Postprocessing of CFD Results
Extracting Engineering Information from CFD Results
Postprocessing activty includes generation of detailed report with the help of quantitative data, qualitative data, contour plots, vector plots, streamlines, areaaverage values, massaverage values, pressure coefficient, lift coefficient, centre of pressure. One of the commonly used term in postprocessing 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 2^{N} 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 2^{8} = 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.
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 postprocessing interpolation on coarse mesh. As theoretically explained, tangent to streamlines gives direction of velocity field at that point.
Contour Plot
Contour plots are "colouredband" 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.
Isosurfaces
Isosurfaces are surface or planes with constant value of a particular variable. CFXpost has feature to create interactively, same feature is available in FLUENT through Isosurface option. Hence, to create a plane parallel to XY plane, Z value will remain constant. Isosurfaces are also useful to visualize the effect of one variable on any other variable over the entire domain.
Massweighted or Areaweighted?
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 "areaweighted average" or "massweighted average" feature available in the postprocessing tools. But, the choice of areaweighting or massweighting should be based on the gradients of the chosen field variable. For example, to estimate average temperature at a given section for internal flow, massweighted option is the correct method as explained below.
In the pipe flow example above, for calculation of temperature at the planes shown by dahsed lines, areaweighted option may not give the correct result as it is a function of mesh size near wall. In the example below, areaweighted 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.
Separation and Reattachment
There are few postprocessing 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 reattachment, 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 backfacing step.

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 Equiangle 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

Postprocessing
 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".

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 turbomachines uses many nondimensional 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.
Cell by cell data: A histogram can be generated in ANSYS FLUENT to check cell data. For example, CFL number is important in transient simulations. CFL number can be checked by postprocessing operations: Results → Plots → Histogram → Set Up... → Select Velocity... under Histogram of → Select Cell Courant Number from the Velocity... category → Set the value for Divisions to desired value say 50, 100 or 200 → Click Plot.
Flux Values
 The mass flow rate through a boundary is computed by summing the [dot product of the density × the velocity vector] and the area projections over the faces of the zone.
 The total moment vector about a specified center of action is computed by summing the [cross products of the pressure and viscous force vectors] for each face with the moment vector.
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) / A_{REF}
ForceMomentum 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 = (Fx^{2}/Fy)*x + Fy*x
 Hence, x = Mz/(Fx^{2}/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.