On nonlinear K-l and K-ε models of turbulence

1987 ◽  
Vol 178 ◽  
pp. 459-475 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Asymptotic Expansion ◽  
Turbulent Flows ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Turbulent Channel Flow ◽  
Secondary Flows ◽  
Separated Flows ◽  
Future Research ◽  
Reynolds Stresses

The commonly used linear K-l and K-ε models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-ε models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

scholarly journals Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

2014 ◽  
Vol 11 (7) ◽  
pp. 1817-1831 ◽  
Author(s):  
Y. P. Wang ◽  
B. C. Chen ◽  
W. R. Wieder ◽  
M. Leite ◽  
B. E. Medlyn ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Microbial Biomass ◽  
Soil Carbon ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Oscillatory Behavior ◽  
Carbon Pools ◽  
Carbon Decomposition ◽  
Pool Model

Abstract. A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √(ϵ−1−1) Ks/Vs in the two-pool model, and to √(ϵ−1−1) Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and /Vs and /Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period of between 5 and 15 years depending on other parameter values, and has smaller amplitude at soil temperatures between 0 and 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input are notable features in these nonlinear models that are somewhat unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

scholarly journals Predicting the Electrical Energy Consumption of Electric Arc Furnaces Using Statistical Modeling

Metals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 959 ◽  
Author(s):  
Leo S. Carlsson ◽  
Peter B. Samuelsson ◽  
Pär G. Jönsson
Keyword(s):  
Statistical Modeling ◽  
Statistical Models ◽  
Linear Models ◽  
Nonlinear Models ◽  
Electrical Energy ◽  
Electric Arc ◽  
Future Research ◽  
Published Data ◽  
Industrial Setting ◽  
Input Variables

Statistical modeling, also known as machine learning, has gained increased attention in part due to the Industry 4.0 development. However, a review of the statistical models within the scope of steel processes has not previously been conducted. This paper reviews available statistical models in the literature predicting the Electrical Energy (EE) consumption of the Electric Arc Furnace (EAF). The aim was to structure published data and to bring clarity to the subject in light of challenges and considerations that are imposed by statistical models. These include data complexity and data treatment, model validation and error reporting, choice of input variables, and model transparency with respect to process metallurgy. A majority of the models are never tested on future heats, which essentially renders the models useless in a practical industrial setting. In addition, nonlinear models outperform linear models but lack transparency with regards to which input variables are influencing the EE consumption prediction. Some input variables that heavily influence the EE consumption are rarely used in the models. The scrap composition and additive materials are two such examples. These observed shortcomings have to be correctly addressed in future research applying statistical modeling on steel processes. Lastly, the paper provides three key recommendations for future research applying statistical modeling on steel processes.

scholarly journals Experimental and Analytical Study of Axial Turbulent Flows in an Interior Subchannel of a Bare Rod Bundle

1976 ◽  
Vol 98 (2) ◽  
pp. 262-268 ◽  
Author(s):  
P. Carajilescov ◽  
N. E. Todreas
Keyword(s):  
Velocity Field ◽  
Turbulent Flows ◽  
Length Distribution ◽  
Secondary Flows ◽  
Reynolds Stresses ◽  
Rod Bundle ◽  
Aspect Ratios ◽  
Fuel Elements ◽  
Velocity Turbulence ◽  
Rod Array

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the bundles in the space between the rods. Heat transfer calculations form an important part in the design of such elements, which can only be carried out if information of the velocity field is available. A one-equation statistical model of turbulence is applied to compute the detailed description of velocity field (axial and secondary flows) and the wall shear stress distribution of steady, fully developed turbulent flows with incompressible, temperature-independent fluid, flowing through triangular arrays of rods with different aspect ratios (P/D). Also experimental measurements of the distributions of the axial velocity, turbulence kinetic energy, and Reynolds stresses were performed using a laser Doppler anemometer (LDA), operating in a “fringe” mode with forward scattering, in a simulated interior subchannel of a triangular rod array with P/D = 1.123 and L/DH = 77. From the experimental results, a new mixing length distribution is proposed. Comparisons between the analytical results and the results of this experiment as well as other experimental data available in the literature are presented. The results are in good agreement.

Modeling and Control of the Oxygen Saturation in Neonatal Infants

2009 ◽  
Author(s):  
Timothy Keim ◽  
Ramak Amjad ◽  
Roger Fales
Keyword(s):  
Oxygen Saturation ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Error Model ◽  
Modeling And Control ◽  
Varying Parameters ◽  
Performance Specifications ◽  
And Performance ◽  
Neonatal Infants

In this work, a nonlinear model is developed to simulate the respiratory system of neonatal infants. The nonlinear model is based on a model proposed by other researchers, but with varying parameters based on the oxygen saturation output [1]. The nonlinear model response is compared to the response of a linearized model given small and large step inputs. For small step sizes, the nonlinear and linear models responses are nearly identical. For larger step sizes, the nonlinear model has a higher steady state response. The linear and nonlinear models are also compared to clinical data taken from a bedside monitor. An error model is also developed given known ranges for model parameter variations. Since the varying parameters change performance, a robust controller is designed using the error model and performance specifications using a μ-synthesis optimization. The controller is shown to have robust stability and performance.

Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework

2020 ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner
Keyword(s):  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Mixing ◽  
Equivalence Ratio ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Computational Domain ◽  
Reynolds Stresses ◽  
Mean Flow

Abstract In this paper a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier-Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields, which serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These in this study are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then the method is applied to predict the convection, mean flow dispersion and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with Direct Numerical Simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs, when the DNS mean flow and Reynolds stresses are provided. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

scholarly journals Impact of chart image characteristics on stock price prediction with a convolutional neural network

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0253121
Author(s):  
Guangxun Jin ◽  
Ohbyung Kwon
Keyword(s):  
Stock Price ◽  
Linear Models ◽  
Nonlinear Models ◽  
Numerical Data ◽  
Future Research ◽  
Stock Price Prediction ◽  
Price Prediction ◽  
Image Characteristics ◽  
The Subject ◽  
Accuracy Of Prediction

Stock price prediction has long been the subject of research because of the importance of accuracy of prediction and the difficulty in forecasting. Traditionally, forecasting has involved linear models such as AR and MR or nonlinear models such as ANNs using standardized numerical data such as corporate financial data and stock price data. Due to the difficulty of securing a sufficient variety of data, researchers have recently begun using convolutional neural networks (CNNs) with stock price graph images only. However, we know little about which characteristics of stock charts affect the accuracy of predictions and to what extent. The purpose of this study is to analyze the effects of stock chart characteristics on stock price prediction via CNNs. To this end, we define the image characteristics of stock charts and identify significant differences in prediction performance for each characteristic. The results reveal that the accuracy of prediction is improved by utilizing solid lines, color, and a single image without axis marks. Based on these findings, we describe the implications of making predictions only with images, which are unstructured data, without using large amounts of standardized data. Finally, we identify issues for future research.

On Turbulent Secondary Flows by Using Linear and Nonlinear k–ω Model

2000 ◽  
Author(s):  
B. Song ◽  
R. S. Amano
Keyword(s):  
Linear Model ◽  
Nonlinear Model ◽  
Vortex Structure ◽  
Rotational Speed ◽  
Nonlinear Models ◽  
Suction Side ◽  
Secondary Flows ◽  
Pressure Side ◽  
Square Duct ◽  
Linear And Nonlinear

Abstract In the present study, the fully developed turbulent secondary flows inside rotating and non-rotating square duct are numerically simulated using the linear and nonlinear k–ω models. For non-rotating duct, an eight-vortex structure is well captured by the nonlinear k–ω model. For rotating duct, it is interesting to notice that the two vortices are generated when Ro = 0.05, four vortices are presented when Ro = 0.15, and two vortices appeared when the rotational speed is increased up to Ro = 0.35. Although the linear and nonlinear models all produce reasonable results, the different results are also exhibited with these models. For example, the nonlinear model produces a stable effect in the pressure side and predicts less distortion region than the linear model. In the suction side, the linear k–ω model produces greater gradients than the linear model which seems to be realistic.

scholarly journals Forecasting Stock Prices With Linear And Nonlinear Settings: A Comparison

2013 ◽  
Vol 17 (4) ◽  
pp. 257
Author(s):  
Dimitri Tsoukalas
Keyword(s):  
Stock Prices ◽  
Linear Models ◽  
Financial Time Series ◽  
Nonlinear Models ◽  
Future Research ◽  
Regression Splines ◽  
Forecasting Models ◽  
Non Linear ◽  
Adaptive Regression ◽  
Adaptive Regression Splines

This paper is devoted to the application and comparison of linear (VAR) and nonlinear Multiple Adaptive Regression Splines (MARS) forecasting models, in estimating, evaluating, and selecting among linear and non-linear forecasting models for economic and financial time series. We argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. Nonlinear models reduce nonlinearity and Gaussianity in the residuals of the linear models. Linear models, however, demonstrate better forecasts than nonlinear. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Probability density function/Monte Carlo simulation of near-wall turbulent flows

1998 ◽  
Vol 357 ◽  
pp. 141-166 ◽  
Author(s):  
THOMAS D. DREEBEN ◽  
STEPHEN B. POPE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Flows ◽  
Turbulent Channel Flow ◽  
Reynolds Stresses ◽  
Langevin Model ◽  
Near Wall

Probability density function (p.d.f.) methods are extended to include modelling of wall-bounded turbulent flows. A p.d.f. near-wall model is developed in which the generalized Langevin model is combined with a model for viscous transport. This provides exact treatment of viscous inhomogeneous effects, and enables consistent imposition of the no-slip condition in a particle framework. The method of elliptic relaxation is combined with additional boundary conditions and with the generalized Langevin model to provide an analogy for the near-wall fluctuating continuity equation. This provides adequate representation of the near-wall anisotropy of the Reynolds stresses. The model is implemented with a p.d.f./Monte Carlo simulation for the joint p.d.f. of velocity and turbulent frequency. Results are compared with DNS and experimental profiles for fully developed turbulent channel flow.

scholarly journals Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

2013 ◽  
Vol 10 (12) ◽  
pp. 19661-19700 ◽  
Author(s):  
Y. P. Wang ◽  
B. C. Chen ◽  
W. R. Wieder ◽  
Y. Q. Luo ◽  
M. Leite ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Microbial Biomass ◽  
Soil Carbon ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Oscillatory Behavior ◽  
Carbon Pools ◽  
Carbon Decomposition ◽  
Pool Model

Abstract. A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √ (ϵ −1−1)Ks/Vs in the two-pool model, and to √ (ϵ −1−1)Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and Vs and Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period between 5 and 15 yr depending on other parameter values, and has smaller amplitude at soil temperatures between 0 °C to 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input in the nonlinear models are unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

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