A Turbulence Model for Pulsatile Arterial Flows

2004 ◽  
Vol 126 (5) ◽  
pp. 578-584 ◽  
Author(s):  
B. A. Younis ◽  
S. A. Berger
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Solid Wall ◽  
Flow Behavior ◽  
Local Equilibrium ◽  
Fluid Motion ◽  
Circulatory System ◽  
Wave Form ◽  
Mean Flow ◽  
Law Of The Wall

Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the “nonequilibrium” effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the prediction of arterial flows.

A Proposal for Modeling Intermittent Transitional Pulsatile Flows

2003 ◽  
Author(s):  
Stanley A. Berger ◽  
Bassam A. Younis
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Solid Wall ◽  
Local Equilibrium ◽  
Turbulence Models ◽  
Shear Stresses ◽  
Turbulent Transition ◽  
Circular Pipes ◽  
Pulsatile Flows ◽  
Additional Equation

The principal requirements in a turbulence model to be valid for the prediction of arterial flows are the ability to capture the consequences of laminar–turbulent transition that occur at various phases of the cardiac cycle and to yield accurate predictions of the wall shear stresses. These requirements are not immediately met by the majority of turbulence models since these have largely been formulated with reference to data from fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on recent progress in the development of a turbulence model that overcomes some of these limitations. The model is based on the solution of transport equations for two turbulence parameters that are zero–valued at a solid wall and an additional equation for intermittency. Comparisons with measurements obtained in oscillatory transitional flows in circular pipes show substantial improvements over existing closures.

Multidimensional Predictions of In-Cylinder Turbulent Flows: Contribution to the Assessment of k-ε Turbulence Model Variants for Bowl-in-Piston Engines

2003 ◽  
Author(s):  
Andrea E. Catania ◽  
Mirko Baratta ◽  
Ezio Spessa ◽  
Rui L. Liu
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Fluid Motion ◽  
Combustion Process ◽  
Turbulence Models ◽  
Algebraic Equations ◽  
Mean Flow ◽  
Wall Functions ◽  
Simpler Algorithm ◽  
Model Engine

As is well known, the in-cylinder flow phenomena can strongly affect the engine combustion process and the related emission sources. Therefore, a better understanding of the fluid motion is critical for developing new engine concepts with the most attractive operation and emission characteristics. To that end, multidimensional flow computational codes with reliable turbulence models are useful investigation and design tools. This paper is concerned with mean-flow and turbulence simulation in a motored model engine with a compression ratio of 6.7. The flow configurations comprise an axisymmetric combustion chamber with one centrally located valve and each of a flat piston and cylindrical bowl-in-piston arrangements. The calculations are performed using a non-commercial CFD code that was originally developed by the authors. A finite volume conservative implicit method, applying various order-of-accuracy schemes, is employed for the discretization of the partial differential equations modeling the in-cylinder turbulent flow, and the resultant algebraic equations are linearized and sequentially solved by an iterative procedure. Velocity-pressure coupling is ensured by a pressure correction method similar to that of the SIMPLER algorithm. Results of the simulation are presented at the model engine speed of 200 rpm throughout the engine cycle. They were obtained using three versions of the k-ε turbulence model (Standard, Two Scale and RNG) which differ from each other for underlying concepts, complexity and accuracy in capturing flow features. Modified boundary conditions with respect to logarithmic wall-functions were applied. Insight was also gained into the nonlinear effects of stress-strain constitutive relation on turbulence modeling. The effects of the equation differencing schemes and computational grid spacing on flow predictions were tested. Then the numerical results were compared to those of LDV measurements and the influence of the k-ε model variants on the flow field features were examined during the induction stroke and around compression TDC.

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.

Mean Flow Field and Reynolds Stress Behavior in Coannular Jet Flow With Swirl Along a Centerbody

1991 ◽  
Vol 113 (3) ◽  
pp. 445-452
Author(s):  
M. O. Frey ◽  
F. B. Gessner
Keyword(s):  
Reynolds Stress ◽  
Nozzle Exit ◽  
Reynolds Shear Stress ◽  
Local Equilibrium ◽  
Mixing Layer ◽  
Flow Rate Ratio ◽  
Mean Flow ◽  
Wall Functions ◽  
Law Of The Wall ◽  
Flow Situation

An experimental study was conducted of an incompressible turbulent flow which exits from two concentric annular nozzles and develops along an unconfined centerbody. The operating Reynolds number based on centerbody diameter and the axial bulk velocity of the inner stream at the nozzle exit was 8 × 104. Swirl was imparted only to the inner stream, and the outer-to-inner stream mass flow rate ratio was fixed at unity. The results show that streamwise oscillations exist in the mean flow which apparently arise when vortices shed at the nozzle lip separating the two streams interact with the centerbody boundary layer. A comparison of Reynolds shear stress profiles with mean strain rates in the flow indicates that departures from local equilibrium exist in the mixing layer downstream of the nozzle exit. Local law-of-the-wall behavior is observed, however, near the centerbody surface. Analysis of the results shows that the use of conventional wall functions for the turbulence kinetic energy may not be appropriate for this flow situation, and that closure at the full Reynolds stress transport equation level is required for prediction purposes.

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.

scholarly journals Friction Factor Estimation for Turbulent Flows in Corrugated Pipes with Rough Walls

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Maxim Pisarenco ◽  
Bas van der Linden ◽  
Arris Tijsseling ◽  
Emmanuel Ory ◽  
Jacques Dam
Keyword(s):  
Boundary Condition ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Behavior ◽  
Turbulence Models ◽  
Computational Grids ◽  
Law Of The Wall ◽  
Fully Developed Turbulent Flow ◽  
The Right

The motivation of the investigation is the critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k−ϵ and k−ω) are used in the computations. First, the fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions, and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, the turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: The friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric, which is wrapped around the spiral.

Computations of Flow Field and Heat Transfer in a Stator Vane Passage Using the v2¯−f Turbulence Model

2005 ◽  
Vol 127 (3) ◽  
pp. 627-634 ◽  
Author(s):  
A. Sveningsson ◽  
L. Davidson
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Mean Flow ◽  
Stator Vane ◽  
Good Agreement

In this study three-dimensional simulations of a stator vane passage flow have been performed using the v2¯−f turbulence model. Both an in-house code (CALC-BFC) and the commercial software FLUENT are used. The main objective is to investigate the v2¯−f model’s ability to predict the secondary fluid motion in the passage and its influence on the heat transfer to the end walls between two stator vanes. Results of two versions of the v2¯−f model are presented and compared to detailed mean flow field, turbulence, and heat transfer measurements. The performance of the v2¯−f model is also compared with other eddy-viscosity-based turbulence models, including a version of the v2¯−f model, available in FLUENT. The importance of preventing unphysical growth of turbulence kinetic energy in stator vane flows, here by use of the realizability constraint, is illustrated. It is also shown that the v2¯−f model predictions of the vane passage flow agree well with experiments and that, among the eddy-viscosity closures investigated, the v2¯−f model, in general, performs the best. Good agreement between the two different implementations of the v2¯−f model (CALC-BFC and FLUENT) was obtained.

scholarly journals Friction Factor Estimation for Turbulent Flows in Corrugated Pipes With Rough Walls

2009 ◽  
Author(s):  
Maxim Pisarenco ◽  
Bas van der Linden ◽  
Arris Tijsseling ◽  
Emmanuel Ory ◽  
Jacques Dam
Keyword(s):  
Boundary Condition ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Behavior ◽  
Turbulence Models ◽  
Computational Grids ◽  
Law Of The Wall ◽  
Fully Developed Turbulent Flow ◽  
The Right

The motivation of the investigation is critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k–ε and k–ω) are used in the computations. First, fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: the friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric which is wrapped around the spiral.

Computations of Flow Field and Heat Transfer in a Stator Vane Passage Using the v2–f Turbulence Model

2004 ◽  
Author(s):  
Andreas Sveningsson ◽  
Lars Davidson
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Mean Flow ◽  
Stator Vane ◽  
Good Agreement

In this study three-dimensional simulations of a stator vane passage flow have been performed using the v2–f turbulence model. Both an in-house code (CALC-BFC) and the commercial software Fluent are used. The main objective is to investigate the v2–f model’s ability to predict the secondary fluid motion in the passage and its influence on the heat transfer to the endwalls between two stator vanes. Results of two versions of the v2–f model are presented and compared with detailed mean flow field, turbulence and heat transfer measurements. The performance of the v2–f model is also compared with other eddy-viscosity based turbulence models, including a version of the v2–f model, available in Fluent. The importance of preventing unphysical growth of turbulence kinetic energy in stator vane flows, here by use of the realizability constraint, is illustrated. It is also shown that the v2–f model predictions of the vane passage flow agree well with experiments and that, amongst the eddy-viscosity closures investigated, the v2–f model in general performs the best. Good agreement between the two different implementations of the v2–f model (CALC-BFC and Fluent) was obtained.

scholarly journals Dynamics and evolution of turbulent Taylor rolls

2019 ◽  
Vol 870 ◽  
pp. 970-987 ◽  
Author(s):  
Francesco Sacco ◽  
Roberto Verzicco ◽  
Rodolfo Ostilla-Mónico
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Fluid Motion ◽  
Domain Size ◽  
Turbulent Regime ◽  
Computational Domain ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
Angular Velocities ◽  
High Reynolds

In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor–Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocities, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ‘Taylor rolls’ there is a wide variety of structures that differ in the vorticity distribution within the cores, the way they are driven and their effects on the mean flow. We relate the rolls at high Reynolds numbers not to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analysing the effect of the computational domain size, we show that this pinning is not a product of numerics, and that the position of the rolls is governed by a random process with the space and time variations depending on domain size.

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