Hydrodynamics of Pumps Christopher E. Brennen California Institute of Technology, Pasadena, California With many thanks to Allan Acosta, Dave Japikse, innumerable colleagues, a special group of students at Caltech, and a special debt to NASA Marshall, to Loren Gross, Otto Goetz and Henry Stinson.

Prediction of problems: Turbomachine Power proportional to L 5 3 = L 2 ( 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. to L -4/3

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

Geometric Notation:

Streamtube: Velocity Triangle:

Incidence Angle Deviation Angle

Reynolds Number effects:

Non-cavitating pump performance analysis

Using Bernoullis 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 loss mechanisms (m D ):

Deviation from inviscid calculation:

Viscous losses in blade wakes (axial cascade):

Axial cascade losses:

Centrifugal cascade analysis:

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