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Numerical Analysis to Evaluate the Effect of Wall Temperature on Skin Friction and Stanton Number for Turbulent Flows over a Flat Plate from Mach 2–8

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Abstract

The computational approaches of CFD are more powerful than the analytical solutions for high-speed compressible flows over a flat plate. A small number of expensive experimental data can be generated to aid high-speed vehicle design. However, CFD can be used to simulate a large variety of flows with different freestream and wall conditions in a cost-effective manner. The current work aims to numerically calculate the turbulent boundary layer flows over a flat plate at different Mach numbers in the range of 2–8 at different wall conditions and unit Reynolds numbers. The Reynolds-averaged Navier–Stokes method with k − ω turbulence model is applied to resolve the flow over the flat plate at zero angle of attack. The computed skin friction coefficient and Stanton number are compared with the available experimental data in the literature. The calculated results indicate some agreement with the experimental data. An increase in the Mach number and wall temperature decreases the skin friction and the Stanton number. A polynomial curve fit data estimation is proposed for skin friction under adiabatic wall conditions for Mach numbers in the range of 2–8. Numerical simulations over compression corner flows are also presented in the present work. The freestream Mach number influences the thickness of the subsonic layer in the undisturbed boundary layer on the flat plate in compression corner flows. The higher freestream Mach number results in a lower subsonic thickness near the wall, leading to a small separation bubble and lower peak heat transfer in shock/boundary-layer interaction flows.

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Abbreviations

C f :

Skin friction coefficient (–)

C h :

Stanton number (–)

H :

Shape factor (–)

K :

Turbulent kinetic energy (m2 s−2)

M ∞ :

Freestream Mach number (–)

P w :

Wall pressure (Pa)

P ∞ :

Freestream pressure (Pa)

Pr:

Prandtl number (–)

q w :

Wall heat flux (W m−2)

Re∞ :

Reynolds number based on plate length (–)

Re1 :

Freestream unit Reynolds number (m−1)

T ∞ :

Freestream temperature (K)

T wad :

Adiabatic wall temperature (K)

T w :

Wall Temperature (K)

T r :

Recovery wall temperature (K)

V ∞ :

Local velocity (m s−1)

V ∞ :

Freestream velocity (m s−1)

δ :

Boundary-layer thickness at end of a flat plate (m)

δ 0 :

Upstream boundary-layer thickness (m)

Θ:

Momentum thickness (m)

δ * :

Displacement thickness (m)

τ w :

Wall shear stress (N m−2)

ρ :

Density (kg m−3)

ω :

Turbulent kinetic energy dissipation rate (m2 s−3)

wad:

Adiabatic wall condition

w:

Wall condition

∞:

Freestream condition

r:

Recovery

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Acknowledgements

The project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. D-177-135-1442. The authors, therefore, gratefully acknowledge DSR technical and financial support. We would like to thank the high-performance center (HPC) staff for providing us the Aziz supercomputing facility (http://hpc.kau.edu.sa) to perform the numerical simulations. The authors would also like to thank Professor Krishnendu Sinha from the Department of Aerospace Engineering, Indian Institute of Technology Bombay for his kind help.

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Authors and Affiliations

  1. Aerospace Engineering Department, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Amjad A. Pasha, Mohammed Mahdi Abdulla & Khalid A. Juhany

  2. School of Mechanical Engineering, SRM Institute of Science and Technology, Kattankulathur, Chennai, 603203, India

    D. Siva Krishna Reddy

  3. Turbulence and Flow Control Lab, School of Mechanical Engineering, SASTRA Deemed University, Thanjavur, Tamil Nadu, 613401, India

    S. Nadaraja Pillai

  4. Department of Mechanical Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Nazrul Islam

  5. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    V. Mahendra Reddy

  6. Department of Chemical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Abdul Gani Abdul Jameel

  7. Center for Refining and Advanced Chemicals, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Abdul Gani Abdul Jameel

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  1. Amjad A. Pasha
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Correspondence to Amjad A. Pasha.

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Pasha, A.A., Reddy, D.S.K., Abdulla, M.M. et al. Numerical Analysis to Evaluate the Effect of Wall Temperature on Skin Friction and Stanton Number for Turbulent Flows over a Flat Plate from Mach 2–8. Arab J Sci Eng 47, 8243–8256 (2022). https://doi.org/10.1007/s13369-021-06170-w

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