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a steam compressor is operated sisaadly at 30 kpa with quality of 80% and leaves at 8.5 mpa 600c.the velocity of the steam going into the compressor is 1220 m/s.a heat loss of 50 kj/kg is occured during the process. based on the design the compressor has an inlet area of 50cm^2 and an exit area 120cm^2. answer all the following questions: a) list all given and required properties for each state. b) determine mass flow rate of the steam. c) calculate the outlet velocity. d) examine the power input to the compressor
ANSWER|
Part a|
Given: Heat Loss = Qout = 50 kJ/kg
State1: Given: P1 = 30 kPa, x = 0.8 i.e 80% steam and 20% liquid; A1 = 50 cm2 and v1 = 1220 m/s.
This state is saturated mix state. From steam table or table A-5 of Cengel,
at P=30kPa, => Tsat = 69.09 C
at P=30kPa and saturated mixture condition => = 0.001022 m3/kg , = 5.2287m3/kg
Thus,
at P=30kPa and saturated mixture condition => hf= 289.27 kJ/kg , hg = 2624.6 kJ/kg
Thus, h1 = hf + 0.8*(hg-hf) = 2157.534 kJ/kg
State 2: Given: P2 = 8.5 MPa, T2 = 600C; A2 = 120 cm2
The state is superheated state.From steam table or table A-6 of Cengel,
At P = 8 MPa and T = 600 C At P = 9 MPa and T = 600 C
h = 3642.4 kJ/kg h = 3634.1 kJ/kg
By interpolating we get the properties at P = 8.5 MPa and T = 600 C
Part b|
At inlet, Volumetric flow rate of steam V = v1 *A1
Also,
Thus,
Mass fow rate of steam is 1.458 kg/s.
Part c|
Using equation of continuity for the compressor:
Thus the outlet velocity is 508.33 m/s.
Part d|
Given: Heat Loss = qout = 50 kJ/kg
The energy balance for the steady-flow system can be expressed in the rate form as
Putting all values in the above equation:
; ;
and qout = 50 kJ/kg
Thus, power input to compressor is 2231.784 kJ/kg.