Compressibility and Pressure Waves Flashcards
What type of waves are pressure waves?
Longitudinal waves consisting of points of compression and rarefaction.
What speed do pressure waves travel?
Speed of sound
What is formula for speed of sound (kts)?
39* sqrt(K)
What is speed of sound at sea level ISA conditions?
662 knots.
What are pressure waves formed from a Stationary Point Source? Do they remain uniformly spaces as they move away?
- Pressure waves expand out from their source in a circular pattern.
- Yes
What is the wave pattern from a subsonic point source? What is another name for this effect?
- The pressure waves are not uniformly spaced
- The waves ahead of the source are more closely spaced together than those behind because of the relative speed of the point source.
- Pressure waves ahead are still faster than the point source
- This effect is also call Doppler effect.
What is the wave pattern from a sonic point source?
- If the point source is moving at the speed of sound, the pressure waves move at the same speed as the source
- This results in a boundary forming in which no wave can pass and pressure waves cannot influence areas ahead of the source
What is the wave pattern from a supersonic point source?
- If point source is moving at greater the speed of source, the pressure waves are behind the point source
- Waves form a boundary that results in an oblique angle
- Source arrives before waves
What are Mach waves?
- Convergence of individual pressure waves that come from a source moving at or greater than speed of sound that converge in the direction of motion.
- A point in space that experiences a pressure disturbance (as the wave passes the molecules return to previous state)
Is flow effected on a Mach wave?
Not really, pressure change is very small
What is a shock wave?
A mach wave that creates significant changes in pressure and temperature.
Does the amplitude of a pressure wave decrease as it moves away from the source?
Yes
What type of wave pattern are new disturbances unable to propagate ahead of the source and form a boundary through which no wave can pass?
Sonic waves
What is the formula for Mach number?
Mach = V/A where V = TAS of object A = Local speed of sound
What is the free-stream Mach number (Mfs)? What is it also referred to as?
- The Mach number of the flow sufficiently remote from an aircraft to be unaffected by it.
- Also called the Flight Mach Number
What is the Local Mach number (Ml)?
- The ratio of the speed of the flow at a specified point to the speed of sound at the same point
- There are different local Mach numbers at different points on the A/C
What is the Critical Mach Number (Mcrit)?
The free stream Mach number at which a local Mach number first reaches sonic velocity
What is the Critical Drag Rise Mach number (Mcdr)?
- The free stream Mach number at which the drag co-efficient for a given AoA rises sharply
- Usually defined as a Cd rise of 20% of its subsonic value
What is the Detachment Mach number (Mdet)?
The free stream Mach number at which the bow shockwave first attaches to a sharp LE
What are the four flight regimes?
1) Subsonic
2) Transonic
3) Supersonic
4) Hypersonic
What are the characteristics of the airflow at subsonic speeds?
1) All airflow over the A/C is subsonic
2) Air is assumed to be an ideal fluid and is homogenous, continuous, non-viscous and incompressible
3) Free stream mach number is less than critical mach number
What are the characteristics of airflow at transonic speeds?
1) Transition between subsonic and supersonic
2) Local shock waves form in this range
3) Compressible flow is experienced
4) Delineated by Mcrit at lower end and Mdet at upper end
What are the characteristics of airflow at supersonic speeds?
1) All airflow is supersonic
2) All local Mach numbers are greater than 1.0
3) Mfs number is greater than Mdet
What are the characteristics of hypersonic airflow?
1) A subset of the supersonic regime generally defined as being from Mach 5.0 upwards
2) Characterized by highly supersonic flow
What is the formula for speed of sound?
a = sqrt(yRT)
where y = ratio of specific heats (1.4)
R = Gas constant
T = Temp in Kelvin
Do density and pressure effect the speed of sound?
No, except when increase in pressure results in increase in temperature
Does Mach number increase with altitude?
Yes, generally as long as temp is decreasing still.
What is a shockwave?
Very narrow region in which the air undergoes a high state of compression
Does the thickness of the shockwave decrease as the Mach number increases?
Yes it does.
What are the two types of shock wave?
1) Normal - a shockwave that is perpendicular to the airflow
2) Oblique - a Mach wave that is angled to the airflow dependent on the TAs
Does the air temperature increase between the normal shock and the leading edge?
Yes, can be quite significant.
Is airflow always subsonic behind a normal shock wave?
Yes
What are Mach whiskers?
Accelerated airflow over the upper wing camber starts to exceed Ml = 1.0 and small shockwaves are generated.
Do Mach whiskers help in preventing the normal shockwave?
Yes as they smoothly slow down the air, delaying development of normal shockwave.
What is the lambda foot of a shockwave? What causes this?
- The base of the normal shock has a delta shape called a lambda foot
- This is caused because of the pressure rise behind the shock being transmitted forward via the lower layers of the boundary layer (which are at slower speeds closer to the surface).
What is a shock stall?
- Boundary layer thickening and separation occurs due to the intense adverse pressure gradient through the shockwave.
- Can cause buffeting of control surfaces and render them ineffective.
- All flying tail designs are favoured for high speed aircraft.
What is the effect of normal shockwaves on wing lift coefficient (Cl) at transonic speed ranges?
The pressure increases behind the shockwave on the top surface of the wing are greater than the bottom, which reduces the lift coefficient of the wing.
What is the effect on Cp (Centre of Pressure) position in transonic/normal shock wave buildup? What is often incorporated into design to counter this?
- At speed, Cp moves rearwards at high transonic speeds, which causes mach tuck as the Cp moves further from the CoG.
- Mach trimmers are often fitted to counter this effect.
How do shockwaves form on a wings surface?
1) Mcrit is reached
2) Mach whiskers form on the upper surface of wing, which smoothly decelerate the flow back to subsonic
3) Pressure disturbance is created at wing trailing edge, which travels forward until point where Ml = 1.0
4) Pressure wall is formed
5) Pressure rise behind the shock is transmitted forward in subsonic surface boundary layer, generating lambda foot shape at shock base
6) Lamba foot thickened boundary layer presents a compressive corner to the airflow, oblique shockwaves appear that merge into a shockwave.
What occurs to density, static pressure and temperature across the normal shock?
Density, stastic pressure and temperature all increase across the shock.
Describe the typical flow over the wing at subsonic speeds Mach = 0.50?
- Standard incompressible flow
- Upwash ahead of the wing, stagnation point on LE
- Airflow accelerates over the upper surface and encounters an adverse pressure gradient once past the point of maximum thickness
- Adverse pressure gradient results in separated airflow at TE
What occurs at Mcrit? Around 0.72
- Areas over teh wing start to become supersonic, with small pressure disturbances resulting at the point of max acceleration
- Mach whiskers are created
- Lift increased to about 60% of low speed value
- Drag is higher
What starts to occur above Mcrit? Mach 0.77
- Mach whiskers have been swept together
- Pressure disturbances have been transmitted forward far enough that they cannot progress as they have encountered sonic airflow
- Lamda foot results as pressure disturbances can still propogate forward in subsonic boundary layer
- Drag increasing, lift is increased
- Cp has started to move rearwards.
- Shock stall has started to develop
What occurs at Mfs = 0.82?
- Top shock moves rearwards towards the TE
- Shockwave forms on lower surface
- Large reduction in pressure on lower surface of wing
- Cp moves about 15% of chord
- Cl reduces
What occurs at Mach = 0.95?
- Upper and lower shocks have moved rearwards to TE
- Cp moves rearwards to about 45% of chord, resulting in Mach tuck and potential shock stall
- Overall lift is reduced to incompressible values
- Drag is reduced as shocks move rearwards
What occurs at Mach 1.05?
- Bow wave has formed but is ahead of the wing
- Large pressure changes across the bow wave results in high pressure drag
- Cp is now around 45-50% of chord
- Lift is lower and higher overall drag compared to incompressible flow
What are the two main factors that affect the formation of bow shockwaves ?
1) Shape of the leading edge
2) Speed of the aircraft
What speeds will a bow wave form?
Speeds greater than Mach 1.0 but less than Mdet
What type of shock will form for blunt objects?
Combined normal/oblique shockwave and stabilize ahead of the leading edge
What type of shockwave will form for sharp objects?
An oblique shockwave will form and attach to the leading edge
