Steady and Unsteady Computations of Turbulent Flows Induced by a 4/45° Pitched-Blade Impeller

1999 ◽  
Vol 121 (2) ◽  
pp. 318-329 ◽  
Author(s):  
K. Wechsler ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Steady State ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
High Performance ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Computational Effort ◽  
Stirred Tank ◽  
Mean Flow ◽  
Stirred Vessel

The present paper summarizes steady and unsteady computations of turbulent flow induced by a pitched-blade turbine (four blades, 45° inclined) in a baffled stirred tank. Mean flow and turbulence characteristics were determined by solving the Reynolds averaged Navier-Stokes equations together with a standard k-ε turbulence model. The round vessel had a diameter of T = 152 mm. The turbine of diameter T/3 was located at a clearance of T/3. The Reynolds number (Re) of the experimental investigation was 7280, and computations were performed at Re = 7280 and Re = 29,000. Techniques of high-performance computing were applied to permit grid sensitivity studies in order to isolate errors resulting from deficiencies of the turbulence model and those resulting from insufficient grid resolution. Both steady and unsteady computations were performed and compared with respect to quality and computational effort. Unsteady computations considered the time-dependent geometry which is caused by the rotation of the impeller within the baffled stirred tank reactor. Steady-state computations also considered neglect the relative motion of impeller and baffles. By solving the governing equations of motion in a rotating frame of reference for the region attached to the impeller, the steady-state approach is able to capture trailing vortices. It is shown that this steady-state computational approach yields numerical results which are in excellent agreement with fully unsteady computations at a fraction of the time and expense for the stirred vessel configuration under consideration.

CFD Performance Analysis of a Stirred Tank Flowmaker

2006 ◽  
Author(s):  
Lasse A. Rosendahl ◽  
Xiaopeng Wang ◽  
Christian B. Jacobsen
Keyword(s):  
Steady State ◽  
Turbulence Model ◽  
Cfd Simulation ◽  
Flow Characteristics ◽  
Stirred Tank ◽  
Mean Flow ◽  
Solution Quality ◽  
Transient Simulations ◽  
Multiple Frame ◽  
Steady State Simulation

In the present work, the mean flow field in a stirred tank equipped with a commercially available Grundfos AFG.40.230.35 flowmaker is investigated using both steady-state and transient CFD simulation, in order to provide information on the interaction between flow, propeller and wall proximity as well as information on aspects of using numerical tools for this type of fluid machinery. The simulations, carried out with Ansys CFX 10, used a multiple frame of reference (MFR) approach to include a full representation of the flowmaker blade and motor geometry, in order to fully include the effects of the blade shape and variable pitch for both stationary and transient simulations. The influence of grid type, turbulence model and steady vs transient setup on solution quality has been investigated, and the steady state calculations are compared with LDA measurements. The results show that for the steady state calculations, the choice of grid type is decisive in terms of quality of results, and that the transient simulations using the SST turbulence model yields a superior prediction of flow characteristics; however, the computational expenses for transient simulation is around 10 times than steady-state simulation.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

scholarly journals Stochastic Dynamical Modeling of Turbulent Flows

2020 ◽  
Vol 3 (1) ◽  
pp. 195-219 ◽  
Author(s):  
A. Zare ◽  
T.T. Georgiou ◽  
M.R. Jovanović
Keyword(s):  
Turbulent Flows ◽  
High Performance ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Measurement Techniques ◽  
Large Data ◽  
Low Rank ◽  
Structural Constraints ◽  
Mean Velocity ◽  
Linearized Model

Advanced measurement techniques and high-performance computing have made large data sets available for a range of turbulent flows in engineering applications. Drawing on this abundance of data, dynamical models that reproduce structural and statistical features of turbulent flows enable effective model-based flow control strategies. This review describes a framework for completing second-order statistics of turbulent flows using models based on the Navier–Stokes equations linearized around the turbulent mean velocity. Dynamical couplings between states of the linearized model dictate structural constraints on the statistics of flow fluctuations. Colored-in-time stochastic forcing that drives the linearized model is then sought to account for and reconcile dynamics with available data (that is, partially known statistics). The number of dynamical degrees of freedom that are directly affected by stochastic excitation is minimized as a measure of model parsimony. The spectral content of the resulting colored-in-time stochastic contribution can alternatively arise from a low-rank structural perturbation of the linearized dynamical generator, pointing to suitable dynamical corrections that may account for the absence of the nonlinear interactions in the linearized model.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

scholarly journals On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

Vorticity Transport Analysis of Turbulent Flows

1995 ◽  
Vol 117 (3) ◽  
pp. 410-416 ◽  
Author(s):  
J. J. Gorski ◽  
P. S. Bernard
Keyword(s):  
Turbulent Flows ◽  
Transport Theory ◽  
Stokes Equations ◽  
Transport Model ◽  
Plate Boundary ◽  
Separated Flow ◽  
Flow Region ◽  
Leeward Side ◽  
Mean Flow ◽  
Vorticity Transport

Turbulence closure for the Reynolds averaged Navier-Stokes equations based on vorticity transport theory is investigated. General expressions for the vorticity transport correlation terms in arbitrary two-dimensional mean flows are derived. Direct numerical simulation data for flow in a channel is used to evaluate the modeled terms and set unknown scales. Results are presented for a channel, flat plate boundary layer, and flow over a hill. The computed mean flow and kinetic energy compares well with numerical and physical experiments. The vorticity transport model appears to perform better than conventional Boussinesq eddy viscosity Reynolds stress models near the separated flow region on the leeward side of the hill.

scholarly journals THE INFLUENCE OF THE TURBULENCE CLOSURE MODEL ON WAVE-CURRENT INTERACTION MODELING AT A LOCAL SCALE AT A LOCAL SCALE

2012 ◽  
Vol 1 (33) ◽  
pp. 64
Author(s):  
Maria João Teles ◽  
António Pires-Silva ◽  
Michel Benoit
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Local Scale ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Interaction Modeling ◽  
Flow Components

An advanced CFD solver based on the RANS (Reynolds Averaged Navier-Stokes) equations is used to evaluate wave-current interactions through numerical simulations of combined wave-current free surface turbulent flows. The repercussions of various schemes for modeling turbulence effects is addressed with a special attention to the exchanges and fluxes of momentum and energy between the mean flow components and the wave (oscillatory) component. Numerical simulations are compared with experimental data from Klopman (1994).

scholarly journals Stochastic Modelling of Turbulent Flows for Numerical Simulations

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 108 ◽  
Author(s):  
Carlo Cintolesi ◽  
Etienne Mémin
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Stochastic Modelling ◽  
Turbulent Channel Flow ◽  
Alternative Formulation ◽  
Stochastic Representation ◽  
Practical Applications ◽  
Local Variance

Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier–Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy–viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at R e τ = 590 . The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model.

scholarly journals Linear iterative method for closed-loop control of quasiperiodic flows

2019 ◽  
Vol 868 ◽  
pp. 26-65 ◽  
Author(s):  
Colin Leclercq ◽  
Fabrice Demourant ◽  
Charles Poussot-Vassal ◽  
Denis Sipp
Keyword(s):  
Turbulent Flows ◽  
Linear Models ◽  
Stokes Equations ◽  
Linear Time ◽  
Base Flow ◽  
Nonlinear Flow ◽  
Mean Flow ◽  
Loop Control ◽  
Linear Controller ◽  
The Mean

This work proposes a feedback-loop strategy to suppress intrinsic oscillations of resonating flows in the fully nonlinear regime. The frequency response of the flow is obtained from the resolvent operator about the mean flow, extending the framework initially introduced by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to study receptivity mechanisms in turbulent flows. Using this linear time-invariant model of the nonlinear flow, modern control methods such as structured ${\mathcal{H}}_{\infty }$-synthesis can be used to design a controller. The approach is successful in damping self-sustained oscillations associated with specific eigenmodes of the mean-flow spectrum. Despite excellent performance, the linear controller is however unable to completely suppress flow oscillations, and the controlled flow is effectively attracted towards a new dynamical equilibrium. This new attractor is characterized by a different mean flow, which can in turn be used to design a second controller. The method can then be iterated on subsequent mean flows, until the coupled system eventually converges to the base flow. An intuitive parallel can be drawn with Newton’s iteration: at each step, a linearized model of the flow response to a perturbation of the input is sought, and a new linear controller is designed, aiming at further reducing the fluctuations. The method is illustrated on the well-known case of two-dimensional incompressible open-cavity flow at Reynolds number $Re=7500$, where the fully developed flow is initially quasiperiodic (2-torus state). The base flow is reached after five iterations. The present work demonstrates that nonlinear control problems may be solved without resorting to nonlinear reduced-order models. It also shows that physically relevant linear models can be systematically derived for nonlinear flows, without resorting to black-box identification from input–output data; the key ingredient being frequency-domain models based on the linearized Navier–Stokes equations about the mean flow. Applicability to amplifier flows and turbulent dynamics has, however, yet to be investigated.

A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
A. Nakayama ◽  
F. Kuwahara
Keyword(s):  
Porous Media ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Packed Bed ◽  
Volume Averaging ◽  
Packed Beds ◽  
Mean Flow ◽  
Rod Bundles ◽  
And Performance

This study focuses on Nakayama and Kuwahara’s two-equation turbulence model and its modifications, previously proposed for flows in porous media, on the basis of the volume averaging theory. Nakayama and Kuwahara’s model is generalized so that it can be applied to most complex turbulent flows such as cross flows in banks of cylinders and packed beds, and longitudinal flows in channels, pipes, and rod bundles. For generalization, we shall reexamine the extra production terms due to the presence of the porous media, appearing in the transport equations of turbulence kinetic energy and its dissipation rate. In particular, we shall consider the mean flow kinetic energy balance within a pore, so as to seek general expressions for these additional production terms, which are valid for most kinds of porous media morphology. Thus, we establish the macroscopic turbulence model, which does not require any prior microscopic numerical experiments for the structure. Hence, for the given permeability and Forchheimer coefficient, the model can be used for analyzing most complex turbulent flow situations in homogeneous porous media without a detailed morphological information. Preliminary examination of the model made for the cases of packed bed flows and longitudinal flows through pipes and channels reveals its high versatility and performance.

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