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Analysis of the ground effect on development of flow structures around an inclined solar panel

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Abstract

The complex three-dimensional flow that develops around an inclined flat solar panel near the ground is investigated using Computational Fluid Dynamics. The early stage evolution of the flow and the interaction of the shear layers emanating from the sides of the panel, the large separation region behind the panel and the boundary layers on the panel and ground are captured using Delayed Detached-Eddy Simulation to model the turbulence. The mean analysis shows that a small clearance produces a wall-jet like flow in the gap region between the panel and the ground, which tends to elongate the wake region in the downstream direction. On the other hand, a strong upwash is observed for a larger gap, reducing the length of the wake. Transient three-dimensional flow structures are captured using vorticity contours and the λ2-criterion. The early stage development of flow around the panel shows inverted hairpin-like vortices that are shed from the leading edge, touch down on the ground, generate a counter-rotating sheared vortex and a pair of vertical vortex tubes that extend from the ground and curl up into the wake. This pair of vortex tubes appears to be the source of the meandering structures reported in the literature. When the flow reaches a quasi-steady state, there is an asymmetric distorted flow for the smaller gap, whereas there is a nearly symmetric wake pattern for the larger gap.

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Abbreviations

CFD:

Computational Fluid Dynamics

CFL:

Courant number

CL :

Lift coefficient

D:

Edge length, m

DDES:

Delayed Detached-Eddy Simulation

DES:

Detached-Eddy Simulation

H:

Gap height, m

k:

Turbulent kinetic energy, m2/s2

L:

Length of the solar panel, m

LES:

Large Eddy Simulation

p:

Pressure, Pa

RANS:

Reynolds-Averaged Navier–Stokes

Sij :

Shear strain: \(\frac{1}{2}\left( {{\text{U}}_{{{\text{i}},{\text{j}}}} + {\text{U}}_{{{\text{j}},{\text{i}}}} } \right)\), s−1

SIMPLE:

Semi-Implicit Method for Pressure Linked Equations

SST:

Shear-Stress Transport

t:

Time, s

tr :

Reference time, s

t*:

Normalized time, t/tr

U, V, W:

Velocity components, m/s

U(Y):

Streamwise velocity at the distance Y from the bottom wall, m/s

Ug :

Velocity at gradient height Yg, m/s

Ui, j :

Velocity gradients

U0 :

Approaching velocity at the height of the inclined panel leading edge, m/s

\(\overline{u}_{{{\text{rms}}}} ,\overline{v}_{{{\text{rms}}}} ,\overline{w}_{{{\text{rms}}}}\) :

Root mean square of velocity fluctuations, m/s

uτ :

Frictional velocity, m/s

W:

Width of the solar panel, m

X, Y, Z:

Cartesian coordinate directions, m

XAlt, YAlt :

Parallel and perpendicular axes to the inclined panel

Y*:

Normal direction normalized by H for the gap region and Δ for the upper region

Yg :

Gradient height in open terrain, m

Y+ :

Wall normal distance: \(({\text{u}}_{{\uptau }} \cdot\ {\text{Y}})/{\upnu }\)

α:

Constant exponent based on terrain type

Δ:

Projected height of the inclined panel: W·sin(π − ϕ), m

λ:

Eigenvalues

ν:

Kinematic viscosity, m2/s

ρ:

Air density, kg/m3

τw :

Wall shear stress, Pa

ϕ:

Inclination angle of the solar panel, deg

Ωij :

Vorticity: \(\frac{1}{2}\left( {{\text{U}}_{{{\text{i}},{\text{j}}}} - {\text{U}}_{{{\text{j}},{\text{i}}}} } \right)\), s−1

ω:

Specific dissipation rate, s−1

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Acknowledgements

This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada.

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Authors and Affiliations

  1. Department of Mechanical, Automotive and Materials Engineering, University of Windsor, Windsor, ON, N9B 3P4, Canada

    K. Fukuda, R. Balachandar & R. M. Barron

  2. Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON, N9B 3P4, Canada

    R. Balachandar

  3. Department of Mathematics and Statistics, University of Windsor, Windsor, ON, N9B 3P4, Canada

    R. M. Barron

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Fukuda, K., Balachandar, R. & Barron, R.M. Analysis of the ground effect on development of flow structures around an inclined solar panel. Environ Fluid Mech 20, 1463–1489 (2020). https://doi.org/10.1007/s10652-020-09750-w

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