BSA Flow Software Installation and User's Guide - CSI

1
=
N
Mean D mean ui
(7-31)
N
∑ − N 1
i=
0
∑ −1
i=
0
( )
2
Variance σ = Di
− Dmean
(7-32)
2
RMS σ = σ
(7-33)
Table 7-3: Formulas for estimating diameter moments
7.9.3 Statistical data acquisisiton stop criteria from LDA data
Formulas:
Derived quantities:
Confidence limits:
This document describes the algorithms employed in the software.
A crucial condition for employing the stop criteria is that the velocity
samples are statistically independent. To fulfil this, the sampling interval
must be larger than twice the integral time scale τI. A method for
determination of τI is described in the last section of this document.
1 st order moment
∑η iU
i
µ u ≅ U =
(7-34)
(Mean) ∑η
i
2 nd order moment
(Variance)
σ
2
u
2
i ( U i − U)
∑ i
2
∑η 2
≅ u =
(7-35)
η
For transit time weighting the weights ηi will equal the transit time for the
sample in question, while they will equal one for simple arithmetic statistics.
Other weighting schemes exist but will not be discussed here, so in the
following the symbol η is replaced by t for transit time.
RMS
Based on formulas from the following paper:
2
σ u ≅ u
(7-36)
Benedict & Gould: ”Uncertainty estimates for any turbulence statistics”,
Proceedings of the 8 th international symposium on applications of laser
techniques to fluid mechanics, Lisbon, Portugal, 1996, Paper 36.1
Statistic
U
2
u
Assuming normal
distribution
u 2
N
2
2 ( u )
N
2
Valid for any distribution
BSA Flow Software:Reference guide 7-101
u 2
N
u
4 −
u
N
2
2
(7-37)
(7-38)