Descripción: Theory of gas turbines explained by principles of fluid mechanic and turbodynamics
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Gas Turbine Data SheetDescription complète
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TABLE OF CONTENTS
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Description
Page
1
Objective
2
2
Theory
3
3
Apparatus
4
4
Procedure
5
5
Observations
6
6
Results
7
7
Discussion and Conclusion
8
8
References
9
APPENDIX
10
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1. OBJECTIVE The objective of this experiment was to study the design and running of a Rover 1S/60 gas turbine engine using an ideal air-standard analysis Brayton cycle approximation. This was done by conducting a full load test on the engine at steady state and calculating the overall efficiency, power and fuel consumption rate using the data recorded during the observations.
2. THEORY The quality of any gas turbine engine can be evaluated by calculating its fuel consumption, generated power and the overall thermal efficiency. A gas turbine engine is mainly used to produce thrust or shaft work and its working can be closely modeled after a Brayton thermodynamic cycle (Figure 1 below) keeping second law of thermodynamics in mind, provided that an air standard analysis is applied.
Figure 1: A comparison between a Brayton cycle and an actual gas turbine cycle [1]
In a Brayton cycle, air as an ideal gas is used as a working fluid while in an actual turbine, a mixture of various fluids such as air, fuel and combustion products are used. The energy released from these combustion products is then used to provide work. Some of this work goes on to produce shaft work for power while some is used to drive the compressor. The total power generated by the turbine is the addition of those two power values as well as the power 2
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lost due to friction. Rover 1S/60 (Figures 2,3 and4 Apparatus) is the gas turbine used for this experiment. The power generated by this turbine can be calculated using the dynamometer loading times the dynamometer RPM. The value of the dynamometer RPM is the one at which a balancing torque is applied to the stator by rotating the water past the stator vanes. The power generated by the turbine is actually called the brake horsepower and is measured at the output shaft of the turbine. This is given by the equation below:
(Equation 1)
where W is the dynamometer loading (lbf) and N i s the RPM. The total power generated by the turbine can be f ound by means of the following equation:
(Equation 2)
where is the total power, is the compression power and is the power lost due to friction. A mass and energy balance equation is generally used to find the compressor power. The fuel consumption can be found using the concept of brake fuel consumption (BSFC) which can be calculated using the equation:
(Equation 3)
Where is the mass flow rate of the fuel and heat transfer.
is the net rate of work for a given rate of
And finally the overall thermal efficiency of the engine can be calculated using the relationship below:
(Equation 4)
(Note: The theory is derived from references [1] & [2]) 3
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3. APPARATUS
Figure 2: A sketch of Rover 1S/60 Rover Gas Turbine [4]
Figure 3: A general schematic of Rover 1S/60 Gas turbine [5]
Figure 4: Rover 1S/60 gas turbine engine used in the experiment 4
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4. PROCEDURE
1) Atmospheric temperature and pressure was recorded. 2) The type of fuel as well as its heating value and specific gravity was recorded. 3) Start sequence of the engine was initiated 4) Load is added by means of adding water to the dynamometer 5) The torque was balanced using the handwheel 6) The load is increases until the maximum turbine exit temperature reached approx. F. 7) Dynamometer load was recorded including 50 lbf of extra loading. 8) Dynamometer speed was recorded. 9) Air flow meter pressure drop, compressor to turbine pressure drop, turbine exit static pressure and compressor inlet and exit pressures were recorded using the instrumental panel near the engine. 10) Compressor inlet and exit temperature values were recorded. 11) Turbine exit temperature was recorded 12) Fuel pressure was recorded. 13) Flow rate was recorded. 14) Temperature and pressure values of the engine oil as well as dynamometer water was recorded. 15) Engine was shut down and rundown time was recorded.
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5. OBSERVATIONS Fuel HHV fuel Specific gravity of fuel Atmospheric pressure ( pa) Atmospheric Temperature Dynamometer load Dynamometer speed Fuel flow rate Airmeter pressure drop ( ( p)
Compressor to turbine pressure drop Compressor inlet (impeller tip ) pressure ( p1) Compressor exit (comp. delivery ) pressure( p2 ) Compressor inlet temperature ( T 1) Compressor exit (comp. delivery ) temperature ( T 2) Turbine exit pressure Turbine exit temperature ( T 4) Dynamometer pressure Dynamometer temperature Oil pressure Oil temperature Fuel pressure Run down time
Table 1 : Observations as recorded during the experiment
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6. RESULTS
Brake horsepower (b) (Calculation a - Appendix)
38 hp
Mass flow rate of fuel ( f ) (Calculation b - Appendix)
1.44 lbm/min
Total energy added by fuel (Calculation c - Appendix)
28621.44 BTU/min
Equivalent Brayton cycle efficiency ( ) (Calculation d - Appendix)
0.0563
BSFC (Calculation e - Appendix)
0.0379 lbm/(hp.h)
Mass flow rate of air ( a) (Calculation f - Appendix)
1.52 lbm/s
Turbine work( t) (Calculations g & h - Appendix)
171 hp
Turbine inlet temperature (T3) (Calculation i - Appendix)
1380 F
BWR (Back Work Ratio) (Calculation j - Appendix)
0.745
Turbine efficiency using cold-air standard analysis (t) (Calculation k Appendix)
0.157
o
Table 2: Results obtained through calculations Comparison of efficiencies (cold air standard to brake hors epower ) = 64% 7
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7. DISCUSSION & CONCLUSION Table 2 (Results) represents the values obtained from calculations. The percentage difference between the efficiency calculated from cold-air standard analysis and the one calculated using brake horsepower is 64% (Calculation l Appendix) which is significant. This percentage indicates a considerable difference in efficiency using cold air analysis to that of a Brayton cycle analysis but the use of this modeling can still be carried out anyways because cold air analysis assumes turbine to be isentropic as well as ignoring any stray heat transfers between components when compared to the other. Therefore, the experiment was carried out to a successful completion with all the objectives achieved. This also resulted in achieving a familiarity with the Rover engine which would no doubt be trivial in the study and practical use of other gas turbine engines.
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8. REFERENCES [1] AER 423: Applied Thermodynamics and Heat Transfer Laboratory Manual J.V. Lassaline Ryerson 2011
h) Power developed by turbine: Assuming compressor is isentropic, where inlet conditions and the exit pressure are fixed:
