Q4 - Normal Shock

Question 1

Derive general relations for a normal shock from integral form of conservation laws.

Answer 1

1. Process is irreversible(Not isentropic). (P2/P1 =! (T2/T1)^(k/(k-1))
2. Mass conservation: DI of rhovnDa = 0. -v1rho1A1 + v2rho2A2 = 0. rho1v1 = rho2v2.

3.Energy conservation: DI of horhovn*dA = Q. - W. Assume Q. and W. are 0.
h01 = h02. T1 + (v1^2)/2cp = T2 + (v2^2)/2cp

4. Momentum: (DI of vrhovndA + DI of PndA) = 0
   p1+rho1(v1^2)=p2+rho2(v2^2)

Question 2

A blunt-nosed body is re-entering the Earth’s atmosphere at a Mach number of 20. In front of
the body there is a shockwave. Opposite the nose of the body, the shock can be regarded to be
normal to the flow direction. Assume that the air behaves as a perfect gas (neglect
dissociation) with constant = 1.4. The ambient pressure and temperature are 1 kPa and 220
K, respectively.

(b) Determine the temperature to which the nose is subjected.

Answer 2

Provided M1, T1 and P1.

Find M2 (Formula provided in the data sheet) M2^2 = (k1M1^2 +1)/(k*M1^2 - k1)

Now Find (T2/T1) = (1+k1M1^2)/(1+k1M2^2)
And rearrange to Find T2

Question 3

A blunt-nosed body is re-entering the Earth’s atmosphere at a Mach number of 20. In front of
the body there is a shockwave. Opposite the nose of the body, the shock can be regarded to be
normal to the flow direction. Assume that the air behaves as a perfect gas (neglect
dissociation) with constant = 1.4. The ambient pressure and temperature are 1 kPa and 220
K, respectively.

(c) Determine the static pressure to which the nose is subjected.

Answer 3

Use (P2/P1) = (1+kM1^2)/(1+kM2^2) and rearrange to find P2.

Question 4

A blunt-nosed body is re-entering the Earth’s atmosphere at a Mach number of 20. In front of
the body there is a shockwave. Opposite the nose of the body, the shock can be regarded to be
normal to the flow direction. Assume that the air behaves as a perfect gas (neglect
dissociation) with constant = 1.4. The ambient pressure and temperature are 1 kPa and 220
K, respectively.

(d) Determine the stagnation pressure to which the nose is subjected

Answer 4

Find (P02/P01) = (T1/T2)^*(k/(k-1)) *(P2/P1).

Find P01 = P1 * (1+k1*M1^2)^(k/(k-1)).

P02 = P01 * (P02/P01)

Question 5

A blunt-nosed body is re-entering the Earth’s atmosphere at a Mach number of 20. In front of
the body there is a shockwave. Opposite the nose of the body, the shock can be regarded to be
normal to the flow direction. Assume that the air behaves as a perfect gas (neglect
dissociation) with constant = 1.4. The ambient pressure and temperature are 1 kPa and 220
K, respectively.

(e) Determine increase in the specific entropy at the shock near the nose.

Answer 5

As a moving shock is an adiabatic process, we can use the formula
s2 - s1 = -Rg*Ln(P02/P01).