Tools › Aerodynamics › Rotors and Propellers › Tip Clearance Loss

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.

  • Figure of merit against tip gap from Martin and Tung's 10-inch ducted rotor (NASA Ames 7 × 10 ft tunnel, 2004)

  • Shrouded-to-open thrust-to-power ratio against tip clearance from Pereira's four shroud series (2008)

  • Power penalty at constant thrust and thrust penalty at constant power for the entered clearance

  • Chart of both curves with the entered clearance marked, and the clearance at which the duct gains nothing

Tip Clearance Loss

Unit System: /

Fan and Clearance







Tip Clearance and the Duct's Suction Peak | Method page
×

Tip Clearance Loss

Tip Clearance and the Duct's Suction Peak

A duct earns its keep by carrying part of the thrust on its lip: the inflow accelerating around the leading edge creates a suction peak whose axial component is thrust. That peak depends on the rotor pulling the flow through the duct close to the wall. Air leaking through the gap between the blade tips and the wall short-circuits the pressure difference across the rotor near the tip, the suction peak collapses, and the duct's share of the thrust falls away. Martin and Tung's potential-flow pictures (their Figure 9) show the lip pressure distribution shrinking as the gap grows from 1 to 5 percent of the radius.

The data

Two public test series are used. Martin and Tung (NASA Ames, 2004) measured a 10-inch ducted rotor at 9,000 rpm with the tip gap varied from 1.0 to 4.2 percent of the radius; the hover figure of merit fell from 0.67 to 0.47 toward the isolated rotor's 0.44, most of the loss in the first percent. Pereira (University of Maryland, 2008) tested seventeen 16-cm shrouded-rotor models; his Figure 3.17 gives, for four shroud series, the ratio of the shrouded rotor's maximum thrust-to-power to the open rotor's against tip clearance in percent of the tip diameter. The series with the smaller lip radius and the shorter diffuser lose fastest.

How the tool uses them

Each curve is normalized by its value at the tightest clearance tested and treated as the fraction of the zero-gap figure of merit kept. The Martin and Tung curve is extrapolated linearly from 1 percent to zero gap; Pereira's series are averaged over those that cover the entered clearance. Both fractions are scaled to the zero-gap figure of merit entered on the form, and the power penalty at constant thrust (power scales with 1/FM) and the thrust penalty at constant power (thrust with FM2/3) follow. The break-even clearance is where the scaled Martin and Tung figure of merit falls to the entered open-rotor value.

Limits

Both rotors are small (tip Reynolds numbers of order 105), where the lip boundary layer is thick and the loss is severe; a large fan at the same percentage clearance should fare better, so the estimate is conservative for it. The gap under load is what matters: add the centrifugal and thermal growth of the blade and the ovality of the duct to the static clearance. Designs that keep the gap below about half a percent of the radius use a stiff duct and a tip-path controlled by a rigid hub; abradable liners allow a running clearance near zero.



References

Martin, P., and Tung, C. (2004). "Performance and Flowfield Measurements on a 10-inch Ducted Rotor VTOL UAV." In Proceedings of the 60th Annual Forum of the American Helicopter Society, Baltimore, MD.

Pereira, J. L. (2008). Hover and Wind-Tunnel Testing of Shrouded Rotors for Improved Micro Air Vehicle Design. PhD dissertation, University of Maryland, College Park, MD.

Hrishikeshavan, V. (2011). Experimental Investigation of a Shrouded Rotor Micro Air Vehicle in Hover and in Edgewise Gusts. PhD dissertation, University of Maryland, College Park, MD.

DISCLAIMER: The methods and calculation on aNOWysis.com are provided as means to educate the reader. There is no warranty, expessed or implied, as to the relevance or accuracy of the methods or calculations. All calculations should be checked by a qualified analyst for appropriateness and accuracy. We will not be held liable for any damages, injuries or deaths caused by using methods or calculations from this site.