        Improved Fuel Economy with " Controllable Variable Flow "

Euler Equations

The principle Euler turbine equations apply also to this centrifugal coolant pump application which takes advantage of varying inlet swirl vectors. The geometry and notation used to develop the speed triangles for such a typical pump are shown in figure 1.  Using the vector notations shown in figures 1 and 2 and applying the conservation of momentum relationship between torque and the moment of momentum applied to a fixed control volume enclosing the impeller in the tangential direction, the Euler turbine equations can be expressed to describe the theoretical head, a simplified form of which is represented as follows:  H  = ( u x Vt2 ±  u1 x Vt1 ) closed

Hydraulic Principles - Figure 1 Velocity Vectors

The angles α1 and α2 shown in figures 1 and 2 express the tangential components of the absolute velocity vectors, Vt1 and Vt2 . The inlet component Vt1 , written as Vt1 = V1 cos α1 describes the amount and direction of inlet pre-swirl.

Figure 2 shows the entry speed vector triangles for three cases.

The triangles in figure 2 show the relative effect of the inlet angle α1 on the entry vector Vt1 .  So, the magnitude of α1 denotes the effect of the inlet preswirl (or pre-rotation) on the Head, and Velocity vector product which is proportional to Flow.  For example when α1 = 90 degrees (no preswirl), Vt1 = zero.   Similarly for α1 < 90° the sign is negative, effectively reducing the pump Flow and Head output, and conversely for α1 > 90° the pump Head (and Flow) output is increased.

The resulting impact of pump performance is shown in figure 3, which depicts several different pump performance characteristics for variable inlet guide vane positions.   Hydraulic Principles - Figure 2 Variable Performance Range - Figure 3

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