### 21.2.1. Working with Transient Statistics

This section describes the generation and output of running statistics for solution variables. The available statistics are arithmetic average, minimum, maximum, root-mean-square (RMS) and standard deviation.

This follows from the same statistical theory that is used to determine statistical Reynolds Stresses, for example, in turbulence modeling.

#### 21.2.1.1. Statistic Initialization and Accumulation

Arithmetic averages, RMS values, and the minimum and maximum values are initialized using the solution values and are updated with each time step.

Standard deviations are initialized with a value of zero. The type of standard deviation that is computed is the sample standard deviation.

Whenever the standard deviation is computed, the arithmetic average and RMS statistics are also computed.

#### 21.2.1.2. Statistics as Variable Operators

Transient statistics are operators that act on variables (both conservative and hybrid values) identified in the Output Variables List. Like other variable operators, the data written to results files have names like `<variable>.<statistic>` where <variable> is the name of the specified variable and <statistic> is one of the following:

- `Trnmin` (Minimum)

- `Trnmax` (Maximum)

- `Trnavg` (Arithmetic average)

- `Trnrms` (Root mean square)

- `Trnsdv` (Standard deviation)

Tip: To output transient statistics for intermediate results, be sure to select the Output Variable Operators check box on the Transient Results tab.

Choose the Full option if all variable operators are desired.

A significant consequence of treating transient statistics as operators is that only one instance of a `<variable>.<statistic>` exists during the entire simulation. For example, even if multiple transient statistics objects containing the arithmetic average of velocity are requested, only one statistic will ever exist. The potential for specifying different start (stop) iterations for these transient statistics objects is addressed by using the earliest (latest) value specified; that is, statistics are accumulated over the largest range of timesteps possible as defined by the start and stop iterations for all transient statistics objects.

Note: If you want to re-initialize a given statistic (that is, remove the history from the statistic), you must shut down and restart the simulation with a new start (stop) iteration. This step is required to ensure that the new statistic accumulation interval is not included when searching for the earliest and latest start and stop iteration values, respectively.

#### 21.2.1.3. Using Statistics with Transient Rotor-Stator Cases

You can use transient statistics to examine the convergence of a transient/rotor stator case. This is done by obtaining averaged variable data over the time taken for a blade to move through one pitch. By comparing consecutive data sets, you can examine if a pseudo steady-state situation has been reached. Variable data averaged from integer pitch changes should be the same if convergence has been achieved.

Each of the variables that are created by the CFX-Solver can be used in CFD-Post to create plots or perform quantitative calculations.

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