A Novel Algebraic Stress Model with Machine-Learning-Assisted Parameterization

Reynolds-stress closure modeling is critical to Reynolds-averaged Navier-Stokes (RANS) analysis, and it remains a challenging issue in reducing both structural and parametric inaccuracies. This study first proposes a novel algebraic stress model named as tensorial quadratic eddy-viscosity model (TQEVM), in which nonlinear terms improve previous model-form failure due to neglection of nonlocal effects. Then a data-driven regression model based on a fully-connected deep neural network is designed to determine the TQEVM coefficients. The well-trained data-driven model using high-fidelity direct numerical simulation (DNS) data successfully learned the underlying input-output relationships, further obtaining spatial-dependent optimal values of these coefficients. Finally, detailed validations are made in wall-bounded flows where nonlocal effects are expected to be significant. Comparative results indicate that TQEVM provides improvements both for the stress-strain misalignment and stress anisotropy, which are clear advantages over linear and quadratic eddy-viscosity models. TQEVM extends to the scope of resolution to the wall distance y + ≈ 9 as well as provides a realizable solution. RANS simulations with TQEVM are also carried out and the obtained mean-flow quantities of interest agree well with DNS. This work, therefore, results in a high-fidelity representation of Reynolds stresses and contributes to further understanding of machine-learning-assisted turbulence modeling and regression analysis.

Analysis of Turbulent Flow Around Horizontal Axis Wind Turbines Using Algebraic Stress Model

Due to the problems associated with increase of greenhouse gases, and the limited supply of fossil fuels, switching to clean and renewable sources of energy seems necessary. Wind energy is a very suitable form of renewable energy which can be a good choice for those areas around the world with sufficient amount of wind annually. However, in order for the commercial wind turbines to be cost-effective, they need to operate at very high elevations, and therefore, blades with the length as high as 60–70 m are common. Because of the high manufacturing and transportation costs of the wind turbine components, it is necessary to evaluate and predict the performance of the turbine prior to shipping it to the installation site. Computational Fluid Dynamics (CFD) has proven to be a simple, cheap and yet relatively accurate tool for prediction of wind turbine performance, where suitability of different designs can be evaluated at a low cost. Total lift and drag forces can be calculated, from which one can estimate the torque, and ultimately the output power. Reynolds Stress Model (RSM) is a well-known Reynolds Averaged Navier-Stokes (RANS) turbulence model, which is typically more accurate than eddy viscosity models, but it comes with higher computational cost. In the present work, turbulent flow of air around a horizontal axis wind turbine blade is modeled computationally by using a modified version of RSM, known as Algebraic Stress Model (ASM) for the near-blade region. Because of the periodicity nature of the flow domain, only one of three blades is modeled by applying the periodic conditions on the sides of a 120 degree sector of the domain. While the flow is solved in the bulk fluid using the k-epsilon model, in order to better capture the near-wall effects and to make the computations cost effective, it is proposed to apply ASM only in the locations very close to the blade surface. A number of reasonable assumptions are made in ASM in order to convert the transport differential equations of the Reynolds stresses into an algebraic form. The highly coupled system of non-linear equations is then solved concurrently for six Reynolds stress components. Turbulent kinetic energy, turbulent dissipation rate, and mean velocity gradients are calculated from the k-epsilon model and used as initial values and iterated through the ASM computations. To the best of our knowledge, this is the first time that ASM is used for analysis of Reynolds stress for flow around rotating wind turbines blades. Reynolds stresses are obtained at several locations (heights) along the blade, and at different radial distances from the blade. Different variations of implicit and explicit ASM are examined and compared in terms of accuracy. Results indicate that the implicit ASM method using the full form of pressure-strain term tends to show predictions that are closer to the predictions of the fully-resolved RSM simulation, as compared to the other ASM models examined. Therefore, there seems to be a good potential for reducing computational costs for determination of near wall Reynolds stresses and ultimately calculating torque and power generated from wind turbines without sacrificing the accuracy.

Eddy Diffusivities for Momentum and Heat in the Upper Troposphere and Lower Stratosphere Measured by MU Radar and RASS, and a Comparison of Turbulence Model Predictions

Recently, middle- and upper-atmosphere Doppler radar (MU radar) has enabled the measurement of middle-atmosphere turbulence from radar backscatter Doppler spectra. In this work, eddy diffusivities for momentum Km in the upper troposphere and lower stratosphere during clear-air conditions were derived from direct measurements of the Reynolds stress and vertical gradient of mean wind velocity measured by MU radar. Eddy diffusivity for heat Kh below 8 km was determined from measurements of temperature fluctuations by the Radio Acoustic Sounding System (RASS) attached to the MU radar. The eddy diffusivity for momentum was on the order of 10 m2 s−1 in the upper troposphere and decreased gradually in the stratosphere by an order of magnitude or more. The eddy diffusivity for heat was almost of the same order of magnitude as Km. Estimates of eddy diffusivity from the radar echo power spectral width give fairly good values compared with the direct measurement of Km. Applicability of three turbulence models—the spectral width method, the k–ɛ model modified for stratified flows, and the algebraic stress model—were also examined, using radar observation values of turbulent kinetic energy k and turbulent energy dissipation rate ɛ together with atmospheric stability observations from rawinsonde data. It is concluded that the algebraic stress model shows the best fit with the direct measurement of Km, even in the free atmosphere above the atmospheric boundary layer once k and ɛ values are obtained from observations or a model.