Whatever the flow rate, the superimposition of the measurement axes reveals the thermal

axisymmetry of the flow.

2005; Xu 2002) were thoroughly investigated on decay rate of the mean centerline velocity, jet spreading rate, potential core, turbulence intensity, Re stresses, local entrainment and mixing rate, velocity gradient in the shear layer, boundary layer displacement thickness and momentum thickness, kinematic momentum flux and kinematic mass flux, frequency spectrum of the velocity fluctuations, breaking the

axisymmetry and enhancing three-dimensionality in the shear layer, speed of convection and number of large-scale coherent structures in the near field of the nozzle exit, Strouhal number, distribution of vorticity concentration, intermittency in lateral skewness, and flatness moments across the jet and scalar field.

Only half the thickness was modeled to reduce computational time by assuming

axisymmetry.

The simulation takes advantage of the

axisymmetry, the cylindrical shape and the repetitive pattern of the winding sections in the flow path.

begins at the ground floor with by describing probability distributions and densities, then moves to moments, characteristic functions, Gaussian distribution, random functions, random processes in more dimensions, Fourier transforms, tensors, the theory of generalized functions and invariant theory along with isotropy and

axisymmetry.

This assumes

axisymmetry and that radial temperature, velocity and concentration gradients are small in comparison with those perpendiculars to the disc; Coriolis forces, non-Newtonian effects angular slip, and gas-induced shear stresses are all neglected; most importantly, the effects of interfacial waves are also neglected.

Only the half of the geometry and appropriate boundary conditions are used to assure the

axisymmetry of the system (Fig.

Due to the

axisymmetry of construction and flow, only one repeat blade passage is modeled for CFD simulation.

As the dynamics of the film is very complicated and to keep the analysis as simple as possible,

axisymmetry, steady state, and no heat transfer are assumed for both phases; thus, the change of phase for the polymer film close to the freezeline can not be examined here.

However, it should be pointed out that the

axisymmetry simulation cannot capture the surface undulations that a dry gel block undergoes while swelling (11).

Because of

axisymmetry, the principal axes in a disc usually are aligned with the r, [theta] and z directions of the disc.

The displacements of Node 1, 101 and 201 in the 1-axis direction are zero because of

axisymmetry.