T.E. (Mech., Mech. S/W) (Semester II) Examination, 2011 TURBOMACHINES (New) (2008 Pattern)

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1 * * [4063] 218 T.E. (Mech., Mech. S/W) (Semester II) Examination, 2011 TURBOMACHINES (New) (2008 Pattern) Time : 3 Hours Marks : 100 Instructions : 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) Black 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 1. a) A circular jet of water having velocity of 60 m/s impinges tangentially on a series of curved vanes moving uniformly at 25 m/s. The jet makes an angle of 30 degrees with the direction of motion of the vanes. Relative to a vane, the jet turns through an angle of 100 degrees as it flows over the vane. The flow speed along the vane drops by 15% due to frictional loss. Draw neat inlet and outlet velocity triangles showing all the relevant details and determine : i) Vane tip angles at inlet and outlet for smooth flow, ii) Absolute velocity of water leaving the vanes, iii) Work done on the series of vanes per unit mass of water, iv) Power delivered to the vanes if the jet mass flow is 50 kg/s, v) Hydraulic efficiency. What is the pressure of water jet while it is flowing along the vane? Justify your answer. 10 P.T.O.

2 [4063] * * b) Consider a single, symmetric 2D curved vane having centrally impinging 2D water jet. Jet cross-section area is A and density of water is. Velocity of the jet is V and the vane moves at velocity u in the same direction as the jet. The turning angle of the vane on each side is. Derive the expression for hydraulic efficiency η of the vane in terms of the speed ratio u/v and the half angle of the vane. Then derive the condition for maximum efficiency for given angle. Hence obtain the maximum efficiency for : i) a semicircular vane, ii) a flat plate perpendicular to the flow and iii) a flat plate aligned with the flow a) A horizontal-single-jet Pelton wheel works at a hydro-electric power station where the head race level is vertically 450 m above the nozzle centreline. The length of the penstock is 5 km and its diameter is 1 m. Friction factor for the penstock may be taken to be Velocity coefficient for the nozzle is 0.97 and other head losses (in fittings and bends) up to the nozzle exit amount to 10 m of water. Relative flow speed at the bucket exit is 90% of that at the bucket inlet on account of bucket friction. Clearance angle is 15 degrees and speed ratio is Average velocity of water in the penstock is 2 m/s and the density of water is 1000 kg/m 3. Mechanical efficiency, accounting for the mechanical friction losses in bearings, is 95% and the generator efficiency is unknown. If the turbine develops an electrical power output of 5 MW while rotating at 375 rpm, determine : i) Rate of work done by the jet on the wheel, ii) Mean diameter of the bucket pitch circle, iii) Hydraulic efficiency, iv) Generator efficiency. 12 b) Draw a neat schematic of the Pelton-wheel bucket and explain clearly the functions of the following : i) Twin-bucket construction, ii) Splitter edge, iii) Bucket-tip notch, iv) Clearance angle. 4

3 * * -3- [4063] 218 Unit II 3. a) A vertical-shaft mixed-flow Francis turbine (Modern Francis turbine) works between the head race and the tail race having vertical level difference of 150 meters. Frictional head losses in penstock, casing, wicket gates, runner and draft tube are 10 m, 1 m, 0.5 m, 0.5 m and 2 m of water respectively. Water discharges from the draft tube at a velocity of 2 m/s into the tail race. The turbine develops shaft power of MW while running at a speed of 300 rpm. Mechanical efficiency of the system is 95% and the electrical generator is 98% efficient. Outer diameter and axial width of the runner at the inlet are 2.5 m and m respectively. Blockage caused by the runner blades to the flow is negligible. Discharge from the runner is axial and whirl-free. Density of water may be taken to be 1000 kg/m 3. Determine : i) Overall efficiency of the plant, ii) Discharge through the turbine in m 3 /s, iii) Runner blade angle at the inlet and iv) Wicket gate (or inlet guide vane) angle. Draw neat inlet velocity triangle showing all the important details. 12 b) A reaction turbine with a straight divergent draft tube operates under a net head of 30 m of water and develops electrical power of 50 MW. Generator and mechanical efficiencies are 98% and 95% respectively. Inlet of the draft tube is located 3 m above the tail race level where the diameter of the draft tube is 5 m. Frictional head loss in the draft tube is 1 m of water and the efficiency of the draft tube is 64.85%. Density of water may be taken to be 1030 kg/m 3. Determine : i) Diameter of the draft tube at its exit, ii) Gauge pressure head at the draft tube inlet (or runner exit) a) A vertical-shaft Kaplan turbine operates under a net head of 25 m of water and develops hydraulic power of 150 MW. Outer diameter of the tip circle of Kaplan blades is 5 m and the boss (or the hub) diameter is 2 m. Blockage factors, accounting for the thickness of aerofoil-shaped Kaplan blades, are 0.9 and 0.93 at inlet and outlet respectively. The discharge from the turbine is purely axial and hence whirl-free. On inlet side of the runner, the product of the whirl velocity and the blade velocity is constant with respect to the radius

4 [4063] * * (i.e. free-vortex type whirl distribution at inlet to the runner). Rotational speed of the turbine is 150 rpm and density of water is 1000 kg/m 3. Draw inlet and outlet velocity triangles at the tip and root (i.e. at the hub) of a Kaplan blade and determine : i) Inlet blade angles at the blade tip and the blade root and ii) Outlet blade angles at the blade tip and the blade root. 14 b) Why is the draft tube necessary in the case of hydraulic reaction turbines? Explain with neat sketches. Explain the advantage of elbow-type divergent draft tube over a straight divergent draft tube. 4 Unit III 5. The initial pressure and temperature of steam entering a reaction turbine of axial type are 100 bar and 550 C respectively. The steam flows at 120 kg/s and the exit angle of first stage of nozzle blades is 70 degrees. The turbine is a single-stage machine with 50% degree of reaction at the mean blade height. The stage efficiency is 85%. Assuming maximum blade efficiency, determine : i) Rotor blade angles at inlet and outlet, ii) Absolute steam velocity at rotor inlet, iii) Power developed, iv) Final state of the steam after expansion. Mean diameter of rotor is 105 cm and the speed of rotation is 3200 rpm. All angles are measured with respect to axial direction only a) For a certain stage of a 50% reaction axial steam turbine, the mean rotor diameter is 1.35 m and the speed ratio is The rotor speed is 3000 rpm and the outlet blade angle is 55 degrees. Determine : i) Inlet blade angle, ii) Blade efficiency, iii) Maximum blade efficiency. All angles are measured with respect to axial direction only. 10 b) State various methods employed in practice for governing of steam turbines. Discuss any two methods in detail along with a neat schematic. 6

5 * * -5- [4063] 218 SECTION II Unit IV 7. a) A gas-turbine power plant has an output of 100 MW at the generator terminals. The technical details of the plant are as follows : Air compressor inlet pressure : bar Air compressor inlet temperature : 310 K Compressor pressure ratio : 8 Compressor efficiency : 82% Turbine inlet temperature : 1350 K Turbine efficiency : 88% Turbine inlet pressure = 0.98* Compressor exit pressure Turbine exit pressure = 1.03 bar Calorific value of fuel = 42 MJ/kg Combustion efficiency = 99% Mechanical efficiency = 95% Generator efficiency = 97% Neglecting kinetic heads and taking γ a = 1.4, C pa = kj/kgk for air and γ g = 1.33, C pg = kj/kgk for exhaust gases, determine : i) Gas flow rate, ii) Fuel-air ratio, iii) Thermal efficiency of the plant, iv) Overall efficiency of the plant, v) Ideal Joule-Brayton cycle efficiency. 10

6 [4063] * * b) For an actual Joule-Brayton cycle without any pressure drops, derive the condition for maximum plant output in terms of isentropic temperature ratio and compressor and turbine efficiencies a) A turbojet engine takes in 50 kg of air every second and propels an aircraft with a uniform flight speed of 910 km/hr. The isentropic enthalpy change in the nozzle is kj/kg and its velocity coefficient is The fuel to air ratio is 1.3%, the combustion efficiency is 85% and the calorific value of the fuel is 44 MJ/kg. Determine : i) Thrust Specific Fuel Consumption in kg/n-hr, ii) Thrust power, iii) Propulsive power, iv) Propulsive efficiency. 8 b) Describe briefly the construction of a turbofan engine along with a schematic. Also draw an indicative graph comparing the propulsive efficiencies of turboprop, turbofan and turbojet engines. 8 Unit V 9. a) A centrifugal pump discharges 3000 lpm of water and the outer diameter of the impeller is 35 cm. The vanes are curved backwards at an angle of 30 degrees to the wheel tangent at the impeller tip. The thickness of the vanes occupies 10% of the peripheral area. The passage is 50 mm wide and the impeller rotates at a speed of 1500 rpm. If the manometric efficiency is 82%, find the pressure head developed across the impeller in metres of water column. Assume that there is no loss of energy in the impeller and that the flow velocity is constant throughout. 10 b) State the criteria for selection of a centrifugal pump for a given application. 6

7 * * -7- [4063] a) Impeller of a centrifugal pump is 185 mm in diameter and width at the outlet is 60 mm. The blades are curved backwards at an angle of 20 degrees. The H-Q characteristic of the pump is given by : H = Q 1660 Q 2 The pump delivers water through a 150 mm diameter and 80 m long pipe to a static lift of 32 m. Calculate the head developed, discharge and the manometric efficiency if the pump speed is 3200 rpm. Friction factor for the outlet pipe material as and the frictional head loss in the suction pipe is negligible. 10 b) Why is multistaging used for a centrifugal pump? Describe the methods used for multistaging. 6 Unit VI 11. a) An axial compressor has 10 stages with an overall stagnation pressure ratio of Isentropic efficiency of each stage is 90%. Ambient air temperature is 25 C and ambient air pressure is 1 bar. Stagnation pressure ratios of all the stages are equal and overall stagnation pressure ratio is the product of stage stagnation pressure ratios. Same is the case for stagnation temperature ratio. The degree of reaction for each stage is 50% at the mean blade height. The first stage of the compressor has a set of Inlet Guide Vanes (IGVs) followed by rotor and stator rings. Exit angle of the IGVs is 20 degrees with respect to the axial direction and the velocity of flow at the rotor inlet is 150 m/s. Rotor hub diameter to tip diameter ratio is 0.5 for the first stage and compressor speed is rpm. Taking = 1.4 and C p = kj/kgk for air, determine : i) Stage stagnation temperature ratio, ii) Overall isentropic efficiency, iii) Rotor inlet and exit angles and stator inlet angle for first stage, iv) Specific work done on air in the first stage, v) Rotor blade speed at the mean blade height in the first stage, vi) Inner and outer diameters of the first stage rotor annulus. Draw neat inlet and outlet velocity triangles at the mean blade height for the first stage rotor showing all the improtant details. 12 b) Explain slip and prewhirl in connection to centrifugal compressors. 6

8 [4063] * * 12. a) A centrifugal compressor runs at rpm with an overall stagnation pressure ratio of 4. Ambient air conditions are 25 C and 1 bar. Vanes are radial. Slip factor is 0.96 and power input factor (work factor) is Flow in the inlet section up to the impeller entry is isentropic and that in the impeller and the diffuser is adiabatic. There is no prewhirl at axial entry to the impeller. Mechanical efficiency is 96% and the electric motor driving the compressor is 98% efficient. The loss of stagnation pressure from impeller exit to diffuser exit is 0.1 bar. Isentropic efficiency of the impeller alone is 90%. Taking = 1.4 and C p = kj/kgk for air, determine : i) Electrical energy consumed by the electric motor per kg of air, ii) Overall isentropic efficiency of the compressor, iii) Impeller tip diameter. Draw neat T s diagram showing only the stagnation temperatures and pressures involved in the present problem. 12 b) Explain surging and rotating stall with reference to axial compressors. 6 B/II/11/1,560