Volume Uniformity

The uniformity of a scalar quantity is computed in a volume as:

Figure 1. EQUATION_DISPLAY
U n i f o r m i t y i n d e x  of   ϕ = 1 c | ϕ c ϕ ¯ | V c 2 | ϕ ¯ | c V c
(419)

where ϕ ¯ is the volume average of ϕ , ϕ c is the value of the selected scalar in a cell and V c is the cell volume.

When the input is a Lagrangian phase, the volume integral is:

U n i f o r m i t y i n d e x  of   ϕ = 1 p | ϕ p ϕ ¯ | V p 2 | ϕ ¯ | p V p
(420)

where ϕ p is the parcel value of the selected scalar and V p is the parcel volume.

This uniformity index [141] describes the distribution of a certain quantity in a volume. If the quantity is distributed equally, the resulting number is 1. This report is useful in applications where a uniform flow rate is desired throughout an entire volume. Heat exchangers, catalysts, and filters are examples of such applications.

See also the properties of this statistical report.