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Gas Turbine & Jet Propulsion (April 2010)

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Total No. of Questions : 12] P1391 [Total No. of Pages :4 [3764] - 134 B.E. (Mechanical) GAS TURBINE AND JET PROPULSION (2003 Course) Time : 3 Hours] [Max. Marks:100 Instructions to the candidates: 1) Answer any three questions from each section. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables slide rule. Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. SECTION - I Unit - I Q1) a) A convergent-divergent nozzle has a throat area 500 mm2 and an exit area of 1000 mm2. Air enters the nozzle with a stagnation temperature of 360 K and stagnation pressure of 1 MPa. Determine the maximum flow rate, a static pressure, static temperature, Mach number and velocity at exit if (i) the divergent section acts as nozzle (ii) the divergent section acts as a diffuser. [10] b) Show that for an isentropic flow, the mass flow rate per unit area is maximum when Mach number is unity (Start with basic continuity equation). [6] OR Q2) a) Explain with the help of governing equation and T-S diagram, why shock waves causes supersonic flow to jump to subsonic flow. [5] b) Draw the Fanno curve on H-S diagram and discuss the effect of friction in case of subsonic and supersonic flow. [5] c) What do you mean by Rayleigh flow? What are the assumptions made in Rayleigh flow? Explain choking in Rayleigh flow. [6] P.T.O. Unit - II Q3) a) b) A centrifugal blower compresses 4.8 m3/sec of air from 1 bar and 20 C to 1.5 bar. The index of compression is 1.5. The flow velocity at inlet and outlet of the machine is the same and equals to 65 m/s. The inlet and outlet impeller diameters are 0.32 m and 0.62 m. The blower rotates at 8000 rpm. Calculate : (i) blade angles at outlet and inlet of the impeller. (ii) Absolute angle at the tip of the impeller (iii) breadth of the blade at inlet and outlet. Assume that no diffuser is employed and whole pressure increase takes place in the impeller and blades have negligible thickness. [10] Explain the various losses in a centrifugal compressor with the help of Head-discharge diagram. [6] OR Q4) a) b) An axial flow compressor is designed for 50% reaction with inlet and outlet air angles for rotor blades as 80 and 45 respectively measured from axial direction. The mean blade speed is 200m/s and the axial velocity of flow is constant throughout. Assuming a work factor of 0.88, find the number of stages required if the total pressure ratio is 4:1 with an isentropic efficiency of 85%. The stagnation inlet temperature may be taken as 200K. Assume = 1.4, R = 287Nm/kg-K Cp =1.005KJ/kg-K. [11] Compare axial flow compressor and centrifugal compressor on following points : (i) Pressure ratio per stage (ii) isothermal efficiency (iii) frontal area (iv) part load performance (v) delivery pressure possible. [5] Unit - III Q5) a) A 4500 Kw gas turbine generating set operates with two compressor stages; the overall pressure ratio is 9:1. A high pressure turbine is used to drive the compressor and a low pressure turbine drives the generator. The temperature of the gases at entry to the high-pressure turbine is 625 C and the gases are reheated to 625 C after expansion in the first turbine. The exhaust gases leaving the low-pressure turbine are passed through a heat exchanger to heat air leaving the high-pressure stage compressor. The compressors have equal pressure ratio and intercooling is complete between the stages. The air inlet temperature to the unit is 20 C. The isentropic efficiency of each compressor is 0.8 and isentropic efficiency of each turbine stage is 0.85 and the heat exchanger thermal ration is 0.8. A mechanical efficiency of 95% can be assumed for both the power shaft and compressor turbine shaft. Calculate :- (i) thermal efficiency (ii) work ratio pf the plant (iii) mass flow rate in kg/sec neglecting the mass of fuel. [3764]-134 2 b) Q6) a) b) Assume =1.4, R = 287Nm/kg-k Cp =1.005KJ/Kg-K for air. For gases = 1.333, Cp = 1.15KJ/kg-K. [12] Explain the effect on work output and efficiency if pressure ratio is varied between fixed temperature limits of the cycle with the help of T-S diagram. [6] OR Air is taken in a gas turbine plant at 1.1 bar and 20 C. The plant comprises of LP and HP compressors and turbines. The compression in LP stage is up to 3.3 bar followed by intercooling to 27 C. The pressure of air after HP compressor is 9.45 bar. Loss in pressure during intercooling is 0.15 bar. Air from HP compressor is transferred to heat exchanger of effectiveness 0.65 where it is heated by the gases from LP turbine. After heat exchanger, the air passes through combustion chamber. The temperature of gases supplied to HP turbine is 700 C. The gases expand in HP turbine to 3.62 bar and air then reheated to 670 C before expanding in LP turbine. The loss of pressure in reheater is 0.12 bar. Determine (i) overall efficiency (ii) work ratio (iii) mass flow rate when the power generated is 6000KW. Assume isentropic efficiency of compression in both stages = 0.82, isentropic efficiency of expansion in turbines = 0.85 Assume = 1.4, Cp =1.005KJ/Kg-K for air. For gases = 1 .33, [13] Cp = 1.15KJ/kg-K. State merits and demerits of closed cycle gas turbine over open cycle [5] gas turbine. SECTION - II Unit - IV Q7) a) With a neat sketch explain velocity compounding of a multistage impulse turbine. [6] b) The mean diameter of the blades of an impulse turbine with a single row wheel is 105 cm and the speed is 3000 rpm. The nozzle angle is 72 with respect to axial direction, the ratio of blade speed to gas speed at inlet is 0.42 and the ratio of relative velocity at outlet from the blades to that at inlet is 0.84. The outlet angle of the blade is to be made 3 less than the inlet angle. The mass flow rate is 8 kg/s. Calculate the following i) Tangential thrust on blades. ii) axial thrust on blades. iii) power produced. iv) blade efficiency. [10] OR [3764]-134 3 Q8) a) For a fifty percent reaction turbine, prove that maximum work is Vb2, where Vb is the mean blade speed. [8] b) In a stage of reaction turbine, the mean diameter of the rotor is 1.4 m and the velocity ratio is 0.7. Turbine rolates at 5000 rpm. Blade outlet angle is 70 to the axial direction. Find the diagram efficiency and also find the value of maximum diagram efficiency. [8] Q9) a) Describe briefly the factors affecting the combustion chamber design of gas turbines. [8] b) Write a note on combustion chamber geometry. [8] OR Q10)a) b) Why gas turbine blades need cooling? Explain different methods used for blade cooling. [8] Discuss the various fuels that can be used for gas turbines. [8] Q11)a) With the aid of a neat diagram explain the working principle of a ramjet engine. Also draw the thermodynamic cycle of the ramjet engine. What are its advantages and disadvantages. [8] b) A turbojet plant uses aviation kerosene having a calorific value of 43 MJ/ kg. The fuel consumption is 0.18 kg per hour per N of thrust, when the thrust is 9kN. The aircraft velocity is 500 m/s and the mass of air passing through the compressor is 27 kg/s. Calculate the air fuel ratio, thrust power, heat input and overall efficiency. [6] c) What is meant by thrust angmentation and explain how it is effected.[4] OR Q12)a) With the aid of the schematic diagram and thermodynamic cycle, explain the working of a turboprop engine. [6] b) The effective jet exit velocity from a jet engine is 2700 m/s. The forward flight velocity is 1350 m/s. The air flow rate is 78.6 kg/s. Calculate. i) Thrust ii) Thrust power iii) propulsive efficiency. [6] c) What is meant by thrust? Derive the thrust equation for a general propulsions system. [6] kbkb [3764]-134 4

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