EAS 4300 Exam 2 03-09 Solutions

8/14/2019 EAS 4300 Exam 2 03-09 Solutions

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EAS 4300 Exam 3 April 6, 2009

NAME: _SOLUTION SHEET______________________________

1. Mark the statements below true or false by placing a T or F to the left of the letter

introducing the statement:

T (a) Axial flow compressor performance is limited by aerodynamic stallT (b) Increasing the turbine entry stagnation temperature improves performance

F (c) A coarse propeller pitch setting is the best one for take-off performance

F(d) The centrifugal effect is an important contributor to axial flow compressorperformance

T (e) Axial flow turbine performance is limited by choking (15)

2. Define the efficiency of adiabatic compression by showing the process (using arrowsto show direction) on the thermodynamic plane below. The starting point is the entry to

the compressor, denoted by the numeral 2 on the diagram; the final point state should be

denoted by the numeral 3. Label all quantities clearly and complete the equation for c

on the right of the diagram.

3 2

3 2

't tc

t t

h h

h h

=

(10)

3. Write an equation for the percent reaction of an axial flow compressor stage in termsof (a) the relative and absolute velocities entering and leaving the stage (w2, w3 and c2, c3,

respectively) and (b) the static pressure change in the rotor and the static pressure change

in the stage, that is, the rotor and the stator.

(a)

( )

( ) ( )

2 2

2 3

2 2 2 2

2 3 3 2

%rotor

rotor stator

w whr h h w w c c

= = + +

(b) % 100rotor

rotor stator

pr

p p

=

+ (10)

1

pt,3

pt,2h

t,3

ht,3

ht,2

s2s3

s

adiabatic-frictionprocessisentropic

process

ht


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4. Air at standard sea level conditions enters an axial flow compressor rotor with an

absolute velocity c2 = 141m/s and an entry angle 2 = 45o. The air leaves the rotor at an

absolute velocity c3 = 173m/s and an angle 3 = 30o. If the blade passage is located at a

radius r= 0.5m from the axis of rotation, the angular speed of the rotor is = 1000s-1

and the mass flow rate is 1kg/s, (a) what is the tangential force Fu and (b) what is the

powerPrequired by the rotor?

(a)

( ) [ ]

( ) ( ) ( ) ( )

( ) [ ]

3 2 3 2

2

cos30 cos 45

3 2 3 2173 / 141 / 100 3 100 2

2 2 2 2

1 / 150 / 100 / 50 /

50

u u u

u

u

u

F m c c m c c

F m m s m s m

F kg s m s m s kg m s

F N

= =

= =

= =

=

(b)( ) ( ) ( )

11000 0.5 50 25,000 /

25,000 25

q u P T rF s m N N m s

P W kW

= = = = = =

(15)

5. A turbine operating at an efficiency of adiabatic expansion of 92% processes 10kg/s ofa hot gas that enters the turbine with a stagnation temperature of 1500K. If the power

output of the turbine is 5MW what is the stagnation temperature leaving the turbine? You

may assume that the gas properties are as follows: cp=1kJ/kg-K, =3/2, and R= 1/3kJ/kg-K.

Wt = P/m = 5x106W/10kg/s = 5x105J/kg

Wt=cp(Tt4 Tt5) = (1000J/kg-K)[1500K Tt5] = 5x105J/kg

Tt5 = 1500K (5x105J/kg)/(103J/kg-K) = 1500K 500K = 1000K

(15)

2


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6. Make a neat sketch of the performance of an axial flow compressor, that is, a

compressor map. Label all quantities (including the x-axis) clearly

(10)

7. The compressor of a turbojet engine operates with a pressure ratio of 20 and an

efficiency of adiabatic compression of 90%. It processes 50kg/s of air and requires a

work per unit mass of 200kJ/kg to operate. What is the power delivered by the turbine,assuming that the fuel flow rate may be neglected?

Pc = mWc = (50kg/s)(200kJ/kg) = 10,000kJ/s = 10,000kW = 10MW

Pt = Pc =10MW

(10)

3

pt3/p

t2

w 21/2

/ 2 (corrected weight flow)

Surge or stall line

c

(compre

efficienc

N/2

1/2 (corrected rpm)


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8. For the rotor wheel shown below sketch in the rest of the velocity diagrams and theairfoil, in the form of a simple arc, that would properly accommodate them. Label all

quantities clearly

(15)

-----------------------------------------------------------------------------------------------------------

-

Some general equations are listed below:

2

2

1

,2 ,2 ,3

, ,2

1p t t

c

ad c t

c T pW

p

=

4

4

1

,5

, ,4 ,4

,4

1t

t ad e p t

t

pW c T

p

=

1,3

2 2

1ad c ct

t p t

Wp

p c T

= +

u

u

cA

cA

u

c2w

2

c3w3

airfoil sketch

4


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( )

( )

( )

1

3

2

,1

3

1 , 2

1

11 1 1

t

t

ad c

int

i ii ad c t

p

p

p

p

=

=

+

5

EAS 4300 Exam 2 03-09 Solutions

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