Lift Forces in External Flows

• DECEMBER 2019

Real External Flows – Lesson 3 Lift

• We covered the drag component of the fluid force acting on an object, and now we will discuss its counterpart, lift. • Lift is produced by generating a difference in the pressure distribution on the “top” and “bottom” surfaces of the object. • The lift acts in the direction normal to the free-stream fluid motion. • The lift on an object is influenced primarily by its shape, including orientation of this shape with respect to the freestream flow direction. • Secondary influences include Reynolds number, Mach number, the Froude number (if free surface present, e.g., hydrofoil) and the surface roughness. • The pressure imbalance (between the top and bottom surfaces of the object) and lift can increase by changing the angle of attack (AoA) of the object such as an airfoil or by having a non-symmetric shape. Example of Unsteady Lift Around a Baseball

• Rotation of the baseball produces a nonuniform pressure distribution across the ball ‐ clockwise rotation causes a floater. Flow ‐ counterclockwise rotation produces a sinker. • In soccer, you can introduce spin to induce the banana kick.

Baseball Pitcher Throwing the Ball Soccer Player Kicking the Ball Importance of Lift

• Like drag, the lift force can be either a benefit Slats or a hindrance depending on objectives of a Flaps fluid dynamics application. ‐ Lift on a wing of an airplane is essential for the airplane to fly. • Flaps and slats are added to a wing design to maintain lift when airplane reduces speed on its landing approach.

‐ Lift on a fast-driven car is undesirable as it Spoiler reduces wheel traction with the pavement and makes handling of the car more difficult and less safe. • Race cars are equipped with spoilers to counter (“spoil”) unfavorable uplift force. Lift-Generating Devices • Lift-generating devices are specifically designed for efficient and stable generation of lift force at a range of angles of attack . ‐ Angle of attack (AOA) is defined as the angle between the direction of upstream flow and the reference line of the body (usually cord of an airfoil). Flow direction • The most common lifting device is an aircraft wing. positive AoA • Airfoils are 2D sections of a wing which are commonly 푉∞ used for analyzing lift and drag in two dimensions. • Note that many shapes other than specially designed wings can create lift. Flow Separation ‐ A flat plate under a positive AOA will create lift, but it will be a poor choice for an aircraft wing because of highly unsteady flow due to separation at the leading edge even at modest AOAs, which will pose a challenge to controlling the hypothetical airplane. Symmetric vs. Cambered Airfoils and Wings • A symmetric airfoil cannot produce lift at AOA = 0 deg because pressure forces on both sides balance. A symmetric airfoil must be at positive AOA to generate lift. • A carefully designed non-symmetric airfoil can generate lift at AOA = 0 deg. The asymmetry, or Symmetric Airfoil camber, between the two surfaces of the airfoil leads to unequal pressure distribution resulting in non-zero lift force. • A wing is complexly designed to optimize lift and minimize drag, and different sections can have different airfoil profiles. Cambered Airfoil ‐ The stream of air is split into two by the airfoil’s leading edge. More air is deflected downwards under the airfoil thus increasing upward force, and less air flow over the top airfoil’s shape resulting in decrease of the downward force. The net effect is the upward lift force on an airfoil. Example of Cambered Airfoils — NACA Series

• NACA airfoils are probably one of the most studied family of airfoils. • Originally developed by the National Advisory Committee for Aeronautics (NACA) in the 1930s, NACA airfoils since then have been a subject of numerous experimental and numerical studies, and a wealth of data exists for validations of computational predictive methodologies. • The shape of NACA four-digit series is described by four numbers MPXX ‐ 1st digit (M) – maximum camber as percentage of the cords. ‐ 2nd digit (P) – distance of maximum camber from the leading edge in tens of percents of the cord. ‐ 3rd and 4th digits (XX) – airfoil thickness as percentage of the cords. • M = P = 0 corresponds to a symmetric foil

NACA 2412 M XX camber line

P Lift Coefficient vs. Angle of Attack • For thin airfoils, lift is proportional to the AOA for small angles within ~10 degrees of AOA. • As the AOA reaches a critical value, there is a sudden drop 2 in lift, called wing stall. NACA 0012 ‐ Stall is caused by the flow separation which changes flow dynamics on the suction side of the wing. 1.5 ‐ Stall also is characterized by an increase in drag due to sudden Wing Stall onset of a large wake (refer to wake-induced drag in the L 1 previous lesson). C ‐ Predictions of stall are different because of highly unsteady separated flow, and normally either experimental techniques or high-fidelity CFD methods are used to analyze wing behavior in 0.5 near-stall conditions. • Drag also increases with the increase in AOA, primarily due 0 to the increase on the wing frontal area and thickening of 0 5 10 15 20 25 the boundary layer on the suction side. Angle of Attack α Lift Coefficient vs. Angle of Attack

AoA – 0o o AoA – 4 • Increasing the angle of attack causes the flow to separate from the top surface of the airfoil. The separation occurs for angles of attack greater than 5° or 6°.

• Increasing the frontal area of the airfoil increases the drag AoA – 8o AoA – 12o coefficient.

• Increasing the angle of attack eventually causes total separation and the airfoil is essentially a blunt object. Lift-to-Drag Ratio

0.03 • The lift-to-drag ratio is the lift created by an NACA 0012 object divided by its drag. This is an indication of 0.025 the aerodynamic efficiency of an airplane.

0.02 • One of major objectives of aircraft design is higher lift-to-drag ratios.

푫 0.015 푪

0.01 • Note that high-performance wings generate lift which is on the order of two orders of magnitude higher than their drag. 0.005

0 −2 −1 0 1 2 푪푳 Inviscid Methods for Lift Predictions

• Unlike drag, which cannot be accounted for unless fluid viscosity is included in the analysis, lift can actually be predicted with a certain degree of accuracy using the inviscid flow assumption. • The original methodology was proposed independently by German mathematician Maritn Kutta and Russian scientist Nikolay Joukowski, and subsequently received the name Kutta-Joukowski theorem. Kutta-Joukowski Theorem

• Assuming viscous effects are of minor importance in generating lift, the lift force acting on a thin airfoil is:

퐹푙푖푓푡 = න 푝푏 − 푝푡 푑푥

• Applying Bernoulli’s theorem, and assuming velocities on top and bottom sides are nearly equal to freestream, the force becomes: 휌 푝푏 1 2 푝푡 1 2 Ԧ + 푢 = + 푢 퐹 = න 푢푡 + 푢푏 푢푡 − 푢푏 푑푥 ≈ 휌푉∞ න 푢푡 − 푢푏 푑푥 = −휌푉∞ ර 푢 ∙ 푑푙 휌 2 푏 휌 2 푡 2

≈ 2푉∞ circulation Γ

• Kutta-Joukowski Theorem: Any 2D body in relative motion to the ambient fluid with velocity 푉∞ has a lift force, normal to 푉∞, of magnitude

퐹 = −휌푉∞Γ Lattice Vortex Method

• This theorization gave rise to a family of vortex methods for estimating lift. In these methods a lifting surface is approximated by a series of vortex panels, and each vortex panel is represented by local circulation Γ푗.

• Then velocity at a point, expressed in terms of the velocity potential, is: 푁 where coefficient 퐴푖푗 represent the induced ∇휑푖 = ෍ 퐴푖푗 Γ푗 flow on panel 푖 by the vortex on panel 푗. 푗=1

• Applying zero-normal-velocity on each panel results in a system of liner equations for unknown Γ푗

푁 푁

෍ 퐴푖푗 Γ푗 푉∞ + ෍ 퐴푖푗 Γ푗 ∙ 푛 = 0 푗=1 푗=1

• Local force for individual panels are found using Kutta-Joukowski theorem, and they summed up to provide the total force: 푁 Ԧ 퐹푖 = 휌Γ푗(푉∞ + 푢푖) × 푙푖 퐹 = ෍ 퐹푖 푗=1 Inviscid Methods for Lift Predictions

• Vortex methods are quick and relatively accurate in predicting lift, and they are widely used as low-fidelity methods for preliminary conceptual designs of lifting bodies.

NACA 4412 3

퐿 퐶 −20 −10 10 20 −1 Vortex Method −2 Wind Tunnel

Angle of attack High Lift Devices: Slats & Flaps

• Slats are fitted to the leading edge of an aircraft wing to delay flow separation ‐ This allows aircraft to operate at higher AoAs. ‐ The flow between the slat and wing reduces the adverse pressure Slats gradient preventing flow separation at higher angles of attack Flaps compared to the airfoil case. ‐ The flow eventually separates at larger angles of attack. • Flaps are aerodynamics structures fitted towards the trailing edge of the wing. ‐ Flaps can be controlled independently to increase the camber of the wing. This leads to the generation of larger lift force at the same angle of attack. High Lift Devices: Slats & Flaps

• Large commercial aircraft can have more than one flap on their wings. These are called multielement trailing edge flaps. AoA – 20.18 degrees • Deploying the slats and flaps of an aircraft not only increases Re = 3.52E6 the generated lift force but also adversely increases the fluid Mach Number – 0.197 drag. Large commercial aircraft use this increase in drag force to their advantage to land large commercial aircraft. • Depending on the flight phase, we can have three different configurations of slats and flaps. ‐ Take-off configuration ‐ Cruise configuration ‐ Landing configuration Flight Phases: Take-off, Cruise, and Landing

• Take-off: Slat and flaps are partially deployed to increase the lift force on the aircraft. Take-off configuration • Cruise: Slats and flaps are not used. No high-lift devices are necessary, and they are retracted into the wing. Cruise configuration • Landing: Slats and flaps are fully extended to increase the drag force experienced by the Landing configuration aircraft. Lift in Turbomachinery

• Blades of turbomachinery devices are designed using approaches similar to those used for aircraft wings, and the concept of lift (and drag) is also used in turbomachinery to quantify performance of, e. g., turbine or fan blades. ‐ Lift exerted by wind flow on wind turbine blades is what makes them turn. ‐ Lift exerted by rotating blades of a compressor (a fan) generates the flow of fluid Summary

• In this lesson we discussed the lift component of the fluid force acting on an object in an external flow. • We covered some aspects of lift-generating devices using airfoils as an example, such as dependence of lift on the angle of attack and the phenomenon of stall. • We also took a quick look into the inviscid method for predicting lift.