Unit 4: LINEARIZED AERODYNAMICS FOR AEROACOUSTIC APPLICATIONS - Practice Quiz

1 In linearized aerodynamics, how is the total pressure usually represented?

2 Which assumption is fundamental to linearizing the unsteady aerodynamic equations?

3 What happens to products of two small perturbation quantities during linearization?

4 For a uniform fluid at rest, which equation is the linearized continuity equation?

5 Which feature of a vortex flow is most directly associated with sound generation?

6 What physical quantity describes the local rotation of a fluid element?

7 Why can a vortex passing near a solid edge produce sound?

8 In Lighthill's acoustic analogy, turbulence in free space is primarily represented as which type of sound source?

9 What is a blade cascade?

10 Which expression gives the blade-passing frequency for a rotor with blades rotating at frequency ?

11 How is cascade solidity commonly defined?

12 What commonly produces tonal noise in a rotor-stator fan stage?

13 What is the main mechanism of aerodynamic trailing-edge noise?

14 Acoustic liner impedance is commonly defined as the ratio of acoustic pressure to which quantity?

15 Which part of acoustic impedance represents energy dissipation?

16 What is the main purpose of an acoustic liner in a fan or compressor duct?

17 What distinguishes a perforated plate from a solid plate?

18 Where are vortices commonly formed when oscillatory flow passes through a perforated plate?

19 What does the porosity of a perforated plate represent?

20 How can vortex shedding at perforation edges affect an incident sound field?

21 For small perturbations about a uniform mean flow in the -direction, which operator replaces the ordinary time derivative in the linearized acoustic equations?

22 A uniform fluid has density and sound speed . Under an isentropic linearization, what pressure perturbation corresponds to ?

23 For an inviscid uniform medium at rest, the linearized continuity and momentum equations are combined to obtain which equation for ?

24 A plane disturbance in a uniform flow is represented by . For a downstream-propagating acoustic wave, which dispersion relation applies?

25 An isolated vortex translates steadily through an otherwise unbounded, uniform inviscid fluid. Why is its far-field sound generally weak?

26 A compact vortex passes close to a rigid edge and produces a rapidly varying force on it. Which leading acoustic source type best represents this process?

27 In Lighthill's acoustic analogy at low Mach number, vortex-flow sound in the fluid volume is primarily associated with derivatives of which stress contribution?

28 Two equal, like-signed vortices orbit one another. If their separation is reduced while circulation remains fixed, what is the expected qualitative acoustic effect?

29 A cascade has blade chord and pitch . What is its solidity?

30 A harmonic disturbance reaches adjacent cascade blades with a constant phase difference . Which expression describes the complex amplitude on blade number relative to blade zero?

31 For an unlined circular duct without mean flow, a mode has axial wavenumber satisfying . Under which condition is the mode cut on?

32 A rotor with blades rotates at . What is the blade-passing frequency observed by a stationary vane row?

33 In a vortex model of trailing-edge noise, what principally converts a convecting vortical disturbance into propagating sound?

34 The normalized acoustic impedance of a liner is at normal incidence. Using , what is the pressure reflection coefficient?

35 Which impedance limit most closely represents an acoustically rigid wall when impedance is defined as ?

36 A liner impedance is written as . Which component directly represents time-averaged acoustic energy dissipation?

37 When can a perforated plate most reasonably be replaced by a locally reacting, homogenized impedance boundary?

38 A vortex convects toward a perforated plate. Which mechanism can increase sound generation compared with steady passage through an unobstructed flow?

39 For fixed total plate area and fixed acoustic frequency, reducing the open-area ratio generally causes which change in the effective acoustic impedance?

40 Why can adding a moderate bias flow through a perforated plate alter its acoustic resistance?

41 For a uniform mean flow in the -direction, an acoustic disturbance has nondimensional frequency , transverse wavenumber , and . Using , what are the possible values of ?

42 A plane perturbation in a uniform inviscid flow satisfies , , and . Which linear mode does it represent?

43 For the positive-frequency acoustic branch in a uniform subsonic flow, . If is the angle between and the downstream direction, when does the laboratory-frame group velocity have an upstream axial component?

44 A plane acoustic wave is incident at angle from the normal onto a locally reacting boundary of impedance . With no mean flow, what is the pressure reflection coefficient?

45 In Howe's low-Mach-number vortex-sound analogy for homentropic flow, which term acts as the principal source of fluctuations in stagnation enthalpy ?

46 Two compact vortex–body interactions produce equal, opposite, harmonically varying lift forces separated by distance , where . Relative to one isolated interaction, what characterizes their leading combined radiation?

47 An isolated, steady vortex structure translates uniformly through an unbounded, otherwise uniform inviscid fluid. In the low-Mach-number idealization, which statement best describes its acoustic radiation?

48 For otherwise comparable compact low-Mach-number sources, a boundary converts a free-field quadrupole into an unsteady-force dipole. If quadrupole and dipole acoustic powers scale as and , respectively, how does their power ratio scale with Mach number?

49 A rotor with blades interacts with a stator having vanes. At rotor harmonic , Tyler–Sofrin circumferential orders satisfy . Which order has the smallest magnitude?

50 In a hard-walled annular-duct approximation without mean flow, a mode satisfies . If , , and , how is the mode classified?

51 A cascade with identical passages has Bloch circumferential order . Spatial aliasing permits physical orders for integer . Which order is not in this family?

52 A stationary stator distortion has circumferential dependence with . A rotor with blades turns at angular speed . What interblade phase angle does this disturbance impose on adjacent rotor blades, modulo ?

53 In linear trailing-edge scattering theory for a sharp edge, what is the principal role of the unsteady Kutta condition?

54 A trailing-edge noise model has span much larger than the spanwise turbulence coherence length . If is doubled while all local statistics remain unchanged, what is the expected change in total radiated power?

55 At normal incidence and without mean flow, a liner has impedance . Using , what fraction of incident acoustic power is absorbed?

56 For a uniform tangential mean flow , let wall displacement be , let , and impose . For , which effective boundary relation follows?

57 A zero-thickness perforated plate has identical apertures per unit area, each with Rayleigh conductivity . For and , what is the plate impedance ?

58 A perforated plate contains two aperture populations with number densities and Rayleigh conductivities . Neglecting mutual interaction, which effective impedance relates pressure jump to total area-averaged velocity?

59 A convected vortical disturbance drives a periodic row of holes at positions with hole flux . Far-field propagation at angle contributes phase . What condition gives an array-factor maximum?

60 A perforated sheet backed by a rigid cavity has normalized total impedance at normal incidence. Which condition produces critical coupling and zero reflection at a target frequency?