Hydrodynamics of Pumps Christopher E. Brennen California Institute of Technology, Pasadena,...

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