Coupling Mesoscale and Microscale Atmospheric Dynamics for Wind Plant Simulations in Complex Terrain

1. Introduction

This paper's motivation is to be able to simulate the full range of conditions a wind plant may encounter by coupling microscale atmospheric large-eddy simulations (LES) with mesoscale information in complex terrain. There are various ways to perform mesoscale-microscale coupling. One way is to simulate an inflow/outflow microscale domain that uses mesoscale weather model flow field information as boundary conditions. The main difficulty with this method is that mesoscale models essentially solve the unsteady Reynolds-averaged Navier-Stokes (RANS) equations, so the flow field is smooth and the atmospheric boundary layer turbulence is not resolved. Therefore, the method suffers from the problem of how to initiate realistic resolved-scale turbulence with as little distance as possible given the smooth mesoscale model inflow. Kilometers of fetch are necessary for the turbulence to come to some sort of equilibrium state.

As an attempt to circumvent the need for superimposed stochastic perturbations in flat terrain, previous to this work, we have developed a method in which we run periodic microscale simulations that have internal source terms, like large-scale advection, derived from the mesoscale solver. Alternatively, these sources may be computed within the microscale solver such that they drive the plane-averaged solution to match that of the mesoscale solver. In that case, a simple P-controller with height-time varying gains is used to compute the source terms. This method is attractive in that the domain is periodic, and realistic turbulence naturally forms as in any other periodic atmospheric LES, but the mesoscale influence is present. The drawback of this method is that one is constrained to a periodic domain with either flat or periodic terrain. Neither of these drawbacks work well with realistic terrain.

This work bring together the advantages of both methods outlined above for the case of complex terrain with a standalone microscale solver. The idea is simple. The microscale simulation in complex terrain is not periodic, but rather has distinct inflow and outflow boundaries. Velocity and temperature data from the mesoscale solver are interpolated in space and time to create the "base" part of the inflow boundary conditions of the microscale simulation. Rather than add velocity or temperature perturbations from stochastic methods, a separate periodic microscale LES is run with driving mesoscale sources, like the pressure gradient force. The idea is that the conditions simulated, although over flat or periodic terrain with periodic boundary conditions, will be similar enough to the terrain case that the turbulence developed will be similar to that which the terrain case should include. The fluctuating field from this mesoscale-informed precursor LES are extracted and superimposed on the mesoscale-model-derived inflow of the inflow/outflow terrain case. Mathematically, for any inflow quantity, φ (velocity, temperature, etc.), this equates to

φ_inflowMicro = φ_inflowMeso + (φ_precursor - <φ_precursor>)

where φ_inflowMicro is the field being used as inflow boundary conditions for the microscale simulation, φ_inflowMeso is the smooth (no resolved turbulence) inflow from the mesoscale solver, φ_precursor is the precursor LES generated boundary data, and the angle brackets are the mean of the precursor flow. The right hand-side quantity in parentheses is the fluctuating precursor field. Basically, we are replacing the stochastic perturbations with LES-generated perturbations in a hope that less distance from the inflow boundary is needed to create realistic and correct turbulence.

2. Approach

In order to test the idea, we use the OpenFOAM-based Simulator fOr Wind Farm Applications (SOWFA), a wind-plant computational fluid dynamics tool developed at the National Renewable Energy Laboratory. We simulate terrain over the Columbia River, which is shown in Fig. 1 (a). The computational domain is 15 km x 15 km in the horizontal and 4 km in the vertical. The resolution is uniform 20 m in the lowest 1 km of the domain. Above that, the mesh coarsens to 40 m, and then 80 m resolution. Because the mesoscale-inflow precursor has a flat bottom boundary, the turbulence data extracted from it is simply mapped geometrically to the terrain-conforming inflow boundaries of the terrain case.

3. Initial Results

At this point, our results are qualitative but promising. Figure 1 (b) shows contours of instantaneous wind speed in a surface 80 m above the terrain, a height typical of wind turbine rotor hubs. One can see that the turbulence that enters the domain from the north and west is already realistic LES turbulence, so there is no need to transition from stochastic to physical turbulence. The turbulence may still need to adjust to the terrain and the specific mesoscale conditions it then encounters, though. Flow separates over some of the steeper parts of the ridge to the north of the Columbia River and the wind speed becomes very low over the river. By the time the flow has crossed the river, it is horizontally non-homogeneous and clearly influenced by the terrain.

4. Working Toward the Full Paper

In the full paper, we will further this work by enlarging our domain of interest to include an 80 m meteorological mast south of the domain shown in Fig. 1. That will allow us to compare our results against the meteorological mast data for assessment of the performance of the coupling method. The difficulty that will arise is separating the error due to the coupling method from the error inherent in the mesoscale simulation used to drive the microscale simulation. We will also compare the proposed mesoscale-microscale coupling method with other methods that use stochastic perturbations to initiate resolved-scale turbulence in the microscale domain.