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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, ccentre of pressure...


Vector Plot

A vectorplotisaqualitativerepresentationof 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 elocityfield,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 meshes. As theoretically explained, tangent to streamlines gives direction of velocity field at that point.

Streamline Plot

Contour Plot

A contour plot is a "coloured-band" plot 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


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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