Q3. A theoretical engine cycle consists of the following four sequential processes:
Compression according to the law pV1.28 from the initial conditions
Constant volume heat addition
Expansion according to the law pV1.33 to the initial volume
Constant volume heat rejection to the initial temperature.
The initial pressure and temperature are 1 bar and 43ºC.
The volume compression ratio is 13:1.
The heat addition is 1200 kJ/kg of working fluid.
The working fluid has the properties of air throughout.
(a) Sketch the cycle on Pressure-Volume and Temperature-specific entropy diagrams.
(b) Calculate EACH of the following:
(i) The heat transfer during the compression process
(ii) The heat transfer during the expansion process
(iii) The cycle efficiency.
Note: for air Cv = 0.718 kJ/kgK, R = 0.287 kJ/kgK
Q1. Air enters the compressor of simple gas turbine plant at a pressure and temperature of 1.013 bar and 298 K respectively and is compressed through a pressure ratio of 12:1 with an isentropic efficiency of 0.85.
The hot gases enter the turbine at a temperature of 1500 K and expand down to the initial pressure with an isentropic efficiency of 0.9.
The mass flow rate of air is 250 kg/min and the mass flow rate of fuel may be ignored.
(a) Sketch the cycle on a Temperature-specific entropy diagram.
(i) The compressor outlet temperature
(ii) The turbine outlet temperature
(iii) The net power output
(iv) The work ratio
(v) The thermal efficiency of the cycle.
Note: for air γ = 1.4 and Cp = 1.005 kJ/kgK
For the hot gas γ = 1.33 and Cp = 1.15 kJ/kgK
Q2. A producer gas has the following volumetric composition: 49% H2, 20% CH4, 18% CO, 6% N2, 4% CO2, 2% C3H8, and 1% O2. The gas is completely burned in 20% excess air.
Calculate EACH of the following:
(a) The volumetric air/fuel ratio for stoichiometric combustion
(b) The percentage volumetric analysis of the wet combustion products
(c) The gravimetric analysis of the dry products of combustion.
Note: Relative atomic masses Carbon = 12, Hydrogen = 1, Oxygen = 16, Nitrogen = 14.
Air contains 21% oxygen by volume.
Q2. A vapor compression refrigeration plant using R134a operates between saturation temperatures of -20°C and +25ºC.
The plant produces 200 kg/hour of ice at -12°C from water at +20ºC.
The refrigerant enters the expansion valve at the rate of 531 kg/hour with 5 K of sub-cooling.
The isentropic efficiency of the compressor is 93.1%.
(a) Sketch the cycle on p-h and T-s diagrams.
(i) The temperature of the refrigerant entering the compressor;
(ii) The temperature of the refrigerant leaving the compressor;
(iii) The cycle co-efficient of performance.
Note: for water Cp = 4.187 kJ/kg K
For ice Cp = 2.1 kJ/kg K and enthalpy of fusion = 335 kJ/kg
Q2. An insulated container 3 m long, 2.4 m wide and 2.6 m high consists of an insulating layer of 200 mm thick cork placed between an inner layer of 5 mm thick aluminium and an outer layer of 5 mm thick steel.
The exposed surface of the aluminium is at -15ºC when the outside atmosphere is at +25ºC.
(a) The heat flow into the container per hour
(b) The interface temperatures between the cork and the steel
(c) the emissivity of the aluminium at -15ºC when the contents of the container are at -25ºC and the net emissive power from the aluminium is 15% of the value calculated in Q7(a).
Note: Thermal conductivity of aluminium = 205 W/mK
Thermal conductivity of cork = 0.04 W/mK
Thermal conductivity of steel = 54 W/mK
Outer surface heat transfer coefficient =13 W/m2K
Stefan-Boltzmann constant = 56.7 kW/m2K4
Q1. A two stage, single acting reciprocating air compressor is designed for minimum work and has perfect inter-cooling. The pressure and temperature at inlet are 1 bar and 20ºC respectively, the discharge pressure is 36 bar. The swept volume of the first stage is 0.01 m3 and the clearance volume is 3% of the swept volume.
The polytrophic index for all the expansion and compression processes is 1.2, the mechanical efficiency of the compressor is 0.8 and the speed is 240 rev/min.
(a) Sketch the processes on a p-V diagram indicating the pressures and volumes.
(i) The first stage volumetric efficiency
(ii) The mass of air delivered per second
(iii) The input power.
Note: For air R = 0.287 kJ/kgK
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