壁面摩擦系数与第一层网格高度
作者：互联网
1. 第一层网格节点到壁面距离
1.1 雷诺数计算：
\[Re=\frac{\rho u d}{\mu} \]1.2 壁面摩擦系数计算：
更多公式参考http://www.cfd-online.com/Wiki/Skin_friction_coeffcient
The skin friction coefficient, \(C_{f}\), is defined by:
\[C_{f} \equiv \frac{\tau_{w}}{\frac{1}{2} \rho U_{\infty}^{2}} \]Where \(\tau_{w}\) is the local wall shear stress, \(\rho\) is the fluid density and \(U_{\infty}\) is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet). For a turbulent boundary layer several approximation formulas for the local skin friction for a flat plate can be used:
1/7 power law:
\(1 / 7\) power law with experimental calibration (equation \(21.12\) in [3]):
\[C_{f}=0.0592 R e_{x}^{-1 / 5} \text { for } 5 \cdot 10^{5}<R e_{x}<10^{7} \]Schlichting (equation \(21.16\) footnote in [3])
\[C_{f}=\left[2 \log _{10}\left(R e_{x}\right)-0.65\right]^{-2.3} \quad \text { for } \quad R e_{x}<10^{9} \]Schultz-Grunov (equation 21.19a in [3]):
\[C_{f}=0.370\left[\log _{10}\left(R e_{x}\right)\right]^{-2.584} \](equation 38 in [1]):
\[1.0 / C_{f}^{1 / 2}=1.7+4.15 \log _{10}\left(R e_{x} C_{f}\right) \]The following skin friction formulas are extracted from [2],p.19. Proper reference needed:
Prandtl (1927):
Telfer (1927):
\[C_{f}=0.34 R e_{x}^{-1 / 3}+0.0012 \]Prandtl-Schlichting (1932):
\[C_{f}=0.455\left[\log _{10}\left(R e_{x}\right)\right]^{-2.58} \]Schoenherr (1932):
\[C_{f}=0.0586\left[\log _{10}\left(R e_{x} C_{f}\right)\right]^{-2} \]Schultz-Grunov (1940):
\[C_{f}=0.427\left[\log _{10}\left(R e_{x}\right)-0.407\right]^{-2.64} \]Kempf-Karman (1951):
\[C_{f}=0.055 R e_{x}^{-0.182} \]Lap-Troost (1952):
\[C_{f}=0.0648\left[\log _{10}\left(R e_{x} C_{f}^{0.5}\right)-0.9526\right]^{-2} \]Landweber (1953):
\[C_{f}=0.0816\left[\log _{10}\left(R e_{x}\right)-1.703\right]^{-2} \]Hughes (1954):
\[C_{f}=0.067\left[\log _{10}\left(R e_{x}\right)-2\right]^{-2} \]Wieghard (1955):
\[C_{f}=0.52\left[\log _{10}\left(R e_{x}\right)\right]^{-2.685} \]ITTC (1957):
\[C_{f}=0.075\left[\log _{10}\left(R e_{x}\right)-2\right]^{-2} \]Gadd (1967):
\[C_{f}=0.0113\left[\log _{10}\left(R e_{x}\right)-3.7\right]^{-1.15} \]Granville (1977):
\[C_{f}=0.0776\left[\log _{10}\left(R e_{x}\right)-1.88\right]^{-2}+60 R_{x}^{-1} \]Date Turnock (1999):
\[C_{f}=\left[4.06 \log _{10}\left(R e_{x} C_{f}\right)-0.729\right]^{-2} \]References
- von Karman, Theodore (1934), "Turbulence and Skin Friction", J. of the Aeronautical Sciences, Vol. 1, No 1, 1934, pp. 1-20.
- Schlichting, Hermann (1979), Boundary Layer Theory, ISBN 0-07-055334-3, 7th Edition.
1.3 计算壁面切应力
\[\tau_w=(\frac{1}{2}\rho U^2)C_f \]1.4 计算壁面摩擦速度
\[u_\tau=\sqrt{\frac{\tau_w}{\rho}} \]1.5 无量纲距离
\[y^+=\frac{u_\tau y}{\nu}=\frac{\rho u_\tau y}{\nu}=Re_\tau \]标签：10,壁面,frac,log,tau,网格,摩擦系数,right,left 来源： https://www.cnblogs.com/baowee/p/16036385.html