pulse-width modulation (PWM) on the brushless-motor commutation wave (Figure 4) to “chop” main current so that the average current satisfies demand. Although the “chopping loss” may be only about 3%, a much larger system loss will now be revealed.
For an aircraft propeller, both speed and torque may be reduced for cruise. In Figure 5, the electric motor has 60% cruise efficiency continuously energized. But de-energized between power pulses, the motor continues to sustain windage, bearing, and magnetic losses. Here, neither motor alone nor ESC alone can be “blamed” for what becomes poor system efficiency. For this example, the PWM duty cycle (δ) is about 1/7 to match motor and load torques at cruise.
Figure 5. Torque and speed at climb and cruise
In effect, main-current PWM magnifies motor torque losses by the factor (1/δ). Data and theory show that main-current PWM efficiency “alone” is about 50% at cruise, per Figure 6. Again, this is not the “chopping loss,” but instead represents the gross inefficiency of two components, each of good or excellent efficiency, poorly integrated as a system. The PWM efficiency of Figure 6 is factored by the motor efficiency of Figure 5 to yield a system electrical-power efficiency near 30% at cruise. We next introduce a more-efficient alternative for power conditioning in the form of DC-DC conversion.
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Non-dimensional CharacterizationAll Data (6,10,16V), Mfly 180-08-15
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Figure 6. Main-current PWM efficiency, data and theory
Efficient Power Conditioning With DC-DC Conversion We have shown that main-current PWM imposes significant losses at cruise. But in an entirely different role, PWM proves essential to “buck” (step-down) or “boost” (step-up) voltage with a DC-DC converter. In the DC boost converter of Figure 7, the duty cycle of low-voltage PWM at the gate of the single transistor controls the converter voltage gain to efficiently match motor and load, with negligible ripple in the main current.
Figure 7. DC-DC converter Circuit
At “sport-flyer” scale (say ~30kWe climb), DC-DC converter efficiency is about 97% in all regimes, including climb, cruise, and regen. Also with DC conversion, motor voltage is always close to that for say 90% peak motor efficiency. Comparing the products of motor efficiency and power-conditioning efficiency, we find that cruise system efficiency and range can be almost tripled by replacing main-current PWM with DC conversion.
Closure to Part 1
Part 1 herein is dedicated to Michael Faraday, electrochemistry pioneer and inventor in 1821 of the world’s first electric motor. With little formal education, Faraday became “one of the greatest scientific discoverers of all time,” according to Earnest Rutherford. Albert Einstein posted on the wall of his study three images, those of Isaac Newton, James Clerk Maxwell, and Michael Faraday.
Part 2: Propeller, Windprop, and Propfan Aero Introduction Today, 90 years after its publication in what would become a classic text, Hermann Glauert’s blade element method remains the most popular computationally-efficient tool for propeller or wind turbine aerodynamic analysis. The method, however, by ignoring mutual interaction of blade sections from hub to tip is limited to 2D flow. This yields optimistic thrust and renders the method unusable for a square-tip blade. It is also limited to low-speed subsonic flow. However, the method correctly applies the momentum principle to relate wake-induced velocities to local thrust and torque loading gradients. Herein we propose a hybrid lifting line/blade-element method representing 3D flow, using Glauert’s induced-velocity relations, and accommodating transonic flow for swept blades. Glauert’s Blade Element Method (BEM) BEM solves the problem stated by the equations and sketch of Figure 8, where Greek or upper-case symbols (and cL : cD) represent non-dimensional parameters. Fundamental to BEM is the relationship of axial and circumferential wake-induced non-dimensional velocities (Vix : Viθ) to local non-dimensional radial gradients (dT/dR : dQ/dR) of thrust and torque. For the iterative solution, induced velocities are first ignored and then the equation or function series is repeated to convergence.
• BEM interpretation validated• First hint of optimistic thrust
R RR
by permission, Wellcome Library, London
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Next in Figure 10 we illustrate the 2D nature of BEM by applying it to a square-tip blade. As shown, the induced velocities, thrust loading, and torque loading remain tied to the blade shape, but all of these actually vanish at the hub and tip.
Figure 10. Revealing the 2D Limitation of Glauert’s Method
Hybrid Lifting-Line / Blade-element Method Here we numerically integrate helical wake-induced velocities (Figure 11) and apply our “equivalent-flat-plate” boundary condition to solve for bound vortex strength. Knowing the resulting thrust and torque loading, Glauert’s induced velocity formulas are applied. The method matches test data in Figure 12, where we also show the characteristic over prediction of BEM.
Figure 11. Wake and boundary conditions
Figure 12. Hybrid Lifting-line validated & compared to BEM
Method Application: Windprop In Figure13 the hybrid lifting line/BEM is applied to predict the performance of two windprops of the same diameter and climb thrust. The 8-blade rotor has steeper blade angles, lower RPM (lower noise), and slight edge in peak efficiency.
Figure 13. Windprop comparison at given diam. & climb thrust
Method Application: Propfan In Figure 14 we apply the method to predict the performance of a propfan at high-subsonic Mach number. By taking most aero properties normal to the lifting line, the flow remains subsonic from hub to tip whereby, provided the blades are swept, the method obtains an excellent match with test data.
Figure 14. Closure to Part 2
Part 2 herein is dedicated to Hermann Glauert, brilliant aerodynamicist and propeller guru of the 20th century. Glauert solved the thin-airfoil integral, wing lift loading with arbitrary chord and twist, and independently originated the Prandtl-Glauert Rule for transonic flow. And as to our “regen,” Glauert is “father” of the airborne wind turbine.
