3.1. Rotor aerodynamics: introduction

Helicopter definition

a vehicle with one rotor that has the following three functions:

• lift

• propulsion

• control

main rotor functions?

• lift (up, down)

• propulsion (onwards, backwards)

• control

main helicopter producing countries?

• USA

• Russia

• Italy

• France

• Brazil

• India

• China

helicopters as we know them now appeared ___, even though…

post WW2

the concept of rotorcraft took root before fixed wing aircraft

fixed wing milestones (and year)

• 1000BC: chinese kites

• 1400: Da Vinci’s flying machine

• 1843: George Cayley’s biplane

• 1895: Otto Lilienthal’s gliders

• 1900: Invention of internal combustion

• 1903: first flight (Wright brothers)

rotary wing milestones (and year)

• 400BC: chinese toys

• 1400: Da Vinci’s aerial screw

• 1900: Invention of internal combustion

• 1920s: autogiros

• 1945: first production helicopters

• 1950s: turboshaft engines

which sections are in developmental hurdles?

• powerplant, aero and structures

• stability

• control

• ulterior problems

• recovery

why did early designs of helicopters fail?

• inefficient aero (FM 0.5)

• underestimated power

• heavy engine

early designs mainly consisted of ___ rotors

co-axial

wires and structural bracings…

add to drag

structural weight reduction possible with…

AI

what was the key for enabling the technology for vertical flight?

turboshaft engines

the main rotor produces a torque → rotorcraft need…

when did people realize this?

counter torque

until first prototypes

when was the first tail rotor developed? and by who?

1924-1930

AG Von Baumhaeur

rotors produce symmetric or asymmetric lift in forward flight?

asymmetric

to translate control inputs to the main rotor, …

you need a mechanism

when was the first successful implementation of the swash-plate? and by who?

1922

Juan de la Cierva

alternative to swash plate? when developed?

Karman servo flaps

late 1940s

which is the problem with rotor desings for flight?

they expose the system to risk of resonance

when does control saturation happen?

in sustained high g turns

when do rotors lose control authority?

in certain altitudes

Is it possible to recover a helicopter in case of engine failure? How?

Yes. By performing autorotation, where the airflow keeps the rotor spinning and allows a controlled descent.

If the pilot reacts quickly and has enough altitude, a safe landing is possible

How are real helicopter rotor flows?

• highly complex

• extremely complicated to model

is there a jump in flow velocity across the disk? and in pressure?

• no, there’s a smoothly accelerated flow

• there’s a jump in pressure

what happens to the stream tube with increasing velocity?

it contracts

how is velocity variation along the blade? (Hover)

• radially linear

• azimuthally symmetric

is the lift loading the same at each section? (Hover)

no, it’s different

where is the highest velocity (and hence dynamic pressure) (Hover)?

at rotor tips → strong tip vortices

highest velocity implies highest… (Hover)

dynamic pressure

describe the rotor flow in hovering flight

• velocity variation along the blade is radially linear and azimuthally symmetric

• lift loading different at each section

• highest velocity (and hence dynamic pressure) at rotor tips → strong tip vortices

describe the rotor flow in forward flight

• highly asymmetric

• region of flow reversal

• high Mach number

• large range of Mach numbers

• log Re regions

• large range of Re

when and by who was the Froude-Rankine momentum theory? for what? (two theories)

• developed by Rankine in 1865

  • for marine propeller applications

  • considered the rotor as an actuator disk

• expanded later by Froude

  • to capture variations across rotor stations

  • how? by discretizing the rotor as annular rings

how is the rotor idealized in the Froude-Rankine momentum theory?

as an infinitesimally thin actuator disk that produces a pressure difference

advantages of Froude-Rankine momentum theory?

• no need to analyze variations across sections

• power estimate

• rotor performance limits

disadvantages of Froude-Rankine momentum theory

no indications on rotor design and optimization

assumptions of Froude-Rankine momentum theory

• incompressible flow → neglect compressive effects in rotor tips

• steady, inviscid, irrotational flow

• flow is 1D, and uniform through the rotor disk and in the far wake

• ambient pressure in the far stream

• well defined slip stream

what we’re ignoring in the Froude-Rankine momentum theory

• no swirl in the wake

• no tip vortices

what is the streamtube?

the control volume we can define when using the assumptions of the Froude-Rankine momentum theory

when not climbing nor descending, …

v0=vc=0

what does a control volume mean?

the volume is fixed and particles are moving in and out of it

how do I apply conservation laws onto a control volume?

Reynolds transport theorem → for steady flows: formula

mass conservation original formula (momentum theory)

formula

mass conservation formula when applying it to the stream tube (momentum theory)

formula

momentum conservation original formula (momentum theory)

formula

momentum conservation: Glauert (momentum theory)

• year

• statement

• formula

• 1935

• the net pressure force on the fluid inside the control/material volume is zero for an unconstrained flow

momentum conservation formula when applying it to the stream tube (momentum theory)

formula

energy conservation original formula (momentum theory)

formula

energy conservation formula considering adiabatic process (momentum theory)

formula

energy conservation formula when applying it to the stream tube (momentum theory)

formula

mathematical model of momentum theory: formulas and development

formulas

development of pressure variation in momentum theory

development

which are the two dimensional ratios of interest to evaluate rotor performance?

• disc loading

• power loading

disc loading (DL): formula, meaning, units

DL=T/A

thrust produced per rotor area

N/m³

power loading (PL): formula, meaning, units

PL=T/P

thrust produced per unit power consumed

N/W

for an efficient rotor, we want a ___ PL (___ thrust vs. ___ power)

high, high, low

development of v_h (rotor efficiency)

development

what is v_h?

the induced velocity at the rotor disk in hover

do we aim to maximize or minimize the induced velocity?

minimize, because induced power is proportional to it.

vi lower → same thrust with less power → efficiency higher

helicopters consume the ___ power (at equivalent gross weight) to hover compared to any other type of craft

least

what did the advent of turboshaft engines (and leaps in aero knowledge) do?

finally increased the power loading enough for mass production of helicopters