Example

Calculate the performance of a compressor using air for the following conditions:

d = 10.5 in. rotor diameter L/d - 3.5 length-diameter ratio mw = 23

O, = 2,500 acfm inlet volume i. = I00°F inlet temperature Pi. = 14.5 psia inlet pressure P2 --■ 43.5 psia discharge pressure rp = 3.0 pressure ratio k= l .23

w = 138.8 lbs/min weight flow

Step 1. Using Equation 4.2, solve for the displaced volume per revolution. Convert the units using 1728 in.3/ft3,

From Figure 4-6, read a volumetric efficiency for pressure ratio, 3, where Ev -- 89%. Use Equation 4.4 and solve for the total displaced volume.

Qd = 2,809 cfm total displacement volume

Now calculate the required speed by substituting into Equation 4.3. N = 2.809/.450 N = 6,242 rpm rotor speed

Step 2. Find the velocity of sound for air at the inlet conditions given, using Equation 2.32 from Chapter 2.

R = 67 17 specific gas constant a = (1.23 x 67.17 x 32.2 x 560)1/2 a = 1,220.6 fps velocity of sound

Compute the rotor tip velocity using Equation 4.5 and the unit conversions of 12 in./ft and 60 sec/min.

kx 10.5x6242

60 x 12

u = 286.0 fps rotor tip velocity

Refer to Figure 4-4 with pressure ratio = 3.0 and read the rotor Mach number uc/a = .25. Calculate uD, the optimum tip velocity.

u„ = 305 fps optimum tip velocity

Then calculate the tip speed ratio.

Step 3. Refer to Figure 4-7 and select an efficiency at a pressure ratio of 3 and a volume ratio, rv of 2.44. The adiabatic efficiency is 74%. Now, from Figure 4-5, select a value of efficiency ratio using the tip speed ratio just calculated. Because the value is .99+, round off to an even 1.0. With a multiplier of 1.0, the final adiabatic efficiency is the value read directly off the curve or T|a = 74. The molecular weight correction for efficiency, per rule of thumb, is 0.6 for a final efficiency of 73.4.

Step 4. The adiabatic power can be solved by substituting into Equation 3.18.

k/(k - 1) = 1.23/.23 k/(k - I) = 5.34 (k- 1 )/k = . 187

Calculate the power using the conversions of 144 in.2/ft2 and 33,000 ft Ibs/min/hp for a net value of 229.

Substitute into Equation 4.6 for the discharge temperature.

.734

12 = 256.6°F discharge temperature

Step 5. Solve for the shaft power substituting into Equation 4.7.

Ps — 281.0 hp shaft horsepower

Living Off The Grid

Living Off The Grid

Get All The Support And Guidance You Need To Be A Success At Living Off The Grid. This Book Is One Of The Most Valuable Resources In The World When It Comes To When Living Within The Grid Is Not Making Sense Anymore.

Get My Free Ebook


Post a comment