Influence of turbulence anisotropy on RANS predictions of wind-turbine wakes

Simulating wind-turbines in Reynolds-averaged Navier-Stokes (RANS) codes is highly challenging, at least partly due to the importance of turbulence anisotropy in the evolution of the wake. We present a preliminary investigation into the role of anisotropy in RANS simulations of vertical-axis turbines, by comparison with LES. Firstly an LES data-set serving as our ground-truth is generated, and verified against previously published works. This data-set provides raw turbulence anisotropy fields for several turbine configurations. This anisotropy is injected into RANS simulations of identical configurations to determine the extent to which it influences (i) the production of turbulence kinetic energy, (ii) the turbulence momentum forcing, and finally (iii) the mean-flow. In all these quantities we observe the anisotropy has a surprisingly limited effect, and is certainly not the leading-order error in Boussinesq RANS for these cases. Nevertheless we go on to show that it is feasible to predict anisotropy fields for unseen configurations based only on the mean-flow, by using a tensorized version of random-forest regression. Aerodynamic

Aerodynamic Shape Optimization Using the Discrete Adjoint of the Navier-Stokes Equations: Applications towards Complex 3D Configurations

Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy. After describing the theory of the viscous discrete adjoint method and its implementation within the unstructured RANS solver TAU, this paper describes application for aerodynamic shape optimization. First wing and fuselage designs of the DLR-F6 wing-body aircraft are presented. A step forward in complexity is considered by applying the adjoint for flap and slat optimal settings of the DLR-F11 model, a wing-body aircraft in high-lift configuration. On all cases presented, optimization were successfully performed within a limited number of flows evaluations.Aerodynamics & Wind EnergyAerospace Engineerin

Data assimilation for Navier-Stokes using the least-squares finite-element method

We investigate theoretically and numerically the use of the least-squares finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based on a stress-velocity-pressure (S-V-P) first-order formulation, using discrete counterparts of the Sobolev spaces H(div) ×H1 ×L2 for the variables respectively. In general, S-V-P formulations are promising when the stresses are of special interest, e.g., for non-Newtonian, multiphase or turbulent flows. Resolution of the system is via minimization of a least-squares functional representing the magnitude of the residual of the equations. A simple and immediate approach to extend this solver to data assimilation is to add a data-discrepancy term to the functional. Whereas most data assimilation techniques require a large number of evaluations of the forward simulation and are therefore very expensive, the approach proposed in this work uniquely has the same cost as a single forward run. However, the question arises: what is the statistical model implied by this choice? We answer this within the Bayesian framework, establishing the latent background covariance model and the likelihood. Further we demonstrate that—in the linear case—the method is equivalent to application of the Kalman filter, and derive the posterior covariance. We practically demonstrate the capabilities of our method on a backward-facing step case. Our LSFEM formulation (without data) is shown to have good approximation quality, even on relatively coarse meshes—in particular with respect to mass conservation and reattachment location. Adding limited velocity measurements from experiment, we show that the method is able to correct for discretization error on very coarse meshes, as well as correct for the influence of unknown and uncertain boundary conditions.Aerodynamic

Solenoidal filtering of volumetric velocity measurements using Gaussian process regression

Volumetric velocity measurements of incompressible flows contain spurious divergence due to measurement noise, despite mass conservation dictating that the velocity field must be divergence-free (solenoidal). We investigate the use of Gaussian process regression to filter spurious divergence, returning analytically solenoidal velocity fields. We denote the filter solenoidal Gaussian process regression (SGPR) and formulate it within the Bayesian framework to allow a natural inclusion of measurement uncertainty. To enable efficient handling of large data sets on regular and near-regular grids, we propose a solution procedure that exploits the Toeplitz structure of the system matrix. We apply SGPR to two synthetic and two experimental test cases and compare it with two other recently proposed solenoidal filters. For the synthetic test cases, we find that SGPR consistently returns more accurate velocity, vorticity and pressure fields. From the experimental test cases, we draw two important conclusions. Firstly, it is found that including an accurate model for the local measurement uncertainty further improves the accuracy of the velocity field reconstructed with SGPR. Secondly, it is found that all solenoidal filters result in an improved reconstruction of the pressure field, as verified with microphone measurements. The results obtained with SGPR are insensitive to correlation length, demonstrating the robustness of the filter to its parameters.Aerodynamics, Wind Energy & PropulsionAerospace Engineerin

Data-driven modelling of the Reynolds stress tensor using random forests with invariance

A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor for new, unseen flows. The resulting predictions of turbulence anisotropy are used as a turbulence model within a custom RANS solver. Stabilization of this solver is necessary, and is achieved by a continuation method and a modified k-equation. Results are compared to the neural network approach of Ling et al. [29]. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with realizable predictions close to the DNS/LES reference data. Corresponding mean flows for a square duct flow case and a backward facing step flow case show good agreement with DNS and experimental data-sets. Overall, these results are seen as a next step towards improved data-driven modelling of turbulence. This creates an opportunity to generate custom turbulence closures for specific classes of flows, limited only by the availability of LES/DNS data.Aerodynamic

Vortex-in-Cell method for time-supersampling of PIV data

The present work investigates the use of a vortex-in-cell (VIC) inviscid, incompressible Navier-Stokes solver [1,2] to increase temporal resolution of time-resolved 3D fluid-velocity data obtained from tomographic PIV experiments. The measurement rate in such experiments is limited by available laser power, and the requirements of laser pulse energy and quality of particle image digital recordings. The principle of time-supersampling is that by using an interpolation based on a largely complete description of the flow-physics, high spatial-resolution can be leveraged to increase low temporal-resolution. The numerical solver simulating the fluid is applied on a domain corresponding to the 3D measurement volume, and time-integration is performed between each pair of consecutive measurements. Initial conditions are taken from the first measurement field, and time-resolved boundary conditions can be approximated either by linear interpolation or advection-model-based interpolation between the two fields. To obtain a continuous representation of the velocity in time, a weighted-average of forward- and backward-time integration is made. To make the backward integration problem well-posed, viscosity is neglected. This is justified given the short time-interval between measurements. The supersampling method is applied to a turbulent wake, and a cylindrical jet, and compared to reference high-frequency experimental data, as well as an advection-model-based supersampling approach. In both test cases temporal resolution substantially above the Nyquist limit is achieved

Trimmed simulation of a transport aircraft using fluid-structure coupling

The accurate prediction of the aerodynamic coefficients under cruise conditions is of major importance for assessing the aircraft’s fuel consumption. To this end, fluid dynamics, structural mechanics and flight mechanics have to be considered: on the one hand, the structure elastically deforms under the influence of the flow and a state of static aeroelastic equilibrium is reached; on the other hand, the aircraft’s loads are balanced by adjusting control surfaces, which influences the flow. A procedure has been developed to account for this interplay. For the interaction between fluid and structure (FSI), a partitioned approach is followed to make use of highly-specialized solvers for each discipline: for the equations governing the flow, the hybrid RANS DLR-TAU-code is employed, whereas for the structural equations, ANSYS is used. The trimmed states are computed using a Newton method, in which the derivatives are calculated using finite difference approximations or, alternatively, using the discrete adjoint. The first test case shows the trim results for a 2-dimensional wing-tail configuration, comparing the approach using finite difference approximations with the one using the discrete adjoint. The second test case uses finite differences for finding the trimmed state for the DLR-F12 transport aircraft configuration in viscous flow, comparing the results of a rigid aircraft with the ones where the wing was allowed to deform elastically.Aerodynamics & Wind EnergyAerospace Engineerin

Data-driven turbulence modeling for wind turbine wakes under neutral conditions

Currently, the state of the art in wind farm flow physics modeling are Large Eddy Simulations (LES) which resolve a large part of the spectra of the turbulent fluctuations. But this type of model requires extensive computational resources. One wind speed and direction simulation of the Lillgrund wind farm can take between 160k and 3000k processor hours depending on how the turbines are modeled [1, 2]. The next-fidelity model types are Reynolds-Averaged Navier-Stokes (RANS) models which resolve only the mean quantities and model the effect of turbulence fluctuations. These models require about two orders of magnitude less computational time, but generally do not produce accurate predictions of the mean flow field. Proposed modifications made to these models so far do not generalize well and there is room for improvement. Hence, we present the first steps towards using a data-driven approach to aid in deriving new RANS models that generalize well to different turbine types, varying atmospheric stability, and farm layouts. To do so, time-averaged LES data is used to derive corrections to existing RANS models. The approach uses a deterministic symbolic regression method to infer algebraic correction terms to the RANS turbulence transport equations. Optimal correction terms to the RANS equations are derived using a frozen approach where time-averaged flow fields from LES are injected into the RANS equations. The potential of the approach is demonstrated under neutral conditions for multi-turbine constellations at wind-tunnel scale. The results show promise, but more work is necessary to realize the full potential of the approach. Wind EnergyAerodynamic

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3-D Reynolds-averaged Navier-Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced-motion simulations are used to train a time-domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.AerodynamicsWind Energ

Symbolic regression of algebraic stress-strain relation for RANS turbulence closure

In this work recent advancements are presented in utilising deterministic symbolic regression to infer algebraic models for turbulent stress-strain relation with sparsity-promoting regression techniques. The goal is to build a functional expression from a set of candidate functions in order to represent the target data most accurately. Targets are the coefficients of a polynomial tensor basis, which are identified from high-fidelity data using regularised least-square regression. The method successfully identified a correction term for the benchmark test case of flow over periodic hills in 2D at Reh = 10595.Aerodynamic