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MAE 3303 Final Exam
| Question | Answer |
|---|---|
| What is the quasi one dimensional flow approximation? Ch.10 (2/52) | The flow cross-sectional area is changing but the flow at any section can be treated as one-dimensional. |
| For quasi-1D subsonic flow, what will happen to the velocity and pressure if the cross-sectional area is reduced? What will happen to the velocity and pressure if the cross-sectional area is increased? Ch.10 (5/52) | M<1: CS ↓∴u↑,p↓ CS ↑∴u↓,p↑ |
| For quasi-1D supersonic flow, what will happen to the velocity and pressure if the cross-sectional area is reduced? What will happen to the velocity and pressure if the cross-sectional area is increased? Ch.10 (6/52) | M>1: CS ↓∴u↓,p↑ CS ↑∴u↑,p↓ |
| What geometrical feature must be present in order to accelerate an initially subsonic flow to supersonic speeds in a duct with slowly varying areas? Where will the sonic flow be located? Ch.10 (8/52) | - A convergent-divergent duct. - The sonic flow will be located at the throat. |
| What is the maximum exit Mach number we can get with a convergent nozzle? Ch.10 (8/52) | M_e = 1 |
| What is the sonic throat area? Ch.10 (19/52) | A* is the area where the flow is at sonic conditions (M=1), either physical or imaginary. |
| For subsonic flow through a duct, what will happen to Mach number if the cross-sectional area is reduced or increased? Ch.10 (12/52) Note: Isentropic Mach-Area Relation but depends on pressure difference. | M<1: CS ↓∴M ↑ CS ↑∴M ↓ |
| For supersonic flow through a duct, what will happen to Mach number if the cross-sectional area is reduced or increased? Ch.10 (13/52) Note: Isentropic Mach-Area Relation but depends on pressure difference. | M>1: CS ↓∴M↓ CS ↑∴M↑ |
| Is the sonic throat area constant in a steady isentropic duct flow? Is a throat always the sonic throat? Is the sonic throat always located at a throat? Ch. 10 (20/52) | - The sonic throat area is constant in a steady isentropic duct flow. - The throat is not always the sonic throat, can be imaginary. - The sonic throat is always located at the throat. |
| What does it mean for the flow in a nozzle to be choked? Ch. 10 (25/52) | If pe ≤ pe_3, because the sonic flow is reached at the throat and disturbances cannot pass the sonic line and propagate upstream, the flow properties at the throat and throughout the entire subsonic section of the duct become unaffected ("frozen"). |
| Once flow becomes choked in a nozzle, why is it not possible to increase the mass flowrate by decreasing the back pressure? Explain your answer. Ch.10 (25/52) | The mass flow rate reaches its maximum: ṁ = 𝜌_𝑡 𝐴_𝑡 𝑢_𝑡 = 𝜌* 𝐴* 𝑢* with sonic flow at the throat. Further reducing back pressure has no effect bc conditions at the throat are fixed and disturbances cannot propagate upstream past the sonic point. |
| What parameters does the maximum mass flow rate that a CD nozzle can deliver depend on ? Ch. 10 (25/52) | p_0, T_o, A_t, γ, R |
| Can a normal shock wave stand somewhere in the convergent portion of a convergent-divergent nozzle? Why? Ch. 10 (28/52) | No because the maximum Mach number at the exit plane of a convergent nozzle is 1 and the flow needs to be supersonic for a shock wave to occur. |
| What is the exit pressure of a CD nozzle? What is the back pressure of a CD nozzle? Ch. 10 (30/52) | - CD Nozzle Exit Pressure: Pressure at the exit plane of a channel. - CD Nozzle Back Pressure: Ambient pressure created by vacuum pump/valve or locate atmosphere. |
| What is the perfect expansion nozzle back pressure condition? Ch. 10 (31/52) | pₑ = p_b = pₑ₆= pᵢₛ |
| What is an under expanded nozzle exit condition? What flow structure will develop downstream of the nozzle? Ch. 10 (31/52) | p_b < pₑ₆= pᵢₛ and expansion waves develop downstream. |
| What is an overexpanded nozzle exit condition? What flow structure will develop downstream of the nozzle? Ch. 10 (31/52) | pₑ₅ > p_b > pₑ₆= pᵢₛ and shock waves develop downstream. |
| What will happen if the back pressure of a conversion-divergent nozzle is increased to the value that is higher than the exit pressure predicted for a subsonic-supersonic isentropic flow? Ch. 10 (32/52) | 3 Cases: p_b = p_0 (subsonic everywhere) pₑ₆< p_b = pₑ (NSW forms inside the divergent section) p_b = pₑ₆ (Ideal isentropic supersonic flow throughout the nozzle. No shock occurs.) |
| Will a compression wave incident on a free body (constant pressure) reflect as a compression wave or an expansion wave? Will an expansion wave incident on a free boundary (constant pressure) reflect as a compression wave or an expansion wave? | - A compression wave incident on a free body (constant pressure) will reflect as an expansion wave. Ch. 10 (42/52) - An expansion wave incident on a free boundary (constant pressure) will reflect as a compression wave. Ch. 10 (43/52) |
| What is a diffuser? Does the flow velocity increase or decrease along a diffuser? Does the flow pressure increase or decrease along a diffuser? Ch. 10 (45/52) | - Diffuser: Mechanism to slow high speed flows to low speed flows. - The flow velocity decreases along a diffuser. - The flow pressure increases along a diffuser. |
| If there are multiple sonic throats in a steady and adiabatic channel flow, what is the relation between stagnation pressures and sonic throat areas? Ch. 10 (47/52) | p_o1 A*_1 = p_o2 A*_2 |
| What is the definition of irrotational flow? Ch. 11&12 (4,5/61) | Flow has zero vorticity and is inviscid. ζ = ∇ x V = 2ω = 0 |
| For what kind of flows would the velocity potential equation be exact? Ch. 11&12 (11/61) | Any steady, irrotational, isentropic flow: subsonic, transonic, supersonic, hypersonic. |
| For incompressible flow is the velocity potential equation a linear or nonlinear partial differential equation? For compressible flow is the velocity potential equation a linear or nonlinear partial differential equation? Ch 11&12 (11/61) | For incompressible flow the velocity potential equation is a linear partial differential equation. For compressible flow the velocity potential equation is a non-linear partial differential equation. |
| On a physical basis, what is the small-perturbation theory? Ch. 11&12 (12/61) | A uniform flow is perturbed only by a small deviation of its original uniform state. |
| What type of pde the linearized velocity potential equation for subsonic flow is, elliptic, parabolic, or hyperbolic? What type of pde the linearized velocity potential equation for supersonic flow is elliptic, parabolic, or hyperbolic? Ch. 11&12 (18/61) | - The of type pde the linearized velocity potential equation for subsonic flow is, elliptic. - The of type pde the linearized velocity potential equation for supersonic flow is, hyperbolic. |
| State the formula for the linearized pressure coefficient. Ch. 11&12 (21/61) | Cp = -2û/V_inf |
| At what conditions will the linearized velocity potential equation be reasonably valid (but not exact)? Ch. 11&12 (23/61) | Subsonic or supersonic flow over a thing body at small angle of attack. |
| What is the Prandtl-Glauert compressibility correction for pressure coefficient? Ch. 11&12 (27/61) | Cp = Cp,o / Sqrt(1 - (M_inf)^2) |
| What is the utility of the Prandtl-Glauert similarity rule? Ch. 11&12 (27/61) | Relates the pressure coefficient between subsonic and incompressible flow. |
| Why it is not possible to use a simple transformation to connect linearized supersonic flow to incompressible flow? Ch. 11&12 (31/61) | Hyperbolic Type - no real transformation between supersonic flow (hyperbolic) and subsonic or incompressible flow (elliptic). |
| According to linearized supersonic flow theory, both oblique shock and expansion waves are treated as what kind of wave? Ch. 11&12 (32,33/61) | Mach Waves |
| The pressure coefficient in linearized supersonic flow is proportional to what geometric feature.Ch. 11&12 (35/61) | In linearized supersonic flow, the pressure coefficient is proportional to the surface inclination angle θ, measure w.r.t. the free stream flow. |
| According to supersonic linearized theory, the lift coefficient of an airfoil is related to what geometrical feature? Ch. 11&12 (41/61) | Only α [rad] for a given M_ inf |
| According to supersonic linearized theory, the wave drag coefficient of an airfoil is related to what geometrical features? Ch. 11&12 (42/61) | All geometric features: Aoa (α), Mean Camber (z), Thickness (t) |
| According to supersonic linearized theory, the pitching moment coefficient is related to what geometrical features? Ch. 11&12 (43/61) | Aoa (a), Mean Camber (z) |
| For the same thickness envelope and angle of attack, which airfoil has less wave Symmetric drag, symmetric or cambered? Ch. 11&12 (44/61) | Symmetric |
| Where is the center of pressure located on a supersonic thin airfoil? Where is e aerodynamic center located on a supersonic thin airfoil? Ch. 11&12 (44/61) | The center of pressure (cp) and aerodynamic (ac) on a supersonic thin airfoil, are located at the mid-chord. |
| Does the lift coefficient increase or decrease with increasing Mach number in subsonic flow? Does the lift coefficient increase or decrease with increasing Mach number in supersonic flow? Ch. 11&12 (44/61) | The lift coefficient increases with increasing Mach number in subsonic flow. The lift coefficient decreases with increasing Mach number in supersonic flow. |
| What is the definition of the Critical Mach number? Why is the critical Mach number of interest? Ch. 11&12 (50/61) | Critical Mach Number (M_cr): Free stream Mach number at which sonic flow is first achieved on the airfoil surface. The critical Mach number is of interest since it tells us the flight Mach number where locally supersonic flow exists. |
| Will the critical Mach number increase or decrease as the airfoil thickness increases? Ch. 11&12 (50/61) | Decreases |
| What is the critical pressure coefficient of an airfoil? Ch. 11&12 (51/61) | The pressure coefficient at the point where the sonic flow is first achieved on the airfoil surface at the critical Mach number. |
| What is meant by the drag-divergence Mach number? Why does the drag coefficient increase rapidly once the free-stream Mach number reaches the drag-divergence Mach number? Ch. 11&12 (55/61) | The value of the free stream Mach number at which the drag suddenly starts to increase rapidly. The drag coefficient increases rapidly once the free-stream Mach number reaches the drag-divergence Mach number because of BL separation from airfoil surface. |
| Typically by what factor does the drag increase as an aircraft passes through Mach 1? What is meant by the "sound barrier"? Does it really exist? Explain your answer. Ch. 11&12 (56/61) | 10. The myth that sonic speed is the fundamental limit of aircraft flight speed. The sound barrier does not true because drag can be overcame by lift. |
| How is a supercritical airfoil distinguished from a convectional airfoil in geometry? What is the advantage of a supercritical airfoil? Ch. 11&12 (58/61) | A supercritical airfoil has a relative flat top from a convectional airfoil, the advantage is that it has a high M_drag-divergence meaning a higher flight M with lower cd. |
| How will the quarter chord pitching moment coefficient for a supercritical airfoil compare with a conventional airfoil? Ch. 11&12 (58/61) | Higher cm_c/4 |
| State the area rule for transonic flow. Does the area rule require a widening or thinning of the fuselage in the vicinity of the wing? Ch. 11&12 (60/61) | Area rule for transonic flow: To reduce the peak drag near Mach 1, the variation of cross-section area for an airplane should be smooth, with no discontinuities. The area rule requires a thinning of the fuselage in the vicinity of the wing. |
| By what factor can the peak drag near Mach 1 be reduced through use of the area rule? Ch. 11&12 (61/61) | 2 |
| In general, are Mach lines straight lines or curved lines in supersonic flow? Ch. 13 (3/19) | Curved Lines |
| Characteristics lines are Mach lines. True or False? Ch. 13 (3/19) | true |
| How many characteristic lines at a point in supersonic flow? Ch. 13 (3/19) | Characteristic C_I and Characteristic C_II |
| What is the angle between the characteristic line and the flow direction at a point in supersonic flow? Ch. 13 (3/19) | Mach angle, μ |
| What are the two approaches to calculate steady 2D isentropic irrotational supersonic flow properties using the method of characteristics? Ch. 13 (5/19) | Point-to-Point and Region-to-Region |
| How to cancel an incident wave on a wall? Ch. 13 (16/19) | Let the wall turn through an angle Δθ at the point of impingement of the incident wave. |
| What quantities are constant along characteristic lines? | C_I = ν + θ C_II = ν - θ |
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