Closure models for the turbulent scalar flux are an important source of uncertainty in Reynolds-averaged-Navier-Stokes (RANS) simulations of scalar transport. This paper presents an approach to quantify this uncertainty in simulations of complex engineering flows. The approach addresses the uncertainty in modeling the pressure scrambling (PS) effect, which is the primary mechanism balancing the productions in scalar flux dynamics. Inspired by the two classical phenomenological theories of return-to-isotropy (RI) and isotropization-of-production (IP), we assume that the most likely directions of the PS term are around a fan-shaped region bounded by the RI and IP directions. Subsequently, we propose a strategy that requires two additional simulations, defining perturbations of the PS directions towards the RI and IP limits. The approach is applied to simulations of forced heat convection in a complex pin-fin array configuration, and shows favorable monotonic properties and bounding behaviors for various quantities of interest (QoIs) relevant to heat transfer. To conclude, the results are analyzed from the perspective of transverse scalar transport in a shear flow; the analysis indicates that the proposed approach is likely to exhibit monotonic behaviors in a wide range of scalar transport problems.
It is well known that Boussinesq turbulent-viscosity hypothesis can introduce uncertainty in predictions for complex flow features such as separation, reattachment, and laminar-turbulent transition. This study adopts a recent physics-based uncertainty quantification (UQ) approach to address such model form uncertainty in Reynolds-averaged Naiver- Stokes (RANS) simulations. Thus far, almost all UQ studies have focused on quantifying the model form uncertainty in turbulent flow scenarios. The focus of the study is to advance our understanding of the performance of the UQ approach on two differen…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent systems containing a large number of positive Lyapunov exponents results in a rapid growth of small uncertainties, requiring naturally a probabilistic characterization for the evolution of the turbulent system. Uncertainty quantification in turbulent dynamical systems is a grand challenge where the goal is to obtain statistical estimates such as the change …
We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical simulations in three dimensions in periodic boxes. From the spectrum, we find that a significant fraction of the energy is concentrated in modes with wave frequency $ω\approx 0$, even when the external forcing injects no energy directly into these modes. However, for modes for which the period of the inertial waves $τ_ω$ is faster than the turnover time $τ_\textr…
It is well known that the Boussinesq turbulent viscosity hypothesis can yield inaccurate predictions when complex f low features are involved, e.g. laminar-turbulent transition. The focus of the study is to explore the capability of a physics-based uncertainty quantification (UQ) approach to quantify the model-form uncertainty in Reynolds-averaged Naiver-Stokes (RANS) simulations of laminar-turbulent transitional flows over an Selig-Donovan (SD) 7003 airfoil. This methodology perturbs the modeled Reynolds stress tensor in the momentum equations; perturbations are injected into the amplitude, e…
The predictive accuracy of wall-modeled large eddy simulation is studied by systematic simulation campaigns of turbulent channel flow. The effect of wall model, grid resolution and anisotropy, numerical convective scheme and subgrid-scale modeling is investigated. All of these factors affect the resulting accuracy, and their action is to a large extent intertwined. The wall model is of the wall-stress type, and its sensitivity to location of velocity sampling, as well as law of the wall's parameters is assessed. For efficient exploration of the model parameter space (anisotropic grid resolutio…
A stochastic approach based on generalized Polynomial Chaos (gPC) is used to quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving mixing layer flow and its sensitivity to different simulation parameters, viz. the grid stretching in the streamwise and lateral directions and the subgrid scale model constant ($C_S$). The error is evaluated with respect to the results of a highly resolved LES (HRLES) and for different quantities of interest, namely the mean streamwise velocity, the momentum thickness and the shear stress. A typical feature of the considered spatially evolving …
Reynolds Averaged Navier Stokes (RANS) modelling is notorious for introducing the model-form uncertainty due to the Boussinesq turbulent viscosity hypothesis. Recently, the eigenspace perturbation method (EPM) has been developed to estimate the RANS model-form uncertainty. This approach estimates model-form uncertainty through injecting perturbations to the predicted Reynolds stress tensor. However, there is a need for a reliable machine learning method for estimating the perturbed amplitude of the Reynolds stress tensor. Machine learning models are often too complex and data intensive for thi…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows id…
Experiments on the effects due solely to a mobile granular layer on a liquid flow are presented (feedback effect). Nonintrusive measurements were performed in a closed conduit channel of rectangular cross section where grains were transported as bed load by a turbulent water flow. The water velocity profiles were measured over fixed and mobile granular beds of same granulometry by Particle Image Velocimetry. The spatial resolution of the measurements allowed the experimental quantification of the feedback effect. The present findings are of importance for predicting the bed-load transport rate…
A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified $k-ω$ equation for canonical wall bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number ($Re$). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the $k-ω$ equation. Three innovations are introduced: First, an adjustme…
Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change o…
Turbophoresis leading to preferential concentration of inertial particles in regions of low turbulent diffusivity is a unique feature of inhomogeneous turbulent flows, such as free shear flows or wall-bounded flows. In this work, the theory for clustering of weakly inertial particles in homogeneous turbulence is extended to the inhomogeneous case of a turbulent channel flow. The inhomogeneity contributes to the cluster formation in addition to clustering in homogeneous turbulence. A space-dependent rate for the creation of inhomogeneous particle concentration is derived in terms of local stati…
Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely used in aerospace applications but suffers inaccuracies due to the Boussinesq turbulent viscosity hypothesis. The eigenspace perturbation method can estimate the accuracy of a RANS model by injecting perturbations to its predicted Reynolds stresses. However, there lacks a reliable method for choosing the strength of the injected perturbation, while existing machine learning models are often complex and data craving. We examined two light-weighted machine learning models to help select the strength of the injected pertur…
On the rheoscopic measurement of turbulent decay in wall-bounded flows
PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité（PMHC，法国国家科学研究中心，巴黎高等物理化工学院，巴黎文理研究大学，索邦大学，巴黎西岱大学）；Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles（加州大学洛杉矶分校地球、行星与空间科学系）；FAST, CNRS, Université Paris-Saclay（FAST，法国国家科学研究中心，巴黎萨克雷大学）
Direct numerical simulation of a thermal turbulent boundary layer: an analogy to simulate bushfires and a testbed for artificial intelligence remote sensing of bushfire propagation
We present the construction of an original stochastic model for the instantaneous turbulent kinetic energy at a given point of a flow, and we validate estimator methods on this model with observational data examples. Motivated by the need for wind energy industry of acquiring relevant statistical information of air motion at a local place, we adopt the Lagrangian description of fluid flows to derive, from the $3$D+time equations of the physics, a $0$D+time-stochastic model for the time series of the instantaneous turbulent kinetic energy at a given position. Specifically, based on the Lagrangi…
We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, $W(τ)$, of a particle's energy over a time-scale $τ$ is non-Gaussian, and skewed towards negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this $\textit{slow gain}$ and $\textit{fast loss}$. We find that the third moment of $W(…
We introduce a novel end-to-end approach to improving the resolution of PIV measurements. The method blends information from different snapshots without the need for time-resolved measurements on grounds of similarity of flow regions in different snapshots. The main hypothesis is that, with a sufficiently large ensemble of statistically-independent snapshots, the identification of flow structures that are morphologically similar but occurring at different time instants is feasible. Measured individual vectors from different snapshots with similar flow organisation can thus be merged, resulting…
A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator's outputs with respect to uncertain inputs and computational parameters. These parameters are divided into two groups: based on the variation of the first group, a computer experiment is designed, the data of which may become uncertain due to the parameters of the second grou…
The effect of grid resolution on large eddy simulation (LES) of wall-bounded turbulent flow is investigated. A channel flow simulation campaign involving systematic variation of the streamwise ($Δx$) and spanwise ($Δz$) grid resolution is used for this purpose. The main friction-velocity based Reynolds number investigated is 300. Near the walls, the grid cell size is determined by the frictional scaling, $Δx^+$ and $Δz^+$, and strongly anisotropic cells, with first $Δy^+ \sim 1$, thus aiming for wall-resolving LES. Results are compared to direct numerical simulations (DNS) and several quality …
In this brief, we try to develop a comprehensive framework to identify, quantify, isolate, and reduce the uncertainties in the original BHR model \citep {Besnard1992} for variable-density flows. Because the eigenspace perturbation of Reynolds stress successfully accounts for the structural uncertainty in many flows, we first extend this methodology to the BHR model for variable-density flows with different $At$. The philosophy of eigenspace perturbation in Reynolds stress, i.e., quantifying the states of maximizing and minimizing the production mechanism, has led to the proposals of the struct…
A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；Computational Science Center, National Renewable Energy Laboratory（美国国家可再生能源实验室计算科学中心）
Simulations based on Reynolds-Averaged Navier--Stokes (RANS) models have been used to support high-consequence decisions related to turbulent flows. Apart from the deterministic model predictions, the decision makers are often equally concerned about the predictions confidence. Among the uncertainties in RANS simulations, the model-form uncertainty is an important or even a dominant source. Therefore, quantifying and reducing the model-form uncertainties in RANS simulations are of critical importance to make risk-informed decisions. Researchers in statistics communities have made efforts on th…
Vorticity in turbulent flows is often organized into complex geometries that influence the dynamics. We use a relatively novel approach to describe these geometries: that of obtaining segments of vortex lines embedded in the flow. This enables us to quantify the geometric features of these objects. Vortex lines differ widely in their behaviour but we find some unifying features. The decay from high levels of vorticity is shown to happen over a short fraction of the vortex length. The local curvature is inversely related with the vorticity magnitude. Strong parts of vortex lines bundle together…
In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (\textit{Simulation 1}) impinging on a flat plate to provide convective heat transfer (\textit{Simulation 2}). The first approach is the Stochastic Collocation Method (SCM) with Clenshaw-Curtis sparse grids. The concl…
Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flows
School of Data Science, University of Virginia（数据科学学院，弗吉尼亚大学）；Department of Mechanical Engineering, University of Iowa（机械工程系，爱荷华大学）；Department of Mechanical and Aerospace Engineering, University of Virginia（机械与航空航天工程系，弗吉尼亚大学）
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering application. For many practical flows, the turbulence models are by far the largest source of uncertainty. In this work we develop an open-box, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., real…
