## CFD Example Downloads

#### Computational Fluid Dynamics Solutions

You need THREE files to view each CFD solution!

- The CFD3DViewB.exe viewing software. Download it NOW. It's the SAME viewing software for ALL the CFD solutions here so you only download this ONCE. Use at your own risk. Software is subject to change without notice.
- A Grid file that tells the viewing software about the problem domain. ONE grid file may be used for SEVERAL solutions. These are either *.grd files or *grid.exe compressed, self-extracting files.
- The file that contains the numerical solution data. These are either *.cfd files or *.exe compressed, self-extracting files.

Always place the grid file (*.grd) and the solution file (*.cfd) in the same directory so that you can find both with the viewing software.

#### 2D Axisymmetric Entry Flow in a Tube with Circular Cross Section

Download Self-extracting compressed file 2DCConL.exe (13.79 MB) containing the grid file (2DCCon_L3.grd) and solutions for a range of Reynolds numbers (25, 50, 100, 250, 750, 1000, 1250, 1500, 2000). This is a "long" tube (12 diameters) to illustrate how the Reynolds number affects development of the velocity profile.

#### 2D Axisymmetric Flow in a Tube with an "Orifice Plate" stenosis (k-epsilon turbulence model)

Velocity contours for a tube with an orifice plate stenosis showing the location of the vena contracta. The solution is 2-dimensional, as suggested by the figure. Below, streamlines originating at the tube inlet show the paths of fluid elements with velocity conveyed by color.

A wide range of solutions are available, each *.exe file corresponding to a specific geometry (stenosis "severity") bundled with corresponding grid file (*.grd) solutions (*.cfd) at Re = 10, 25, 50, 100, 250, 500, 1000, 2000, and 5000.

2D_CStn04A - Radius ratio 0.9 / Area ratio 0.81

2D_CStn06A - Radius ratio 0.85 / Area ratio 0.7225

2D_CStn08A - Radius ratio 0.8 / Area ratio 0.64

2D_CStn10A - Radius ratio 0.75 / Area ratio 0.5625

2D_CStn12A - Radius ratio 0.7/ Area ratio 0.49

2D_CStn14A - Radius ratio 0.65 / Area ratio 0.4225

2D_CStn16A - Radius ratio 0.6/ Area ratio 0.36

2D_CStn18A - Radius ratio 0.55/ Area ratio 0.3025

2D_CStn20A - Radius ratio 0.5/ Area ratio 0.25

2D_CStn22A - Radius ratio 0.45/ Area ratio 0.2025

2D_CStn24A - Radius ratio 0.4/ Area ratio 0.16

2D_CStn28A - Radius ratio 0.3 / Area ratio 0.09

Here are a whole lot more stenosis calculations for a range of geometries and Reynolds numbers:

2D_CStnS14_A.exe - Area ratio 1/4 / Abrupt sinusoid

2D_CStnS24_A.exe - Area ratio 2/4 / Abrupt sinusoid

2D_CStnS34_A.exe - Area ratio 3/4 / Abrupt sinusoid

2D_CStnS14_B.exe - Area ratio 1/4 / Less Abrupt Sinusoid

2D_CStnS24_B.exe - Area ratio 2/4 / Less Abrupt Sinusoid

2D_CStnS34_B.exe - Area ratio 3/4 / Less Abrupt Sinusoid

2D_CStnS14_C.exe - Area ratio 1/4 / Sinusoid

2D_CStnS24_C.exe - Area ratio 2/4 / Sinusoid

2D_CStnS34_C.exe - Area ratio 3/4 / Sinusoid

2D_CStnS14_D.exe - Area ratio 1/4 / Lazy Sinusoid

2D_CStnS24_D.exe - Area ratio 2/4 / Lazy Sinusoid

2D_CStnS34_D.exe - Area ratio 3/4 / Lazy Sinusoid

Colors and contours (above) depict the pressure field (the "gradient") in the vicinity of a relatively smooth stenosis. **Specifics **of stenosis geometry affect the severity (through the flow dynamics) -- NOT just the area or area ratio.

Here's where the turbulence is (turbulence intensity, *k-epsilon* turbulence model)

#### 3D Rectangular Conduit with 90 degree bend

Download Self-extracting compressed file RCon90.exe (15.01 MB) containing the grid file (RCon90D_20x100.grd) and solutions at Re = 500 and 1000.

Above: Flow in a rectangular conduit with a 90 degree bend, Re = 1000. Uniform velocity flow enters at lower right, exits upper left. Color represents velocity. Note higher velocity at the outside of the bend. Secondary vortices can be viewed downstream of the bend.

Pressure contours (color represents pressure also) show the high pressure region at the outside of the bend that forces the fluid elements into the curved tragectory. Download the files and watch a flow animation.

Here are LARGE versions of the problem: RCon90L_Re500.exe, RCon90L_Re1000.exe, 37.9 MB each! (*grd and *cfd zipped together)

Here are HUGE versions with k-e turbulence modeling: Rcon90Lg_Re1000T.exe, Rcon90Lg_Re2000T.exe, 71.8 MB each! (*grd and *cfd zipped together)

#### 3D Circular Conduit with 90 degree bend

Download Self-extracting compressed file CCon90.exe (15.1 MB) containing the grid file (CConB_20x100.grd) and solutions at Re = 500 and 1000.

Download Self-extracting compressed file CCon90L.exe (39.1 MB) containing the grid file (CCon90L.grd) and solutions at Re = 500 and 1000.

Pressure contours (color represents pressure also) at several cross-sectional surfaces as flow proceeds from lower right to upper left. Download the files and watch a flow animation. Re = 500.

Stopped image from a displacement flow animation for flow in a circular conduit with a 90 degree bend. Re = 500.

#### Arterial Bifurcation Models (Computations in Progress; Coming Soon)

#### 3D Circular T Bifurcation

Blood flow through bifurcations has important implications in both physiology and pathology. While the asymmetrical "T" shaped bifurcation below appears in plumbing throughout the world, it would be a poor design for a mammalian arterial bifurcation and for multiple reasons. However it affords a model to visualize **why** it's a poor design as well as to understand the intricacies of some complex flow patterns.

In these images flow enters from the left and is divided equally into the "straight" and "side" branches. The velocity field (vectors shown above) was used to create an animation (below) that depicts a well-verified curiosity; flow that has already entered into the straight branch can backtrack along the walls near the periphery of the structure and exit via the side branch. Bizarre and true.

A bifurcation flow problem like this has elements of stenosis flow (potentially with large convective accelerations) but with an added degree of freedom - the division of flow between the two branches. I once studied this problem in depth, seeking to determine whether the structure of a bifurcation itself might have some bearing on determining blood flow distribution (not much). Mammalian bifurcations appear to be structured so that blood momentum does NOT affect flow distribution in most cases. Increase the blood momentum significantly however (stenosis flow, regurgitant jets) and the potential arises for blood flow redistribution due to the local geometry of the circulation. You might end up with preferrential flow to a specific limb, lung lobe, or localized pulmonary edema e.g. due to mitral regurgitation directed towards a specific pulmonary vein.

3 dimensional flow through an asymmetrical T bifurcation:

With equal flow division into the two branches:

TBif01_Re100-500.exe Reynolds numbers 100, 250, 500

TBif01_Re1000-2000T.exe Reynolds numbers 1000, 2000 with k-epsilon turbulence model

TBif01_Re1000_NF.exe Reynolds number 1000 with no turbulence model, not converged (NF stands for not final)

With 75% of flow into the right angle side branch:

TBif01A_Re100-250.exe Reynolds numbers 100, 250

TBif01A_Re500-1000T.exe Reynolds numbers 500, 1000 with k-epsilon turbulence model

TBif01A_Re2000T.exe Reynolds numbers 2000 with k-epsilon turbulence model

With 75% of flow into the straight branch:

TBif01B_Re100-500.exe Reynolds numbers 100, 250, 500

TBif01B_Re500-1000T.exe Reynolds numbers 500, 1000 with k-epsilon turbulence model

TBif01B_Re2000T.exe Reynolds numbers 2000 with k-epsilon turbulence model

#### Rectangular T Bifurcation

NOTE: These datasets require an updated version of CFD 3DViewB.exe to view correctly. Download it NOW.

Video is at Reynolds number 1000 with 75% of the flow into the side branch. Similar to the above, the video depicts how flow that has already entered the straight branch flows upstream along the walls into a recirculation region and eventually exits the side branch. The rectangular cross-sectional geometry is a better test bed for the computations.

2 Dimensional Bifurcations (40 cells across inlet)

2DRBif40.exe Includes 25%, 50%, and 75% flow distributions into the side branch at Reynolds numbers 100, 250, 500, 1000, and 2000. k-epsilon turbulence model.

Moderate size 3 Dimensional Bifurcations (20 cells across inlet in each direction)

RBif20_25.exe 25% of flow into side branch at Reynolds numbers 100, 250, 500, 1000, and 2000. k-epsilon turbulence model.

RBif20_50.exe 50% of flow into side branch at Reynolds numbers 100, 250, 500, 1000, and 2000. k-epsilon turbulence model.

RBif20_75.exe 75% of flow into side branch at Reynolds numbers 100, 250, 500, 1000, and 2000. k-epsilon turbulence model.

Velocity contours in a rectangular T bifurcation with 75% of flow directed into the side branch; Reynolds number 500.

HUGE 3 Dimensional Bifurcations (32 cells across inlet in each direction). Only one solution in each compressed file. Each compressed file ~100MB. Not for everyday consumption!

25% flow in side branch / k-epsilon turbulence model

RBif32_25_Re100T.exe

RBif32_25_Re250T.exe

RBif32_25_Re500T.exe

RBif32_25_Re1000T.exe

RBif32_25_Re2000T.exe

50% flow in side branch / k-epsilon turbulence model

RBif32_50_Re100T.exe

RBif32_50_Re250T.exe

RBif32_50_Re500T.exe

RBif32_50_Re1000T.exe

RBif32_50_Re2000T.exe

75% flow in side branch / k-epsilon turbulence model

RBif32_75_Re100T.exe

RBif32_75_Re250T.exe

RBif32_75_Re500T.exe

RBif32_75_Re1000T.exe

RBif32_75_Re2000T.exe

Video of a displacement animation of flow entering the side branch of a T bifurcation with rectangular conduits. Reynolds number 1000 with 75% of the flow going into the side branch. k-epsilon turbulence model

#### Lid Driven Cavity

A bench comparison problem in computational fluid dynamics, these are also quite interesting to help you get the "flavor" of fluid dynamics. Conceptually these models consist of a cube or rectangular cavity where one or more of the cube walls (a "lid") moves parallel to the surface. This sets the fluid within the cavity in motion.

#### 2D Lid Driven Cavity

Download Self-extracting compressed file LDC2D40.exe containing the grid file (LDC2D40.grd) and several solutions at Re = 100, 250, 500, 1000, 2000, and 5000. These files are small, quick, (and dirty). A 40x40 grid is good accuracy and this may be all you need to get a good idea of how the solution depends on Reynold's number

Pressure contours (color for pressure also) for the 2D Lid Driven Cavity at Re = 500. The lid is drawn across the top of the square cavity, left to right. High pressure occurs at the upper right corner where there is a singularity.

Download Self-extracting compressed file LDC2D100.exe containing the grid file (LDC2D100.grd) and several solutions at Re = 100, 250, 500, 1000, 2000, and 5000. These files are medium sized. A 100x100 grid is higher accuracy; maybe a little too much information for viewing pleasure.

Above: Several velocity profiles shown for the lid driven cavity at Re = 1000. Color represents pressure. This is the higher resolution version.

Above: A snapshot several seconds into a flow animation showing how fluid moves (approximate streamlines) in the cavity. Download the file and watch it live. Color depicts pressure.

2D Lid Drivien Cavity with a 2x1 rectangular aspect ratio. Download Self-extracting compressed file LDC2DR.exe containing the grid file (2DLDCx.grd) and several solutions at Re = 100, 1000, 2000, and 5000. These files are medium sized with a 50x100 grid.

Snapshot several seconds into an animation showing fluid tragectories (streamlines) for a 2D rectangular (2x1) lid driven cavity at Re = 2000. Lid at top moves left to right generating 2 main counter-rotating vortices. Color depicts pressure. Download the files and watch it live.

#### 3D Lid Driven Cube

Download Self-extracting compressed file LDC40.exe (14.42 MB) containing the grid file (LDC40.grd) and Re = 1000 solution (LDC40_Re1000_F.cfd).

In the example, the top surface moves to the right and fluid velocity vectors are shown. Color depicts velocity magnitude.

#### 3D Skew Driven Cube

The first set of these is a cube is driven by 2 **adjacent** lids moving at 90 degrees to each other. LDC40_skew1A.exe (32.5 MB) contains the grid file (LDC40_skew.grd), and solutions at Re = 100, 250 and 500; LDC40_skew1B.exe (24.0 MB) includes the grid and Re 1000 and 2000.

The second set is a cube driven by 2 **opposiing** lids moving at 90 degrees to each other. LDC40_skew2A.exe (33.2 MB) contains the grid file (LDC40_skew2.grd), and solutions at Re = 100, 250 and 500; LDC40_skew2B.exe (24.0 MB) includes the grid and Re 1000 and 2000. (Apparently I thought this was pretty interesting.)

Grids are 40x40x40 cells.

#### 3D Asymmetrically Driven Cube

This cube is driven by just 1 lid, but at 30 degrees relative to the intrinsic (orthogonal) cube orientation

Download Self-extracting compressed file LDC40_asym.exe (24.05 MB) containing the grid file (LDC40_asym.grd), Re = 500 solution (LDC40_asym_Re500_F.cfd), and Re = 1000 solution (LDC40_asym_Re1000_F.cfd).

The fluid in this asymmetrically driven cavity has deformed (mind-boggling). Run an animation and watch how that happens by downloading the files. Color depicts velocity.

Here's a 3D rectangular LDC driven asymmetrically at Re 500 (download).