Differential Equation Specification of Integral Turbulence Length Scales

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Richard J. Jefferson-Loveday ◽  
Paul G. Tucker ◽  
John D. Northall ◽  
V. Nagabhushana Rao
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Dirichlet Boundary Conditions ◽  
Recirculation Region ◽  
Mean Flow ◽  
Length Scales ◽  
Measured Velocity ◽  
Drag Coefficients ◽  
Rans Models ◽  
Turbulence Length

A Hamilton–Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee–Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in re-attachment length is improved by 180% compared with the steady RANS k-ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case, the HJ–NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

Differential Equation Specification of Integral Turbulence Length Scales

2012 ◽  
Author(s):  
Richard Jefferson-Loveday ◽  
Paul Tucker ◽  
V. Nagabhushana Rao ◽  
John Northall
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Dirichlet Boundary Conditions ◽  
Recirculation Region ◽  
Mean Flow ◽  
Length Scales ◽  
Measured Velocity ◽  
Drag Coefficients ◽  
Rans Models ◽  
Turbulence Length

A Hamilton-Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee-Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in reattachment length is improved by 180% compared with the steady RANS k–ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case the HJ-NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

Numerical Simulation of a Three-Dimensional Axisymmetric Hill: Performance Evaluation of Hybrid RANS-LES Models

2021 ◽  
Author(s):  
Tausif Jamal ◽  
Varun Chitta ◽  
Dibbon K. Walters
Keyword(s):  
Eddy Viscosity ◽  
Turbulence Modeling ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Wake Flow ◽  
Dynamics Simulation ◽  
Recirculation Region ◽  
Mean Flow ◽  
Large Eddy ◽  
Rans Models

Abstract Computational fluid dynamics simulation of flow over a three-dimensional axisymmetric hill presents a unique set of challenges for turbulence modeling. The flow past the crest of the hill is characterized by boundary layer separation, complex vortical structures, and unsteady wake flow. As a result, traditional eddy-viscosity Reynolds-averaged Navier-Stokes (RANS) models have been found to perform poorly for this benchmark test case. Recent studies have focused on the use of large-eddy simulation (LES) and hybrid RANS-LES (HRL) methods to improve accuracy. In this study, several different HRL models are investigated and results from the different models are evaluated relative to each other, to an eddy-viscosity RANS model, and to previously documented high-fidelity large-eddy simulations and experimental data. Results obtained from the simulations in terms of mean flow statistics, surface pressure distribution, and turbulence characteristics are presented and discussed in detail. Results indicate that HRL models can significantly improve predictions over RANS models, but only when the development of turbulent velocity fluctuations in the separated shear layer and recirculation region are well resolved.

Asymmetry and transition to turbulence in a smooth axisymmetric constriction

2008 ◽  
Vol 607 ◽  
pp. 351-386 ◽  
Author(s):  
J. VÉTEL ◽  
A. GARON ◽  
D. PELLETIER ◽  
M.-I. FARINAS
Keyword(s):  
Reynolds Number ◽  
Wavelet Transforms ◽  
Transition To Turbulence ◽  
Sudden Expansion ◽  
Recirculation Region ◽  
Discrete Wavelet ◽  
Spectral Structure ◽  
Mean Flow ◽  
Number Range ◽  
Structure Of Flow

The flow through a smooth axisymmetric constriction (a stenosis in medical applications) of 75% restriction in area is measured using stereoscopic and time-resolved particle image velocimetry (PIV) in the Reynolds number range Re ~ 100–1100. At low Reynolds numbers, steady flow results reveal an asymmetry of the flow downstream of the constriction. The jet emanating from the throat of the nozzle is deflected towards the wall causing the formation of a one-sided recirculation region. The asymmetry results from a Coanda-type wall attachment already observed in symmetric planar sudden expansion flows. When the Reynolds number is increased above the critical value of 400, the separation surface cannot remain attached and an unsteady flow regime begins. Low-frequency axial oscillations of the reattachment point are observed along with a slow swirling motion of the jet. The phenomenon is linked to a periodic discharge of the unstable recirculation region inducing alternating laminar and turbulent flow phases. The resulting flow is highly non-stationary and intermittent. Discrete wavelet transforms are used to discriminate between the large-scale motions of the mean flow and the vortical and turbulent fluctuations. Continuous wavelet transforms reveal the spectral structure of flow disturbances. Temporal measurements of the three velocity components in cross-sections are used with the Taylor hypothesis to qualitatively reconstruct the three-dimensional velocity vector fields, which are validated by comparing with two-dimensional PIV measurements in meridional planes. Visualizations of isosurfaces of the swirling strength criterion allow the identification of the topology of the vortices and highlight the formation and evolution of hairpin-like vortex structures in the flow. Finally, with further increase of the Reynolds number, the flow exhibits less intermittency and becomes stationary for Re ~ 900. Linear stochastic estimation identifies the predominance of vortex rings downstream of the stenosis before breakdown to turbulence.

A random-jet-stirred turbulence tank

2008 ◽  
Vol 604 ◽  
pp. 1-32 ◽  
Author(s):  
EVAN A. VARIANO ◽  
EDWIN A. COWEN
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Homogeneous Region ◽  
Gas Transfer ◽  
Water Interface ◽  
Mean Flow ◽  
Length Scales ◽  
Air Water Interface

We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylor's frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.

Simulating flow separation from continuous surfaces: routes to overcoming the Reynolds number barrier

2009 ◽  
Vol 367 (1899) ◽  
pp. 2885-2903 ◽  
Author(s):  
Michael Leschziner ◽  
Ning Li ◽  
Fabrizio Tessicini
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Major Elements ◽  
Wall Layer ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Rans Models ◽  
High Reynolds ◽  
Near Wall

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence

2021 ◽  
Author(s):  
Yaomin Zhao ◽  
Richard D. Sandberg
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Suction Side ◽  
Rotor Blades ◽  
High Fidelity ◽  
Mean Flow ◽  
High Pressure Turbine ◽  
Flow Shear ◽  
Phase Lock ◽  
The Mean

Abstract We present the first wall-resolved high-fidelity simulations of high-pressure turbine (HPT) stages at engine-relevant conditions. A series of cases have been performed to investigate the effects of varying Reynolds numbers and inlet turbulence on the aerothermal behavior of the stage. While all of the cases have similar mean pressure distribution, the cases with higher Reynolds number show larger amplitude wall shear stress and enhanced heat fluxes around the vane and rotor blades. Moreover, higher-amplitude turbulence fluctuations at the inlet enhance heat transfer on the pressure-side and induce early transition on the suction-side of the vane, although the rotor blade boundary layers are not significantly affected. In addition to the time-averaged results, phase-lock averaged statistics are also collected to characterize the evolution of the stator wakes in the rotor passages. It is shown that the stretching and deformation of the stator wakes is dominated by the mean flow shear, and their interactions with the rotor blades can significantly intensify the heat transfer on the suction side. For the first time, the recently proposed entropy analysis has been applied to phase-lock averaged flow fields, which enables a quantitative characterization of the different mechanisms responsible for the unsteady losses of the stages. The results indicate that the losses related to the evolution of the stator wakes is mainly caused by the turbulence production, i.e. the direct interaction between the wake fluctuations and the mean flow shear through the rotor passages.

INVESTIGATION ON HEAT TRANSFER ENHANCEMENT IN A CORRUGATED FIN-AND-TUBE COMPACT HEAT EXCHANGER

2016 ◽  
Vol 78 (10-2) ◽  
Author(s):  
Ahmadali Gholami ◽  
Mazlan A. Wahid ◽  
Hussein A. Mohammed ◽  
A. Saat ◽  
M. Y. M. Fairus ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Loss ◽  
Boundary Layer Separation ◽  
Performance Criteria ◽  
Recirculation Region ◽  
Moderate Pressure ◽  
Compact Heat Exchangers ◽  
Heat Transfer Augmentation

Heat transfer augmentation and pressure loss penalty in the fin-and-tube compact heat exchangers (FTCHEs) with the corrugated shape as a special form of the fin are numerically investigated to improve heat transfer performance criteria in low Reynolds numbers. The corrugated fin as the newly design of fin pattern is presented in this study. The influence of applying corrugated design adjustments on the thermal and hydraulic characteristics of air flow are analyzed on the in-line tube arrangements. The performance of air-side heat transfer and fluid flow is investigated by numerical simulation for Reynolds number ranging from Re = 400 to 800 based on the tube collar diameter, with the corresponding frontal air velocity ranging from 0.35 to 0.72 m/s. The outcomes of simulation revealed that the corrugated fin could significantly improve the heat transfer augmentation of the FTCHEs with a moderate pressure loss penalty. The computational results indicated that some eddies were developed behind the fluted domain of corrugated finwhich produce some disruptions to fluid flow and enhance heat transfer compared with plain fin. The corrugated form of fins could enhance the thermal mixing of the fluid, delay the boundary layer separation, and reduce the size of the wake and the recirculation region behind tubes compared with the conventional form of the fin at the range of Reynolds number used in this study. In addition, the results showed that the average Nusselt number for the FTCHE with corrugated fin increased by 7.05–10.0% over the baseline case and the corresponding pressure loss decreased by 5.0–6.2%.

Velocity and Pressure Measurements Along a Row of Confined Cylinders

2006 ◽  
Author(s):  
Barton L. Smith ◽  
Jack J. Stepan ◽  
Donald M. McEligot
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Symmetry Plane ◽  
Field Measurements ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Recirculation Region ◽  
Pressure Measurements ◽  
Layer Transition ◽  
Flow Experiments

The results of flow experiments performed in a cylinder array designed to mimic a VHTR Nuclear Plant lower plenum design are presented. Pressure drop and velocity field measurements were made. Based on these measurements, five regimes of behavior are identified that are found to depend on Reynolds number. It is found that the recirculation region behind the cylinders is shorter than that of half cylinders placed on the wall representing the symmetry plane. Unlike a single cylinder, the separation point is found to always be on the rear of the cylinders, even at very low Reynolds number. Boundary layer transition is found to occur at much lower Reynolds numbers than previously reported.

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