Parameterization
MULTI-F features a 2D axisymmetric and a 3D non-axisymmetric nozzle parameterization. The parameterization should be specified in the config file using the PARAMETERIZATION= 3D keyword and assignment. However, a 2D or 3D analysis can be run using either parameterization (by specifying 2D or 3D in the model definitions in the config file). When a 3D parameterization is specified but a 2D model is run, information will be lost during the mapping used to 'downsize' the 3D non-axisymmetric nozzle. In contrast, a 2D parameterization can also be 'scaled up' to a 3D model where a 3D analysis is then run.
The figure below shows the defining elements of the internal wall geometry for the 3D non-axisymmetric nozzle. A mapping is used to 'downsize' the 3D non-axisymmetric nozzle to an equivalent 2D axisymmetric nozzle, as described below.
The 2D axisymmetric parameterization uses a B-spline to parameterize the radius of the inner wall. Wall layer thicknesses are parameterized using piecewise linear distributions. All nozzle variation occurs in the X-coordinate.
The 3D non-axisymmetric parameterizaiton uses 3 B-splines and 2 additional parameters (WALL_SHOVEL_HEIGHT and WALL_SHOVEL_START_ANGLE) to define the shape of the inner wall. The B-splines are used to parameterize the shape of the nozzle centerline and major and minor axes of vertical elliptical cross-sections as a function of X. A shovel height and starting angle are used to define how the nozzle geometry morphs from axisymmetric before the throat to a flattened 'shovel'-like shape after the throat. Wall layer thicknesses are parameterized using piecewise bilinear distributions, as a function of the X-coordinate, and the angular coordinate in the Y-Z plane. The angle = 0 ray points parallel in the direction of the positive Y-axis. Thus, nozzle variation occurs in the X- and angular coordinate in the Y-Z plane.
The centerline is ignored and set to be along the X-axis. The axisymmetric inner wall is determined to have the equivalent vertical plane cross-sectional area as that of the non-axisymmetric inner wall. Thickness distribution variation in the angular coordinate is averaged out.
The equivalent 3D nozzle geometry is simply chosen to be the same 2D axisymmetric nozzle. Thus the 3D nozzle is also axisymmetric. This mapping is useful for comparing the 3D and 2D code results since the same axisymmetric geometry is used for both.