Lead Session Chair:
Stephan Barth, Managing Director, ForWind - Center for Wind Energy Research, Germany
Anshul Mittal (1) F P W. Roger Briley (1) Lafayette Taylor (1) Kidambi Sreenivas (1)
(1) SimCenter, University of Tennessee at Chattanooga, Chattanooga, United States
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Presenter's biographyBiographies are supplied directly by presenters at OFFSHORE 2015 and are published here unedited
Anshul Mittal graduated in 2003 from Indian Institute of Technology Roorkee where he obtained a Bachelor's degree in Mechanical Engineering. He moved to Cleveland, Ohio to obtain a Master's degree in Mechanical Engineering from Case Western Reserve University where he started his research on the placement of wind turbines in a wind farm. He is presently a graduate student pursuing a Ph.D. in Computational Engineering from the SimCenter at the University of Tennessee at Chattanooga where he is working on high fidelity, low cost models for wind turbine wakes.
A Parabolic Method without Pressure Approximations for a Wind Farm
Wakes in wind farms cause loss of power production and increased maintenance costs. High-fidelity computer simulations have become feasible with current high performance resources. These computations typically consist of Navier-Stokes equations with either blade-resolved or Actuator disk/line models. However, these simulations are still impractical for industrial application. Conversely, runtimes utilizing analytical wake models can be measured in seconds but at greatly reduced accuracy. A numerical simulation using a parabolized Navier-Stokes formulation has the capability to offer high-resolution results for forecasting/micro-siting purposes in a reasonable amount of time on a commodity desktop computer.
A new parabolized Navier-Stokes (PNS) formulation for wind turbines is developed based on the three-dimensional viscous primary/secondary flow approximation. This model predicts the wake and secondary-flow velocity fields consistent with the axial momentum and streamwise vorticity equations. The streamwise pressure-gradient field, consistent with these primary and secondary flows, is a dependent variable of the nonlinear modeling equations without further approximations. Turbines are modeled as Actuator Disks with forces computed using NREL’s FAST code and imposed as source terms. The solution is initialized well upstream of a turbine and spatially marched through the near-wake and far-wake regions.
Main body of abstract
For a wind farm, the prevailing wind defines the primary-flow direction and the solution is spatially marched in this direction. The key to the parabolized Navier-Stokes model is in the viscous and inviscid approximations used. Viscous terms representing streamwise diffusion are neglected. The inviscid approximation is based on a vector decomposition of the transverse velocity field into rotational and irrotational component vectors. The equations are parabolized by neglecting the potential components in the transverse momentum equations that govern the streamwise vorticity, based on order-of-magnitude estimates analogous to those of boundary layer theory but extended to three-dimensional flows with large secondary velocity. The final equation set of five equations is solved by spatial marching using a sequentially decoupled, semi-implicit algorithm.
The developed PNS model has been validated using several test cases. For laminar and turbulent flows past a flat plate, the model gives excellent agreement with theoretical/experimental results. A simple case of a convecting vortex was simulated with the PNS model and a Navier-Stokes code (7th order spatially accurate scheme). The PNS model is less dissipative of streamwise vorticity and gives more accurate solutions than the CFD simulations on a similar mesh. The PNS model was verified for wind turbines by CFD simulations of flow through a NREL 5-MW wind turbine and comparing the PNS results with the CFD solutions. In the final paper, results for the flow through an array of wind turbines will be presented, and the details of the computational cost (runtime and memory requirements) will be discussed.
Accurate solutions for flow through a wind farm can be obtained using the parabolized primary-secondary flow approximation without the need of a supercomputer. The advantage of the present formulation is that the flowfield for each turbine does not have to be reinitialized based on additional simulations or experimental data. Moreover, there is no need to neglect or prescribe the streamwise pressure gradient field. The methodology can be applied for forecasting of power or micro-siting and the model can be easily extended to include atmospheric stability effects.
- New parabolized Navier-Stokes method for wind farm applications
- No approximations for the streamwise pressure gradient field
- Wind turbine modeled as an Actuator Disk