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Revisiting T+ Versus Pry+ Scaling in Turbulent Flows With 0.01 ≤ Pr ≤ 760 Using RANS

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Fluid Mechanics and Fluid Power

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

This paper presents the computational analysis of thermally and hydraulically developing two-dimensional incompressible turbulent flow over the smooth flat plate with different fluids (liquid metal to oil) having a Prandtl number (Pr) in the range 0.01–760 with ANSYS. Assessment of non-dimensional temperature (T+) with normalized wall distance (y+) over the entire range of Pr reveals a possible dependence of initiation of log-law region on Pr. This allows investigating the scaling of T+ with Pry+ over the wide range of Pr. Finally, some limitations of wall functions at extreme Pr are presented.

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Abbreviations

\(\alpha\) :

Thermal diffusivity of fluid

\(\alpha_{t}\) :

Turbulent thermal diffusivity

i, j :

Indices for Newtonian summation

k :

Von Karman constant (=0.41) in wall laws

\(v\) :

Kinematic viscosity

\(v_{t}\) :

Eddy viscosity

\(\varphi\) :

A flow variable

Pr :

Prandtl number

Pr t :

Turbulent Prandtl number

Re :

Reynolds number

\(\overline{u}_{1}\) :

Time-average velocity component along xi

U ∞ :

Free stream velocity

U ∞ :

Free stream temperature

x1 or x:

Axial direction

x2 or y:

Cross-stream direction

\(\overline{T}\) :

Time-averaged temperature

\(T^{ + }\) :

Non-dimensional statistical temperature

U ∞ :

Free stream temperature

y + :

Non-dimensional height

()′:

Fluctuating quantities

References

  1. Pardeshi R, Tiwari S, Sharma P, Pardeshi R, Chandra L, Shekhar R (2015) Solar convective furnace for metals processing. JOM 67(11):2697–2704

    Google Scholar 

  2. Chandra L, Roelofs F, Houkema M, Jonker B (2009) A stepwise development and validation of a RANS based CFD modeling approach for the hydraulic and thermal-hydraulic analyses of liquid metal flow in a fuel assembly. Nucl Eng Des 239:1988–2003

    Article  Google Scholar 

  3. Wang X, Castillo L, Araya G (2008) Temperature scalings and profiles in forced convection turbulent boundary layers. J Heat Transf 130 (021701): 1–17

    Google Scholar 

  4. Grötzbach G (2013) Challenges in low-Prandtl number heat transfer simulation and modelling. Nucl Eng Des 264:41–55

    Article  Google Scholar 

  5. Kader BA (1981) Temperature and concentration profiles in fully turbulent boundary layers. Int J Heat Mass Transf 24(9):1541–1544

    Google Scholar 

  6. Bejan A (2013) Convection heat trasfer. Wiley, Hoboken, New Jersey

    Book  Google Scholar 

  7. Suga K, Craft TJ, Iacovides H (2006) An analytical wall-function for turbulent flows and heat transfer over rough walls. Int J Heat Fluid Flow 27:852–866

    Article  Google Scholar 

  8. Craft TJ, Gerasimov AV, Iacovides H, Launder BE (2002) Progress in the generalization of wall-function treatments. Int J Heat Fluid Flow 23: 148–160

    Google Scholar 

  9. Vigdorovich II (2017) Turbulent thermal boundary layer on a plate. reynolds analogy and heat transfer law over the entire range of Prandtl numbers. Fluid Dyn 52(5): 631–645

    Google Scholar 

  10. Nagano Y, Shimada M (1996) Deveopment of a two-equation heat transfer model bsaed on direct simulations of turbulent flows with different Prandltl number. Phys Fluids 8:3379–3402

    Article  Google Scholar 

  11. Kasagi N, Kuroda A, Hirata M (1989) Numerical investigation of near wall turbulent heat transfer taking into account the unsteady heat conduction in the solid wall. J Heat Transf 111:385–392

    Article  Google Scholar 

  12. Dong YH, Lu XY, Zhuang LX. An investigation of the Prandtl number effect on turbulent heat transfer in channel flows by large eddy simulation. Acta Mechanica 159: 39–51

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology (BHU) Varanasi, Varanasi, Uttar Pradesh, 221005, India

    Kunal Kumar, Kuldeep Aswal, Manish Kumar Rajwade, Ankit Kumar, S. S. Mondal & L. Chandra

Authors
  1. Kunal Kumar
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  2. Kuldeep Aswal
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  3. Manish Kumar Rajwade
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  4. Ankit Kumar
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  5. S. S. Mondal
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  6. L. Chandra
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Corresponding author

Correspondence to Ankit Kumar .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, PSG College of Technology, Coimbatore, Tamil Nadu, India

    T. Prabu

  2. Department of Mechanical Engineering, PSG College of Technology, Coimbatore, Tamil Nadu, India

    P. Viswanathan

  3. Department of Mechanical Engineering, Indian Institute of Technology (IIT) Bombay, Mumbai, Maharashtra, India

    Amit Agrawal

  4. Department of Mechanical Engineering, S. V. National Institute of Technology Surat, Surat, Gujarat, India

    Jyotirmay Banerjee

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Kumar, K., Aswal, K., Rajwade, M.K., Kumar, A., Mondal, S.S., Chandra, L. (2021). Revisiting T+ Versus Pry+ Scaling in Turbulent Flows With 0.01 ≤ Pr ≤ 760 Using RANS. In: Prabu, T., Viswanathan, P., Agrawal, A., Banerjee, J. (eds) Fluid Mechanics and Fluid Power. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-0698-4_45

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  • DOI: https://doi.org/10.1007/978-981-16-0698-4_45

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-0697-7

  • Online ISBN: 978-981-16-0698-4

  • eBook Packages: EngineeringEngineering (R0)

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