scholarly journals Turbulence statistics from three different nacelle lidars

2021 ◽  
Author(s):  
Wei Fu ◽  
Alfredo Peña ◽  
Jakob Mann
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Wind Velocity ◽  
Sonic Anemometer ◽  
Volume Averaging ◽  
Doppler Spectrum ◽  
Probe Volume ◽  
Reynolds Stress Tensor ◽  
Multiple Beams ◽  
Velocity Variance

Abstract. Atmospheric turbulence can be characterized by the Reynolds stress tensor, which consists of the second-order moments of the wind field components. Most of the commercial nacelle lidars cannot estimate all components of the Reynolds stress tensor due to their limited number of beams; most can estimate the along-wind velocity variance relatively well. Other components are however also important to understand the behavior of, e.g., the vertical wind profile and meandering of wakes. The SpinnerLidar, a research lidar with multiple beams and a very high sampling frequency, was deployed together with two commercial lidars in a forward-looking mode on the nacelle of a Vestas V52 turbine to scan the inflow. Here, we compare the lidar-derived turbulence estimates with those from a sonic anemometer using both numerical simulations and measurements from a nearby mast. We show that from these lidars, the SpinnerLidar is the only one able to retrieve all Reynolds stress components. For the two- and four-beam lidars, we study different methods to compute the along-wind velocity variance. By using the SpinnerLidar's Doppler spectra of the radial velocity, we can partly compensate for the lidar's probe volume averaging effect and thus reduce the systematic error of turbulence estimates. We find that the variances of the radial velocities estimated from the maximum of the Doppler spectrum are less affected by the lidar probe volume compared to those estimated from the median or the centroid of the Doppler spectrum.

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

Experimental study of particle-driven secondary flow in turbulent pipe flows

2012 ◽  
Vol 709 ◽  
pp. 1-36 ◽  
Author(s):  
R. J. Belt ◽  
A. C. L. M. Daalmans ◽  
L. M. Portela
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Cross Section ◽  
Circular Pipe ◽  
Horizontal Pipe ◽  
Pipe Cross Section ◽  
Reynolds Stress Tensor ◽  
Pipe Flows

AbstractIn fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, $\partial {\tau }_{rr} / \partial r$ and $\partial {\tau }_{\theta \theta } / \partial \theta $. Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.

Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer

1998 ◽  
Vol 120 (2) ◽  
pp. 280-284 ◽  
Author(s):  
A. Mazouz ◽  
L. Labraga ◽  
C. Tournier
Keyword(s):  
Surface Roughness ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Pipe Flow ◽  
Duct Flow ◽  
Reynolds Stress Tensor ◽  
Entire Thickness ◽  
Anisotropy Tensor ◽  
Flow Turbulence

The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

Large-eddy simulation subgrid modelling using neural networks

2020 ◽  
Author(s):  
Robin Stoffer ◽  
Caspar van Leeuwen ◽  
Damian Podareanu ◽  
Valeriu Codreanu ◽  
Menno Veerman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Grid Point ◽  
A Priori ◽  
Flow Fields ◽  
Training Dataset ◽  
Reynolds Stress Tensor ◽  
Eddy Simulation ◽  
The Neural Networks

<p><span>Large-eddy simulation (LES) is an often used technique in the geosciences to simulate turbulent oceanic and atmospheric flows. In LES, the effects of the unresolved turbulence scales on the resolved scales (via the Reynolds stress tensor) have to be parameterized with subgrid models. These subgrid models usually require strong assumptions about the relationship between the resolved flow fields and the Reynolds stress tensor, which are often violated in reality and potentially hamper their accuracy.</span></p><p><span>In this study, using the finite-difference computational fluid dynamics code MicroHH (v2.0) and turbulent channel flow as a test case (friction Reynolds number Re<sub>τ</sub> 590), we incorporated and tested a newly emerging subgrid modelling approach that does not require those assumptions. Instead, it relies on neural networks that are highly non-linear and flexible. Similar to currently used subgrid models, we designed our neural networks such that they can be applied locally in the grid domain: at each grid point the neural networks receive as an input the locally resolved flow fields (u,v,w), rather than the full flow fields. As an output, the neural networks give the Reynolds stress tensor at the considered grid point. This local application integrates well with our simulation code, and is necessary to run our code in parallel within distributed memory systems.</span></p><p><span>To allow our neural networks to learn the relationship between the specified input and output, we created a training dataset that contains ~10.000.000 samples of corresponding inputs and outputs. We derived those samples directly from high-resolution 3D direct numerical simulation (DNS) snapshots of turbulent flow fields. Since the DNS explicitly resolves all the relevant turbulence scales, by downsampling the DNS we were able to derive both the Reynolds stress tensor and the corresponding lower-resolution flow fields typical for LES. In this calculation, we took into account both the discretization and interpolation errors introduced by the finite staggered LES grid. Subsequently, using these samples we optimized the parameters of the neural networks to minimize the difference between the predicted and the ‘true’ output derived from DNS.</span></p><p><span>After that, we tested the performance of our neural networks in two different ways:</span></p><ol><li><span>A priori or offline testing, where we used a withheld part of the training dataset (10%) to test the capability of the neural networks to correctly predict the Reynolds stress tensor for data not used to optimize its parameters. We found that the neural networks were, in general, well able to predict the correct values. </span></li> <li><span>A posteriori or online testing, where we incorporated our neural networks directly into our LES. To keep the total involved computational effort feasible, we strongly enhanced the prediction speed of the neural network by relying on highly optimized matrix-vector libraries. The full successful integration of the neural networks within LES remains challenging though, mainly because the neural networks tend to introduce numerical instability into the LES. We are currently investigating ways to minimize this instability, while maintaining the high accuracy in the a priori test and the high prediction speed.</span></li> </ol>

The Development of the Reynolds Stress Tensor in a Turbulent Shear Flow

1970 ◽  
Vol 92 (4) ◽  
pp. 836-842
Author(s):  
S. J. Shamroth ◽  
H. G. Elrod
Keyword(s):  
Shear Flow ◽  
Stress Tensor ◽  
Linear Model ◽  
Reynolds Stress ◽  
Experimental Results ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stress Tensor ◽  
Theoretical Predictions

The development of the normalized Reynolds stress tensor, uiuj/q2, in the region upstream of a fully developed, turbulent shear flow is investigated. An inviscid, linear model is used to predict values of the normalized Reynolds stress tensor as a function of position. The theoretical predictions are then compared with experimental results.

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