From 99a39fee888507ba50e2f1e566087a52593691a3 Mon Sep 17 00:00:00 2001
From: "Singh, Atul" <atul.singh@tuwien.ac.at>
Date: Wed, 15 Jan 2025 16:22:09 +0100
Subject: [PATCH] 10fluent y+estimation

---
 .../fluent_images/wallfunc-applicable.png     | Bin 0 -> 120184 bytes
 docs/images/fluent_images/ypluscalc.png       | Bin 0 -> 16344 bytes
 .../packages/Fluent/best_practices.md         |  67 +++++++++++++++++-
 3 files changed, 65 insertions(+), 2 deletions(-)
 create mode 100644 docs/images/fluent_images/wallfunc-applicable.png
 create mode 100644 docs/images/fluent_images/ypluscalc.png

diff --git a/docs/images/fluent_images/wallfunc-applicable.png b/docs/images/fluent_images/wallfunc-applicable.png
new file mode 100644
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diff --git a/docs/images/fluent_images/ypluscalc.png b/docs/images/fluent_images/ypluscalc.png
new file mode 100644
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diff --git a/docs/software/packages/Fluent/best_practices.md b/docs/software/packages/Fluent/best_practices.md
index 73faf31..703718c 100644
--- a/docs/software/packages/Fluent/best_practices.md
+++ b/docs/software/packages/Fluent/best_practices.md
@@ -92,7 +92,6 @@ Increasing computatinal cost of each turbulent approach in Fluent.
 
 Using non-dimensional velocity and non-dimensional distance from the wall results in a predictable boundary layer profile for a wide range of flows. 
 
-
 - For CFD, the most important are the viscous sublayer, immediately adjacent to the wall and log-layer, slightly further away from the wall. 
 - Different turbulent models require different inputs depending on whether the simulation eneds to resolve teh viscous sublayer with the mesh. 
 - Using wall functions to involve utilizing predictable dimensionless boundary layer profile shown on slides 9 & 10 to determine conditions at wall from conditions at the centroid of the wall adjacent mesh cell. 
@@ -112,4 +111,68 @@ Using non-dimensional velocity and non-dimensional distance from the wall result
 
 Red line indicates the first node wall distance reflected by y+ value. 
 
-
+## Example $y^+$ calculation 
+
+A sample $y^+$ calculation is indicated for the following smooth plate flow as follows, 
+
+![](../../../images/fluent_images/ypluscalc.png)
+
+Flow over flat plate with air at 20m/s, at a given density and viscosity. 
+
+$$
+Re = \frac{\rho V L}{\mu} = 1.4 \cdot 10^6 \\
+$$
+
+The target $y^+$, after rearranging, is 
+$$
+y^+ = \frac{\rho U_{\tau} y } {\mu}
+$$
+$$
+y = \frac{y^+ \mu}{U_{\tau} \rho}
+$$
+
+$U_{\tau}$ is now requried  which is obtained as, 
+$$
+U_{\tau} = \sqrt {\frac {\tau_{w}}{\rho}}
+$$
+
+The wall shear stress or $\tau_{w}$ can be found from the skin friction coefficient, $C_f$ as,
+$$
+\tau_w = \frac{1}{2} C_f \rho U_{\infty} ^2 
+$$
+
+For a smooth plate as shown in the figure, skin friction is obtained as 
+$$
+C_f = 0.058 Re_{l} ^ {-0.2}
+$$
+
+Re being known, will yield the $C_f$ as follows, aiming for a $y^+$ of 50,
+$$
+C_f = 0.0034
+$$
+$$
+\tau_w = \frac{1}{2} C_f \rho U_{\infty} ^2  = 0.83 (kg/ (ms^2))
+$$
+$$
+U_{\tau} = \sqrt{\frac {\tau_{w}}{\rho}} = 0.82 m/s
+$$
+$$
+y = \frac{y^+ \mu}{U_{\tau} \rho} = 9 \cdot 10^{-4} m
+$$
+
+Meaning, the very first cell next to the boundary should have the heigt of approximately 1mm. Aiming for a $y^+$ of 1, 50 will be replaced with 1 in the above formula, giving 
+$$
+y=1.8 \cdot 10^{-5}
+$$
+
+- Wall functions however also have some limitations. In some situation, such as boudnary layer separation, the boundary layer profile is not logarathmic which means that wall functions, which are based on logarithmic velocity profile, do not correctly predict the boundary layer. 
+
+![](../../../images/fluent_images/wallfunc-applicable.png)
+
+Lastly for for turbulent inlet conditions, 
+
+- Normal turbulent intensities range from 1% to 5%.
+- Default turbulent intensity value 5% is sufficient for nominal turbulence through a circular inlet, and is good estimate in absense of experimental data. 
+- For external flows, turbulent viscosity ratio of 1-10 is typically good. 
+- For internal flows, turbulent viscosity ratio of 10-100 is typically good. 
+- For fully developed pipe flow at Re=50000, the turbulent viscosity ratio is around 100. 
\ No newline at end of file
-- 
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