Homework: Centrifugal Compressor

ME3280 / ME6160 Turbines and Centrifugal Machinery Fall 2017 Dr. T. J. Barber

Problem 4.1: Nondimensionalization

Suppose one know that the force F on a particular body immersed in a stream of fluid depended only on  body length, L  stream velocity, U  fluid density,   fluid viscosity,  that is F f L, U , ,   Suppose further that the geometry and flow conditions are so complicated that integral or differential theories fail to yield the solution for the force F.

Reduce the number of dimensional variables using Buckingham’s pi theorem, where each pi =  is the product of a number of dimensional variables.

Problem 4.2: Scaling

The design point of a compressor is defined as follows:  Inlet total pressure=1.5 bars  Inlet total temperature=345K  Mass flow rate=3.8 kg/s  Physical speed=45,000 rpm  Total temperature rise=320 K

These operating conditions are tested using air under standard sea-level conditions on 1 bars and 288K, respectively, using the full-scale compressor. Calculate the mass flow rate, speed and total temperature rise during the test.

Problem 4.3: Centrifugal Compressor

Given a centrifugal compressor with the following operating and geometric conditions:

 Flow 5 lb/sec  Pt1 14.7 psia  Tt1 519 °R

N  a1 30°  N 20,000 RPM  h 82%

rtip = 5.35"

rod = 3.192"

rid = 1.596"

Assume radial exit flow in rotating frame of reference, ie, b2 = 0°

1. Sketch inlet & exit velocity diagram 2. Calculate impeller pressure ratio