The Type setting has the following options:

The Title setting specifies a title for the Chart object. Clear the Display Title check box if you don’t require a chart title.

The Caption is the description of the Chart object that appears in the report.

The Fast Fourier Transform check box can be selected only for Transient or Sequence charts. When the Fast Fourier Transform check box is selected, the following options are available:

 

12.16.1.1.4.1. Fast Fourier Transform (FFT) Theory

When interpreting time-sequence data from a transient solution, it is often useful to look at the data's frequency attributes. For instance, you may want to determine the major vortex-shedding frequency from the time-history of the drag force on a body recorded during a simulation, or you may want to compute the frequency distribution of static pressure data recorded at a particular location on a body surface. Similarly, you may need to compute the frequency distribution of turbulent kinetic energy using data for fluctuating velocity components.

To interpret some of these time-dependent data, you need to perform Fourier transform analysis. The Fourier transform enables you to take any time-dependent data and resolve it into an equivalent summation of sinusoids.

The CFD-Post FFT module assumes that the input data have been sampled at equal intervals and are consecutive (in the order of increasing time).

The lowest non-zero frequency that the FFT module can pick up, , is given by , where is the total number of samples, and is the sampling interval (or timestep size). If the sampled sequence contains frequencies lower than this, these frequencies will be aliased into higher frequencies.

The highest frequency that the FFT module can pick up, , is given by . Note that the floor function has been applied to to round it down to the nearest integer. Note that, when is even, .

The value at zero frequency represents the mean value. The mean value can be taken out of the plot by selecting Subtract mean check box.

 

12.16.1.1.4.1.1. Windowing in Fast Fourier Transforms

The discrete FFT algorithm is based on the assumption that the time-sequence data passed to the FFT corresponds to a single period of a periodically repeating signal. Because in most situations the first and the last data points will not coincide, the repeating signal implied in the assumption can have a large discontinuity. The large discontinuity produces high-frequency components in the resulting Fourier modes, causing an aliasing error. You can condition the input signal before the transform by "windowing" it, in order to avoid this problem.

Suppose there are consecutive discrete (time-sequence) data that are sampled with a constant interval :

(12–43)

Windowing is done by multiplying the original input data () by a window function :

(12–44)

There are four different window functions:

Hamming's window:

(12–45)

Hanning's window:

(12–46)

Barlett's window:

(12–47)

Blackman's window:

(12–48)

These window functions preserve 3/4 of the original data, affecting only 1/4 of the data the ends.

 

12.16.1.1.4.1.2. Using Fast Fourier Transforms

The Fourier transform utility enables you to compute the Fourier transform of a signal, , a real-valued function, from a finite number of its sampled points.

For a periodic set of sampled points, , the discrete Fourier transform expresses the signal as a finite trigonometric series:

(12–49)

where the series coefficients are computed as

(12–50)

The previous two equations form a Fourier transform pair that enables you to determine one from the other.

Note that when you vary from 0 to in Equation 12–49 or Equation 12–50, the following is true:

• and form a complex conjugate pair.

• The value at is unique and corresponds to zero frequency.

• When is even, the range of index corresponds to positive frequencies, and the range of index corresponds to negative frequencies. The frequency at , called the Nyquist frequency, is a unique value.

• When is odd, the range of index corresponds to positive frequencies, and the range of index corresponds to negative frequencies. In this case, the Nyquist frequency does not exist.

For the actual calculation of the transforms, the CFD-Post adopts the Fast Fourier transform (FFT) algorithm, which significantly reduces operation counts in comparison to the direct transform. Specifically, CFD-Post uses the FFT algorithm from the Intel Math Kernel Library. This FFT algorithm allows for the processing of an N-point FFT where N can be even or odd.

Performing a refresh means re-reading files; therefore refreshing data from a series of files (such as transient files for a transient case) is potentially a time-consuming operation. If necessary, CFD-Post automatically performs a refresh of all charts when printing a chart and when generating or refreshing a report. At other times, you have control over when to perform a "refresh" of the data. When the General tab is set to create an XY transient or sequence chart, settings appear that control how charts are refreshed:

At the top of the Data Series tab is a list of the data series for the chart. The icons beside the list enable you to:

Corresponding functions are available when you right-click a data series name.

The fields in the Data Source area become enabled after you create an initial series.

[Name]
Velocity Profile

[Data]
 Z [ m ],Velocity [ m s^-1 ]
-0.10000000,4.53693390
-0.09797980,4.54303789
-0.09595960,4.54667473
-0.09393939,4.54347515
-0.09191919,4.54762697
...

The File Variable Selection settings are available when you are defining a data series from a file. They indicate which data, within the selected file, is to be used to define the data series.

Section Name is used to select a section of data from the file. This setting does not appear if there is only one section of data in the data source file.

X Axis Variable and Y Axis Variable specify which two columns of data are to be used to generate a chart line.

The Custom Data Selection Controls settings are available when you are defining a data series from a location or expression, with General > Fast Fourier Transform not selected.

When selected, the Custom Data Selection controls enable you to override the settings on the X Axis and Y Axis tabs for each series individually. See Chart: X Axis Tab and Chart: Y Axis Tab for more details on what each setting means.

You can also specify the use of Hybrid or Conservative values or to use the absolute value of data points. For help on the use of Hybrid or Conservative values, see Hybrid and Conservative Variable Values.

Other available settings depend on the chart type; see X Axis Data Selection for details.

The Monitor Variable Selection settings are available when you are defining a data series from monitor data or solution residuals.

Set Source to one of:

X Axis Variable and Y Axis Variable specify which variables are to be used to generate a chart line.

Take absolute value of data points controls whether the values of data points are always positive.

The Data Selection settings control which variable is used as the data source and how the data is processed:

When General > Type is XY or Histogram, the Variable field can be set to any variable. Hybrid vs. Conservative sets how conservation equations for the boundary control volumes are solved. See Hybrid and Conservative Variable Values for details. Take absolute value of data points controls whether the values of data points are always positive.

When General > Type is XY — Transient or Sequence, the Expression field can be set to expressions provided in CFD-Post or to expressions that you have defined. For example, you could use this option to plot areaAve(Temperature)@Outlet as a function of time.

When General > Type is XY — Transient or Sequence and Fast Fourier Transform is selected, you can define an X Function.

 

12.16.1.3.1.1. Specifying an X Function

The options for the X Function are related to the discrete frequencies at which the Fourier coefficients are computed. You can apply the following specific analytic functions. Because the corresponding definitions for the y-axis functions include contributions from both elements of a complex conjugate pair (i.e. and ), definitions are provided for when is even, and when is odd.

Frequency is defined as:

(12–51)

where N is the number of data points used in the FFT.

Strouhal Number is the nondimensionalized version of the frequency defined in the equation for Frequency:

(12–52)

where and are the reference length and velocity scales. Note that you can set and by clicking Reference Values on the General tab.

Fourier Mode is the index in

(12–53)

and/or

(12–54)

which represents the nth or kth term in the Fourier transform of the signal.

Octave Band Full is a range of discrete frequency bands for different octaves within the threshold of hearing. The range of each octave band is double to that of the previous band (see Table 12.3: Octave Band Frequencies and Weightings).

One Third Full is a range of discrete frequency bands within the threshold of hearing. Here the range of each band is one-third of an octave, meaning that there are three times as many bands for the same frequency range.

Table 12.3: Octave Band Frequencies and Weightings

Lower Freq. (Hz)	Center Freq. (Hz)	Upper Freq. (Hz)	dB A	dB B	dB C
11	16	22	-56.7	–28.5	-8.5
22	31.5	45	-39.4	-17.1	-3.0
45	63	90	-26.2	-9.3	-0.8
90	125	180	-16.1	-4.2	-0.2
180	250	355	-8.6	-1.3	0.0
355	500	710	-3.2	-0.3	0.0
710	1000	1400	0.0	0.0	0.0
1400	2000	2800	1.2	-0.1	-0.2
2800	4000	5600	1.0	-0.7	-0.8
5600	8000	11200	-1.1	-2.9	-3.0
11200	16000	22400	-6.6	-8.4	-8.5

These controls are enabled when the chart type is Histogram.

If Category Divisions are set to Automatic, you are able to specify the Number of Divisions. If Category Divisions are set to User Defined, you are able to specify the Division Values.

The Division Values field enables you to type points where you want to create histogram boundaries. You can either enter user-defined category divisions by typing a comma-separated ordered list directly into the Division Values field, or click More   to open up an editor for the division values (which includes the ability to set the values in a particular unit). If you use the editor, then the values do not need to be entered in order as you will be offered the chance to sort the values when you close the editor.

You can choose to Determine ranges automatically or to set Min and Max values. To get the range for the Min and Max values, click Get range from existing chart  .

The default X-axis scale is linear but can be set to be a Logarithmic scale. Select Invert Axis to reverse the direction of the scale.

You can have axis numbers set automatically or choose the format yourself:

You can choose to Use data for axis labels, or to use a Custom Label.

When the General tab is set to create an XY or an XY transient or sequence chart, the Data Selection includes a Variable that you can set; you can also control whether the boundary data is Hybrid or Conservative, and whether or not to take the absolute value of data points.

When the General tab is set to create a histogram, the Y axis Value can be:

The Weighting can be:

The weighting setting changes the shape of the histogram by removing mesh dependencies. For example, if mesh density varies along a line, counts are biased towards areas of higher density; the Geometrical setting removes that bias.

When the General tab is set to Fast Fourier Transform, a Y Function field appears where you can choose one of the following settings. The definitions are provided for when is even, and when is odd. The definitions include contributions from both elements of a complex conjugate pair: and .

Figure 12.2: A-, B-, and C-weighting Functions

On the General tab, if Fast Fourier Transform is selected, the line type is controlled by the FFT Line Type setting, otherwise, the line type is controlled by the Line Type setting; the applicable setting is shown.

Both the FFT Line Type and Line Type settings have the following options:

When Fill Area is selected, you can choose to have a fill color generated automatically or at all times (Always On). The Automatic setting generates a fill when the chart's General tab's Type is set to Histogram.

The legend is the text that you entered in the Name field on the Data Series tab displayed beside the line color that represents its data source.

When Display Legend is selected, the chart's legend appears, either Outside Chart or Inside Chart.

When Outside Chart is selected, set the Location and Justification of the legend:

When Inside Chart is selected, the legend is displayed in a box that appears on the chart. Use the X Justification and Y Justification controls to locate a fixed-size box at standard locations, optionally using Width/Height to change the size of the box. Alternatively, set X Justification and Y Justification to None so that you can use Position and Width/Height to control the size and position of the box exactly.

Here you set the width of the line and the size of the symbol (if any) that you defined on the Line Display tab. These sizes apply to all lines and all symbols (you cannot set sizes for individual lines or symbols).

Here is where you control the font type and size of the Title (which you defined on the General tab), the Axes Titles, the Axes values, and the Legend.

Here is where you configure the background grid (if any) and the thickness of its major and minor lines.