Gas turbine combustor - Propulsion - Aerospace Engineering Previous Year Questions

1

2007 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2007

A spring-mass-damper system is excited by a force F_0 sin ωt. The amplitude at resonance is measured to be 1 cm. At half the resonant frequency, the amplitude is 0.5 cm. The damping ratio of the system is

A

0.1026

B

0.3242

C

0.7211

D

0.1936

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2

2007 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2007

A gas turbine engine operates with a constant area duct combustor with inlet and outlet stagnation temperatures 540 K and 1104 K respectively. Assume that the flow is one dimensional, incompressible and frictionless and that the heat addition is driving the flow inside the combustor. The pressure loss factor (stagnation pressure loss non-dimensionalized by the inlet dynamic pressure) of the combustor is

A

0

B

0.489

C

1.044

D

2.044

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3

2007 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2007

The purpose of a fuel injection system in the combustor is

A

to accelerate the flow in the combustor

B

to increase the stagnation pressure of the fuel-air mixture

C

to ignite the fuel-air mixture

D

to convert the bulk fuel into tiny droplets

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4

2007 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2007

The two natural frequencies of the system are given as

A

\(\sqrt{\frac{4 \pm \sqrt{5}}{3} \frac{k}{m}} \)

B

\(\sqrt{\frac{4 \pm \sqrt{3}}{3} \frac{k}{m}} \)

C

\(\sqrt{\frac{4 \pm \sqrt{7}}{3} \frac{k}{m}} \)

D

\(\sqrt{\frac{4 \pm \sqrt{11}}{3} \frac{k}{m}} \)

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5

2007 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2007

The natural frequencies \( \omega \) of the fixed-free rod can then be obtained using

A

\(\cos(\frac{\omega l}{c})=0 \)

B

\(\sin(\frac{\omega l}{c})=0 \)

C

\(\cos(\frac{\omega c}{l})=0 \)

D

\(\cos(\frac{\omega l}{c})=0 \)

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6

2009 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2009

The division of feed air to an aircraft gas-turbine combustor into primary and secondary streams serves which of the following purposes?
P. a flammable mixture can be formed
Q. cooling of combustor liner and flame tube can be accomplished
R. specific fuel consumption can be reduced

A

P and R

B

Q and R

C

P and Q

D

P, Q and R

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7

2009 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2009

If the \( n^{th} \) mode shape of torsional vibration of the above shaft is \( \sin \left( \frac{n\pi x}{L} \right) \), then the \( n^{th} \) natural frequency of vibration, i.e., \( \omega_n \), is given by

A

\(\omega_n = \frac{n\pi}{L} \sqrt{\frac{GJ}{I}} \)

B

\(\omega_n = \frac{(2n+1)\pi}{2L} \sqrt{\frac{GJ}{I}} \)

C

\(\omega_n = \frac{n\pi}{2L} \sqrt{\frac{GJ}{I}} \)

D

\(\omega_n = \frac{(2n+1)\pi}{L} \sqrt{\frac{GJ}{I}} \)

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8

2010 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2010

During an under-damped oscillation of a single degree of freedom system, in the time-displacement plot the third peak is of magnitude 100 and the tenth peak is of magnitude 10. The damping ratio \(\zeta\) is approximately:

A

0.052

B

0.023

C

0.366

D

0.159

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9

2011 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2011

Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of \(m\), \(c\) and \(k\), respectively. The logarithmic decrement of this system can be calculated using

A

\(\frac{2\pi}{\sqrt{4mk - c^2}}\)

B

\(\frac{\pi}{\sqrt{4mk - c^2}}\)

C

\(\frac{2\pi}{\sqrt{mk - c^2}}\)

D

\(\frac{2\pi}{\sqrt{mk - 4c^2}}\)

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10

2011 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2011

Consider a single degree of freedom spring-mass system of spring stiffness \(k_1\) and mass \(m\) which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness \(k_2\) and mass \(m\) which has a natural frequency of 20 rad/s. The spring stiffness \(k_2\) is equal to

A

\(k_1\)

B

\(2k_1\)

C

\(\frac{k_1}{4}\)

D

\(4k_1\)

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11

2012 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2012

The logarithmic decrement measured for a viscously damped single degree of freedom system is 0.125. The value of the damping factor in % is closest to

A

0.5

B

1.0

C

1.5

D

2.0

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12

2012 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2012

The mode shapes of an un-damped two degrees of freedom system are \(\begin{Bmatrix}1 \\ 0.5\end{Bmatrix}^T\) and \(\begin{Bmatrix}1 \\ -0.675\end{Bmatrix}^T\). The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of \(\begin{Bmatrix}2 \\ 1\end{Bmatrix}^T\) (in mm) and zero initial velocities is ____.

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13

2012 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2012

The boundary condition of a rod under longitudinal vibration is changed from fixed-fixed to fixed-free. The fundamental natural frequency of the rod is now \(k\) times the original frequency, where \(k\) is

A

\(\frac{1}{2}\)

B

2

C

\(\frac{1}{\sqrt{2}}\)

D

\(\sqrt{2}\)

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14

2012 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2012

A spring-mass system is viscously damped with a viscous damping constant \(c\). The energy dissipated per cycle when the system is undergoing a harmonic vibration \(X \cos \omega_n t\) is given by

A

\(\pi c \omega_n X^2\)

B

\(\pi \omega_n X^2\)

C

\(\pi c \omega_n X\)

D

\(\pi c \omega_n^2 X\)

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15

2014 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2014

A damped single degree of freedom system whose undamped natural frequency, \(\omega_n = 10\text{Hz}\), is subjected to sinusoidal external force. Power is half of the maximum for the two frequencies of 60.9469 rad/s and 64.7168 rad/s. The damping factor associated with the vibrating system (in %) is __________.

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16

2014 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2014

The boundary conditions for a rod with circular cross-section, under torsional vibration, are changed from fixed-free to fixed-fixed. The fundamental natural frequency of the fixed-fixed rod is \(k\) times that of fixed-free rod. The value of \(k\) is

A

1.5

B

\(\pi\)

C

2.0

D

0.5

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17

2014 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2014

1kg mass is hanging from a spring of stiffness 500N/m attached to a massless, symmetric beam of length 0.6m, moment of inertia about the bending axisI = 8.33 × 10^-11m⁴ and Young's modulus E=210GPa as shown in the figure. The fundamental natural frequency (in rad/s) of the system is

A

3.24

B

20.36

C

22.36

D

3.56

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18

2014 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2014

A single degree of freedom system is vibrating with initial (first cycle) amplitude of 5cm. The viscous damping factor associated with the vibrating system is 2%. Vibration amplitude of the fifth cycle (in cm) is

A

1.65

B

4.41

C

2.67

D

3.02

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19

2015 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2015

Air enters an aircraft engine at a velocity of \( 180 \; m/s \) with a flow rate of \( 94 \; kg/s \). The engine combustor requires \( 9.2 \; kg/s \) of air to burn \( 1 \; kg/s \) of fuel. The velocity of gas exiting from the engine is \( 640 \; m/s \). The momentum thrust (in \( N \)) developed by the engine is

A

43241

B

45594

C

47940

D

49779

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20

2016 · Aerospace Engineering · Propulsion · Gas turbine combustor

Aerospace Engineering (AE) 2016

Combustion in gas turbine engines is ideally represented as the following process:

A

Adiabatic

B

Isentropic

C

Isobaric

D

Isochoric

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