- CFD, Fluid Flow, FEA, Heat/Mass Transfer

Post-processing of CFD Results (- Last update on 24-Apr-2023 -)

Post-processing activity 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 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 1 byte per channel, with 3 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. Z-buffer is the element of the computer hardware/software that is expected to manage the depth of the image (in the z-direction - into the plane of the screen).

Excerpts from ParaView tutorial manual: "the process of visualization is taking raw data and converting it to a form that is viewable and understandable to humans. This allows us to get a better cognitive understanding of our data. Scientific visualization is specifically concerned with the type of data that has a well defined representation in 2D or 3D space. Data that comes from simulation meshes and scanner data is well suited for this type of analysis. There are 3 basic steps to visualizing your data: reading, filtering and rendering. First, your data must be read into ParaView. Next, you may apply any number of filters that process the data to generate, extract or derive features from the data. Finally, a viewable image is rendered from the data."

STAR --- The output shows maximum temperature limited to 5000 in 3468 no. of cells... These messages very often indicate a problem with mesh or unreasonably high heat flux. Check the quality of it before running: Right click on your Region ---> Remove Invalid Cells ---> Preview ---> The boxes should indicate 0 problem cells found for a good mesh. Additionally, visualize where this (unrealistic) minimum or maximum temperature is taking place by making a threshold: Representations ---> Expand Volume Mesh ---> Right click on Cell Sets ---> Threshold). Create a lower threshold for unreasonable low temperature and higher threshold for unreasonably high temperatures. Note that temperature thresholds are ALWAYS in Kelvin no matter how solution units are set. **In FLUENT one can try turning secondary gradient OFF. **

**Checklist for Simulation Result**

No. | Checkpoint | Record |

01 | Has the overall mass imbalance of ≤ 0.01% achieved? | |

02 | Do the velocity and pressure profiles at inlets and outlets been checked for uniformity? | |

03 | Has the pressure drop reported for porous domains been checked with expected value as per P-Q curve? | |

04 | Has the contour plot been set as banded instead of continously coloured? | |

05 | Has the precision of labels (number of decimal places) set as per the range of data on legend? | |

06 | Has the format of number labels on legend set as per magnitude of values: float, decimal or exponential? | |

07 | Has the material properties at inlets and outlets checked to be closed to expected and/or specified values? |

- This should be small enough to have a distinct interval and high enough to keep it legible and easy to read and distinguish.
- 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.

For this sample grid, the average velocity is 1.550 [m/s], the area-weighted average velocity = 2.171 [m/s], mass-weighted average velocity = 3.251 [m/s], average temperature = 37.7 [°C], area-averaged temperature = 32.9 [°c] and mass-weighted average temperature = 27.8 [°C]

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.

- 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 turbulence parameters.
- Tabulated summary of solver setting: discretization scheme, wall function, relaxation factors
- Contour plots
- Limit the number of colour bands to 10
- Set the decimal notation to FLOAT, INTEGER or SCIENTIFIC (exponential) based on mangnitude. E.g. for values ≤ 1000, it is better to use decimal notation istead of exponential format
- Chose the unit easy to read and interpret: e.g. [K] for temperature is difficult to quicky visualize in mind. For most of us, 37 [°C] which is out body temperature or 25 [°C] which is standard ambient temperature serves as reference
- Similarly, a value of 0.075 [m] takes more time to interpret than 75 [mm]. It is quicker to deal with integers than fractions

Note that an STL file is a surface file and cannot represent a volumetric region even if the surface is a closed one. This means that if you cut through it say to generate Iso Clip, you shall get the appearance of edges rather than a solid object. Steps to generate STL surfaces are: Slice or create post-processing surfaces using edges/boundaries of original geometry in SpaceClaim ---> Save as .STL using

**Surface Groups and Clipped Surfaces **

- Chose font size ≥ 11 px, font-type should be easy to read. Calibri, Arial are few good fonts.
- Use line spacing of 1.50 or higher. For bullet points, it can be reduced to 1.25
- If paragraphs are not indented, quadruple-space the paragraphs i.e. add extra space before the pargraphs
- Keep margin of 20 ~ 25 [mm] on each side
- Add page number centred under footer
- Maintain uniformity of font sizes such as for Paragraphs, Headers, Captions...
- Use unique symbols for variables
- Do not use mix of small letters and capital letters for same variables such as u or U, p or P
- Use over-dot for mass flow rates such as ṁ
- List standard (Roman) alphabets and Greek alphabets separately
- Arrange the variable names in alphabetical order
- Keep a separate list for subscripts and superscripts
- Add page number in references, typically any documents (books, journals, theses, research papers...) having number of pages ≥ 5
- Do not use superscript of 'o' or '0' as degree symbol. All of the MS-Office programs Excel, Word and PowerPoint provide degree symbol (°).
- Do not use underline for words containing g, j, p, q, y
- Write all units within square brackets [...]
- No space should be left in front of (before) a punctuation mark
- It is better to write inline reference with page number (e.g. Sukhatme, 1998, p. 21)
- For all title of in-text citations, the first letter of every word except articles (a, an, the), prepositions (such as in, on, under...), and conjunctions (such as and, because, but, however ...) should be capitalized, unless they occur at the beginning of the title or subtitle
- In-text citations must provide the name of the author or authors and the year the source was published
- The references page should be double-spaced and lists entries in alphabetical order by the authorâ€™s last name

- Note that there is no space before any of the punctuations such as . (full stop) , (comma) : (colon) ; (semi-colon) closing ' (apostophe) and closing " (double quote)
- There are some words which spell check cannot identify as error. There are words generated due to nearby key on the kewords: e.g. [any:nay], [out:our], [neat:near], [near:hear], [below:bellow], [field:filed], [from:form], [for:fro], [its:it's], [though:through], [it is:it it]
- Check all the occurrences of 'it' and ensure 'it' and 'is' are used appropriately. Note that its and it's are not same
- Do not use &
- Full stop is used only at the end of last entry of a bulletted list.

In ANSYS FLUENT pre-post (V19 or earlier), walls and section planes are diplayed along with partition boundaries. To remove the partition boundaries - try (cxg-stitch-shells). This SCHEME command needs to be used after every new plot operation. Alternatiely, you can try TUI: "define beta yes" followed by "display set duplicate yes".

- 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".

- 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 governing 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.

Flux values are important to check the conservation of mass, momentum and energy. Note that in case there are reverse flows at the outlet, the area-weighted average values of temperature and pressure may signficantly deviate from expected value. In other words, the gain in internal energy of fluid as calculated from [mass flow rate] x [specific heat capacity] x [T_{EX} - T_{IN}] may not be equal to the heat gained by the air through the walls and the heat soures. However, this is more of a data interpolation error on finite cells at the outlet and has less implication on the global energy balance. In case of flows with heat transfer, it is important to set the temperature of fluid entering into the computational domain at the outlets (the reverse flows) close to the expected values to reduce the deviation with respect to thermodynamics energy balance described above.

The discrepancies increases with reduction in mass flow rates such as buoyancy-driven flows. Hence, it is important to move the outlet plane to a location where such reverse flows are not expected.

- 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.

**Probe Function**

**Plot HTC (Heat Transfer Coefficient) in ANSYS FLUENT**

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}

- 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.

**For circular, squre or nearly circular channels**

**For rectangular channels**

No. | Checkpoint | Record [Y/N] |

01 | Have the fluid and solid zones named as per material type say by adding air, ss, al, pl, cr (ceramics)... as suffix? | |

02 | Have appropriate prefixes been added to the boundary names as per boundary type: e.g. mf for mass-flow, vi for velocity inlets, po for pressure outlets... | |

03 | Has the mesh quality been checked for skewness and aspect ratios (for boundary layers and for freestream elements)? | |

04 | Have sliver elements been collapsed? With minimum size ~ 0.05 [mm], elements having area < 0.002 [mm^{2}] or volume 0.0001 [mm^{3}] are unreasonable. | |

05 | Have the areas of the boundaries been checked and matched with the values used to estimate boundary condition parameters? | |

06 | Have the walls been grouped into logical surface-groups easy to maintain during solution and post-processing? | |

07 | Have the inlet and outlet planes of a porous domain been assigned to separate internal patches? | |

08 | Has the basic checks been made: scale of mesh, quality, default interfaces settings (CFX may create unwanted interfaces)? | |

09 | Has the density, viscosity and thermal conductivity of fluid been correctly assigned as per operating temperature and pressure? | |

10 | Has the auto-save frequency and file name correctly defined? For runs on clusters, specify only file name without full path. | |

11 | For transient simulations, have the specific heat capacity and density of solids been correctly assigned? | |

12 | Has the relaxation factors for k, ε and turbulent viscosity been reduced to value lower than 1.0 say 0.25 or 0.50? | |

13 | Has the convergence criteria been set to low value such as 1e-05 or lesser? Run may stop early if set to higher number such as 1e-3. | |

14 | Has the discretization schemes set to first order for initial 500 ~ 1000 iterations? Gradually move to second order. | |

15 | Has the monitor points been created for global mass imbalance? | |

16 | In FLUENT, have contour plots been created? This helps avoid repeating the process on repeated set-up of different cases. | |

17 | Has a monitor for heat transfer through all walls been created? Do not include inlets and outlets. | |

18 | Has a interface of porous and fluid domains changed to internal? |

Step | Description of the Step | Activities Performed | Tool Name |

01 | Prepare the geometry | Rename the parts as per identifier such as applicable boundary condition, material or interface type | ANSYS SpaceClaim, HyperMesh, ANSA |

02 | Inspect geometry | Check for interferences, gaps, proximities and leakages to ensure volumes do not mix and merge | SpaceClaim, HyperMesh, ANSA |

03 | Create named selection or names zones / patches | To apply required mesh setting and boundary conditions - easy to filter and select in subsequent operations | SpaceClaim, HyperMesh, ANSA |

04 | Prepare geometry for pre-processor | Merge volumes, imprint surfaces, share topology (merge overlapping surfaces) | SpaceClaim |

05 | Import the CAD geometry in pre-processor (meshing) | Get boundary mesh and required refinement at curvatures | FLUENT Mesher |

06 | Correct surface mesh for topological and quality issues | Intersections, proximities, leakages, skewed cells, high aspect ratio (sliver elements) | FLUENT Mesher |

07 | Define meshing parameters | Global mesh controls, local mesh controls, boundary layer controls | FLUENT Mesher |

08 | Compute volume | Regenerate volumes for fluid and solid zones, ensure each volume is correctly identified | FLUENT Mesher |

09 | Generate volume mesh | Check quality of volume mesh: skewness (≤ 0.90), orthogonality (≥ 0.10) and aspect ratio (≤ 50) | FLUENT Mesher |

10 | Improve mesh quality | Use mesh improvement tools (move and merge nodes, refine mesh) to meet required target | FLUENT Mesher |

11 | Export mesh into solver format and read into pre-processor | Check the mesh, scale into metric units | FLUENT Pre-Post |

12 | Apply solver settings | Define materials, boundary conditions, turbulence models, relaxation factors | FLUENT Pre-Post |

13 | Identify run-time variables | Define monitor points and planes, section planes for contours, result back-up frequency | FLUENT Pre-Post |

14 | Make runs | Monitor convergence residuals | FLUENT Solver and Cluster |

15 | Post-process result | Create contour plots, vector plots, streamlines, animations | FLUENT Pre-Post, CFD-Post |

16 | Create special plots | Overlap of contour and vectors, Iso-volumes, Import special planes for post-processing, uniformly spaced vectors | FLUENT Pre-Post, CFD-Post |

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 the contents.

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