Computational Fluid Dynamics Analysis of Turbulent Flow
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Multiscale Computational Fluid Dynamics
energies Review Multiscale Computational Fluid Dynamics Dimitris Drikakis 1,*, Michael Frank 2 and Gavin Tabor 3 1 Defence and Security Research Institute, University of Nicosia, Nicosia CY-2417, Cyprus 2 Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1UX, UK 3 CEMPS, University of Exeter, Harrison Building, North Park Road, Exeter EX4 4QF, UK * Correspondence: [email protected] Received: 3 July 2019; Accepted: 16 August 2019; Published: 25 August 2019 Abstract: Computational Fluid Dynamics (CFD) has numerous applications in the field of energy research, in modelling the basic physics of combustion, multiphase flow and heat transfer; and in the simulation of mechanical devices such as turbines, wind wave and tidal devices, and other devices for energy generation. With the constant increase in available computing power, the fidelity and accuracy of CFD simulations have constantly improved, and the technique is now an integral part of research and development. In the past few years, the development of multiscale methods has emerged as a topic of intensive research. The variable scales may be associated with scales of turbulence, or other physical processes which operate across a range of different scales, and often lead to spatial and temporal scales crossing the boundaries of continuum and molecular mechanics. In this paper, we present a short review of multiscale CFD frameworks with potential applications to energy problems. Keywords: multiscale; CFD; energy; turbulence; continuum fluids; molecular fluids; heat transfer 1. Introduction Almost all engineered objects are immersed in either air or water (or both), or make use of some working fluid in their operation. -
CFD-Driven Symbolic Identification of Algebraic Reynolds-Stress Models
CFD-driven Symbolic Identification of Algebraic Reynolds-Stress Models Isma¨ılBEN HASSAN SA¨IDIa,∗, Martin SCHMELZERb, Paola CINNELLAc, Francesco GRASSOd aInstitut A´erotechnique, CNAM, 15 Rue Marat, 78210 Saint-Cyr-l'Ecole,´ France bFaculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 2, Delft, The Netherlands cInstitut Jean Le Rond D'Alembert, Sorbonne Universit´e,4 Place Jussieu, 75005 Paris, France dLaboratoire DynFluid, CNAM, 151 Boulevard de l'Hopital, 75013 Paris, France Abstract A CFD-driven deterministic symbolic identification algorithm for learning ex- plicit algebraic Reynolds-stress models (EARSM) from high-fidelity data is de- veloped building on the CFD-free SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD- driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simula- tions. A preliminary sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space and the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters within a realizable search space. The resulting turbulence models are numerically robust and ensure conservation of mean kinetic energy. Furthermore, the CFD-driven procedure enables training of models against any target quantity of interest com- putable as an output of the CFD model. -
Turbulence Momentum Transport and Prediction of the Reynolds Stress in Canonical Flows
Turbulence Momentum Transport and Prediction of the Reynolds Stress in Canonical Flows T.-W. Lee Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, 85287 Abstract- We present a unique method for solving for the Reynolds stress in turbulent canonical flows, based on the momentum balance for a control volume moving at the local mean velocity. A differential transform converts this momentum balance to a solvable form. Comparisons with experimental and computational data in simple geometries show quite good agreements. An alternate picture for the turbulence momentum transport is offered, as verified with data, where the turbulence momentum is transported by the mean velocity while being dissipated by viscosity. The net momentum transport is the Reynolds stress. This turbulence momentum balance is verified using DNS and experimental data. T.-W. Lee Mechanical and Aerospace Engineering, SEMTE Arizona State University Tempe, AZ 85287-6106 Email: [email protected] 0 Nomenclature C1 = constants Re = Reynolds number based on friction velocity U = mean velocity in the x direction Ue = free-stream velocity V = mean velocity in the y direction u’ = fluctuation velocity in the x direction urms’ = root-mean square of u’ u’v’ = Reynolds stress = boundary layer thickness m = modified kinematic viscosity Introduction Finding the Reynolds stress has profound implications in fluid physics. Many practical flows are turbulent, and require some method of analysis or computations so that the flow process can be understood, predicted and controlled. This necessity led to several generations of turbulence models including a genre that models the Reynolds stress components themselves, the Reynolds stress models [1, 2]. -
Deep Learning Models for Turbulent Shear Flow
DEGREE PROJECT IN MATHEMATICS, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018 Deep Learning models for turbulent shear flow PREM ANAND ALATHUR SRINIVASAN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Deep Learning models for turbulent shear flow PREM ANAND ALATHUR SRINIVASAN Degree Projects in Scientific Computing (30 ECTS credits) Degree Programme in Computer Simulations for Science and Engineering (120 credits) KTH Royal Institute of Technology year 2018 Supervisors at KTH: Ricardo Vinuesa, Philipp Schlatter, Hossein Azizpour Examiner at KTH: Michael Hanke TRITA-SCI-GRU 2018:236 MAT-E 2018:44 Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci iii Abstract Deep neural networks trained with spatio-temporal evolution of a dy- namical system may be regarded as an empirical alternative to conven- tional models using differential equations. In this thesis, such deep learning models are constructed for the problem of turbulent shear flow. However, as a first step, this modeling is restricted to a simpli- fied low-dimensional representation of turbulence physics. The train- ing datasets for the neural networks are obtained from a 9-dimensional model using Fourier modes proposed by Moehlis, Faisst, and Eckhardt [29] for sinusoidal shear flow. These modes were appropriately chosen to capture the turbulent structures in the near-wall region. The time series of the amplitudes of these modes fully describe the evolution of flow. Trained deep learning models are employed to predict these time series based on a short input seed. Two fundamentally different neural network architectures, namely multilayer perceptrons (MLP) and long short-term memory (LSTM) networks are quantitatively compared in this work. -
Development of a Wake Model for Wind Farms Based on an Open Source CFD Solver
Development of a wake model for wind farms based on an open source CFD solver. Strategies on parabolization and turbulence modeling PhD Thesis Daniel Cabezón Martínez Departamento de Ingeniería Energética y Fluidomecánica, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid (UPM), Madrid, Spain Abstract Wake effect represents one of the most important aspects to be analyzed at the engineering phase of every wind farm since it supposes an important power deficit and an increase of turbulence levels with the consequent decrease of the lifetime. It depends on the wind farm design, wind turbine type and the atmospheric conditions prevailing at the site. Traditionally industry has used analytical models, quick and robust, which allow carry out at the preliminary stages wind farm engineering in a flexible way. However, new models based on Computational Fluid Dynamics (CFD) are needed. These models must increase the accuracy of the output variables avoiding at the same time an increase in the computational time. Among them, the elliptic models based on the actuator disk technique have reached an extended use during the last years. These models present three important problems in case of being used by default for the solution of large wind farms: the estimation of the reference wind speed upstream of each rotor disk, turbulence modeling and computational time. In order to minimize the consequence of these problems, this PhD Thesis proposes solutions implemented under the open source CFD solver OpenFOAM and adapted for each type of site: a correction on the reference wind speed for the general elliptic models, the semi-parabollic model for large offshore wind farms and the hybrid model for wind farms in complex terrain. -
Simulation of Turbulent Flows
Simulation of Turbulent Flows • From the Navier-Stokes to the RANS equations • Turbulence modeling • k-ε model(s) • Near-wall turbulence modeling • Examples and guidelines ME469B/3/GI 1 Navier-Stokes equations The Navier-Stokes equations (for an incompressible fluid) in an adimensional form contain one parameter: the Reynolds number: Re = ρ Vref Lref / µ it measures the relative importance of convection and diffusion mechanisms What happens when we increase the Reynolds number? ME469B/3/GI 2 Reynolds Number Effect 350K < Re Turbulent Separation Chaotic 200 < Re < 350K Laminar Separation/Turbulent Wake Periodic 40 < Re < 200 Laminar Separated Periodic 5 < Re < 40 Laminar Separated Steady Re < 5 Laminar Attached Steady Re Experimental ME469B/3/GI Observations 3 Laminar vs. Turbulent Flow Laminar Flow Turbulent Flow The flow is dominated by the The flow is dominated by the object shape and dimension object shape and dimension (large scale) (large scale) and by the motion and evolution of small eddies (small scales) Easy to compute Challenging to compute ME469B/3/GI 4 Why turbulent flows are challenging? Unsteady aperiodic motion Fluid properties exhibit random spatial variations (3D) Strong dependence from initial conditions Contain a wide range of scales (eddies) The implication is that the turbulent simulation MUST be always three-dimensional, time accurate with extremely fine grids ME469B/3/GI 5 Direct Numerical Simulation The objective is to solve the time-dependent NS equations resolving ALL the scale (eddies) for a sufficient time -
An Introduction to Turbulence Modeling for CFD
An Introduction to Turbulence Modeling for CFD Gerald Recktenwald∗ February 19, 2020 ∗Mechanical and Materials Engineering Department Portland State University, Portland, Oregon, [email protected] Turbulence is a Hard Problem • Unsteady • Many length scales • Energy transfer between scales: ! Large eddies break up into small eddies • Steep gradients near the wall ME 4/548: Turbulence Modeling page 1 Engineering Model: Flow is \Steady-in-the-Mean" (1) 2 1.8 1.6 1.4 1.2 u 1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 t ME 4/548: Turbulence Modeling page 2 Engineering Model: Flow is \Steady-in-the-Mean" (2) Reality: Turbulent flows are unsteady: fluctuations at a point are caused by convection of eddies of many sizes. As eddies move through the flow the velocity field changes in complex ways at a fixed point in space. Turbulent flows have structures { blobs of fluid that move and then break up. ME 4/548: Turbulence Modeling page 3 Engineering Model: Flow is \Steady-in-the-Mean" (3) Engineering Model: When measured with a \slow" sensor (e.g. Pitot tube) the velocity at a point is apparently steady. For basic engineering analysis we treat flow variables (velocity components, pressure, temperature) as time averages (or ensemble averages). These averages are steady (ignorning ensemble averaging of periodic flows). ME 4/548: Turbulence Modeling page 4 Engineering Model: Enhanced Transport (1) Turbulent eddies enhance mixing. • Transport in turbulent flow is much greater than in laminar flow: e.g. pollutants spread more rapidly in a turbulent flow than a laminar flow • As a result of enhanced local transport, mean profiles tend to be more uniform except near walls. -
Modeling and Simulation of High-Speed Wake Flows
Modeling and Simulation of High-Speed Wake Flows A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Michael Daniel Barnhardt IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Graham V. Candler, Adviser August 2009 c Michael Daniel Barnhardt August 2009 Acknowledgments The very existence of this dissertation is a testament to the support and en- couragement I’ve received from so many individuals. Foremost among these is my adviser, Professor Graham Candler, for motivating this work, and for his consider- able patience, enthusiasm, and guidance throughout the process. Similarly, I must thank Professor Ellen Longmire for allowing me to tinker around late nights in her lab as an undergraduate; without those experiences, I would’ve never been stimulated to attend graduate school in the first place. I owe a particularly large debt to Drs. Pramod Subbareddy, Michael Wright, and Ioannis Nompelis for never cutting me any slack when I did something stupid and always pushing me to think bigger and better. Our countless hours of discussions provided a great deal of insight into all aspects of CFD and buoyed me through the many difficult times when codes wouldn’t compile, simulations crashed, and everything generally seemed to be broken. I also have to thank Travis Drayna and all of my other friends and colleagues at the University of Minnesota and NASA Ames. Dr. Matt MacLean of CUBRC and Dr. Anita Sengupta at JPL provided much of the experimental results and were very helpful throughout the evolution of the project. -
A Mixing-Length Formulation for the Turbulent Prandtl Number in Wall-Bounded flows with Bed Roughness and Elevated Scalar Sources ͒ John P
PHYSICS OF FLUIDS 18, 095102 ͑2006͒ A mixing-length formulation for the turbulent Prandtl number in wall-bounded flows with bed roughness and elevated scalar sources ͒ John P. Crimaldia Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428 Jeffrey R. Koseff and Stephen G. Monismith Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305-4020 ͑Received 7 November 2005; accepted 20 June 2006; published online 5 September 2006͒ Turbulent Prandtl number distributions are measured in a laboratory boundary layer flow with bed roughness, active blowing and sucking, and scalar injection near the bed. The distributions are significantly larger than unity, even at large distances from the wall, in apparent conflict with the Reynolds analogy. An analytical model is developed for the turbulent Prandtl number, formulated as the ratio of momentum and scalar mixing length distributions. The model is successful at predicting the measured turbulent Prandtl number behavior. Large deviations from unity are shown in this case to be consistent with measurable differences in the origins of the momentum and scalar mixing length distributions. Furthermore, these deviations are shown to be consistent with the Reynolds analogy when the definition of the turbulent Prandtl number is modified to include the effect of separate mixing length origin locations. The results indicate that the turbulent Prandtl number for flows over complex boundaries can be modeled based on simple knowledge of the geometric and kinematic nature of the momentum and scalar boundary conditions. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2227005͔ I. INTRODUCTION For flows over rough surfaces, the nature of the roughness 9 has been shown to only slightly alter Prt. -
7. Turbulence Turbulent Jet
7. Turbulence Turbulent Jet Instantaneous Mean Turbulent Boundary Layer y U(y) Instantaneous Mean What is Turbulence? • A “random”, 3-d, time-dependent eddying motion with many scales, superposed on an often drastically simpler mean flow • A solution of the Navier-Stokes equations • The natural state at high Reynolds numbers • An efficient transporter and mixer • A major source of energy loss • A significant influence on drag: ‒ increases frictional drag in non-separated flow ‒ delays, or sometimes prevents, boundary-layer separation on curved surfaces, so reducing pressure drag. ● “The last great unsolved problem of classical physics” Momentum Transfer in Laminar and Turbulent Flow • Laminar: ‒ smooth ‒ no mixing of fluid ‒ momentum transfer by viscous forces • Turbulent: ‒ chaotic ‒ mixing of fluid ‒ momentum transfer mainly by the net effect of intermingling ρ푈퐿 푈퐿 Regime determined by Reynolds number: Re = = μ ν “Low” Re laminar; “high” Re turbulent “High” or “low” depends on the flow and the choice of 푈 and 퐿 Reynolds’ Decomposition v u + mean fluctuation 푢 = 푢ത + 푢′ 푣 = 푣ҧ + 푣′ 푝 = 푝ҧ + 푝′ Alternative Notations • Overbar for mean, prime for fluctuation: 푢 + 푢′ −ρ푢′푣′ • Upper case for mean, lower case for fluctuation: 푈 + 푢 −ρ푢푣 Reynolds Averaging of a Product 푢 = 푢 + 푢′ 푢′ = 0 cf statistics: σ 푢2 2 2 ′2 σ2 = 푢′2 = − 푢ത2 푢 = 푢 + 푢 Variance 푁 σ 푢푣 푢푣 = 푢 푣 + 푢′푣′ ρ ≡ 푢′푣′ = − 푢ത푣ҧ Covariance 푁 푢푣 = (푢 + 푢′)(푣 + 푣′) = 푢 푣 + 푢푣′ + 푢′푣 + 푢′푣′ 푢푣 = 푢 푣 + 푢푣ഥ′ + 푢ഥ′푣 + 푢′푣′ 푢푣 = 푢 푣 + 푢′푣′ Effect of Turbulence on the Mean Flow (i) Mass vA Mass flux: ρ푣퐴 Average mass flux: ρ푣퐴 The mean velocity satisfies the same continuity equation as the instantaneous velocity Effect of Turbulence on the Mean Flow (ii) Momentum vA (푥-)momentum flux: (ρ푣퐴)푢 = ρ(푢푣)퐴 u Average momentum flux : (ρ푣퐴)푢 = ρ(푢 푣 + 푢′푣′)퐴 extra term Net rate of transport of momentum per unit area ρ푢′푣′ from LOWER to UPPER .. -
Intrinsic Plasma Rotation and Reynolds Stress at the Plasma
Measurements of Reynolds Stress and its Contribution to the Momentum Balance in the HSX Stellarator by Robert S. Wilcox A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering) at the University of Wisconsin–Madison 2014 Date of final oral examination: 12/2/2014 The dissertation is approved by the following members of the Final Oral Committee: David T. Anderson, Professor, Electrical Engineering Amy E. Wendt, Professor, Electrical Engineering Chris C. Hegna, Professor, Engineering Physics Paul W. Terry, Professor, Physics Joseph N. Talmadge, Associate Scientist, Electrical Engineering c Copyright by Robert S. Wilcox 2014 All Rights Reserved i ABSTRACT In a magnetic configuration that has been sufficiently optimized for quasi-symmetry, the neoclas- sical transport and viscosity can be small enough that other terms can compete in the momentum balance to determine the plasma rotation and radial electric field. The Reynolds stress generated by plasma turbulence is identified as the most likely candidate for non-neoclassical flow drive in the HSX stellarator. Using multi-tipped Langmuir probes in the edge of HSX in the quasi-helically symmetric (QHS) configuration, the radial electric field and parallel flows are found to deviate from the values calculated by the neoclassical transport code PENTA using the ambipolarity con- straint in the absence of externally injected momentum. The local Reynolds stress in the parallel and perpendicular directions on a surface is also measured using the fluctuating components of floating potential and ion saturation current measurements. Although plasma turbulence enters the momentum balance as the flux surface averaged radial gradient of the Reynolds stress, the locally measured quantity implies a significant contribution to the momentum balance. -
Computational Fluid Dynamics Techniques for Flows in Lapple Cyclone Separator
COMPUTATIONAL FLUID DYNAMICS TECHNIQUES FOR FLOWS IN LAPPLE CYCLONE SEPARATOR A. F. Lacerda, L. G. M.Vieira, A. M. Nascimento, S. D. Nascimento, J. J. R. Damasceno and M. A. S. Barrozo. Federal University of Uberlândia, Faculty of Chemical Engineering -FEQUI, Block K, Campus Santa Mônica, Uberlândia-MG - Brazil. ZIP: 38400-902 – Fax: 55-034-32394188 E-mail: [email protected] Keywords: Separation; Lapple; Cyclones; Computational Fluid Dynamics; Fluent Abstract A two-dimensional fluidynamics model for turbulent flow of gas in cyclones is used for available the importance of the anisotropic of the Reynolds stress components. This study presents consisted in to simulate through computational fluid dynamics (CFD) package the operation of the Lapple cyclone. Yields of velocity obtained starting from a model anisotropic of the Reynolds stress are compared with experimental data of the literature, as form of validating the results obtained through the use of the Computational fluid dynamics (Fluent). The experimental data of the axial and swirl velocities validate numeric results obtained by the model. 1 - Introduction Cyclones are equipment used for the separation and suspended solid collection in gaseous chains. Its popularity if must mainly to the its simplicity of construction, absence of mobile parts, what it guarantees a low necessity of maintenance. Cyclones are among the oldest of industrial particulate control equipment and air sampling device. The primary advantages of cyclones are economy and simplicity in construction and designs. By using suitable materials and methods of construction, cyclones may be adapted for use in extreme operating conditions: high temperature, high pressure, and corrosive gases. Therefore, cyclones have found increasing utility in the field of air pollution [1].