## THERMAL SCIENCE

International Scientific Journal

### NEW NON-ORTHOGONALITY TREATMENT FOR ATMOSPHERIC BOUNDARY LAYER FLOW SIMULATION ABOVE HIGHLY NON-UNIFORM TERRAINS

**ABSTRACT**

In this paper we validate an improved finite volume approximation of Reynolds Averaged Navier-Stokes equations for simulation of wind flows in body-fitted grids generated by algebraic extrusion from digital terrain elevation data, proposed in N. Mirkov et. al. J. Comput. Phys. 287, 18-45(2015), [1]. The approach is based on second-order accurate finite volume method with collocated variable arrangement and pressure-velocity coupling trough SIMPLE algorithm. The main objective is the attenuation of spurious pressure field oscillations in regions with discontinuity in grid line slopes, as encountered in grids representing highly non-uniform terrains. Moreover, the approach relaxes the need for grid generation based on elliptic PDEs or grid smoothing by applying fixed point iterations (i.e. Gauss-Seidel) to initial grid node positions resulting from algebraic grid generators. Drawbacks of previous approaches which ignored treatment of finite volume grid cell cases with intersection point offset in non-orthogonality corrections are removed. Application to real-life wind farm project at Dobrič (Srvljig, Serbia) is used to assess the effectiveness of the method. The results validate the view in which accurate discretization of governing equations play more important role than the choice of turbulence modelling closures. [Projekat Ministarstva nauke Republike Srbije, br. TR-33036]

**KEYWORDS**

PAPER SUBMITTED: 2015-10-25

PAPER REVISED: 2015-11-04

PAPER ACCEPTED: 2015-11-05

PUBLISHED ONLINE: 2015-12-13

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Supplement 1**, PAGES [S223 - S233]

- Mirkov, N., Rašuo, B., Kenjereš, S., On the improved finite volume procedure for simulation of turbulent flows over real complex terrains, Journal of Computational Physics, 287 (2015) pp. 18-45.
- Wind energy scenarios for 2020. retrieved from: www.ewea.org.
- Taylor, P.A., Teunissen H.W., The Askervein Hill project: Report on September/October 1983 main field experiment, Rep. MSRB-84-6. Technical report, Atmospheric Environment Service, Ontario, Canada, 1985.
- Beljaars, A.C.M., Walmsley, J.L., Taylor P.A., A mixed spectral finite-difference model for neutrally stratified boundary-layer flow over roughness changes and topography. Boundary Layer Meteorology, 38 (1987), pp.273-303.
- Undheim O., Andresson, H.I., Berge, E., Non-linear, microscale modelling of the flow over Askervein hill, Boundary Layer Meteorology, 120 (2006), pp.477-495.
- Stevanović, Ž., Mirkov, N., Stevanović, Ž., Stojanović, A., Validation of atmospheric boundary layer turbulence model by on-site measurements, Thermal Science, 14 (2010), 1, pp.199-207.
- Bechmann, A., Sorensen, N.N., Berg, J., Mann, J., Rethore, P.E., The Bolund experiment, part II: Blind comparison of microscale flow models, Boundary-Layer Meteorology, 141 (2011) 2, pp.245-271.
- Prospathopoulos, J.M., Politis, E.S., Chaviaropoulos, P.K., Application of a 3D RANS solver on the complex hill of Bolund and assessment of the wind flow predictions. Journal of Wind Engineering and Industrial Aerodynamics, 107-108 (2012) pp.149-159.
- Vuorinen, V., Chaudhari, A., Keskinen, J.P., Large-eddy simulation in a complex hill terrain enabled by a compact fractional step OpenFOAM solver, Advances in Engineering Software, 79 (2015), pp.70-80.
- Berg, J., Mann, J., Bechmann, A., Courtney, M. S., Jorgensen, H. E., The Bolund experi-ment, part I: Flow over a steep, three-dimensional hill. Boundary Layer Meteorology, 141 (2011), pp.219-243.
- Mathur, S.R., Murthy, J.Y., A pressure-based method for unstructured meshes., Numer- ical Heat Transfer, Part B: Fundamentals, 31 (1997), 2, pp.195-215.
- Gosman, A.D., Jasak, H., Weller, H.G., High resolution NVD differencing scheme for arbitrarily unstructured meshes. International Journal for Numerical Methods in Fluids, 31 (1999), pp.431-449.
- WindSim, User Documentation.(www.windsim.com).
- Phoenics Documentation, CHAM ltd. (www.cham.co.uk).
- Ferry, M., New Features of MIGAL solver. In Proceedings of 9th Phoenics user conference, Moscow, 2002.
- Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B., Speziale, C.G., Development of turbulence models for shear flows by a double expansion technique, Physics of Fluids A, 4 (1992), 7, pp.1510-1520.
- Wilcox, D., Turbulence Modeling for CFD, DCW Industries, La Caada, 2nd edition, 1998.
- Patankar, S.V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New-York, 1980.
- Ferziger, J.H., Perić, M.,Computational Methods for Fluid Dynamics, Springer, 2nd edition, 1999.
- Rhie, C.M., Chow, W.L., Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 2 (1983), pp.1525-1532.
- Waterson, N.P., Deconinck, H., Design principles for bounded higher-order convection schemes - a unified approach, Journal of Computational Physics, 224 (2007), pp.182-207.
- Stone., H., Iterative soluton of implicit approximations of multi-dimensional partial differential equations, SIAM Journal on Numerical Analysis, 5 (1968), pp.530-568.
- Stevanović, Ž., Mirkov, N., Stevanović, Ž., Grubor, B.,Djurović-Petrović, M., Referent Wind Speed and Turbulence Intensity Estimation and on-Site Wind Turbines Classification, Proceedings of the 16th Symposium on Thermal Science and Engineering of Serbia, Sokobanja, Serbia, October 22-25, 2013.
- Retreived from: pedja.supurovic.net/veza/312.