Hydrodynamics of Pumps

Christopher E. BrennenCalifornia Institute of Technology,

Pasadena, California

With many thanks to Allan Acosta, Dave Japikse, innumerable colleagues, a special group of students

at Caltech, anda special debt to NASA Marshall, to Loren Gross,

Otto Goetz and Henry Stinson.

Prediction of problems:

Turbomachine Power proportional to L53 = L2(L)3

Therefore, same power, same fluid, if L decreases then L must increase

and since is prop. to (L)-2

cavitation must increase

Also…

Since fluid pressures prop. to (L)2

Then blade stresses prop. to

(L)2 (L/T)2

And therefore for the same power,same fluid, same geometry,

blade stress is prop. toL-4/3

Lecture One:

Introduction Specific Speed and Pump Design Non-cavitating performance Secondary flows incl. Prerotation

Geometric Notation:

Streamtube:

VelocityTriangle:

Incidence Angle Deviation Angle

Reynolds Number effects:

Non-cavitating pump performance analysis

Using Bernoulli’s equation in rotating coordinates, a simple expression for the viscous losses (f),

assuming simple geometry,zero deviation, and no preswirl,

leads to a simple pump performance analysis:

And with only slightly more complex lossmechanisms (mD):

Deviation from inviscid calculation:

Viscous losses in blade wakes (axial cascade):

Axial cascade losses:

Centrifugalcascadeanalysis:

Displacement component of inviscid flow:

Busemann slip factor for inviscid flow:

Viscous wakes in centrifugal pumps:

Three-dimensional analysis:A radial equilibrium

calculation

Secondary Flows

Some secondary flows:

Within the blade passage At inlet – tip clearance flow and backflow for an unshrouded impeller Shrouded centrifugal pump Cutwater separation in volute

Prerotation

Widespread misunderstanding Prerotation may be caused only by

Backflow

or

Upstream Asymmetry