A Brayton Gas turbine cycle produces 14 MW with an inlet state of the compressor is T10C, P1 kPa, and a compression ratio of rP. The heat added in the combustion is 960 kJ/kg. Determine the mass flow rate of air in kg/s.Where,T1=190CP1= 115 kParP=15:1Specific heat at a constant pressure of air, CP= 1.004 kJ/kg kPolytropic Index, n for compressor, turbine and combustion chamber=1.4
Question
A Brayton Gas turbine cycle produces 14 MW with an inlet state of the compressor is T10C, P1 kPa, and a compression ratio of rP. The heat added in the combustion is 960 kJ/kg. Determine the mass flow rate of air in kg/s.Where,T1=190CP1= 115 kParP=15:1Specific heat at a constant pressure of air, CP= 1.004 kJ/kg kPolytropic Index, n for compressor, turbine and combustion chamber=1.4
Solution
To solve this problem, we need to use the Brayton cycle equations and the given parameters.
Step 1: Convert all temperatures to Kelvin. T1 = 190C = 190 + 273.15 = 463.15 K.
Step 2: Calculate the temperature at the end of the compression process (T2) using the formula for adiabatic compression: T2 = T1 * (rP)^(n-1/n) = 463.15 K * (15)^(1.4-1/1.4) = 1089.5 K.
Step 3: Calculate the temperature at the end of the heat addition process (T3). Since the heat added in the combustion is 960 kJ/kg, we can use the formula Q = m * Cp * (T3 - T2) to find T3. Rearranging the formula gives T3 = Q/(mCp) + T2 = 960 kJ/kg / (1.004 kJ/kgK) + 1089.5 K = 1856.6 K.
Step 4: Calculate the work done by the turbine (Wt) using the formula for adiabatic expansion: Wt = Cp * (T3 - T4), where T4 is the temperature at the end of the expansion process. We can find T4 using the formula for adiabatic expansion: T4 = T3 / (rP)^(n-1/n) = 1856.6 K / (15)^(1.4-1/1.4) = 779.8 K. Substituting these values into the formula for Wt gives Wt = 1.004 kJ/kg*K * (1856.6 K - 779.8 K) = 1081.2 kJ/kg.
Step 5: Calculate the work done by the compressor (Wc) using the formula Wc = Cp * (T2 - T1) = 1.004 kJ/kg*K * (1089.5 K - 463.15 K) = 628.6 kJ/kg.
Step 6: The net work done by the cycle is the difference between the work done by the turbine and the work done by the compressor: Wnet = Wt - Wc = 1081.2 kJ/kg - 628.6 kJ/kg = 452.6 kJ/kg.
Step 7: The power output of the cycle is given as 14 MW = 14,000 kW. The mass flow rate of the air can be found by dividing the power output by the net work done per kilogram of air: m = P/Wnet = 14,000 kW / 452.6 kJ/kg = 30.9 kg/s.
So, the mass flow rate of air is approximately 30.9 kg/s.
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