Speed Of Sound Flashcards
What are the airflow TAS ranges and airflow ranges for sonic flight?
TAS: MfsMdet supersonic
Airflow: M<1 subsonic
M=1 sonic
M>1 supersonic
Define Mfs, Mcrit, Ml
Mfs is the ratio of the TAS to the freestream speed of sound.
Ml is the ratio of the local airspeed to local speed of sound.
Mcrit is the Mfs when any Ml=1.
What equations may be used in compressible flow?
Euler equation
Continuity equation
IGL
Energy equation
What is the critical point?
Describe the properties of air before and after the critical point
The critical point is where v=a so M=1. So the temperature is named the critical temperature at this point, and the velocity= speed of sound so is known as the critical Vs.
Using the energy equation CpT+(v^2/2)=CpT0, it can be seen that when temperature increases, the velocity decreases. And as temperature changes, so will the speed of sound (T proportional a^2).
When T=0, a=0 and V=max.
When V=0, T=max and a=max.
At some point these curves intercept which is the critical point.
There will be a speed of sound at every temperature, but Vs does not necessarily equal the v, only at the intersection of the curves do they equal. Refer to graph.
What are the equations for a(max), V(max), Ac, Tc, energy equation?
The following are not in the equation sheets, however there are longer ways using equations in the formula sheet.
a(max)= SQRT(Cp(y-1)T0)= SQRT(RmT0y)
V(max)= SQRT(2CpT0)= SQRT((2yRmT0)/(y-1))
Ac=SQRT( (2y-1/y+1)CpT0) = SQRT(2yRmT0/y+1)
Tc=2T0/y+1
Energy eq= (a^2/y+1) + (v^2/2)
What are the relationships between Vmax and Ac, Tc and T0?
What are the adiabatic equations to find critical or stagnation pressure/density. What is the relation between the critical and stagnation pressure/density?
Vmax/ac = SQRT (y+1/y-1) Tc= 2T0/y+1
P0/P= (T0/T)^(y/y-1), Pc/P=(Tc/T)^(y/y-1)
pc/p= (Tc/T)^(1/y-1), p0/p=(T0/T)^(1/y-1)
Where P is px and p is density
Pc=(2/y+1)^(y/y-1)P0
pc=(2/y+1)^(y/y+1)p0
What is the velocity coefficient?
How is this useful?
It is a form of Mach number, where M*=v/ac.
V is the airspeed along a streamline and ac is the critical speed of sound along the streamline.
As temperature affects the speed of sound, and temperature will change with different velocities (energy equation), the velocity coefficient measures against ac which is constant? It is therefore able to tell us if a flow is sub or supersonic.
What is the relationship between M and M*?
From the equation given in the equation sheet, it can be seen that when:
M<1, M1, M>M>1
In simpler terms, M* represents if M is sub/supersonic and will always be a value closer to 1 than M. Ie) the true Mach number (M) is a more extreme value.
Explain how airflow (velocity and pressure) behaves in a converging nozzle in sub/supersonic airspeeds.
(Divergent nozzle is the same logic with dA/A>0)
dA/A = (M^2 -1) dv/v and dA/A = (1-M^2)/yM^2 dp/p.
Subsonic:
If dA/A<0 and (M^2 -1) is a negative value, dv/v must be increasing.
If dA/A<0 and (1-M^2) is a positive value, dp/p must be decreasing.
Supersonic:
If dA/A<0 and (M^2 -1) is a positive value, dv/v must be negative.
If dA/A<0 and (1-M^2) is a negative value, dp/p must be positive.
Is there a speed limit on converging nozzles?
Yes, this is as subsonic airflow will increase in speed in a converging nozzle until it reaches supersonic speeds, for which it will begin to decrease in speed. So unless the nozzle diverges, the speed limit is M=1
This point is the critical point where M=1 and v=a and should occur within the critical section (throat) where dA/A=0 (ie at a local minimum).
What are the equations for T0 and Tc?
T0= T + v^2/2Cp = T + (y-1)v^2/2yRm Tc=2T0/y+1 = 1/y+1 x (2T + (y-1)v^2/yRm)
How can air properties at 2 points in a converging/diverging nozzle be found?
By using the IGL, energy equation or adiabatic relationship.
Some long complicated equations can be used (in notes) but stated those above will work.
Describe the formation of a shockwave
The required conditions are:
-air particles must travel greater than the speed of sound
-there must be a compression pressure disturbance
A pressure disturbance will only travel at the speed of sound, whilst supersonic airflow (air particles) travels faster than the speed of sound. Ie) the source of the disturbance (air particles) travels faster than the disturbance.
So the disturbance can never catch up to the source. This means the air properties are not uniform and not continuous, since the disturbances accumulate and form a wave front or shockwave.
Shockwaves are about 1mm thick, and air properties will change across a shockwave.
Compare the air properties enforce and after a shockwave.
Assume a non viscous, adiabatic flow where area change in nil.
Airspeed will decrease across a shockwave
-so if flow before a shockwave is supersonic, flow after will be subsonic (1=M1M2) for a normal shock.
-the higher the speed before a shockwave, the lower the speed after
T0 remains the same but not P0
All properties of the air will increase in value after a shockwave except velocity
The higher the Mach number, the higher the intensity of the shockwave.
Ac^2=v1v2 is for normal shock too.
How could you calculate air properties across a shockwave?
Normal and oblique
The first equations on the formula sheet.
As across a shockwave is a irreversible adiabatic process, the normal adiabatic equations do not apply (only apply on a single side of shockwave).
ac^2=v1v2
1=M1M2
