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ISENTROPIC EFFICIENCY CALCULATIONS for POSITIVE-DISPLACEMENT ROTARY-LOBE BLOWERS

ISENTROPIC EFFICIENCY CALCULATIONS for POSITIVE-DISPLACEMENT ROTARY-LOBE BLOWERS. Roger E. Blanton, P.E. District Sales Manager Kaeser Compressors, Inc. EFFICIENCY. All air and gas compressors are less than 100% efficient. P1 V1 T1. Position 1. P2 V2 T2. Position 2. EFFICIENCY.

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ISENTROPIC EFFICIENCY CALCULATIONS for POSITIVE-DISPLACEMENT ROTARY-LOBE BLOWERS

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  1. ISENTROPIC EFFICIENCY CALCULATIONS for POSITIVE-DISPLACEMENT ROTARY-LOBE BLOWERS Roger E. Blanton, P.E. District Sales Manager Kaeser Compressors, Inc.

  2. EFFICIENCY • All air and gas compressors are less than 100% efficient

  3. P1 V1 T1 Position 1 P2 V2 T2 Position 2 EFFICIENCY P2 > P1 V2 < V1 T2 > T1

  4. EFFICIENCY • Entropy is a measure of the energy loss

  5. COMPRESSION MODEL • Constant entropy (isentropic) process is ideal • No heat loss and perfectly reversible

  6. ISENTROPIC COMPRESSION • Follows this relationship, P2 /P1 = (v1/ v2)k » Pvk= a constant where: v = specific volume [ft3/lb] P1, P2 = initial and final pressure [Pabs] k = Cp/Cv = specific heat ratio = 1.4 for air

  7. COMPRESSOR WORK • For continuous isentropic compression of a gas obeying the previous relationship, work per unit mass (ft·lb/lb) is Wis = vdP = P1 * v1 * [k / (k-1)] * [(P2 / P1)((k-1) / k) – 1] BHF = Big Hairy Formula !!!

  8. POWER • hpis = Wis * m / 60 / 550 where m is mass flow rate in lb/min

  9. EFFICIENCY • Isentropic efficiency of a compressor is the ratio of the ideal isentropic work to the actual work required is = Wis / Wact = hpis / hpact

  10. EXAMPLE CALCULATION • Brand K model 42 @ 2000 rpm • P1 = 14.7 psia • P2 = 10 psig (24.7 psia) • T1 = 68° F • ρ1 (density) = 0.075 lb/ft3 • K = 1.4 (air) • BHP = 13.2 (from performance table) • CFM = 222 (from performance table) • m = 222 * 0.075 = 16.65 lb/min

  11. EXAMPLE CALCULATION (cont’d) • v1 = 1/ ρ1 = 1 / 0.075 = 13.33 ft3/lb • k / (k-1) = 1.4 / (1.4 – 1) = 1.4 / 0.4 = 3.5 • P2 / P1 = 24.7 / 14.7 = 1.68 • (k-1) / k) = (1.4 -1) / 1.4 = 0.4 / 1.4 = 0.286 • (P2 / P1)((k-1) / k) = 1.680.286 = 1.16

  12. EXAMPLE CALCULATION (cont’d) Back to the Big Hairy Formula Wis = P1 * v1 * [k / (k-1)] * [(P2 / P1)((k-1) / k) – 1] Wis = 14.7 * 13.33 * 3.5 * [1.16 -1] * 144 = 15,801 ft·lb/lb

  13. EXAMPLE CALCULATION (cont’d) • hpis = Wis * m / 60 / 550 • hpis = 15801 * 16.65 / 60 / 550 = 8 hp

  14. EXAMPLE CALCULATION (cont’d) • is = hpis / hpact • is = 8 / 13.2 = 61% efficient

  15. CONCLUSION • Repeat this procedure for different blowers at the same pressure

  16. CONCLUSION • Perform this calculation on blowers bid for a project to evaluate efficiency • Look at blower efficiency, not just price when making a decision

  17. CONCLUSION • Perform a Life Cycle Cost (LCC) analysis • Typically a 20 year project horizon is considered • Include installation, estimated maintenance, and operating costs • Discount the expenses to net present value (NPV) for comparison

  18. CONCLUSION • Operating cost greatly outweighs first cost • Blower efficiency is important for customer satisfaction

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