A MULTIFUNCTIONAL HIGH-SPEED SPINDLE FOR MICROMACHINING MEDICAL MATERIALS - Medical Device Manufacturing - page 116

kinetic energy and ε is the turbulence eddy dissipation. The total energy heat
transfer model was considered as kinetic energy effects are important in the
model.
Applied Boundary Conditions
The following boundary conditions were applied to the model:

 Static pressure of 60 psi at the inlets;

 Static pressure of 0 (zero) at the outlet;

 A no-slip (moving) wall boundary condition on the rotor. A constant

angular speed of the rotor was specified;

 A no-slip (stationary) wall boundary condition on the housing and

inlet surfaces.

Governing Equations
The governing equations of three-dimensional fluid flow were represented

as:

Continuity Equation:

 (  )

(1)

i

 0

 X

i

Momentum Equation:

 (  U U )  U

 P   U

(2)

i j j

   ( 

i

  )

eff eff

 x  x  x  x  x

j i j j i

where repeated indices imply summation from 1 to 3, ρ is density, U i are the
cartesian velocity components, P is pressure, X i are the coordinate axes, and
μ eff is the effective viscosity, which is defined as:

2

k

     ; (3)

μ

t 

C ρ

eff t μ

ε

where μ t is the eddy viscosity, C is a constant and is equal to 0.09, k is the
turbulence kinetic energy and ε is the turbulence eddy dissipation. The
turbulence model is given by: