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# re 34power.pptx

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# re 34power.pptx

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### re 34power.pptx

1. 1. Compressor Data Compressor inlet pressure, P01 = 101.325 kPa Compressor inlet temperature, T01 = 288 K Compressor inlet density, ρa = 1.225 kJ/kgK Specific heat capacity of air, Cpa = 1.005 kJ/kgK Gas constant, R = 287 J/kgK Specific heat ratio of air, γa = 1.4 Isentropic efficiency, ηc = 0.85 Compressor slip factor, σc = 0.7 Specific speed of compressor, Ns = 1 rpm Compressor pressure ratio, P02 / P01= 2.5 Compressor mass flow rate, m° a = 0.3 kg/s Compressor impeller diameter, D2 = 0.05 m Compressor eye root diameter, dr = 0.015 m Compressor eye tip diameter, dt = 0.03 m
2. 2. Compressor calculation Compressor outlet pressor, P02 = 2.5 × P01 = 7 × 101.325 = 253.3125 kPa Compressor outlet isentropic temperature, T02 ′ = T01 × P02 P01 γa−1 γa = 288 × 2.5 1.4−1 1.4 = 374.187808 K Compressor outlet temperature, T02 = T02 ′ −T01 ηc + T01 = 374.187808−288 0.85 + 288 = 389.397421 K
3. 3. Compressor work done, Wc = m° a Cpa (T02 – T01) = 0.3 × 1.005 × (389.397421 – 288) = 30.5713224 kW Enthalpy drop, Δh0,1-2 = Cpa (T02 – T01) = 1.005 × (389.397421 – 288) = 101.904408 kJ/kg Impeller velocity, U2 = ∆h0,1−2 σc = 101.904408 ×103 0.6 = 381.546492 m/s
4. 4. Eye impeller area, a = π 4 × dt 2 − dr 2 = π 4 × (0.032−0.0152) = 0.0005301437 m3 C1 = ma ° ρ a = 0.3 1.225×0.0005301437 = 461.94637 m/s Assume C2r = C1 = 461.94637 m/s C2w = σc × U2 = 0.7 × 381.546492 = 267.082544 m/s
5. 5. C2 = C2r 2 + C2w 2 = 461.94637 2 + 267.082544 2 = 533.598663 m/s Compressor exit temperature, T2 = T02 - C2 2 2cp = 398.397421 - 533.598663 2 2×1.005×103 = 247.741931
6. 6. Compressor exit pressure, P2 = P02 × T2 T02 γa γa−1 = 253.3125 × 247.741931 389.397421 1.4 1.4−1 = 52.033038 kPa Compressor exit density, ρ2 = P2 RT2 = 52.033038×103 287×247.741931 = 0.731809 kg/m3
7. 7. H = m° ρ2πD2×C2r = 0.3 0.731809×π×0.05×461.94637 = 0.005649 m Compressor exit area, A2 = πD2H = π × 0.05 × 0.005649 = 0.00088734 m2 Cr2 = m° ρ2A2 = 0.3 0.731809×0.00088734 = 461.99092 m/s
8. 8. Compressor outlet volume flow rate, v2 ° = 1 ρ2 = 1 0.731809 = 1.366476 m3 Compressor speed, N = 60× Δh0,1−2 3 4×Ns 2π v2 ° = 60× 101.904408×103 3 4×1 2×π× 1.366476 = 46592.40256 rpm
9. 9. Eye mean diameter, dm = dt+dr 2 = 0.03+0.015 2 = 0.0225 m Eye mean impeller velocity, Um = πdmN/60 = π ×0.0225× 46592.40256/60 = 54.890381 m/s Eye mean impeller angle, αm = tan-1( C1 Um ) = tan-1 461.94637 54.890381 = 83.223651 °
10. 10. Eye root diameter, dr = 0.015 m Eye root impeller velocity, Uer = πdrN/60 = π × 0.015 × 46592.40256/60 = 36.593587 m/s Eye root impeller angle, αer = tan-1 C1 Uer = tan-1 461.94637 36.593587 = 85.470710 ° Eye tip diameter, dt = 0.03 m Eye tip impeller velocity, Uet = πdtN/60 = π × 0.03 × 46592.40256 /60 = 73.187174 m/s
11. 11. Eye tip impeller angle, αet = tan−1 C1 Uet = tan−1 461.94637 73.187174 = 80.997331 ° Compressor exit impeller angle, β2 = tan−1 C2r C2w = tan−1 461.990538 267.082544 = 59.967252 ° Number of blade of compressor, Z = 6.5× D2+dm D2−dm × sin β2+β1 2 = 6.5× 0.05+0.0225 0.05−0.0225 × sin 59.967252 +0 2 = 8.563940 ~ 8 blades
12. 12. Turbine Data Turbine outlet pressure,P04 = P01 = 101.325 kPa Turbine inlet temperature, T03 = 700 K Specific heat capacity of gas, Cpg = 1.051 kJ/kgK Gas constant, R = 287 J/kgK Specific heat ratio of gas, γg = 1.33 Isentropic efficiency, ηt = 0.9 Turbine slip factor, σt = 0.9 Turbine speed, N = 46592.40256 rpm Turbine expression ratio, P03 / P04 = 2 Turbine mass flow rate, m° g = 0.2 kg/s Turbine impeller diameter, D3 = 0.045 m Turbine eye root diameter, d4r = 0.012 m Turbine eye tip diameter, d4t = 0.032 m Head, H = m
13. 13. Turbine calculation Turbine inlet pressure, P03 = P04 × 2 = 101.325 × 2 = 202.65 kPa Turbine outlet isentropic temperature, T04 ′ = T03 P03 P04 γg−1 γg = 700 2 1.33−1 1.33 = 589.394918 K
14. 14. Turbine outlet temperature, T04 = T03 - T03−T04 ′ ηt = 700 - 700−589.394918 0.9 = 577.105464 K Turbine work done, Wt = mg ° Cpg T03 − T04 = 0.2 × 1.051 × (700 – 577.105464) = 25.832431 kW Enthalpy drop, Δh0,3-4 = Cpg (T03 – T04) = 1.051 × (700 - 577.105464 ) = 129.162157 kW
15. 15. U3 = Δh0,3−4 σt = 129.162157×103 0.9 = 378.831767 m/s Turbine impeller diameter, D3 = U3×60 π×N = 378.831767 ×60 π ×46592.40256 = 0.155286 m