Mesh sensitivity analysis of cfd wind flow model for complex terrain

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CFD software: OpenFOAM 1.7.1 

Atmospheric and Surface Boundary Layer

The atmospheric boundary layer (ABL) is defined as the part of the troposphere directly influenced by the presence of the earth’s surface and responds to its forcings such as frictional drag, evaporation, heat transfer, pollutant emission and terrain induced flow modification (Stull (2009)). These forces give rise to the main characteristic of the ABL: the TURBULENCE. Meteorological phenomena taking place at this layer have a timescale of an hour or less. Typically, the ABL is divided in three differents sub-layers: The surface boundary layer (SBL), the mixed layer and the entrainment zone.
The surface boundary layer is located at the bottom of the ABL and in contact with the surface. Its height is the 10% of the total ABL. SBL is characterized by high vertical gradients of wind speed, humidity and temperature. In the mixed layer, the turbulence is mainly due to heat transfer between warm ground surface and radiative cooling from the top of the mixed layer.
The entrainment zone is a stable layer at the top of the mixed layer acting as a lid restraining the domain of turbulence (Stull (2009)).

Turbulence modelling

Wilcox (1994) wrote during the nineties a reference book about turbulence modelling for CFD.
Doing an overview to highlighted ideas, it could be learned that:
a. An ideal model should introduce the minimum amount of complexity while capturing the essence of the relevant physics. (Wilcox (1994))
b. Practical engineering flows are mostly turbulent.
c. Turbulence has a strongly rotational nature so it must be three dimensional.
d. Difficult to simulate the turbulence due to its complexity, multitude of length scales and its three dimensional and time dependence.
e. The time-dependent and three-dimensional Navier-Stokes equation contains all of the physics of a given turbulent flow.
f. A turbulent model has a wide range of plossible modeling, between the simple algebraic mixing length model to a complete solution to the Navier Stokes equation.
g. Turbulent kinetic energy is transfered on the average from larger eddies to smaller eddies until it dissipates into heat through the action of molecular viscosity.
h. An N-equations model means a model requiring solution for n additional differential transport equations in addition to conservation of mass, momentum and energy (i.e. k−ε turbulence model is a two-equation model and the additional equations that must be solved are: Turbulent kinetic energy (k) and dissipation (ε) of turbulence).
i. Desirable type of turbulence model: Model that can be applied by determining at most the appropiate boundary and/or initial conditions. No advance knowledge of the flow is necessary

More Turbulence Models

Besides RANS models, several turbulence models  have been built and applied along last decades in wind engineering, depending on terrain and analyzed results.
First of all, linear models as WAsP are not based on CFD. These linear analytical models can generalise a long-term meteorological data series at a (reference) site which may then be used to estimate conditions at other sites. The results are obtained in an accurate and quickly way as far as the computational domain is flat. Once the terrain became slightly irregular, the results became wrong due to the bad prediction of the separation and the flow recirculation. (Bowen and Mortensen (1996))
Large eddy simulation (LES) allow better fidelity than RANS simulations. It is a mathematical model for turbulence which resolves larges scales and models the smallest ones (Bakker (2002)). Despite showing better results than RANS, LES requires a very fine subgrid in the near-wall region of attached turbulent boundary layers. So, the computational time increases considerably and when the available computing power is limited it is not advisable.

Wind flow model: CFDWind 1.0

General Features

CFDWind 1.0 is an inhouse Surface Boundary Layer model developped at CENER since 2005 and solved through Ansys. Since 2010, CFDWind 1.0 has been adapted and solved through OpenFOAM. It has been validated over theBolund blind test (Bechmann et al. (2009b)) showing very accurate results. According to Cabezón et al. (2011a), the model is adapted for the simulation of wind speed and turbulence based on the Monin-Obukhov theory (see Sanz et al. (2008)) and on Richards and Hoxey (1993) computational approach. Mixing length is considered strictly increasing with height z as lm = κz. In addition, the atmosphere is considered as neutral since thermal effects and Coriolis force are neglected because of the arguments presented previously.

CFD software: OpenFOAM 1.7.1

Since the seventies, many CFD softwares have been created and optimized. Probably, the most significant way to separate them is between open source and commercial codes. This work is done by means of OpenFOAM 1.7.1. OpenFOAM (Open Field Operation And Manipulation) is a free, open source numerical simulation software with extensive CFD and multi-physics capabilities produced by OpenCFD Ltd. It is written under C++ language. OpenFOAM offers a wide range of components and capabilities  among which: Polyedral Finite Volume Method, second order scheme in space and time, parallelism in domain decomposition mode, incompressible flow (segregated pressure-based algorithms) and RANS for turbulent flows. All of them will be used in this work.

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Execution of OpenFOAM

As well as other CFD softwares, OpenFOAM is characterised by linking three main stages: pre-processor, solver, and post-processor.
During pre-processor the user prepares the simulation case. The computational domain has to be defined and then discretized on a finite number of elements (cells). The physical models representing wind speed or turbulence are selected and set. The fluid is chosen by defining its properties (density, viscosity). Finally, the user has to specify the boundary conditions, determine the discretization schemes used to calculate the physical fields and fix the timing of the iteration of the simulation.
The finite volume method is the numerical analysis used CFD codes as PHOENICS, FLUENT or OpenFOAM among others. After Versteeg and Malalasekera (2007) and Ansys (2009), the method presents different steps. Once the domain is divided into discrete finite control volume using the computational grid, a formal integration of the governing equations is done over all the (finite) control volumes of the solution domain to construct algebraic equations for the discrete dependent variables such as velocities, pressure, turbulence, etc. The discretized equation expresses the conservation principle for the variable inside the control volume. Finally, the discretized equations are linearized and solved by an iterative method. The solution satisfies conservation equation’s at every single cell and at the whole computational domain.
During post-processor, visualisation tools are used to observe the results of the simulations. Grid display, vector plots, 2D and 3D plots, view manipulation, etc. Post processing is helpfull for the understanding.

Selected solver (from the options offered by OpenFOAM)

Since air is considered an incompressible flow, simpleFoam solver is chosen for the first part of this work where freestream inlet profile is developped over complex terrain. simpleFoam is a steady-state solver for incompressible and turbulent flow. During the second study (of the wake model) over offshore wind farm, the solver used is simple Wind Foam. It has the same characteristics as simple Foam and allows to add external source terms in the momentum equation to simulate wind turbines.
The key word « simple » at the beginning of both solver name’s means Semi-Implicit Method for Pressure-Linked Equation. This is pressure-based segregated algorithm allowing to face the governing equations with an iterative procedure and solving them one after another. The segregated algorithm presents the advantadge of being memory efficient since the discretized equations need only be stored in the memory one at a time. However, it presents an inconvenient in convergence time, inasmuch as the equations are solved in a decoupled manner Ansys (2009). The different iterative steps are:
a. Set the boundary conditions.
b. Solve the discretized momentum equation, one after another, using the recently updated values of pressure and face mass fluxes.
c. Solve the pressure correction equation using the recently obtained velocity field and the mass-flux.
d. Correct face mass fluxes, pressure, and the velocity field using the pressure correction obtained from previous step.
e. Solve the equations for additional scalars if any, such as turbulent quantities or energy using the current values of the solution variables.
f. Update the source terms arising from the interactions among different phases.
g. Check for the convergence of the equations.
h. Repeat till convergence fixed by the user in the file fvSolution of OpenFOAM.

Table of contents :

INTRODUCTION
CHAPTER 1 LITERATURE REVIEW 
1.1 Atmospheric and Surface Boundary Layer
1.2 Numerical modelling 
1.2.1 Governing Equations
1.2.2 Turbulence modelling
1.2.2.1 Description and characteristics
1.2.2.2 RANS models: k −ε
1.2.2.3 More Turbulence Models
1.2.3 Wind flow model: CFDWind 1.0
1.2.3.1 General Features
1.2.3.2 Boundary conditions
1.3 CFD software: OpenFOAM 1.7.1 
1.3.1 Execution of OpenFOAM
1.3.2 Selected solver (from the options offered by OpenFOAM)
1.3.3 Selected turbulence model (from the options offered by OpenFOAM)
CHAPTER 2 THE BOLUND EXPERIMENT: BLIND COMPARISON OF FLOW MODELS 
2.1 The experiment setup
2.2 The blind comparison
2.3 Computational domain
2.4 Verification of CFDWind1 using Open FOAM 1.7
2.4.1 Graphics
2.4.2 Errors and discussion
CHAPTER 3 MESH SENSITIVITY ANALYSIS OF CFD WIND FLOW MODEL FOR COMPLEX TERRAIN
3.1 Definition and choice of the Sensitivity Analysis Method 
3.2 Test case 
3.3 Sensitivity Analysis
3.3.1 Base case
3.3.2 Other cases
3.4 Sensitivity results 
3.4.1 Criteria
3.4.2 Average relative error
3.4.3 Discussion on the selection of input parameters
3.5 Validation results
CHAPTER 4 MESH SENSITIVITY ANALYSIS OF CFD WAKE MODEL OVER OFFSHORE WIND FARM
4.1 Offshore wind farms: Advantages and disadvantages 
4.2 Horns Rev Wind Farm 
4.3 Computational Domain 
4.4 Limitations of the numerical model and simpleWindFoam solver
4.4.1 Actuator Disk Model
4.4.2 Iterative algorithm of simpleWindFoam
4.5 Sensitivity Analysis
4.5.1 Base case
4.5.2 Other cases
4.6 Sensitivity results
4.6.1 Discussion on the selection of input parameters
4.7 Validation results
CONCLUSION

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