Development of Empirically-Driven Axisymmetric Turbulence Models Using a Symmetry-Based Approach PDF Download
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Author: Jeremy Pannebaker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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This thesis analyzes a high Reynolds number, axisymmetric, turbulent pipe flow for the purpose of developing a turbulence model that describes the mean velocity and two-point correlation statistics. The work utilizes analytical and experimental methods in the form of Lie theory and planar PIV to construct mathematical models for the chosen statistics. Lie theory is a classical method of solving differential equations by using symmetries that are inherent in the equations under analysis. This work analyzes the Reynolds-averaged Euler equations to identify a family of scaling solutions for the mean velocities and two-point correlations of a turbulent, cylindrical pipe flow. Using the scaling solutions, the theoretical findings are tested experimentally by collecting and analyzing planar PIV data from the core region of a fully-developed, axisymmetric, turbulent pipe. The Lie theory analysis results in various scaling parameters being manifested in the scaling solutions, so curves are fit to the experimental data using a nonlinear least squares approach to quantify the parameters. Through this process, sufficient curve fits to the experimental data could be achieved for the mean streamwise velocity and axial direction Reynolds stress, however, the scaling parameters do not agree across the chosen statistics. Theoretically, the scaling parameters are expected to be universal for all statistics. This thesis also evaluates the Reynolds stress because it is a special case of the two-point correlation equations and serves as a check of the theory before proceeding into the more complex two-point correlation fittings with spatial separations. Future work will aim at finding universal scaling parameters and curve fitting the two-point correlations with spatial separations. In the current literature, to date, there has not been any work that identified symmetry solutions for two-point correlations and used experimental data to validate the results in this manner.
Author: Jeremy Pannebaker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis analyzes a high Reynolds number, axisymmetric, turbulent pipe flow for the purpose of developing a turbulence model that describes the mean velocity and two-point correlation statistics. The work utilizes analytical and experimental methods in the form of Lie theory and planar PIV to construct mathematical models for the chosen statistics. Lie theory is a classical method of solving differential equations by using symmetries that are inherent in the equations under analysis. This work analyzes the Reynolds-averaged Euler equations to identify a family of scaling solutions for the mean velocities and two-point correlations of a turbulent, cylindrical pipe flow. Using the scaling solutions, the theoretical findings are tested experimentally by collecting and analyzing planar PIV data from the core region of a fully-developed, axisymmetric, turbulent pipe. The Lie theory analysis results in various scaling parameters being manifested in the scaling solutions, so curves are fit to the experimental data using a nonlinear least squares approach to quantify the parameters. Through this process, sufficient curve fits to the experimental data could be achieved for the mean streamwise velocity and axial direction Reynolds stress, however, the scaling parameters do not agree across the chosen statistics. Theoretically, the scaling parameters are expected to be universal for all statistics. This thesis also evaluates the Reynolds stress because it is a special case of the two-point correlation equations and serves as a check of the theory before proceeding into the more complex two-point correlation fittings with spatial separations. Future work will aim at finding universal scaling parameters and curve fitting the two-point correlations with spatial separations. In the current literature, to date, there has not been any work that identified symmetry solutions for two-point correlations and used experimental data to validate the results in this manner.
Author: Jean Piquet
Publisher: Springer Science & Business Media
ISBN: 3662035596
Category : Technology & Engineering
Languages : en
Pages : 767
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Book Description
obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.
Author: Manuel D. Salas
Publisher: Springer Science & Business Media
ISBN: 9401147248
Category : Science
Languages : en
Pages : 385
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Book Description
Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.
Author: Konstantin Volkov
Publisher: BoD – Books on Demand
ISBN: 9535133497
Category : Science
Languages : en
Pages : 252
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Book Description
Accurate prediction of turbulent flows remains a challenging task despite considerable work in this area and the acceptance of CFD as a design tool. The quality of the CFD calculations of the flows in engineering applications strongly depends on the proper prediction of turbulence phenomena. Investigations of flow instability, heat transfer, skin friction, secondary flows, flow separation, and reattachment effects demand a reliable modelling and simulation of the turbulence, reliable methods, accurate programming, and robust working practices. The current scientific status of simulation of turbulent flows as well as some advances in computational techniques and practical applications of turbulence research is reviewed and considered in the book.
Author: Xinyi Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Turbulence modeling, including wall models in large-eddy simulations (LESs) and RANS models in Reynolds-averaged Navier-Stokes (RANS) simulations, is usually not considered for non-canonical flows, including rotating flows and stratified flows. Modeling non-canonical flows encounters difficulties. Some of the main difficulties lie in the fact that these flows have multiple flow controlling parameters (FCPs), and thus, the flow behavior is hard to explore, let alone get accurate modeling. The data-driven approach is considered a possible solution to this. The increasing computational resources and shared turbulence data allow another way to utilize the data other than pure human analyses of the physics. However, pure data-driven methods are often criticized for their weak interpretability and generalizability. In this work, multiple data-driven techniques are applied to some persistent problems in turbulence modeling under the circumstances of rotating flows and stratified flows. The problems include not only the accurate modeling of the flow but also the efficient FCP space exploration, model selection, uncertainty quantification, etc. Both the dataset and existing knowledge of physics are utilized, and then data-driven approach shows the interpretability and generalizability. They show how these traditionally difficult problems can be tackled through physics-informed data-driven approach, which significantly saves human labor. To be more specific, data-driven approach to wall modeling is compared to physics-based approach for a spanwise rotating channel, and it shows a more accurate yet still generalizable behavior. When modeling is extended to an arbitrarily directional rotating channel, a surrogate model is efficiently developed through the utilization of Bayesian optimization, when such behavior is never understood in the existing literature. Data-driven approach is also applied to RANS modeling. The diverse modeling makes model selection awkward for a newbie, and we train a recommender system to provide guidelines. Modeling itself for non-canonical cases, e.g., stratified flows, is also troublesome, because the multi-stage behavior of the flow requires automated switching of modeling between different models as the flow develops. A linear logistic regression is developed for automating the classification. The models can then be evaluated through a global epistemic uncertainty quantification (UQ) method, which allows the exploration of dominating terms in a RANS model and determining a priori if a calibration can generalize to other flow conditions. In general, data-driven approach has been used for multiple applications in turbulence modeling, and they show their capability and interpretability.
Author: N. Rajaratnam
Publisher: Elsevier
ISBN: 0080869963
Category : Science
Languages : en
Pages : 315
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Book Description
Turbulent Jets
Author: Yangmo Zhu
Publisher:
ISBN:
Category :
Languages : en
Pages : 135
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Author: Michel Bergmann
Publisher: Frontiers Media SA
ISBN: 2832510701
Category : Science
Languages : en
Pages : 178
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Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 232
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Author: David C. Wilcox
Publisher:
ISBN: 9781928729082
Category : Fluid dynamics
Languages : en
Pages : 522
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