Dear Readers,

I am writing to request assistance in obtaining numeric or number format data related to turbulent flow in ducts, specifically focusing on square, rectangular, and other geometries. I require data for cases of steady, fully developed flow in the cross section of the duct, with a particular interest in cross-sectional details.

The data I am seeking should be presented in a format that includes the following parameters:

- Horizontal coordinate (x2)

- Vertical coordinate (x3)

- Flow properties: main velocity (U), secondary velocities (V and W), turbulent kinetic energy (K), turbulent viscosity, turbulence dissipation rate (e), turbulent stresses (shear and normal), pressure distribution in the cross section, boundary shear stress, and flow parameters (longitudinal pressure gradients, duct geometry dimensions, friction factor, fluid density and viscosity, wall roughness conditions, etc.).

I have come across several articles that contain relevant information, but the data is presented in graphical form, making it challenging to extract the specific numeric values. Therefore, I kindly request your assistance in providing the data in numeric or number format, as described above.

Examples of experimental data sources include:

- Leutheusser, H.J. 1963. "Turbulent flow in rectangular ducts." J. Hydr. Div. ASCE 89 (3), 1–19.

- Brundrett, E., Baines, W. D. 1964. "The Production and Diffusion of Vorticity in Duct Flow." J. Fluid Mech., 19 (3), pp. 375-394.

- Gessner, F. B., Jones, J. B. 1965. "On Some Aspects of Fully-Developed Turbulent Flow in Rectangular Channels." J. Fluid Mech., 23 (4), pp. 689-713.

- Gessner, F. B. 1973. "The Origin of Secondary Flow in Turbulent Flow along a Corner." J. Fluid Mech., 58 (1), pp. 1-25.

- Melling, A., and Whitelaw, J.H. 1976. "Turbulent flow in a rectangular duct." J. Fluid Mech. 78, 289.

- Gessner and Emery. 1980. [Additional information needed]

- Leutheusser, H. J. 1984. "Velocity distribution and skin friction resistance in rectangular ducts." J. Wind Eng. Ind. Aero. 16, 315–327.

- Thangam, S., Speziale, C. G. 1987. "Non-Newtonian Secondary Flows in Ducts of Rectangular Cross-Section." Acta Mech., 68 (3-4), pp. 121-138.

- Rokni, M., et al. 1998. "Numerical and Experimental Investigation of Turbulent Flow in a Rectangular Duct." Int. J. Numer. Meth. Fluids, 28 (2), pp. 225-242.

Additionally, I am interested in numeric data, such as numerical predictions and Direct Numerical Simulation (DNS) data, from studies conducted by Naot and Rodi (1982) and Demuren and Rodi (1984):

- Naot, D.; Rodi, W. 1982. "Calculation of secondary currents in channel flow." ASCE J. Hydraul. Div. 108, 948–968.

- Demuren, A.O.; Rodi, W. 1984. "Calculation of turbulence driven secondary motion in noncircular ducts." J. Fluid Mech. 140, 189–222.

Furthermore, if any numeric data is available for other flow types, such as flow in cavities, flow at backward-facing steps, flow around cylinders, and flow around square rods, it would be greatly appreciated.

Thank you in advance for your assistance and contributions toward fulfilling this request. Your support will significantly contribute to the advancement of turbulent flow research.

Sincerely and best Regards,

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