Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network

2019 ◽  
Vol 22 (6) ◽  
pp. 1675-1688 ◽  
Author(s):  
Pavan Pranjivan Mehta ◽  
Guofei Pang ◽  
Fangying Song ◽  
George Em Karniadakis
Keyword(s):  
Neural Network ◽  
Couette Flow ◽  
Turbulent Flows ◽  
Fractional Order ◽  
Scaling Law ◽  
Variable Order ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Fractional Model ◽  
Better Than

Abstract The first fractional model for Reynolds stresses in wall-bounded turbulent flows was proposed by Wen Chen [2]. Here, we extend this formulation by allowing the fractional order α(y) of the model to vary with the distance from the wall (y) for turbulent Couette flow. Using available direct numerical simulation (DNS) data, we formulate an inverse problem for α(y) and design a physics-informed neural network (PINN) to obtain the fractional order. Surprisingly, we found a universal scaling law for α(y+), where y+ is the non-dimensional distance from the wall in wall units. Therefore, we obtain a variable-order fractional model that can be used at any Reynolds number to predict the mean velocity profile and Reynolds stresses with accuracy better than 1%.

scholarly journals Variable-Order Fractional Models for Wall-Bounded Turbulent Flows

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 782
Author(s):  
Fangying Song ◽  
George Em Karniadakis
Keyword(s):  
Fractional Derivative ◽  
Turbulent Flows ◽  
Fractional Order ◽  
Variable Order ◽  
Universal Curve ◽  
Reynolds Stresses ◽  
Continuous Change ◽  
Mean Velocity ◽  
Symmetric Variable ◽  
Fractional Models

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with relatively slow progress in the last few decades beyond the log law, which only describes the intermediate region in wall-bounded turbulence, i.e., 30–50 y+ to 0.1–0.2 R+ in a pipe of radius R. Here, we propose a fundamentally new approach based on fractional calculus to model the entire mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of variable-order that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing databases from direct numerical simulations (DNSs) to lean the variable-order function and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous change in rate of turbulent diffusion from the wall as well as the strong nonlocality of turbulent interactions that intensify away from the wall. Moreover, we propose alternative formulations, including a divergence variable fractional (two-sided) model for turbulent flows. The total shear stress is represented by a two-sided symmetric variable fractional derivative. The numerical results show that this formulation can lead to smooth fractional-order profiles in the whole domain. This new model improves the one-sided model, which is considered in the half domain (wall to centerline) only. We use a finite difference method for solving the inverse problem, but we also introduce the fractional physics-informed neural network (fPINN) for solving the inverse and forward problems much more efficiently. In addition to the aforementioned fully-developed flows, we model turbulent boundary layers and discuss how the streamwise variation affects the universal curve.

Errors Characterization of a RANS Simulation

2021 ◽  
Author(s):  
Hugo D. Pasinato ◽  
Ezequiel Arthur Krumrick
Keyword(s):  
Shear Stress ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Strain Tensor ◽  
Numerical Code ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Rans Simulation ◽  
Eddy Viscosity Model ◽  
The Mean

Abstract This research uses data from direct numerical simulation (DNS) to characterize the different errors associated with a Reynolds-averaged Navier-Stokes (RANS) simulation. The statistics from DNS (Reynolds stresses, kinetic energy of turbulence, $\kappa$, and dissipation of turbulence, $\epsilon$), are fed into a RANS simulation with the same Reynolds number, geometry, and numerical code used for DNS. Three integral metrics error based on the mean velocity, the moduli of the mean rate-of-strain tensor, and the wall shear stress are used to characterize the errors associated with the RANS technique, with the RANS model, and with the linear eddy viscosity model (LEVM). For developed and perturbed flow, it is found that the mean velocity of the RANS simulations with the DNS statistics is almost the same as the mean velocity from DNS data. This procedure enables the study of the relative importance of the different Reynolds stresses in a particular flow. It is shown that for the bounded perturbed turbulent flows studied here, almost all the necessary effects of turbulence are contained in the Reynolds shear stress.

Turbulent flow in a rectangular duct

1976 ◽  
Vol 78 (2) ◽  
pp. 289-315 ◽  
Author(s):  
A. Melling ◽  
J. H. Whitelaw
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Laser Doppler Anemometer ◽  
Laser Doppler ◽  
Rectangular Duct ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Fully Developed Flow ◽  
Developing Flow ◽  
Better Than

A detailed experimental study of developing turbulent flow in a rectangular duct was made using a laser-Doppler anemometer. The purposes of the work were to obtain data of value to fluid mechanicists, particularly those interested in the development and testing of mathematical turbulence models, and to evaluate the performance of the anemometer. For the first purpose, contours of axial mean velocity and turbulence intensity were measured in the developing flow, and all three mean velocity components and five of the six Reynolds stresses were obtained in the nearly fully developed flow.The symmetry of the present flow appears to be better than that of previous measurements and the range of measurements is more extensive. In addition, the laser-Doppler anemometer has the potential advantage, particularly in the measurement of secondary velocities, of avoiding probe interference.

scholarly journals CirBiTree: Citrullination Site Inference Based on a Fuzzy Neural Network and Flexible Neural Tree

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chuandong Song ◽  
Haifeng Wang
Keyword(s):  
Neural Network ◽  
Fuzzy Neural Network ◽  
Classification Model ◽  
Peptide Sequence ◽  
Sequence Information ◽  
Post Translational Modification ◽  
Fuzzy Neural ◽  
Human Complex ◽  
Better Than

Emerging evidence demonstrates that post-translational modification plays an important role in several human complex diseases. Nevertheless, considering the inherent high cost and time consumption of classical and typical in vitro experiments, an increasing attention has been paid to the development of efficient and available computational tools to identify the potential modification sites in the level of protein. In this work, we propose a machine learning-based model called CirBiTree for identification the potential citrullination sites. More specifically, we initially utilize the biprofile Bayesian to extract peptide sequence information. Then, a flexible neural tree and fuzzy neural network are employed as the classification model. Finally, the most available length of identified peptides has been selected in this model. To evaluate the performance of the proposed methods, some state-of-the-art methods have been employed for comparison. The experimental results demonstrate that the proposed method is better than other methods. CirBiTree can achieve 83.07% in sn%, 80.50% in sp, 0.8201 in F1, and 0.6359 in MCC, respectively.

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals STUDY OF A MA16-BASED VERTEX TRIGGER FOR THE CDF EXPERIMENT

1995 ◽  
Vol 06 (05) ◽  
pp. 681-692
Author(s):  
R. ODORICO
Keyword(s):  
Neural Network ◽  
Response Time ◽  
Impact Parameter ◽  
Electronic Components ◽  
The Neural Network ◽  
Viable Solution ◽  
Impact Parameters ◽  
Input Variables ◽  
Better Than

A Neural Network trigger for [Formula: see text] events based on the SVT microvertex processor of experiment CDF at Fermilab is presented. It exploits correlations among track impact parameters and azimuths calculated by the SVT from the SVX microvertex detector data. The neural trigger is meant for implementation on the systolic Siemens microprocessor MA16, which has already been used in a neural-network trigger for experiment WA92 at CERN. A suitable set of input variables is found, which allows a viable solution for the preprocessing task using standard electronic components. The response time of the neural-network stage of the trigger, including preprocessing, can be estimated ~10 μs. Its precise value depends on the quantitative specifications of the output signals of the SVT, which is still in development. The performance of the neural-network trigger is found to be significantly better than that of a conventional trigger exclusively based on impact parameter data.

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