Journal of Computational Applied Mechanics

Numerical Simulation of Atmospheric Boundary Layer Over Laboratory Scale Two-Dimensional Hill Using Pressure-Driven Boundary Condition

Document Type : Research Paper

Authors

National Institute of Technology Sikkim, Ravangla, Sikkim, India

Abstract

The atmospheric boundary layer (ABL) is the lowest part of the atmosphere directly impacted by the earth's surface. ABL simulation is essential for predicting wind load, pollutant dispersion, and wind capacity over a terrain. ABL can be modeled using the computational fluid dynamics (CFD) tool. Maintaining horizontal homogeneity is critical for a more accurate ABL simulation. Researchers have proposed various boundary conditions for obtaining homogeneously homogeneous ABL. This study investigates pressure-driven boundary conditions for the atmospheric boundary layer over a laboratory-scale two-dimensional (2D) hill. For complex terrains, such as a 2D hill, the numerical analysis of pressure-driven flow has not yet been considered. The validation was done using the experimental results from the ERCOFTAC 69 case, namely a simplified 2D hill. The results are also compared with the shear-driven boundary conditions. The results of simulations of ABL employing pressure-driven boundary conditions using different turbulence models have also been compiled. From MAPE analysis, it is found that the results of ABL simulation using pressure-driven boundary conditions produced lower MAPE values, resulting in superior outcomes compared to the shear-driven boundary conditions.

Keywords

[1]          S. E. Hosseinidoost, A. Sattari, M. Eskandari, D. Vahidi, P. Hanafizadeh, P. Ahmadi, Techno-economy study of wind energy in Khvaf in Razavi Khorasan Province in Iran, Journal of Computational Applied Mechanics, Vol. 47, No. 1, pp. 53-66, 2016.
[2]          F. Mebarek-Oudina, Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths, Engineering science and technology, an international journal, Vol. 20, No. 4, pp. 1324-1333, 2017.
[3]          V. N. Mishra, Some problems on approximations of functions in Banach spaces,  Thesis, Ph. D. thesis, 2007.
[4]          M. Farhan, Z. Omar, F. Mebarek-Oudina, J. Raza, Z. Shah, R. Choudhari, O. Makinde, Implementation of the one-step one-hybrid block method on the nonlinear equation of a circular sector oscillator, Computational Mathematics and Modeling, Vol. 31, No. 1, pp. 116-132, 2020.
[5]          I. Chabani, F. Mebarek-Oudina, A. A. I. Ismail, MHD Flow of a Hybrid Nano-fluid in a Triangular Enclosure with Zigzags and an Elliptic Obstacle, Micromachines, Vol. 13, No. 2, pp. 224, 2022.
[6]          L. N. Mishra, M. Sen, R. N. Mohapatra, On existence theorems for some generalized nonlinear functional-integral equations with applications, Filomat, Vol. 31, No. 7, pp. 2081-2091, 2017.
[7]          R. Djebali, F. Mebarek-Oudina, C. Rajashekhar, Similarity solution analysis of dynamic and thermal boundary layers: Further formulation along a vertical flat plate, Physica Scripta, Vol. 96, No. 8, pp. 085206, 2021.
[8]          H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.
[9]          S. Asemi, A. Farajpour, H. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[10]        S. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.
[11]        S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, pp. 1541-1546, 2014.
[12]        M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650048, 2016.
[13]        M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[14]        A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.
[15]        A. Farajpour, M. R. Hairi Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016/04/15/, 2016.
[16]        A. Farajpour, M. Mohammadi, A. R. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011/08/01/, 2011.
[17]        A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014/04/01/, 2014.
[18]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017/03/15/, 2017.
[19]        A. Farajpour, A. R. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012/04/01/, 2012.
[20]        A. Farajpour, M. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, No. 7, pp. 1849-1867, 2016.
[21]        M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm‐based electromechanical sensors via higher‐order non‐local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[22]        N. Ghayour, A. Sedaghat, M. Mohammadi, Wave propagation approach to fluid filled submerged visco-elastic finite cylindrical shells, 2011.
[23]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.
[24]        M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 659-682, 2014.
[25]        M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy Type Solution for Nonlocal Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.
[26]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature Effect on Vibration Analysis of Annular Graphene Sheet Embedded on Visco-Pasternak Foundati, Journal of Solid Mechanics, Vol. 5, No. 3, pp. 305-323, 2013.
[27]        M. Mohammadi, A. Farajpour, M. Goodarzi, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014.
[28]        M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.
[29]        M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.
[30]        M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.
[31]        M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, 2012.
[32]        M. Mohammadi, M. Goodarzi, M. Ghayour, A. Farajpour, Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, Vol. 51, pp. 121-129, 2013.
[33]        M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics-A/Solids, Vol. 77, pp. 103793, 2019.
[34]        M. Mohammadi, A. Moradi, M. Ghayour, A. Farajpour, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 437-458, 2014.
[35]        M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, An Int'l Journal, Vol. 69, No. 2, pp. 131-143, 2019.
[36]        M. Mohammadi, A. Rastgoo, Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium, Mechanics of Advanced Materials and Structures, Vol. 27, No. 20, pp. 1709-1730, 2020/10/15, 2020.
[37]        M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, No. 8, pp. 2207-2232, 2016.
[38]        H. Moosavi, M. Mohammadi, A. Farajpour, S. Shahidi, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 1, pp. 135-140, 2011.
[39]        M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, 2015.
[40]        M. Mohammadi, A. Farajpour, A. Moradi, M. Hosseini, Vibration analysis of the rotating multilayer piezoelectric Timoshenko nanobeam, Engineering Analysis with Boundary Elements, Vol. 145, pp. 117-131, 2022/12/01/, 2022.
[41]        B. E. Launder, D. B. Spalding, The numerical computation of turbulent flows,  in: Numerical prediction of flow, heat transfer, turbulence and combustion, Eds., pp. 96-116: Elsevier, 1983.
[42]        S. Azad, A. Riasi, H. Mahmoodi Darian, H. Amiri Moghadam, Parametric study of a viscoelastic RANS turbulence model in the fully developed channel flow, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 65-74, 2017.
[43]        T. Cebeci, P. Bradshaw, Momentum transfer in boundary layers, Washington, 1977.
[44]        J. Nikuradse, Laws of flow in rough pipes, 1950.
[45]        K. Choudhary, A. K. Jha, L. N. Mishra, M. Vandana, Buoyancy and chemical reaction effects on mhd free convective slip flow of newtonian and polar fluid through porousmedium in the presence of thermal radiation and ohmic heating with dufour effect, Facta Universitatis. Series: Mathematics and Informatics, Vol. 33, No. 1, pp. 001-029, 2018.
[46]        M. Choudhury, G. C. Hazarika, The effects of variable viscosity and thermal conductivity on mhd flow due to a point sink, Matemáticas: Enseñanza Universitaria, Vol. 16, No. 2, pp. 21-28, 2008.
[47]        P. Richards, R. Hoxey, Appropriate boundary conditions for computational wind engineering models using the k-ϵ turbulence model, Journal of wind engineering and industrial aerodynamics, Vol. 46, pp. 145-153, 1993.
[48]        B. Blocken, T. Stathopoulos, J. Carmeliet, CFD simulation of the atmospheric boundary layer: wall function problems, Atmospheric environment, Vol. 41, No. 2, pp. 238-252, 2007.
[49]        J. Franke, A. Hellsten, K. Schlünzen, B. Carissimo, Best practice guideline for the CFD simulation of flows in the urban environment-a summary, in Proceeding of, Cambridge Environmental Research Consultants, pp.
[50]        D. Hargreaves, N. G. Wright, On the use of the k–ε model in commercial CFD software to model the neutral atmospheric boundary layer, Journal of wind engineering and industrial aerodynamics, Vol. 95, No. 5, pp. 355-369, 2007.
[51]        Y. Yang, M. Gu, S. Chen, X. Jin, New inflow boundary conditions for modelling the neutral equilibrium atmospheric boundary layer in computational wind engineering, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 97, No. 2, pp. 88-95, 2009.
[52]        C. v. Gorlé, J. Van Beeck, P. Rambaud, G. Van Tendeloo, CFD modelling of small particle dispersion: the influence of the turbulence kinetic energy in the atmospheric boundary layer, Atmospheric environment, Vol. 43, No. 3, pp. 673-681, 2009.
[53]        A. Parente, C. Gorlé, J. van Beeck, C. Benocci, A comprehensive modelling approach for the neutral atmospheric boundary layer: consistent inflow conditions, wall function and turbulence model, Boundary-layer meteorology, Vol. 140, No. 3, pp. 411-428, 2011.
[54]        M. Balogh, A. Parente, Realistic boundary conditions for the simulation of atmospheric boundary layer flows using an improved k–ε model, Journal of wind engineering and industrial aerodynamics, Vol. 144, pp. 183-190, 2015.
[55]        P. Richards, S. Norris, Appropriate boundary conditions for a pressure driven boundary layer, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 142, pp. 43-52, 2015.
[56]        P. J. Richards, S. E. Norris, Appropriate boundary conditions for computational wind engineering: Still an issue after 25 years, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 190, pp. 245-255, 2019.
[57]        C. Greenshields, The OpenFOAM foundation user guide 7.0, The OpenFOAM Foundation Ltd: London, United Kingdom, 10th July, 2019.
[58]        R. Lakshman, R. Basak, Analysis of transformed fifth order polynomial curve for the contraction of wind tunnel by using OpenFOAM, in Proceeding of, IOP Publishing, pp. 012048.
[59]        R. Lakshman, R. Basak, Analysis of transformed sixth-order polynomial for the contraction wall profile by using OpenFOAM,  in: Recent advances in theoretical, applied, computational and experimental mechanics, Eds., pp. 133-144: Springer, 2020.
[60]        R. Lakshman, N. Pal, R. Basak, Comparative Analysis of Inlet Boundary Conditions for Atmospheric Boundary Layer Simulation Using OpenFOAM, in Proceeding of, Springer, pp. 79-86.
[61]        I. Abohela, On the Horizontal Homogeneity of the Atmospheric Boundary Layer Profile in CFD Simulations, Appl. Math, Vol. 12, No. 4, pp. 825-829, 2018.
[62]        L. H. Khurshudyan, W. H. Snyder, I. V. Nekrasov, Flow and dispersion of pollutants over two-dimensional hills, Environment Protection Agency Report no EPA-600/4-81-067. Research Triangle Park, 1981.
Journal of Computational Applied Mechanics
Volume 53, Issue 3
September 2022
Pages 379-392
  • Receive Date: 15 May 2022
  • Revise Date: 14 July 2022
  • Accept Date: 14 July 2022