ISENTROPIC EFFICIENCY CALCULATIONS POSITIVE-DISPLACEMENT

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ISENTROPIC EFFICIENCY CALCULATIONS POSITIVE-DISPLACEMENT
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

EFFICIENCY P1 V1 T1 Position 1 P2 > P1 V2 < V1 T2 > T1

EFFICIENCY Entropy is a measure of the energy loss

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

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

COMPRESSOR WORK BHF = Big Hairy Formula !!!
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 !!!

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

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

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

EXAMPLE CALCULATION (cont’d)
v1 = 1/ ρ1 = 1 / = 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) = = 1.16

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 * * 3.5 * [ ] * 144 = 15,801 ft·lb/lb

EXAMPLE CALCULATION (cont’d)
hpis = Wis * m / 60 / 550 hpis = * / 60 / 550 = 8 hp

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

CONCLUSION Repeat this procedure for different blowers at the same pressure

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

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

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