Numerical Techniques for Steady Supersonic Flow topics include: Characteristics philosophy, two dimensional irrotational flow, compatibility equations determination, dependencies domain, steady supersonic flow nozzle design, finite differences basics, macCormack’s technique, boundary conditions, cfl criterion, conservation versus nonconservation form equations.
 

Aerodynamics Practice Test: Numerical Techniques for Steady Supersonic Flow

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15 Questions

1. For subsonic flows, the characteristics through a flow field point are imaginary.

FalseMaybeTrueDon't know

2. K₊ and K_– constant along the characteristic lines are analogous to the Reimann constants.

MaybeFalseTrueDon't know

3. How many characteristics pass through a point in the flow field if the Mach number is greater than 1?

1042

4. Which partial differential equation is used to define the characteristic at sonic condition?

Hyperbolic partial differential equationCircular partial differential equationElliptic partial differential equationParabolic partial differential equation

5. Which of these represent compatibility equation along C₊ characteristic line?

dθ = \(\sqrt {M^2 – 1} \frac {dV}{V}\) dθ = \(\sqrt {M^2 + 1} \frac {dV}{V}\) dθ = tan⁡(θ – μ)\(\frac {dV}{V}\) dθ = tan⁡(θ – μ)

6. If we know the value of θ₁,ν₁ at point 1 and θ₂,ν₂ in a flow, then what is the flow field condition at an internal point 3 lying at the intersection of characteristic lines passing from points 1 and 2?

θ3 = \(\frac {(K_- )_1 + (K_- )_2 + (K_- )_3}{2}\) θ3 = \(\frac {(K_- )_1 + (K_+ )_3}{2}\) θ3 = \(\frac {(K_+ )_1 + (K_+ )_2 + (K_+ )_3}{2}\) θ3 = \(\frac {(K_- )_1 + (K_+ )_2}{2}\)

7. If the flow conditions at point 1 near the nozzle wall is given, then what is the flow conditions at point 2 on the wall?

ν2 = θ2 – θ1ν2 = θ2 + θ1ν2 = θ2 – θ1 + ν3ν2 = θ2 + θ1 – ν3

8. What is the value of derivative of flow field along characteristic line?

IndeterminateZero0.5One

9. K₊ and K_– constant along the characteristic lines related velocity to J₊ and J_– constants.

MaybeFalseTrueDon't know

10. Which of these represents K₊ constant along the C₊ characteristic line?

θ – ν(M) = constθ – 2ν(M) = constθ + 2ν(M) = constθ + ν(M) = const

11. Where is methods of characteristics used?

Designing fuselage’s bulkheadDesigning diamond airfoil for supersonic flowComputing optimum wing camberDesigning supersonic nozzle

12. Which of these is not an application of a hodograph?

Solution for method of characteristicsDetermining temperatureSwinging Artwood’s machineObtaining motion of celestial objects

13. Characteristic curves passing through a point in a flow field are straight lines.

MaybeTrueFalseDon't know

14. How many characteristic lines pass through the flow field in supersonic flow?

2401

15. Which of these equations defines the characteristic curve in an x – y plane?

\(\frac {dy}{dx_{char}} = \frac {- \frac {uv}{a^{2}} ± (\frac {u^2 + v^{2}}{a^{2}}) – 1}{1 – \frac {u^{2}}{a^{2}}}\) \(\frac {dy}{dx_{char}} = – \frac {uv}{a^{2}} ± \sqrt {(\frac {u^2 + v^{2}}{a^{2}})-1}\) \(\frac {dy}{dx_{char}} = \frac {- \frac {uv}{a^{2}} ± \sqrt {(\frac {u^{2} + v^{2}}{a^{2}})}}{\frac {u^{2}}{a^{2}}}\) \(\frac {dy}{dx_{char}} = \frac {- \frac {uv}{a^{2}} ± \sqrt {(\frac {u^2 + v^{2}}{a^{2}})-1}}{1 – \frac {u^{2}}{a^{2}}}\)