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Rotors and Propellers

9 tools in the Aerodynamics area.

Thrust, torque, power and figure of merit of a ducted fan whose blade geometry is known, from blade-element momentum theory: the chord and pitch at a few stations from hub to tip, the airfoil's lift and drag polynomials, the rotor speed and the climb or inlet velocity. The induced velocity of every annulus is solved exactly from the balance of the blade-element thrust with the momentum thrust (the Ducted Fan Optimization tool's small-angle inflow is a few percent higher at the hub). One operating point is written out in full and a sweep of rotor speed, inlet velocity or a pitch offset draws thrust, power and figure of merit against the swept variable: the inverse of the optimizer, which designs the blade for one power.

Duct Thrust Share

Momentum theory of the ducted fan: how the thrust divides between the rotor and the duct lip, the induced velocity at the disk, the exit velocity, the ideal power and the power saving against an open rotor of the same diameter at the same thrust, all as functions of the duct's exit area ratio σ_d (exit area over disk area). A cylindrical duct (σ_d = 1) puts half the thrust on the lip and needs 1/√2 of the open rotor's ideal power; a diffuser (σ_d > 1) moves more thrust to the duct and saves more power until its walls separate. An optional hover figure of merit turns the ideal power into shaft power, and the chart sweeps σ_d so the diffuser's worth can be read against its length and separation risk.

Fan Motor Matching

Operating point of a ducted fan on a brushless DC motor: where the motor's torque-speed line meets the fan's torque curve. The fan is described by its torque at one reference speed (from the Ducted Fan Performance tool or a test), scaled with the square of the speed, and the motor by its speed constant K_v, winding resistance R_m and no-load current I_0 at the supply voltage, with the throttle setting as the fraction of that voltage. The tool solves the operating speed, current, electrical and shaft power, efficiency and the thrust at that speed, checks the motor's current limit, and charts the two torque curves and the throttle sweep so the margin to full throttle can be read.

Multi-Fan Vehicle Sizing

First-order hover and climb power budget of a vehicle lifted by several ducted fans: from the takeoff weight, the number of fans, their diameter and exit area ratio, the disk loading, the ideal and actual hover power with a figure of merit and a drive efficiency, the thrust margin for control, the power to climb at a given rate, and the battery energy and mass for a required hover time from the pack's specific energy and usable fraction. Everything comes from momentum theory, so the result is a sizing estimate to decide how many fans of what size a weight can afford before any blade is drawn; the Ducted Fan Performance tool then checks a blade against the thrust each fan must deliver.

Fan Noise Estimate

Far-field noise of a fan or propeller from its thrust, shaft power, speed, diameter, blade count and blade area: the rotational (tonal) noise of the first harmonics of the blade-passing frequency by Gutin's theory in the engineering form of NACA TN 2968, and the vortex (broadband) noise by Yudin's sixth-power law with Hubbard's constant from the same report. The levels are given at the observer's distance and angle from the thrust axis, summed to an overall level, and charted against distance and angle. The estimate is for an unducted rotor in still air; a duct shields part of the tonal field and adds its own sources, so the result is a starting point and an upper bound for the rotor alone.

2 worked examples reproduced, listed on the tool page.

Tip Clearance Loss

What the gap between the blade tips and the duct wall costs a ducted fan: the fall of the hover figure of merit and of the thrust-to-power ratio with the tip clearance as a fraction of the rotor radius or diameter, read from two published test series, the 10-inch ducted rotor of Martin and Tung (NASA Ames, 2004: figure of merit against tip gap in percent of radius) and the 16-cm shrouded rotors of Pereira (University of Maryland, 2008: the ratio of the shrouded to the open rotor's maximum thrust-to-power against tip clearance in percent of diameter, four shroud shapes). The tool reads both curves at the entered clearance, scales them to the entered no-gap figure of merit, and gives the thrust and power penalties, so a designer can see whether the duct is worth building at the tolerance the shop can hold.

Inlet Flow and Crosswind

A ducted fan in a crosswind or in forward flight sees the free stream at an angle to its axis. Momentum theory with the free stream resolved along and across the axis gives the induced velocity, the ideal power and the momentum drag and pitching moment that the duct feels in turning the inflow; the upstream lip separates when the angle of attack exceeds a limit that falls with the thrust coefficient, and NASA's full-scale test of a 7-foot ducted propeller (TN D-4142, Figure 15) gives that limit against 1/T_c for a well-rounded lip. The tool evaluates the entered speed and angle, reports the power rise over hover, the momentum drag, the ram pitching moment and the margin to lip separation, and sweeps the crosswind speed so the designer sees where the inlet gives up.

Fan Blade Stress

Centrifugal force, flapwise and lagwise bending moments, combined stress and the first bending frequencies of a ducted-fan blade from its planform, section, material and operating point. The aerodynamic loads along the span come from the same blade-element momentum model as the Ducted Fan Performance tool; the blade sections are modeled as solid or thin-shell ellipses of the entered chord and thickness (their area and second moments by the site's section-geometry library) and pitched with the local blade angle, so the thrust and in-plane moments resolve into flap and lag bending about the section axes. The tool reports the root loads, the stress along the span with the critical station, margins against yield and ultimate with a factor of safety, the blade mass, and the first flap and lag frequencies at rest and at speed (Rayleigh with Southwell's centrifugal stiffening) on a Campbell diagram against the per-rev harmonics.

Other Aerodynamics sections

Airfoils and Wings · Aircraft Performance · Stability and Control · Atmosphere and Flight Conditions · Propulsion