5 Numerical Simulation of Taylor Vortex Flows …
51
Fig. 5.1 Geometry of
computational domain and
grid in two sections
Figure 5.1 demonstrates the calculation domain between the cylinders and the
grid in two sections.
The grid is uniform in the longitudinal and circumferential directions. Near the
surfaces of the cylinders, the grid has a concentration along the normal to these
surfaces, which makes it possible to improve the description of the velocity and
temperature gradients in these areas. The calculations were made on the grid of 57
× 361 × 57 nodes (along the radius, in the circumferential direction and along the
axis of the cylinders).
The adhesion conditions in accordance with the given cylinder rotation speed are
set on the surface of the cylinders; the given temperature is fixed. The periodicity
conditions are set along the axis of the cylinders on the edges of the computational
domain. In this case, the gas-dynamic parameters for both edges at the two extreme
layers are replaced by the values of the parameters in the inner layers from the other
edge.
The calculations were made on the multiprocessor computing machinery, and
parallelization was made with the help of the geometric decomposition of the
computational domain.
5.3 Results of the Calculations
Let us examine the results of the numerical simulation using the example of calculating the flow between the endless cylinders: The radius of the inner cylinder is r =
1, and the radius of the outer cylinder is R = 1.5. The simulation calculates only a part
of the endless cylinders: This is a section along the axis for the L length. Hereinafter,
the L parameter is named the given periodicity size.
In the first variant of the calculations, the solution is found by the relaxation
method from the initially given plane flow with a discontinuity in speed in the middle
51
Fig. 5.1 Geometry of
computational domain and
grid in two sections
Figure 5.1 demonstrates the calculation domain between the cylinders and the
grid in two sections.
The grid is uniform in the longitudinal and circumferential directions. Near the
surfaces of the cylinders, the grid has a concentration along the normal to these
surfaces, which makes it possible to improve the description of the velocity and
temperature gradients in these areas. The calculations were made on the grid of 57
× 361 × 57 nodes (along the radius, in the circumferential direction and along the
axis of the cylinders).
The adhesion conditions in accordance with the given cylinder rotation speed are
set on the surface of the cylinders; the given temperature is fixed. The periodicity
conditions are set along the axis of the cylinders on the edges of the computational
domain. In this case, the gas-dynamic parameters for both edges at the two extreme
layers are replaced by the values of the parameters in the inner layers from the other
edge.
The calculations were made on the multiprocessor computing machinery, and
parallelization was made with the help of the geometric decomposition of the
computational domain.
5.3 Results of the Calculations
Let us examine the results of the numerical simulation using the example of calculating the flow between the endless cylinders: The radius of the inner cylinder is r =
1, and the radius of the outer cylinder is R = 1.5. The simulation calculates only a part
of the endless cylinders: This is a section along the axis for the L length. Hereinafter,
the L parameter is named the given periodicity size.
In the first variant of the calculations, the solution is found by the relaxation
method from the initially given plane flow with a discontinuity in speed in the middle