rr322105 high speed aerodynamics

5/26/2018 Rr322105 High Speed Aerodynamics

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Code No: RR322105 Set No. 1

III B.Tech II Semester Supplementary Examinations, Aug/Sep 2006HIGH SPEED AERODYNAMICS

(Aeronautical Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

1. (a) Elaborate that entropy is an extensive property and

(b) That for a real process occur only if the change is larger than the value ofQ

T

.

(c) Show thatUS

V

=T, Thermodynamic temperature andUV

S

=p pres-sure. U is the internal energy of a system under equilibrium. [6+5+5]

2. (a) Prove the relation M22 = 1+

1

2 M2

1

M2

11

2

for a Normal shock and

(b) Comment on the situation when M1 = 1.

(c) What happens whenM1 just becomes greater than 1. [8+4+4]

3. (a) How does a shock wave differ from a Mach wave?

(b) Illustrate the characteristics of oblique shock waves with sketches and plots.

(c) Hence demonstrate with calculations across an oblique shock that the changesacross an oblique shock wave are governed only by the component of velocitynormal to the wave. [5+6+5]

4. Air at M1 = 2.0 and at a pressure of 70 kPa flows along a wall which bends awayat an angle of 120 from the direction of flow. Determine the Mach number andpressure after the bend. If in another case the flow experiences a compression overthe concave wall which actually bends through the same angle, determine the Machnumber and pressure with the same free stream conditions. Sketch the flow fieldsin both the cases. [16]

5. Consider the equation of continuity under isentropic flow conditions and define thenon-dimensional mass flow parameter .Show that the value of maximum mass flow

parameters is as given below mT0

Ap0

R

= 0.0404 [16]

6. Describe the behavior of flow in a convergent-divergent nozzle when it is operatedat

(a) the design pressure ratio,

(b) pressure ratio higher than the design value,

(c) pressure ratio lower than the design value. Make use of sketches and plots toillustrate your answer. [16]

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7. Make use of the partial differential equation for compressible subsonic irrotationaland isentropicflow field, develop the linearized potential equation for subsonic com-pressible and isentropic flow as given below; (1 M2)xx + yy = 0 in usualnomenclature. [16]

8. Consider an airfoil placed in a trisonic wind tunnel. Some systematic studies weremade for studying flow over it up to sonic speed. Present the variation of lift anddrag through plots and sketches with illustrations over this Mach number range.

[16]

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1. (a) Define the terms enthalpy, stagnation temperature and stagnation pressure.Air at a temperature of 288 K and a Pressure of 1 atm (101,325 kPa ) flowsisentropically at a velocity of 300 m/s. Assuming air to behave as a perfectgas of constant specific heats,

(b) Calculate the enthalpy, stagnation temperature and stagnation pressure .

(c) Explain the significance of stagnation properties. [6+6+4]

2. Consider upstream and downstream Mach numbers across a Normal shock .Nowdemonstrate from the equations developed that

(a) entropy increase takes place across a shock wave.

(b) there is an increase in static temperature across the shock wave.

(c) there is an increase in static pressure across a shock wave and

(d) that velocity decreases across a Normal shock. Show these variations across anormal shock wave as a function of Mach number on a single plot. [4x4=16]

3. Consider a supersonic flow with M =2, p = 1 atm and T =288 K.The flow is defected

at a compression corner through 200 . Calculate M ,p, T ,p0 and T0 behind theresulting oblique shock. [16]

4. Consider a 2D circular cylinder, a thin wedge, a thick wedge, compression corner,low speed airfoil section and a high speed airfoil section. Detail out characteristicsof supersonic flow around each of these sections. Sum up your work in a para.explain with sketches and plots. [16]

5. Consider the equation of continuity under isentropic flow conditions and define thenon-dimensional mass flow parameter .Obtain the relationship for the same as given

below mT0

Ap0R

= 2

+1(+1)/2(1) 2

1 2

+1(1)/(1) 1 [16]

6. A Conical diffuser has entry and exit diameters of 15 cm and 30 cm respectively.The pressure, temperature and velocity of air at entry are 0.69 bar, 340 K and 180m/s. Determine the exit velocity and pressure and the force exerted on the diffuserwalls .Assume isentropic flow conditions. [16]

7. Given that V = , where = (x,y) , then obtain for isentropic flows the equa-tion

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1 1a2

x

2 2x2

+

1 1

a2

y

22y2

2a2

x

y

2xy

= 0 Elaborate the na-

ture of this partial differential equation . State the conditions under which thisapplication is used for obtaining approximate flow field around a given object.How does it differ from the Laplace s equation? [16]

8. Define the following terminology in the compressible aerodynamics; critical Machnumber, sub-critical Mach number, super critical Mach number, crest critical Machnumber and transonic Mach number. Hence present all of the above on a singleplot and comment in as much details as possible with reference to the flight of asatellite launch vehicle from t = 0 , at the launch till it reaches supersonic speed.

[16]

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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 ) flowsisentropically at a velocity of 310 m/s. Assuming air to behave as a perfectgas of constant specific heats,

(b) Calculate the enthalpy, stagnation temperature and stagnation pressure .

(c) Explain the significance of stagnation properties [6+6+4]

2. (a) Prove the relationM1 M2 = 1 Hence

(b) Show that M22 = 1+1

2 M2

1

M211

2

.

(c) And show that the downstream Mach number is function of the upstreamMach number alone.

(d) Comment on the situation when M1 = 1. [5+5+3+3]

3. (a) Consider a wedge and a cone with the same semi wedge /semi vertex angle= 200 in a stream of Mach number = 2.

i. Sketch the flows over the two configurations and compare the same. What

differences do you notice?ii. Provide your detailed comments

(b) Consider an oblique shock wave with = 350 and pressure ratio p2/p1 =3.Calculate the upstream Mach number. [6+6+4]

4. Air at M1 = 2.4 and at a pressure of 70 kPa flows along a wall which bends awayat an angle of 120 from the direction of flow. Determine the Mach number andpressure after the bend. If in another case the flow experiences a compression overthe concave wall which actually bends through the same angle, determine the Machnumber 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 definethe non-dimensional mass flow parameter .Obtain the relationship for the same in

terms of the area ratio as given below mT0

Ap0

R =

2+1

(+1)/2(1)A

A [16]

6. Air flows isentropically through a nozzle of throat area 6cm2 and exit area 24cm2

. Ifp0 = 600 kPa and T0 = 2000C, compute the mass flow, exit pressure and exit

mach number for

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(a) subsonic flow,

(b) supersonic flow. [16]

7. The equation of 2-D motion of fluid in small perturbation potential is given by(1M2)

2x2

+ 2

y2 =M2(+ 1)

x

2x2

, where is the perturbation potential and

M is the free stream Mach number of the flow. Develop the expression for thepressure coefficient Cp [Cp = pp12V2

in incompressible flow ] in terms of the flow

over a planar wing. [16]

8. State the Prandtl-Glauert rule. What are its basis of this correction for compress-ibility?(Hint: consider the small perturbation potential equation) . Hence showthatcl,c =

cl,i1M2

where cl,iandcl,c are the coefficients of lift at incompressible and

compressible Mach numbers. [16]

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1. (a) Define the stagnation state, stagnation pressure, stagnation enthalpy , stag-nationtemperature and stagnation velocity of sound. Obtain from the a

2

a20

+ V2

V2max= 1

, and

(b) Describe various regimes of compressible flow from a v/s V plot. [10+6]

2. (a) Prove the relation M22 = 1+ 1

2 M2

1

M21

1

2

for a Normal shock and

(b) Comment on the situation when M1 = 1.

(c) What happens whenM1 goes to infinity?. [8+4+4]

3. (a) How does a shock wave differ from a Mach wave?

(b) Illustrate the characteristics of oblique shock waves with sketches and plots.

(c) Hence demonstrate with calculations across an oblique shock that the changesacross an oblique shock wave are governed only by the component of velocitynormal to the wave. [5+6+5]

4. The - - M relation for an oblique shock wave is given bytan = 2 cot M2

1sin2 1

M21(+cos2)+2

.Consider the - - M diagram and explain the fol-

lowing situations;

(a) If in a given physical problem is fixed and M1 is increased

(b) if > max. Make use of sketches and plots along with a drawn - - Mdiagram on your answer sheet. [16]

5. Derive the quasi-one dimensional form of the area-velocity relationship isdAdV

= (1 M2)AV

Explain the behavior of area v/s curve when

(a) M>1(b) M = 0

(c) M < 1.Explain with one example each for the Mach number . [16]

6. Air flows isentropically through a nozzle of throat area 6cm2 and exit area 24cm2

. Ifp0 = 600 kPa and T0 = 2000C, compute the mass flow, exit pressure and exit

mach number for

(a) subsonic flow,

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(b) supersonic flow. [16]

7. Given that V = , where = (x,y), then obtain for isentropic flows theequation for flow over an airfoil which introduces small perturbation potential inthe flow. Specify the limitations .You may make use of the velocity potentialequation developed for compressible, isentropic flow. [16]

8. Define the compressibility of air as a medium in aerodynamics. Establish the lowestMach number at which it starts showing its presence. Show that the pressurecoefficient Cp at Mach number is different from that in an incompressible flow.Can you show it by another method? Make use of sketches and plots. [16]

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rr322105 high speed aerodynamics

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