The friction parameter of the turbulent boundary layer over the rough surface with 2D and 3D roughness elements.
Turbulent boundary layer in pressure gradient.
Figure 1. The scheme of the turbulent flow over a rough surface (left), and the roughness elements geometry: spheres, spherical segments, conical elements (3D) and transverse rectangular roods (2D).
Figure 2. Roughness density effect on the turbulent flow in a case of 3D roughness elements: a) spheres; b) spherical segments; c) cones; d) the generalised correlation.
The mean velocity profile is given by . The roughness density parameter proposed by Dvorak (1969) is given by , where S is the total roughness area, is the whole area. The universal roughness density parameter for 3D roughness elements depends on the Dvorak's roughness density parameter , where a is the geometrical parameter defined as coefficient in the equation for the averaged roughness element height , b0 is the friction parameter of the roughness elements.
Figure 3. Roughness density effect on the turbulent flow in a case of 2D roughness elements: the experimental data of various authors are shown with symbols 1-24. The universal roughness density parameter depends on the Dvorak's parameter as follows , here f is the re-circulation zones parameter: .
The mean velocity profile parameter is given by where b1 =0.12.
To read more about the turbulent flows over rough surfaces please copy Chapter3.zip file 556K with MS Word97 doc Model of turbulent flows over rough surfaces by A P Trunev .
The constructive model of turbulence has been developed for the case of turbulent boundary layer flow in pressure gradient as follows:
where is the dynamic Reynolds number.
This model is based on three assumptions:
1) the turbulent mixing parameter c depends on the transition layer scale lt;
2) the mean velocity profile in the inner layer depends on the transition layer scales and on the dimensionless pressure gradient ;
3) the mean velocity profile in the outer region depends on the outer layer variable , where y0 is the middle position of the mixing layer, z* is the mixing layer parameter.
Figure 4. The estimated mean velocity profiles in the turbulent boundary layer in adverse pressure gradients for p+=0.00898; 0.0251 - the solid lines 1-2 accordingly, and the experimental data (symbols) by Nagano et al (1992).
The function of pressure gradient parameter estimated from the experimental data by Nagano et al (1992) for the turbulent boundary layer in adverse pressure gradients at low Reynolds number as follows
The mixing layer parameters also have been established from the experimental data and they shown to be z* =0.27, y0=H/2.
The computed mean velocity profiles together with the experimental data by Nagano et al (1992) are shown in Figure 4.
To read more about the constructive theory of turbulence copy ZIP file (261K) with MS Word2000 doc: "Theory and constants of wall turbulence" by A P Trunev.
Trunev A. P. Theory of Turbulence, Russian Academy of Sciences, Sochi, 1999.
Dvorak , F. A. Calculation of Turbulent Boundary Layer on Rough Surface in Pressure Gradient. AIAA Journal 7, 9, 1969.
Nagano, Y., Kasagi, N., Ota, T., Fujita, H., Yoshida, H. & Kumada, M. 1992 Data-Base on Turbulent Heat Transfer, Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya, DATA No. FW BL004.