Rr322105-high-speed-aerodynamics

Set No. 1

Code No: RR322105

III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 HIGH SPEED AERODYNAMICS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) What is the relationship between internal energy and enthalpy? Carbon dioxide expands isentropically through a nozzle from a pressure of 3.0 bar to 1.0 bar. If the initial temperature is 463 K, determine (b) The final temperature, (c) The enthalpy drop and (d) The change in the internal energy. 2. (a) Prove the relation M22 =

M12 1+ γ−1 2

[4x4=16] for a Normal shock and

γM12 − γ−1 2

(b) Comment on the situation when M1 = 1. (c) What happens when M1 goes to infinity?.

[8+4+4]

3. (a) Develop the Prandtl relation in supersonic flows for oblique shocks and (b) Show that the normal shock may be considered as the limiting case for a strong oblique shock in which the shock angle is 900 and (c) That the deflection angle of the streamline is zero.

[6+6+4]

4. A supersonic flow with M1 = 1.7 , p1 = 1 atm ,and T1 = 288 K is expanded around a sharp corner through a deflection angle of 150 . Calculate M2 , p2 , T2 , p0,2 , T0,2 and the angles that the forward and rearward Mach lines make with respect to the up stream flow. [16] 5. Consider the equation of continuity under isentropic flow conditions and obtain the   relation for area ratio as

A∗ A

=



(γ−1)/γ

p p0 γ−1 1/2 2

1−

1/2





1/γ p p0 (1/2)(γ+1)/(γ−1)

2 ( ) ( γ+1 ) of this equation in one dimensional gas dynamics.

. Explain the significance [16]

6. Air at velocity of 210 m/s decelerates through a diffuser to a velocity of 60 m/s The temperature and pressure at the inlet are 278 K and 80 kPa with the exit pressure of 90 kPa. Assuming 1-D steady flow, calculate (a) The change in stagnation pressure , (b) The change in entropy, and (c) The diffuser efficiency.

[16]

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Set No. 1

Code No: RR322105

7. Making use of the velocity potential equation for compressible isentropic flows, develop "  ∧ 2 # ∧  2 # ∧ "  ∧ ∧  ∧ ∧ 2φ 2φ ∂ φ ∂ ∂ ∂ φ ∂2 φ ∂ φ = 0, where a2 − V∞ + ∂x + a2 − ∂y −2 V∞ + ∂x ∂∂yφ ∂x∂y ∂x2 ∂y 2 ∧

φ is the perturbation potential due to the placing of a thin airfoil in the flow field. Application of B.C.may be clearly stated. [16] 8. Define critical Mach number and plot lift and drag coefficient v/s Mach number for a conventional airfoil. Now describe a supercritical airfoil due to Whitcomb and plot the aerodynamic characteristics for this airfoil section on the same plot. Illustrate further with Cp plot. [16] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: RR322105

III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 HIGH SPEED AERODYNAMICS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define internal energy and enthalpy . (b) How are the two related? 3.0 Kgs of air is to be discharged through a smooth circular duct at a velocity of 10 m/s.The pressure and temperature of air in the pipe are 1.5 bar and 300 K respectively. (c) Determine the enthalpy and (d) Internal energy of air and dia. (e) of the duct.(R = 0.287 kJ/kg-K, Cp = 1.005kJ/kg-K).

[4+3+3+3+3]

2. (a) Define strong shock and weak shock wave in a compressible flow . (b) Illustrate with sketches and plots. (c) Hence develop the famous Prandtl relation for normal shock waves. (d) Provide detailed comments on this relation.

[3+3+7+3]

3. Consider a Mach 3 supersonic flow. It is desired to slow this flow to a subsonic speed (a) As the first option pass it through a normal shock. (b) let the flow pass through an oblique shock with a 350 wave angle, and then subsequently through a normal shock. i. ii. iii. iv.

Prepare a sketch of both the cases. Carry out calculations of all parameters . Obtain the total pressure values in both the cases and compare the results. Which case gives smaller change in entropy? Give detailed comments. [3+5+5+1+2]

4. Air at M1 = 2.3 and at a pressure of 70 kPa flows along a wall which bends away at an angle of 120 from the direction of flow. Determine the Mach number and pressure after the bend. If in another case the flow experiences a compression over the concave wall which actually bends through the same angle, determine the Mach number and pressure with the same free stream conditions. Sketch the flow fields in both the cases. [16] 5. Consider the equation of continuity under isentropic flow conditions and define the non-dimensional mass parameter .Obtain the relationship for the same as given s flow  2/γ  (γ+1)/γ   √ pγ p m T0 2 . [16] − pp0 below Ap0 = R γ−1 p0 1 of 2

Set No. 2

Code No: RR322105

6. A supersonic nozzle expands air from p0 = 25 bar and T0 = 1050 K to an exit pressure of 4.35 bar; the exit area of the nozzle is 100cm2 . Determine : The throat area; pressure and temperature at throat; temperature at exit; exit velocity and mas flow rate. [16] , andv = ∂φ , show that the partial 7. If V = ∇φ , where φ = φ(x,y) , then u = ∂φ ∂x ∂y differential for   equation  compressible subsonic isentropic flow is given below;  v2 ∂u ∂u ∂v u2 − 2 uv =0 [16] 1 − a2 ∂x + 1 − a2 ∂y a2 ∂y

8. Explain the effect of compressibility of flow on the magnitude of pressure coefficient ∞ Cp which in the compressible flow is given as Cpi = 1p−p . Hence define the ρ V2 2 ∞ ∞ compressibility of fluids and the Mach number at which it becomes apparent. How does it affect the lift on an airfoil? Make use of sketches and plots. [16] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: RR322105

III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 HIGH SPEED AERODYNAMICS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define the stagnation state, stagnation pressure, stagnation enthalpy, stagnation temperature and stagnation velocity of sound. (b) Obtain from the fundamentals the equation of adiabatic steady flow ellipse. (c) Hence define and obtain various regimes of flow in the compressible fluid dynamics. [5+6+5] 2. (a) Prove the relation M22 =

M12 1+ γ−1 2 γM12 − γ−1 2

for a Normal shock and

(b) Comment on the situation when M1 = 1. (c) What happens when M1 goes to infinity?.

[8+4+4]

3. (a) Consider a 2-step compression corner such that the two oblique shocks so generated intersect. Explain the phenomenon with a detailed sketch and its description. (b) Consider the flow over a 220 half-angle wedge. If M1 = 2.5, p1 = 1 atm and T1 = 300K, calculate the wave angle and p2 , T2 , and M2 . [8+8] 4. Consider a diamond wedge airfoil of half wedge angle of 20 . The airfoil is aligned at an angle of 80 to the chord line in a free stream Mach number =2.5. Calculate the lift and wave drag coefficients for the airfoil with C =2m. Make use of shockexpansion technique. [16] 5. Consider the equation of continuity under isentropic flow conditions and define the non-dimensional mass flow Obtain the relationship for the same as s parameter.    (γ+1)/γ  √ q 2/γ p m T0 R 2 [16] = γ−1 p0 − pp0 given below Ap0 γ 6. Air at 403K and 1 atm enters a C-D nozzle at a velocity of 150 m/s and expands isentropically to an exit pressure of 76kPa. If the inlet area of the nozzle is 5X10−3 m2 , find (a) The stagnation temperature , pressure and enthalpy, (b) Minlet, (c) Temperature, Mexit, Aexit (d) What must be the back pressure, temperature and flow rate if sonic conditions are attained at the exit? Assume air to be a perfect gas with Cp /Cv = 1.4.[16]

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Set No. 3

Code No: RR322105

7. Consider a 2-D, irrotational isentropic flow over an arb. Shaped object, given as below:  h  2  2
i
 ∂φ  ∂ 2 φ ∂ φ ∂φ 2 ∂ 2 φ ∂φ ∂φ 1 2 1 = 0, where φ = φ(x, y) + 1 − − 1 − a2 ∂x ∂x2 a2 ∂y ∂y 2 a2 ∂x ∂y ∂x∂y ∧

.Now φ = V∞ x + φ , introduces perturbation potential. Obtain the perturbation velocity equation. Present your work. [16]

8. Describe the effect of profile / shape of the object (streamlined or blunt) on the local flow over it when placed in a fluid stream. Hence consider the corresponding change in local Mach number over the profile by taking a circular cylinder and an airfoil. Now present your work through sketches and plots. [16] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: RR322105

III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 HIGH SPEED AERODYNAMICS (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define the terms enthalpy, stagnation temperature and stagnation pressure. Air at a temperature of 293 K and a pressure of 1 atm (101,325 kPa ) flows isentropically at a velocity of 300 m/s. Assuming air to behave as a perfect gas of constant specific heats (b) Calculate the enthalpy, stagnation temperature and stagnation pressure. (c) Explain the significance of stagnation properties.

[4+8+4]

2. The state of a gas (γ = 1.3, R = 0.469 kJ/kg K ) upstream of a normal shock wave is given by the following data: M∞ =2.6, p∞ = 2 bar, T∞ =285 K. (a) Calculate the Mach number, pressure, temperature and velocity of the gas down stream of the shock. (b) Verify your calculations from the gas tables.

[12+4]

3. Show with sketches and plots that a normal shock wave can be transformed in to an oblique shock wave if a constant tangential velocity component is superimposed on the velocities pertaining to a normal shock. Make use of a polar diagram in this respect. [16] 4. Air at M1 = 2.3 and at a pressure of 70 kPa flows along a wall which bends away at an angle of 120 from the direction of flow. Determine the Mach number and pressure after the bend. If in another case the flow experiences a compression over the concave wall which actually bends through the same angle, determine the Mach number and pressure with the same free stream conditions. Sketch the flow fields in both the cases. [16] 5. Consider the equation of continuity under isentropic flow conditions and define the non-dimensional mass flow parameter. Obtain the relationship for the same in √ q m T0 R M [16] = terms of Mach number as given below Ap0 (γ+1)/2(γ−1) . γ M 2) (1+ γ−1 2 6. Air flows isentropically through a nozzle of throat area 6cm2 and exit area 24cm2 . If p0 = 630kPa and T0 = 2100 C, compute the mass flow, exit pressure and exit mach number for (a) Subsonic flow, (b) Supersonic flow.

[16]

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Set No. 4

Code No: RR322105 7. Develop the velocitypotential equation  2  2 h
i ∂ φ ∂φ 2 ∂ 2 φ 1 1 + 1 − a2 ∂φ − a22 1 − a2 ∂x ∂x2 ∂y ∂y 2

∂φ ∂x


 ∂φ  ∂y

∂2φ ∂x∂y

= 0 , where φ = φ(x,y)

. Specify the application of boundary conditions for a 2-D object.

[16]

8. Define the term critical Mach number. Hence present the variation of lift and drag coefficients over a selected aerodynamic shape with Mach number. Is the critical Mach number unique in the consideration of such flows? Make use of illustrated sketches and plots. [16] ⋆⋆⋆⋆⋆

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