[Paper Review] Model-form uncertainty quantification in RANS simulations of wakes and power losses in wind farms

Ali Eidi, Reza Ghiassi+2 more|arXiv (Cornell University)|May 8, 2021

Wind Energy Research and DevelopmentEngineering67 references34 citations

TL;DR

This study quantifies model-form uncertainty in RANS simulations of wind farm wakes and power losses by comparing multiple RANS models against large-eddy simulation (LES) data. The realizable k−ε model is identified as the most accurate baseline, and perturbations to the eigenvalues of the Reynolds stress tensor—representing turbulence anisotropy—successfully bound LES results for mean velocity deficit, turbulence intensity, and power output, with δ = 0.5 providing a robust uncertainty bound across aligned and staggered wind farm configurations.

ABSTRACT

Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, the applicability of RANS-based methods is always limited by the accuracy of turbulence closure models, which introduce various uncertainties into the models. In this study, we estimate model-form uncertainties in RANS simulations of wind farms. For this purpose, we compare different RANS models to a large-eddy simulation (LES). We find that the realizable k-epsilon model is a representative RANS model for predicting the mean velocity, the turbulence intensity, and the power losses within the wind farm. We then investigate the model-form uncertainty associated with this turbulence model by perturbing the Reynolds stress tensor. The focus is placed on perturbing the shape of the tensor represented by its eigenvalues. The results show that the perturbed RANS model successfully estimates the region bounding the LES results for quantities of interest (QoIs). We also discuss the effect of perturbation magnitude on various QoIs.

Motivation & Objective

• To quantify model-form uncertainty in RANS simulations of wind farm wakes and power losses due to turbulence model assumptions.
• To evaluate the performance of multiple RANS models (standard k−ε, RNG k−ε, realizable k−ε, SST k−ω, fp k−ε) against high-fidelity LES data.
• To identify a representative RANS model that best captures mean velocity, turbulence intensity, and power deficits in wind farms.
• To apply eigenvalue-based perturbation of the Reynolds stress tensor to quantify structural uncertainty in the realizable k−ε model.
• To assess the impact of perturbation magnitude (δ = 0.25, 0.5, 1) on uncertainty bounds for key quantities of interest (QoIs).

Proposed method

• Conduct RANS simulations using the realizable k−ε model as the baseline, validated against LES data for mean velocity, turbulence intensity, and power output.
• Apply eigenvalue-based perturbation to the Reynolds stress tensor to represent extreme anisotropic states: one-component, two-component, and three-component (isotropic) turbulence.
• Use three perturbation magnitudes: δ = 0.25 (least conservative), δ = 0.5 (from prior studies), and δ = 1 (extremely conservative).
• Perform simulations for both aligned and staggered wind farm layouts with varying turbine spacing (5D and 7D) to test robustness.
• Compare perturbed RANS results against LES data to evaluate whether the perturbed models bound the LES solution across different configurations.
• Conduct grid convergence studies to ensure solution independence, using medium-resolution grids (234 × 40 × 58) for final results.

Experimental results

Research questions

• RQ1 Which RANS model most accurately predicts mean velocity deficit, turbulence intensity, and power output in wind farm simulations compared to LES?
• RQ2 Can perturbation of the Reynolds stress tensor's eigenvalues (representing turbulence anisotropy) effectively bound the LES solution for key wind farm QoIs?
• RQ3 How does the magnitude of perturbation (δ) affect the uncertainty bounds for velocity deficit, turbulence intensity, and power loss?
• RQ4 Does the proposed uncertainty quantification framework remain robust under different wind farm configurations, such as staggered layouts and closer turbine spacing?
• RQ5 What is the optimal perturbation magnitude (δ) that balances conservatism and accuracy in bounding LES results?

Key findings

• The realizable k−ε model demonstrates the best agreement with LES data for mean velocity deficit, turbulence intensity, and power output, and is selected as the baseline RANS model.
• Perturbation of the Reynolds stress tensor toward three-component (isotropic) turbulence leads to faster wake recovery and reduced turbulence intensity, increasing downstream turbine power output.
• Perturbation toward one-component turbulence increases wake deficit and turbulence intensity, reducing downstream power output, indicating the opposite trend.
• Perturbation toward two-component turbulence produces intermediate results, lying within the bounds of one- and three-component perturbations, and does not significantly alter predictions compared to the baseline.
• A perturbation magnitude of δ = 0.5 successfully bounds the LES results for all key QoIs across both aligned and staggered wind farm configurations, demonstrating robustness.
• The uncertainty quantification framework effectively captures the structural uncertainty in RANS simulations, even under partial wake interaction scenarios (e.g., staggered layouts), confirming its generalizability.