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Numerical Study of Turbulent Airflow Structure and Transfer of Heat Having Trapezoidal Baffles Attached on the Walls and Centerline of the Rectangular Channel

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Abstract

Numerically, we have studied different characteristics of turbulent air flow (flow structure, axial velocity profiles, dimensionless coefficient of skin friction, normalized friction factor),and heat transfer (local Nusselt number, and average Nusselt number) phenomena through a rectangular channel having trapezoidal baffles attached on its walls, and along the centerline of it. The governing equations have been solved using the finite volume method and to visualize the simulation results, fluent software has been employed. It is shown that the maximum value of pressure drop occurs on the upstream, and minimum value attains in the downstream section of the channel. It is ensured that an increase in the Reynolds number (Re) causes increase in normalize friction factor (F), and average Nusselt number (Nuav). The simulation results of this work will help to design and monitor flow phenomena through many thermal applications.

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Data Availability

Enquiries about data availability should be directed to the authors.

Abbreviations

\(C\) :

Empirical constant, \(C_{\mu }\) = 0.09, \(C_{1\epsilon }\) = 1.44, \(C_{2\epsilon }\) = 1.92, \(\sigma_{k}\) = 1.0, \(\sigma_{\epsilon } = 1.3\)

\(C_{p}\) :

Average pressure coefficient

Cf(x):

Skin friction coefficient

f0 :

Friction factor of smooth channel [Petukhov[1]] = \(\left( {0.79 \ln {\text{Re}} - 1.64} \right)^{ - 2}\) for \(\le {\text{Re}} \le 500,000\)

F:

Average friction factor = \(\frac{2\Delta p H}{{L \rho u_{0 }^{2} }}\)

F:

Normalize friction factor = \(\frac{f}{{f_{0} }}\)

\(G_{k}\) :

Production rate of kinetic energy due to

h(x):

Coefficient of heat transfer

H:

Channel width (m)

HT:

Heat transfer

kf :

Thermal conductivity (Wm−1 K−1)

\(k\) :

Turbulent kinetic energy = \(\frac{1}{2}\overline{{u_{i}^{{\prime }} u_{j}^{{\prime }} }}\)

L:

Length of channel

M:

Meter

Ne :

Total number of elements

p:

Pressure

p1 :

Pressure at inlet

p2 :

Pressure at outlet

\(\Delta p\) :

Absolute pressure drop =|(p2-p1)|

T:

Temperature

Tw :

Wall temperature = 375 K

\(u_{i}^{\prime } ,u_{j}^{\prime }\) :

Fluctuation velocity components in in xi and xj directions

u0 :

Input velocity [ms−1]

\(\rho\) :

Density (kg m−3)

\(\mu\) :

Dynamic viscosity [Pa.s]

Re:

Reynolds number = \(\frac{{u_{0 } \rho H}}{\mu }\)

Nu:

Nusselt number

\(Nu\left( x \right)\) :

Local Nusselt number \(= \frac{h\left( x \right)L}{{k_{f} }}\)

Nuav :

Average Nusselt number = \(\frac{1}{L}\mathop \smallint \limits_{0}^{L} Nu\left( x \right) dx\)

\(Nu_{0}\) :

Average Nusselt number of smooth channel [Dittus and Boelter [2]] = \(0.023 {\text{Re}}^{0.8} \Pr^{0.4}\) for \({\text{Re}} \ge 10,000\)

Nuna :

Normalized average Nusselt number

NCf(x):

Normalize skin friction coefficient = Cf(x)/f0

FVM:

Method of finite volume

Pr:

Prandtl number

\(\frac{\mu }{Pr}\) :

Molecular diffusivity

\(\frac{{\mu_{t} }}{{Pr_{t} }}\) :

Turbulent thermal diffusivity

\(\mu_{t}\) :

Turbulent viscosity = \(\rho C_{\mu } \frac{{k^{2} }}{\epsilon }\)

\(\delta_{ij}\) :

Kronecker delta

\(Y^{ + }\) :

Normalize distance of the walls

\(k_{p}\) :

Kinetic energy of turbulence at position P

\(y_{p}\) :

Distance from position P to the wall

E:

= 9.81

r:

= 0.42

v:

Velocity in y direction

x:

Y, Cartesian coordinate

ui :

Uj, components of mean velocity [ms−1] in xi and xj directions

Tin :

Inlet temperature = 300 K

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Acknowledgements

The authors wish to thank the reviewers for their valuable suggestions, which helped a lot to improve this work.

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Authors and Affiliations

  1. Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, 517325, India

    Sandip Saha

  2. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India

    Pankaj Biswas

  3. Department of Mathematics, Alipurduar University, Alipurduar, West Bengal, 736121, India

    Apurba Narayan Das

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Correspondence to Sandip Saha.

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Saha, S., Biswas, P. & Das, A.N. Numerical Study of Turbulent Airflow Structure and Transfer of Heat Having Trapezoidal Baffles Attached on the Walls and Centerline of the Rectangular Channel. Int. J. Appl. Comput. Math 8, 104 (2022). https://doi.org/10.1007/s40819-022-01252-1

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