- Information
- AI Chat
Introduction to Viscous Flows
Civil Engineering
Bicol University
Recommended for you
Preview text
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
Fundamentals of Aerodynamics
Basic Aerodynamic Principles:
- Introduction to Viscous Flows
What is Viscous Flow? A flow where the effects of viscosity, thermal conduction, and mass diffusion are important.
Viscosity The property of fluid to resist shearing stress The sticky or adhesive characteristic of a fluid
Frictionless flow on an airfoil
Real life flow on an airfoil, with friction
Boundary Layer - the region of viscous flow which has been retarded owing to friction at the surface.
A flow field can be split into two regions, one region in which friction is important, namely, in the boundary layer near the surface, and another region of frictionless flow (sometimes called potential flow) outside the boundary layer. The boundary layer thickness d grows as the flow moves over the body; that is, more and more of the flow is affected by friction as the distance along the surface increases. In addition, the presence of friction creates a shear stress at the surface τw. This shear stress has dimensions of force/area and acts in a direction tangential to the surface. τw gives rise to a drag force called skin friction drag,
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
Velocity profile through a boundary layer
The velocity starts out at zero at the surface and increases continuously to its value of V 2 at the outer edge.
Shear Stress at the Wall
Absolute Coefficient of Viscosity
For liquids, μ decreases as T increases (we all know that oil gets "thinner“ when the temperature is increased). But for gases, μ increases as T increases (air gets "thicker" when temperature is increased).
Absolute Coefficient of Viscosity for air at standard sea level temperature:
Two basic types of viscous flows:
Laminar Flow – flow in which the streamlines are smooth and regular and the fluid element moves smoothly along the streamline.
Turbulent Flow – flow in which the streamlines break up and a fluid element moves
in a random, irregular, and tortuous fashion.
Factors that Affect the Type of Flow in the Boundary Layer: Smoothness of the flow approaching the body the shape of the body the surface roughness the pressure gradient Reynold’s Number
0
y
w dy
dV
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
Relationship between laminar and turbulent shear stresses
Standard Airfoil Pressure Distribution Laminar Flow Airfoil Pressure Distribution
Advantage of Laminar Flow Airfoil Low Skin friction drag have excellent high-speed properties, postponing to a higher flight Mach number the large drag rise due to shock waves and flow separation encountered near Mach 1
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
Disadvantage of Laminar Flow Airfoil Laminar flow is a sensitive phenomenon; it readily gets unstable and tries to change to turbulent flow. For example, the slightest roughness of the airfoil surface caused by such real-life effects as protruding rivets, imperfections in machining, and bug spots can cause a premature transition to turbulent flow in advance of the design condition.
Results for Laminar Boundary Layer
Laminar Boundary Layer Thickness:
Where:
V x
Rex
Laminar Local Skin Friction Coefficient Cfx
Where:
Laminar Flow Total Skin Friction Drag Formula Laminar flow Total skin friction drag coefficient Cf
Skin Friction Drag
Limitations of the laminar formulas apply to laminar boundary layers only These equations are exact only for low-speed (incompressible) flow. reasonably accurate for high-speed subsonic flows as well
x
x
Re
2.
q V
Cfx W W
2 2
1 x
Cfx
Re
.0 664
V x
Rex
V L
q L Df
.1 328
q S
D
C
f f
L
Cf
Re
.1 328
Df cfqS
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
- For the flat plate in sample problem 1 of laminar flow, calculate and compare the local shear stress at the locations 1 and 5 cm from the front edge (the leading edge) of the plate, measured in the flow direction. Assume now the flow is completely turbulent
Practice Problem: The wing of the Fairchild Republic A-1 OA twin-jet close-support airplane is approximately rectangular with a wingspan (the length perpendicular to the flow direction) of 17 m and a chord (the length parallel to the flow direction) of 3 m. The airplane is flying at standard sea level with a velocity of 200 m/s. If the flow is considered to be completely laminar, calculate the boundary layer thickness at the trailing edge and the total skin friction drag. Assume the wing is approximated by a flat plate. Assume incompressible flow.
Compressibility Effects in Skin Friction
Transition from laminar to turbulent boundary layer
Critical Reynold’s Number for Transition
Factors which encourage transition from laminar to turbulent flow: Increased surface roughness increased turbulence in the free stream adverse pressure gradients heating of the fluid by the surface Similarity parameters of the flow (Mach Number and Reynolds Number)
Sample Problems: 1. Assume that you have an airfoil of given surface roughness in a flow at a free-stream velocity of 150 m/s. How far from the leading edge the transition will take place. Rexcr =5 x 105
cr
xcr
V x Re
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
- If now you double the free stream velocity to 300 m/s, the transition point is still governed by the critical Reynolds number Rexcr = 5 x 10 5 .Thus,
- The wingspan of the Wright Flyer I biplane is 40 ft 4 in, and the planform area of each wing is 255 ft 2. Assume the wing is rectangular (obviously not quite the case, but not bad), as shown in Fig. 4. lf the Flyer is moving with a velocity of 30 mi/h at standard sea-level conditions, calculate the skin friction drag on the wings. Assume the transition Reynolds number is 6 x 10 5. The areas of laminar and turbulent flow are illustrated by areas A and B, respectively, in Fig. 4.
Flow Separation
Friction also causes another phenomenon, called flow separation, which, in turn, creates another source of aerodynamic drag, called pressure drag due to separation (Form Drag).
Pressure Drag due to separation on sphere
Qualitative comparison of pressure distribution, lift, and drag for attached and separated flows on an airfoil:
Engr. Kenneth M. Talag References: Department of Aeronautical Engineering Introduction to Flight, 5th Edition, Holy Angel University Fundamentals of Aerodynamics, 3rd Edition Elements of Practical Aerodynamics Airplane Aerodynamics and Performance
Laminar Flow vs Turbulent Flow
LAMINAR TURBULENT
Less skin friction drag; pressure drag predominates
Greater skin friction drag
Unstable, tends to favor flow separation
More stable; disorder is favored by nature
Transition region is closer to leading edge
Transition region is farther aft
“Thinner” velocity profile Fuller velocity profile
Thinner boundary layer Thicker boundary layer
Introduction to Viscous Flows
Course: Civil Engineering
University: Bicol University
- Discover more from:Civil EngineeringBicol University999+ Documents
- More from:Civil EngineeringBicol University999+ Documents
