Viscous Flow

Question 1

What is viscosity?

What are the 2 types?

Answer 1

The MEASURE of RESISTANCE to the RELATIVE MOVEMENT between TWO NEIGHBOURING PARTICLES of a fluid;
DYNAMIC viscosity (μ): A MEASURE of INTERNAL RESISTANCE on the TANGENTIAL FORCE per unit REQUIRED to MOVE HORIZONTAL PLANE with respect to another at a unit VELOCITY while maintaining a unit DISTANCE APART (Pa.s);
KINEMATIC viscosity (ν): The RATIO of DYNAMIC viscosity to DENSITY ν = μ/ρ (m^2/s)

Question 2

What is viscous shear stress?
What is the equation?
What does each component represent?

Answer 2

The FORCE due to the INTERACTION BETWEEN fluid PARTICLES, PROPORTIONAL to the VELOCITY CHANGE in the DIRECTION PERPENDICULAR to VELOCITY;
τ = μ(∂u/∂y);
μ: DYNAMIC VISCOSITY of the the fluid;
u: VELOCITY of the FLUID particle along its STREAMLINE;
y: DIRECTION PERPENDICULAR to u

Question 3

What is the effect of increasing temperature on viscosity?

Answer 3

Normally, VISCOSITY of LIQUID DECREASES as the BONDS between molecules become more RELAXED, and the MOLECULES are LESS RESTRICTED;
VISCOSITY of GASES will INCREASE as the INTERNAL ENERGY INCREASES so the MOLECULES move FASTER and COLLISIONS occur more FREQUENTLY causing more RESISTANCE of the CHANGE of RELATIVE VELOCITY

Question 4

What is the effect of increasing pressure on viscosity?

Answer 4

INCREASING PRESSURE will INCREASE VISCOSITY of LIQUID and GAS as the MOLECULES are COMPRESSED CLOSER together, INCREASING SHEAR STRESS;
However, for a LIQUID to CHANGE VISCOSITY, SIGNIFICANT PRESSURE must be APPLIED as they often have LITTLE to NO COMPRESSIBILITY

Question 5

Explain why Bernoulli’s equation must be changed when considering a viscous fluid?

Answer 5

When a VISCOUS fluid travels from A to B ENERGY is CONSUMED to OVERCOME the FRICTION BETWEEN fluid PARTICLES and BETWEEN FLUID and the SURFACE;
This means H will be LESS at B and PRESSURE will be LOST so hf is added to the equation to ACCOUNT for LOSS of PRESSURE HEAD along the STREAMLINE

Question 6

What is Reynolds number?
What is the equation?
What does each component represent?

Answer 6

A DIMENSIONLESS number which is used to CHARACTERISE the REGIME of a FLOW by showing the RATIO of INERTIAL FORCE of the FLUID to FRICTION due to VISCOSITY of fluid;
Re = ρvL/μ or Re = vL/ν;
ρ: DENSITY of fluid (kg/m^3);
v: MEAN VELOCITY of fluid (m/s);
L: CHARACTERISTIC LENGTH of fluid (m);
μ: DYNAMIC VISCOSITY of fluid (Pa.s);
ν: KINEMATIC VISCOSITY of fluid (m^2/s)

Question 7

What are the two regimes of fluid flow?

Give a brief description of each?

Answer 7

LAMINAR flow: Fluid PARTICLES move in ORDERLY LAYERS;

TURBULENT flow: Fluid PARTICLES may ROTATE, COLLIDE with each other and move RANDOMLY in DIFFERENT DIRECTIONS

Question 8

For internal pipe flow, what are the Re values that determine the regime of the flow?

Answer 8

LAMINAR: Re < 2000
TURBULENT: Re > 4000
TRANSITION: 2000 < Re < 4000

Question 9

Explain the main characteristics of the structure of the boundary layer on an aerofoil?

Answer 9

The boundary layer is a LAYER of FLUID in the PROXIMITY of a SURFACE where the EFFECTS of VISCOSITY are SIGNIFICANT;
At the SURFACE the SPEED is 0m/s and INCREASES with DISTANCE PERPENDICULAR to the SURFACE until reaching the SPEED of the MAIN FLOW;
The THICKNESS is determined by the DISTANCE between the SURFACE and the location where SPEED is 0.99 of the FULL LOCAL SPEED;
As air moves from LEADING EDGE it ENTERS LAMINAR BOUNDARY layer, which has a relatively THIN, UNIFORM FLOW and the SPEED INCREASES approximately LINEARLY PERPENDICULAR to the surface;
The air experiences a TRANSITION PERIOD in the INCREASING X DIRECTION from LAMINAR to TURBULENT known as the TRANSITION REGION;
The air then enters the TURBULENT BOUNDARY layer which has THICKER, more RANDOM flow and SPEED INCREASES STEEPLY close to the SURFACE then becomes UNIFORM near the EDGE of the BOUNDARY layer;
The TURBULENT layer also has a VISCOUS LAMINAR SUB-LAYER just over the SURFACE and BUFFER ZONE between the TRANSITION from LAMINAR SUB-LAYER to main TURBULENT BOUNDARY layer

Question 10

How does pressure change within the boundary layer?

Answer 10

PRESSURE remains CONSTANT in PERPENDICULAR DIRECTION to the surface;
PRESSURE will CHANGE with the PRESSURE OUTSIDE the BOUNDARY LAYER in the PARALLEL DIRECTION to the surface;
According to BERNOULLI’S and the CONTINUITY equation, at the LEADING EDGE the FLOW path gets NARROWER causing PRESSURE to DECREASE and as the air flows OVER the MOST CAMBERED POINT the air PRESSURE INCREASES

Question 11

How does velocity change within the boundary layer?*****

Answer 11

In LAMINAR boundary layer SPEED INCREASES approximately LINEARLY in the DIRECTION PERPENDICULAR to the SURFACE;
In TURBULENT boundary layer SPEED INCREASES SIGNIFICANTLY/EXPONENTIALLY in the DIRECTION PERPENDICULAR to the SURFACE when it is very CLOSE to the SURFACE then the INCREASE SLOWS as the VERTICAL DISTANCE from the surface INCREASES

Question 12

For flow over a flat plate, what are values determine the regime of the flow?

Answer 12

LAMINAR: Re < 5x10^5
TURBULENT: Re > 5x10^6
TRANSITION: 5x10^5 < Re < 5x10^6

Question 13

How does viscous shear stress relate to skin drag?

Answer 13

There is SHEAR STRESS in the BOUNDARY LAYER due to the CHANGE in VELOCITY PERPENDICULAR to the surface which ACTS PARALLEL to the surface;
When this SHEAR STRESS occurs the INTEGRATION of it provides SKIN DRAG therefore the HIGHER the VISCOUS SHEAR STRESS the GREATER the SKIN DRAG

Question 14

Compare the speed profiles of the laminar and turbulent boundary layers NEAR THE SURFACE?

Answer 14

The TURBULENT SPEED PROFILE graph is much FLATTER than the LAMINAR over the THICKNESS of the BOUNDARY LAYER;
This means the AVERAGE SPEED of the TURBULENT layer is GREATER and therefore the PARTICLES have MORE KINETIC ENERGY;
Because of the GREATER CHANGE in VELOCITY in the Y DIRECTIONS, SHEAR STRESS is GREATER in TURBULENT layer τ = μ(∂u/∂y) meaning the SKIN DRAG will also be GREATER

Question 15

What happens to the size of the boundary layer as the distance increases from the leading edge? Why?

Answer 15

In VISCOUS flow, fluid must CONSUME KINETIC ENERGY to OVERCOME the RESISTANCE caused by VISCOSITY;
The LONGER the fluid TRAVELS along the SURFACE, the MORE KINETIC ENERGY will be LOST and the MORE VERTICAL DISTANCE is required to INCREASE the SPEED to MAIN STREAM;
This means the BOUNDARY LAYER will LOSE MORE MOMENTUM, and get THICKER and THICKER along the surface

Question 16

What is the equation for the thickness of the laminar and turbulent boundary layer?
What does each component represent?

Answer 16

LAMINAR: δ = 4.64𝑥(Re𝑥^-0.5);
TURBULENT: δ = 0.383𝑥(Re𝑥^-0.2);
𝑥: The DISTANCE from LEADING EDGE to LOCATION on surface;
Re𝑥: LOCAL REYNOLDS NUMBER on AEROFOIL

Question 17

What is the standard equation for friction coefficient on the surface?
What does each component represent?

Answer 17

Cf = f/(0.5 x ρ x v^2 x b x L);
f: VISCOUS FRICTION FORCE;
ρ: DENSITY of FLUID;
v: SPEED of FLUID;
b: WIDTH of the SURFACE/SPAN;
L: LENGTH of the SURFACE/CHORD

Question 18

What is the equation for the friction coefficient in the laminar and turbulent boundary layer?
What does each component represent?

Answer 18

LAMINAR: Cf = 1.372(ReL^-0.5)
TURBULENT: Cf = 0.074(ReL^-0.2)
ReL: OVERALL REYNOLDS NUMBER

Question 19

What does the Reynolds number and skin drag coefficient graph show?

Answer 19

The SKIN DRAG COEFFICIENT is LOWER in the LAMINAR than the TURBULENT boundary layer;
The SKIN DRAG COEFFICIENT DECREASES with INCREASE in REYNOLDS NUMBER in the LAMINAR and TURBULENT boundary layer;
The SKIN DRAG COEFFICIENT INCREASES with INCREASE in REYNOLDS NUMBER in TRANSITION layer

Question 20

How does airspeed affect Reynolds number?

Answer 20

Re = ρvL/μ or Re = vL/ν;

An INCREASE in v will INCREASE REYNOLDS NUMBER

Question 21

How does pressure and airspeed change over an aerofoil outside the boundary layer?
What equations does this consider?

Answer 21

According to BERNOULLI’S and the CONTINUITY equation, at the LEADING EDGE the FLOW path gets NARROWER causing air SPEED to INCREASE and air PRESSURE to DECREASE;
As the air flows OVER the MOST CAMBERED POINT, the air SPEED to DECREASES and the air PRESSURE INCREASES

Question 22

What is boundary layer separation?

Why does it occur?

Answer 22

When the AIR PARTICLES LEAVE the SURFACE;
Due to VISCOUS FRICTION/SKIN DRAG, the airflow within the BOUNDARY LAYER LOSES KINETIC ENERGY and the INCREASE in SPEED in the Y DIRECTION gets SMALLER;
At the STAGNATION POINT there is NOT enough ENERGY to support the INCREASE in SPEED in the Y DIRECTION (∂v/∂y = 0)
In the VICINITY of the STAGNATION POINT there becomes IDLING air PARTICLES;
Due to the ADVERSE PRESSURE GRADIENT (∂p/∂x > 0) the INCREASE in PRESSURE causes PARTICLES to be PUSHED AWAY from the surface and form TURBULENT SWIRLS/EDDIES in addition to BACKWARD FLOW

Question 23

What is the stagnation point?

Why does this point exist?

Answer 23

The POINT along an AEROFOIL where ∂u/∂y = 0;
Due to VISCOUS FRICTION/SKIN DRAG, the airflow within the BOUNDARY LAYER LOSES KINETIC ENERGY and the INCREASE in SPEED in the Y DIRECTION gets SMALLER;
At the STAGNATION POINT there is NOT enough ENERGY to support the INCREASE in SPEED in the Y DIRECTION

Question 24

How does boundary layer separation cause an aircraft to stall?

Answer 24

The BOUNDARY LAYER SEPARATION causes a CHANGE in PRESSURE DISTRIBUTION around an AEROFOIL;
The SECTION of the aerofoil WHERE the BOUNDARY layer SEPARATES CANNOT produce LIFT;
This DECREASES the CL and CENTRE of PRESSURE moves FORWARD;
When the SEPARATION of the boundary layer OCCURS TOO EARLY over the aerofoil the PRESSURE DISTRIBUTION which PRODUCES LIFT can be DESTROYED;
The subsequent LOSS in LIFT CAUSES a STALL

Question 25

What is the adverse pressure gradient?

Answer 25

The PORTION of the AEROFOIL where ∂p/∂x > 0;

Ie: PRESSURE INCREASES in the X DIRECTION

Question 26

What is form drag?

What are the methods of reducing form drag?

Answer 26

When there is SEPARATION from STREAMLINE FLOW around a BODY causing a FORE-AFT PRESSURE DIFFERENCE;
CAUSED by NON-STREAMLINE SURFACES, SUDDEN CHANGES in surface SHAPE and ADVERSE PRESSURE GRADIENTS;
REDUCED by STREAMLINING SURFACES

Question 27

Which boundary layer separates more easily? Why?

Answer 27

LAMINAR BOUNDARY LAYER;
The PARTICLES have LESS SPEED therefore LESS KINETIC ENERGY and LESS MOMENTUM;
This means LESS ENERGY is REQUIRED to cause BOUNDARY SEPARATION

Question 28

How does ice accretion over a wing affect its aerodynamic properties?

Answer 28

INCREASES WEIGHT which INCREASES LIFT required;
CL must INCREASE to MAINTAIN LEVEL flight which INCREASES AoA;
DECREASES the VERTICAL COMPONENT of LIFT further;
CHANGES the PROFILE of the BOUNDARY LAYER;
QUALITY of SURFACE will CHANGE INCREASING TURBULENT FLOW INCREASING SKIN DRAG;
NO longer STREAMLINE, SEPARATION may occur EARLIER INCREASING FORM and SKIN DRAG;
May LEAD to EARLY STALL

Question 29

What factors will encourage a stall?

What are some factors to avoid?

Answer 29

LOW SPEED, HIGH AOA;
ACCELERATED STALL;
AILERON REVERSAL;
SUDDEN NOSE UP and NON SMOOTH SURFACE