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Post-processing of CFD Results

Extracting Engineering Information from CFD Results

Post-processing activty includes generation of detailed report with the help of quantitative data, qualitative data, contour plots, vector plots, streamlines, area-average values, mass-average values, pressure coefficient, lift coefficient, centre of pressure. One of the commonly used term in post-processing and visualization technique is 'rendering'. This refers to the process of converting underlying mathematical representation of solid geometry into visual forms. The screen is represented by a 2D array of locations called pixels. One of 2N intensities or colors are associated with each pixel, where N is the number of bits per pixel. Greyscale typically has one byte per pixel, for 28 = 256 intensities. Color often requires one byte per channel, with three color channels per pixel: red, green, and blue. An "image map" or 'bitmap' or " frame buffer" is a array or variable to store color data.


Vector Plot

A vector plot is qualitative representation of spatial magnitude. The only limitation is that it can be drawn plane or a 3D twisted surface. For any vector or contour plot, one of the important consideration is to selection the number of colour bands (also called the legend).
  • This should be small enough to have a distinct interval and high enough to keep it legible and easy to read and distiguish.
  • A value between 8 and 16 normally is a good choice.
  • Note the example below has 20 bands (with 21 values) and how cluttered it looks. There are 2 colours very close in intensity and cannot be easily distinguished looking at the plots.

Vector Plot

Streamlines

Streamlines are very good representation of velocity field, at least to beginners in CFD. It is closely related to velocity vector and any inconsistency may arise only because of post-processing interpolation on coarse mesh. As theoretically explained, tangent to streamlines gives direction of velocity field at that point.

Streamline Plot

Contour Plot

Contour plots are "coloured-band" plots of any variable where range of value is represented by a single colour band. This is good presentation of information in both the qualitative and quantitative format.

Contour Plot

Iso-surfaces

Iso-surfaces are surface or planes with constant value of a particular variable. CFX-post has feature to create interactively, same feature is available in FLUENT through Iso-surface option. Hence, to create a plane parallel to X-Y plane, Z value will remain constant. Iso-surfaces are also useful to visualize the effect of one variable on any other variable over the entire domain.

Mass-weighted or Area-weighted?

The features explained above are more qualitative in nature and may not be used directly in design calculatios which usually require a discrete value. This can be obtained by "area-weighted average" or "mass-weighted average" feature available in the post-processing tools. But, the choice of area-weighting or mass-weighting should be based on the gradients of the chosen field variable. For example, to estimate average temperature at a given section for internal flow, mass-weighted option is the correct method as explained below.

area-weighted averaging recommendation

In the pipe flow example above, for calculation of temperature at the planes shown by dahsed lines, area-weighted option may not give the correct result as it is a function of mesh size near wall. In the example below, area-weighted average velocity at inlet and the two outlets will not be in the ratio of flow areas even though flow is assumed incompressible. This is because of the error in integration or summation due to sharp gradient of velocity in the boundary layer and mesh may not be fine enough to capture it. Also note that the narrower sections have 4 boundary layers as compared to 2 boundary laters in inlet section.

area-weighted averaging error


Separation and Re-attachment

There are few post-processing operations which require not only a good insight into the flow physics but experience as well. For example, the estimation of separation length (the reattachment point) needs careful evaluation. There are many methods, one recommended method can be generation of y+ plot. By virtue of re-attachment, the velocity necessarily has to go close to zero and hence y+ or shear stress will follow the same variation. The following image represents y+ plot for flow over back-facing step.

Re-attachment point


  • General Recommendations for Report Preparation

    Pre and Solver
    • One picture or sketch (preferably an isometric or sectional view) representing the extent, origin and axes of computation domain, boundaries and moving walls (if any).
    • Sectional view of mesh in area of interest highlighting the boundary layer, growth and orthogonality.
    • Mesh quality matrix, worst values of mesh Equi-angle skewness and aspect ratios.
    • The description of material properties and its thermodynamic behaviour.
    • Tabulated summary of boundary conditions and tubulence parameters.
    • Tabulated summary of solver setting: discretization scheme, wall function, relaxation factors
  • Post-processing
    • Use same lower and upper limits of legends for contour as well as vector plots
    • Use decimal notation if variables are > 0.01. Even though scientific notations can be used, it is easier for human mind to read numbers as compared to exponential notations.
    • Use number of significant digits judiciously. For example, for most of the industrial applications, it is not important to specify velocity to the 1/10 of mm/s. The number of significant digit is also dependent on the units chosen. For example, 3 decimal places for [Pa] such as 1045.368 [Pa] is irrelevant where as it is a need if unit chosen is [bar] or [kPa] such as 1.034 [kPa]. Followings are more information about "number of significant figures or digits".

      Number Significant Digits

  • Recommendations for Rotating Reference frame
    • Clearly specify the rotating and stationary domain, direction of rotation , location of the interfaces.
    • Show the overlapping view of meshes at the interfaces, if not 1:1.
    • Mention the location of the place used to estimate pressure heads developed by the machine. It is further recommended to use 3 or more close locations on the upstream as well as downstream sides to estimate the grand average values of the pressure.
    • The physics governign performance of turbo-machines uses many non-dimensional coefficients. Include the plots of important performance parameters such as pressure coefficients on the blades
    • On all the plots dealing with flow passage and blades, explicitly mention the suction and pressure sides.

Centre of Pressure

Centre of pressure - CofP (which depends on the location of each cell and pressure force acting on it) is not same as coefficient of pressure - Cp (which depends on the total pressure force and a arbitrarily chosen reference area. The center of pressure is the point on a body where the total sum of a pressure field acts, causing a force and no moment about that point.

CofP = ∫(x * P.dA)/∫(P.dA) or discretely as ∑(xi * π *Ai)/∑(π * Ai), Cp = ∫(P dA) / AREF

Force-Momentum equation about origin:
  • Let {F} = (Fx, Fy, Fz) and {M} = (Mx, My, Mz)
  • Mx = 0*x + Fz*y - Fy*z
  • My = -Fz*x + 0 *y + Fx*z
  • Mz = Fy*x - Fx*y + 0*z
  • As diagonal of the [F] matrix in {M} = [F] {x} is zero, they are singular (i.e. one or more equations are not independent). inv(F) does not exist and det[F] = 0.
  • Unit vector in force direction {f} = {F}/|F| = (Fx, Fy, Fz)/|F| where |F| = sqrt(Fx*Fx + Fy*Fy + Fz*Fz)
  • Moment parallel to F (pure couple) can be calculated by taking component of {M} along {f}. Thus: {MF} = [{M}.{F}] {f} = (Fx, Fy, Fz) * (Mx*Fx + My*Fy + Mz*Fz) / |F| / |F|
  • We need to find a location about which Mz = 0 then using the equations Mz = Fy*x - Fx*y + 0*z we get 0 = Fx*x - Fy*y. Thus, y = (Fx*x)/Fy
  • Mz = -Fx *y + Fy * x and y = (Fx*x)/Fy. Thus: Mz = -Fx*(Fx*x)/Fy) + Fy*x = (-Fx2/Fy)*x + Fy*x
  • Hence, x = Mz/(-Fx2/Fy + Fy)
  • Note: The equations used to calculate the CofP location cannot be used to calculate the moment at the CofP. The moments in those equations are the moments about the origin.
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The content on CFDyna.com is being constantly refined and improvised with on-the-job experience, testing, and training. Examples might be simplified to improve insight into the physics and basic understanding. Linked pages, articles, references, and examples are constantly reviewed to reduce errors, but we cannot warrant full correctness of all content.