BSA Flow Software Installation and User's Guide - CSI

7.8 Optical transform
7.8.1 General 3D setup
The non-cartesian velocity components (u1, u2, u3) are transformed to
cartesian coordinates (u, v, w) using the transformation matrix C:
⎧ u ⎫ ⎧C
C C
⎪ ⎪ ⎪
⎨ v ⎬ = ⎨C
C C
⎪ ⎪ ⎪
⎩⎪
w⎭⎪
⎩⎪
C C C
11 12 13
21 22 23
31 32 33
⎫ ⎧ u1
⎫
⎪ ⎪ ⎪
⎬ ⋅ ⎨ u 2 ⎬
⎪ ⎪ ⎪
⎭⎪
⎩⎪
u 3 ⎭⎪
A typical 3-D LDA setup requiring coordinate transformation is depicted in
Figure 7-73, where 3-dimensional velocity measurements are performed
with a 2-D probe positioned at off-axis angle α1 and a 1-D probe positioned
at off-axis angle α2.
2-D Probe
1-D Probe
u3 u2 α α1 2
Figure 7-73 Typical configuration of a 3-D LDA system.
(7-18)
The velocities actually measured in Figure 7-73 are u1, u2 and u3, but the
velocities desired are in the directions u, v and w. While u1 corresponds to u
directly, v and w must be calculated from u2 and u3 knowing the angles α1
and α2.
7-96 BSA Flow Software: Reference guide
v
u 1
u
w