http://www.cfd-online.com/W/index.php?title=Special:Contributions/Jack1980&feed=atom&limit=50&target=Jack1980&year=&month=CFD-Wiki - User contributions [en]2016-02-07T11:14:33ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2010-12-10T15:58:00Z<p>Jack1980: /* References */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m/s. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. Because the problem is symmetric in the central vertical plane, I model only one half of the problem. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh. For the fine mesh the cell width at the NACA boundary is 1.7 mm, resulting in a wall y+ = 52±17. This permits the application of a Standard Wall Function.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 1% of the mean value.<br />
<br><br><br />
A possible improvement: The turbulence model was "k-epsilon" over the complete chordlength. Results might improve if a critical Reynold's point of Re=5E5 is set, and the model turned to "laminar" in the leading area.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2010-04-06T08:54:19Z<p>Jack1980: /* Lift Curve */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the [[Spalart-Allmaras model | Spalart-Allmaras]] turbulence model.<br />
<br><br />
<br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell structured C-grid. The chord length is 1 m. The width of the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5e5, which is the flat plate transition point.[2]<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[3] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire. (Later note: I have come to think that the presence of a stall angle has some element of luck. It turns out to be quite difficult to get one in Fluent.)<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. H. Slichting, K. Gersten, ''Boundary Layer Theory'', Springer-Verlag, Berlin/Heidelberg (2000), p. 33<br><br />
3. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2010-01-05T15:15:11Z<p>Jack1980: /* Results */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m/s. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. Because the problem is symmetric in the central vertical plane, I model only one half of the problem. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh. For the fine mesh the cell width at the NACA boundary is 1.7 mm, resulting in a wall y+ = 52±17. This permits the application of a Standard Wall Function.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 1% of the mean value.<br />
<br><br><br />
A possible improvement: The turbulence model was "k-epsilon" over the complete chordlength. Results might improve if a critical Reynold's point of Re=5E5 is set, and the model turned to "laminar" in the leading area.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to [mailto:j.h.s.debaar@gmail.com send] your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-11T10:53:25Z<p>Jack1980: </p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the [[Spalart-Allmaras model | Spalart-Allmaras]] turbulence model.<br />
<br><br />
<br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell structured C-grid. The chord length is 1 m. The width of the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5e5, which is the flat plate transition point.[2]<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[3] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. H. Slichting, K. Gersten, ''Boundary Layer Theory'', Springer-Verlag, Berlin/Heidelberg (2000), p. 33<br><br />
3. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-11T10:41:39Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the [[Spalart-Allmaras model | Spalart-Allmaras]] turbulence model.<br />
<br><br />
<br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell structured C-grid. The chord length is 1 m. The width of the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5e5, which is the flat plate transition point.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-11T10:13:46Z<p>Jack1980: /* Drag Coefficient */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the [[Spalart-Allmaras model | Spalart-Allmaras]] turbulence model.<br />
<br><br />
<br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width of the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5e5, which is the flat plate transition point.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-11T10:13:13Z<p>Jack1980: /* Drag Coefficient */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the [[Spalart-Allmaras model | Spalart-Allmaras]] turbulence model.<br />
<br><br />
<br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width of the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5e5.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T19:16:06Z<p>Jack1980: /* References */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T19:11:16Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall ''y+'' = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T19:08:57Z<p>Jack1980: </p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire2.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve3.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve3.JPGFile:Naca0012 lift curve3.JPG2009-11-10T19:08:44Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_cd_tripwire2.JPGFile:Naca0012 cd tripwire2.JPG2009-11-10T19:07:21Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T19:00:26Z<p>Jack1980: /* Lift Curve Slope */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1] Experimental results are both with and without trip wire; again the lift coefficient is less sensetive to the transition point than the drag coefficient.<br />
<br><br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:58:51Z<p>Jack1980: /* Lift Curve */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2] Because the lift coefficient is less sensitive to the transition point, the experimental data is for an airfoil without trip wire.<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:57:19Z<p>Jack1980: /* Drag Coefficient */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:56:58Z<p>Jack1980: /* Drag Coefficient */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero angle of attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
<br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:56:14Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the airfoil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
<br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:55:26Z<p>Jack1980: </p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the foil boundary is 0.02 mm. At Re = 3e6 and zero angle of attack, this results in a wall y+ = 1.3 ± 0.4, which is low enough for the turbulence model to resolve the sub layer. The mesh shown is for an angle of attack of 6 degrees.<br />
<br><br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire, which forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil. Note that the calculated drag coefficient is somewhat higher than the experimental one. Possibly, the modeled boundary layer is turbulent from the beginning, while in reality the trip wire is not at the very leading edge of the foil.<br />
<br />
<br><br />
Modeling the NACA 0012 airfoil without a trip wire is more complicated, since Fluent itself is unable to predict the point along the chord where the transition from a laminar to a turbulent boundary layer takes place. One option is to manually set this transition point at Re = 5.5e6.<br />
<br><br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the angle of attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:46:59Z<p>Jack1980: /* Lift Curve */</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the foil boundary is 0.02 mm. At Re = 3e6 this results in a wall y+ = 1.3 ± 0.4 . The mesh shown is for an Angle of Attack of 6 degrees.<br />
<br><br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire that forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil.<br />
<br><br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve2.JPG]]<br />
<br><br><br />
The lift coefficient depends on the Angle of Attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
<br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve2.JPGFile:Naca0012 lift curve2.JPG2009-11-10T18:46:24Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve.JPGFile:Naca0012 lift curve.JPG2009-11-10T18:45:23Z<p>Jack1980: uploaded a new version of "Image:Naca0012 lift curve.JPG"</p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve.JPGFile:Naca0012 lift curve.JPG2009-11-10T18:43:30Z<p>Jack1980: uploaded a new version of "Image:Naca0012 lift curve.JPG"</p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:42:05Z<p>Jack1980: </p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br><br />
== Mesh ==<br />
<br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the foil boundary is 0.02 mm. At Re = 3e6 this results in a wall y+ = 1.3 ± 0.4 . The mesh shown is for an Angle of Attack of 6 degrees.<br />
<br><br />
== Drag Coefficient ==<br />
<br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire that forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil.<br />
<br><br />
== Lift Curve ==<br />
<br />
[[Image:Naca0012 lift curve.JPG]]<br />
<br><br><br />
The lift coefficient depends on the Angle of Attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br><br />
== Lift Curve Slope ==<br />
<br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br><br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:40:17Z<p>Jack1980: </p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br />
== Mesh ==<br />
<br><br />
[[Image:Naca0012 mesh final.JPG]]<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the foil boundary is 0.02 mm. At Re = 3e6 this results in a wall y+ = 1.3 ± 0.4 . The mesh shown is for an Angle of Attack of 6 degrees.<br />
<br />
== Drag Coefficient ==<br />
<br><br />
[[Image:Naca0012 cd tripwire.JPG]]<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire that forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil.<br />
<br />
== Lift Curve ==<br />
<br><br />
[[Image:Naca0012 lift curve.JPG]]<br />
<br><br><br />
The lift coefficient depends on the Angle of Attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br />
== Lift Curve Slope ==<br />
<br><br />
[[Image:Naca0012 lift curve slope.JPG]]<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve_slope.JPGFile:Naca0012 lift curve slope.JPG2009-11-10T18:39:59Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_lift_curve.JPGFile:Naca0012 lift curve.JPG2009-11-10T18:39:28Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_cd_tripwire.JPGFile:Naca0012 cd tripwire.JPG2009-11-10T18:38:43Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Naca0012_mesh_final.JPGFile:Naca0012 mesh final.JPG2009-11-10T18:37:00Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/NACA0012_airfoilNACA0012 airfoil2009-11-10T18:36:27Z<p>Jack1980: New page: == Introduction == The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spala...</p>
<hr />
<div>== Introduction ==<br />
The NACA 0012 airfoil is widely used. The simple geometry and the large amount of wind tunnel data provide an excellent 2D validation case. For this case I use the Spalart-Allmaras turbulence model.<br />
<br />
== Mesh ==<br />
<br><br />
<br />
<br><br><br />
The mesh is a 30,000 cell C-grid. The width off the first cell at the foil boundary is 0.02 mm. At Re = 3e6 this results in a wall y+ = 1.3 ± 0.4 .<br />
<br />
== Drag Coefficient ==<br />
<br><br />
<br />
<br><br><br />
The drag coefficient at zero Angle of Attack depends on the Reynold's number. The experimental data is for an airfoil with a trip wire that forces the experimental boundary layer to be completely turbulent.[1] This corresponds to the Fluent model, which has an active turbulence model over the complete airfoil.<br />
<br />
== Lift Curve ==<br />
<br><br />
<br />
<br><br><br />
The lift coefficient depends on the Angle of Attack. For Re = 2e6 I compare the lift coefficient to experimental results.[2]<br />
<br />
== Lift Curve Slope ==<br />
<br><br />
<br />
<br><br><br />
The initial slope of the lift curve depends on the Reynold's number. Here I compare the lift curve slope to experimental results.[1]<br />
<br />
== References ==<br />
1. W. J. McCroskey, ''A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil'', NASA Technical Memorandum 10001 9 (1987) <br><br />
2. L. Lazauskus, [http://http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm NACA 0012 Lift Data]</div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-11-03T16:19:37Z<p>Jack1980: /* Results */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m/s. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. Because the problem is symmetric in the central vertical plane, I model only one half of the problem. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh. For the fine mesh the cell width at the NACA boundary is 1.7 mm, resulting in a wall y+ = 52±17. This permits the application of a Standard Wall Function.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 1% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to [mailto:j.h.s.debaar@gmail.com send] your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-11-03T16:18:42Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m/s. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. Because the problem is symmetric in the central vertical plane, I model only one half of the problem. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh. For the fine mesh the cell width at the NACA boundary is 1.7 mm, resulting in a wall y+ = 52±17. This permits the application of a Standard Wall Function.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to [mailto:j.h.s.debaar@gmail.com send] your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-11-03T16:16:56Z<p>Jack1980: /* Introduction */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m/s. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to [mailto:j.h.s.debaar@gmail.com send] your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T13:21:12Z<p>Jack1980: /* References */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to [mailto:j.h.s.debaar@gmail.com send] your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T13:20:32Z<p>Jack1980: /* References */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, ''Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries'', J. Comp. Phys. '''39''', pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, ''Assessment of the volume of fluid method for free-surface wave flow'', J. Mar. Sci. Technol. '''10''', pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please feel free to send your comment.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T13:11:40Z<p>Jack1980: /* References */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis. Please send your comment to j.h.s.debaar[at]gmail.com<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T13:11:02Z<p>Jack1980: /* References */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
[1] C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
[2] Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br><br><br />
This wiki is based on part of a draft chapter for my TU Delft master's thesis.<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T13:00:59Z<p>Jack1980: /* Appendix: Experimental Values */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==<br />
As found in Ref. 2:<br><br />
<br><br />
Chord Experiment<br><br />
0.00 0.082<br><br />
0.03 0.069<br><br />
0.06 0.049<br><br />
0.09 0.029<br><br />
0.12 0.007<br><br />
0.15 -0.007<br><br />
0.18 -0.026<br><br />
0.21 -0.043<br><br />
0.24 -0.056<br><br />
0.27 -0.072<br><br />
0.30 -0.082<br><br />
0.33 -0.095<br><br />
0.36 -0.108<br><br />
0.39 -0.115<br><br />
0.42 -0.121<br><br />
0.45 -0.128<br><br />
0.48 -0.128<br><br />
0.51 -0.118<br><br />
0.54 -0.105<br><br />
0.57 -0.092<br><br />
0.60 -0.072<br><br />
0.63 -0.056<br><br />
0.66 -0.052<br><br />
0.69 -0.046<br><br />
0.72 -0.059<br><br />
0.75 -0.049<br><br />
0.78 -0.059<br><br />
0.81 -0.049<br><br />
0.84 -0.049<br><br />
0.87 -0.046<br><br />
0.90 -0.043<br><br />
0.93 -0.049<br><br />
0.96 -0.043<br><br />
0.99 -0.023<br><br />
1.02 -0.033<br><br />
1.05 -0.033<br><br />
1.08 -0.033<br><br />
1.11 -0.023<br><br />
1.14 -0.020<br><br />
1.17 -0.010<br><br />
1.20 -0.013<br></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:52:32Z<p>Jack1980: /* Results */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br><br />
[[Image:vofnaca0024results.jpg]]<br />
<br><br><br />
I compare the calculated wave height along the profile to that from the experiment [Ref. 2]. As can be seen in the figure above, the calculated solution is quite good except at the area around a chord of roughly 0.5 m. This is a well known difficulty and is related seperation, an effect responsible for the development of bubbles – see first figure – in that area.<br />
<br><br><br />
The accuracy of the solution can be expressed by the Root Mean Squared (RMS) difference between experiment and calculation. For the coarse mesh the RMS = 0.0225, for the fine mesh it reduces to RMS = 0.0206. Since the solution becomes more accurate for the finer mesh, one can be confident that it at least part of the error could dissappear on an even finer mesh. <br />
<br><br><br />
Finally, it should be noted that the drag coefficient does not reach a steady state but appears to oscillate with a frequency of roughly 1 Hz and an amplitude of roughly 3% of the mean value.<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024results.jpgFile:Vofnaca0024results.jpg2009-10-16T12:51:33Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:47:25Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:47:02Z<p>Jack1980: /* Mesh */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br><br><br />
[[Image:vofnaca0024meshdetails.jpg]]<br><br><br />
The mesh for this problem contains 118,800 cells. The solution is time dependent. I monitor the drag coefficient on the profile to see when the problem has reached a stationary solution. I start with a flat free-surface and run the calculations on a coarse mesh. Then I use the solution of the coarse mesh as an initial solution for the fine mesh.<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024meshdetails.jpgFile:Vofnaca0024meshdetails.jpg2009-10-16T12:46:48Z<p>Jack1980: uploaded a new version of "Image:Vofnaca0024meshdetails.jpg"</p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024meshdetails.jpgFile:Vofnaca0024meshdetails.jpg2009-10-16T12:46:09Z<p>Jack1980: </p>
<hr />
<div></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:44:10Z<p>Jack1980: /* Introduction */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br><br><br />
<br />
[[Image:vofnaca0024experimentalsetup.jpg]]<br><br><br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024experimentalsetup.jpgFile:Vofnaca0024experimentalsetup.jpg2009-10-16T12:42:15Z<p>Jack1980: uploaded a new version of "Image:Vofnaca0024experimentalsetup.jpg"</p>
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<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024experimentalsetup.jpgFile:Vofnaca0024experimentalsetup.jpg2009-10-16T12:20:05Z<p>Jack1980: </p>
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<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024_results.JPGFile:Vofnaca0024 results.JPG2009-10-16T12:18:04Z<p>Jack1980: </p>
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<div></div>Jack1980http://www.cfd-online.com/Wiki/File:Vofnaca0024_experimental_setup.JPGFile:Vofnaca0024 experimental setup.JPG2009-10-16T12:17:43Z<p>Jack1980: </p>
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<div></div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:14:45Z<p>Jack1980: /* References */</p>
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<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br />
<br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br><br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:14:00Z<p>Jack1980: /* Introduction */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br />
<br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52E6. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980http://www.cfd-online.com/Wiki/Free-Surface_Piercing_NACA_0024_HydrofoilFree-Surface Piercing NACA 0024 Hydrofoil2009-10-16T12:09:36Z<p>Jack1980: /* Introduction */</p>
<hr />
<div>==Introduction==<br />
This is a validation case for a 3-dimensional Volume of Fluid [Ref. 1] method.<br />
<br />
<br />
The above picture was taken from Ref. 2. It is a photograph of the experimental setup of the surface piercing foil. It shows a NACA 0024 profile with a chord of 1.2 m, which moves horizontally through the water at a velocity of 1.27 m s-1. This situation corresponds to a Froude number of 0.37 and a Reynold’s number of 1.52x106. When the flow has evolved to a steady situation, the height of the free-surface is measured at a number of positions along the profile.<br />
<br />
==Mesh==<br />
<br />
==Results==<br />
<br />
==References==<br />
1. C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, pp. 201-225 (1981)<br />
2. Shin Hyung Rhee, Boris P. Makarov, H. Krishinan, Vladimir Ivanov, Assessment of the volume of fluid method for free-surface wave flow, J. Mar. Sci. Technol. 10, pp. 173-180 (2005)<br />
<br />
==Appendix: Experimental Values==</div>Jack1980