scholarly journals Characteristics of Fiber Suspension Flow in a Turbulent Boundary Layer

2013 ◽  
Vol 8 (1) ◽  
pp. 155892501300800
Author(s):  
Jianzhong Lin ◽  
Suhua Shen ◽  
Xiaoke Ku
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Dissipation Rate ◽  
Viscosity Coefficient ◽  
Fiber Suspension ◽  
Fiber Concentration ◽  
Turbulent Dissipation ◽  
Fiber Aspect Ratio ◽  
Eddy Viscosity Coefficient

The equations of averaged momentum, turbulence kinetic energy, turbulence dissipation rate with the additional term of the fibers, and the equation of probability distribution function for mean fiber orientation are derived and solved numerically for fiber suspension flowing in a turbulent boundary layer. The mathematical model and numerical code are verified by comparing the numerical results with the experimental ones in a turbulent channel flow. The effects of Reynolds number, fiber concentration and fiber aspect-ratio on the mean velocity profile, turbulent kinetic energy, Reynolds stress, turbulent dissipation rate and eddy viscosity coefficient are analyzed. The results show that the velocity profiles become full, and the turbulent kinetic energy, Reynolds stress and eddy viscosity coefficient increase, while turbulent dissipation rate decreases, as the Reynolds number, fiber concentration and fiber aspect-ratio increase. The effect of the fiber aspect-ratio on the turbulent properties is larger than that of the Reynolds number, but smaller than that of the fiber concentration in the range of parameters considered in this paper.

NUMERICAL RESEARCH ON THE EFFECT OF FIBERS ON THE PROPERTY OF TURBULENT FIBER SUSPENSION IN A CHANNEL

2009 ◽  
Vol 23 (03) ◽  
pp. 509-512 ◽  
Author(s):  
SUHUA SHEN ◽  
JIANZHONG LIN
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Fiber Suspension ◽  
Additional Stress ◽  
Mean Velocity ◽  
Navier Stokes Equation ◽  
Fiber Concentration

To explore the rheological property in turbulent channel flow of fiber suspensions, the equation of probability distribution function for mean fiber orientation and the Reynolds averaged Navier-Stokes equation with the term of additional stress resulted from fibers were solved with numerical methods to get the distributions of the mean velocity and turbulent kinetic energy. The simulation results show that the effect of fibers on turbulent channel flow is equivalent to an additional viscosity. The turbulent velocity profiles of fiber suspension become gradually sharper by increasing the fiber concentration and/or decreasing the Reynolds number. The turbulent kinetic energy will increase with increasing Reynolds number and fiber concentration.

Assessment of Simple RANS Turbulence Models for Stall Delay Applications at Low Reynolds Number

2017 ◽  
Vol 863 ◽  
pp. 260-265
Author(s):  
M. Arif Mohamed ◽  
Y. Wu ◽  
Martin Skote
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Radial Flow ◽  
Turbulence Models ◽  
Energy Dissipation Rate ◽  
Rotating Blade ◽  
Rans Turbulence Models ◽  
Delay Phenomenon

This paper assesses the performance of three two-equation turbulence models viz. the SST k-ω, the RNG and realizable k-εfor the simulations of a rotating blade in a wind tunnel experiment where k, ε and ω are turbulent kinetic energy, dissipation rate and specific dissipation respectively. The experiments showed the stall-delay phenomenon at the inboard of the rotating blade at a Reynolds number of 4800. This trend of suction peaks was captured by all three turbulence models albeit not matching the experimental coefficient of pressure accurately. All three models also showed radial flow at the inboard which is consistent with the experiments while the SST predicted the least k at low wall values.

A Velocity and Length Scale Approach to k–ε Modeling

1996 ◽  
Vol 118 (4) ◽  
pp. 857-863 ◽  
Author(s):  
O. Kwon ◽  
F. E. Ames
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Eddy Viscosity ◽  
Normal Component ◽  
Transport Equations ◽  
Length Scale ◽  
Wall Region ◽  
Wide Range

This paper describes a velocity and length scale approach to low-Reynolds-number k–ε modeling, which formulates the eddy viscosity on the normal component of turbulence and a length scale. The normal component of turbulence is modeled based on the dissipation and distance from the wall and is bounded by the isotropic condition. The model accounts for the anisotropy of the dissipation and the reduced length of mixing in the near wall region. The kinetic energy and dissipation rate were computed from the k and ε transport equations of Durbin (1993). The model was tested for a wide range of turbulent flows and proved to be superior to other k–ε based models.

Research on wind buffeting noise characteristics of a vehicle based on ILRN and DES-ILRN methods

2020 ◽  
Vol 235 (1) ◽  
pp. 114-127
Author(s):  
Anqian Yu ◽  
Yang Yi ◽  
Zhengqi Gu ◽  
Ledian Zheng ◽  
Zhengtong Han ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Wind Tunnel Test ◽  
Turbulence Models ◽  
Viscosity Coefficient ◽  
The Road ◽  
Noise Characteristics ◽  
Calculation Results ◽  
Low Reynolds ◽  
Eddy Viscosity Coefficient

In view of the unsatisfactory calculation accuracy of common turbulence models, two improved models, called improved low-Reynolds number (ILRN) k− ε and Detached EddySimulation (DES)-ILRN are proposed. Basing on the low-Reynolds number (LRN k− ε) turbulence model in this paper, revised concepts include the introduction of turbulence time scale, eddy viscosity coefficient limitation concept and separation perception model. Otherwise, the DES model is improved by introducing the ILRN model. The accuracy of the two models is validated through wind tunnel test. Then, the wind buffeting noise from rear windows is received by ILRN and DES-ILRN turbulence models, and the obtained results are compared with the road test. The accuracy of ILRN and DES-ILRN turbulence models in calculating wind buffeting noise of a real vehicle is validated by experiment. ILRN and DES-ILRN models are applied to research the wind buffeting noise, and good calculation results are obtained. They are promising methods to solve wind buffeting noise problems.

Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties

2014 ◽  
Vol 747 ◽  
pp. 73-102 ◽  
Author(s):  
Matthias Kaczorowski ◽  
Kai-Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Heat Flux ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Thermal Plumes ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Very High

AbstractGeometrical confinement of turbulent Rayleigh–Bénard convection (RBC) in Cartesian geometries is found to reduce the local Bolgiano length scale in the centre of the cell $L_{B,centre}$ and can therefore be used to study cascade processes in the bulk of RBC. The dependence of $L_{B,centre}$ versus $\varGamma $ suggests a cut-off to the local $L_B$, which depends on the Prandtl number $Pr$ and is of the order of the cell’s smallest dimension. It is also observed that geometrical confinement changes the topology of the flow, causing the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate (averaged over the centre of the cell and normalized by their respective global averages) to exhibit a maximum at a certain $\varGamma $, which roughly coincides with the aspect ratio at which the viscous and thermal boundary layers of the two opposite lateral walls merge. As a result the mean heat flux through the core region also exhibits a maximum. Unlike in the cubic case, we find that geometrical confinement of the flow results in a local balance of the heat flux and the turbulent kinetic energy dissipation rate for $Pr= 4.38$ for all values of the Rayleigh number $Ra$ (up to $10^{10}$), while no balance is observed for $Pr= 0.7$. The need for very high bulk resolution to accurately resolve the gradients of the flow field at high $Ra$ is shown by analysing the second-order structure functions of the vertical velocity and temperature in the bulk of RBC. Under-resolution of the temperature field yields a large error in the dissipative range scaling, which is believed to be an effect of intermittently penetrating thermal plumes. The resolution contrast resulting from the requirement to resolve the thermal plumes and the homogeneous and isotropic background turbulence scales as $\delta _T / \langle \eta _k \rangle _{centre} \sim Ra^{0.1}$ and should therefore be taken into account when tackling very high $Ra$. In the case studied here, under-resolution can have a significant effect on the local heat flux through the centre of the cell.

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.

scholarly journals Inertia–Gravity Waves Breaking in the Middle Atmosphere at High Latitudes: Energy Transfer and Dissipation Tensor Anisotropy

2020 ◽  
Vol 77 (9) ◽  
pp. 3193-3210
Author(s):  
Tiago Pestana ◽  
Matthias Thalhammer ◽  
Stefan Hickel
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Scaling Law ◽  
Energy Dissipation Rate ◽  
Inertia Gravity Waves

Abstract We present direct numerical simulations of inertia–gravity waves breaking in the middle–upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave’s least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.

Complete self-preservation on the axis of a turbulent round jet

2016 ◽  
Vol 790 ◽  
pp. 57-70 ◽  
Author(s):  
L. Djenidi ◽  
R. A. Antonia ◽  
N. Lefeuvre ◽  
J. Lemay
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Longitudinal Velocity ◽  
Order Structure ◽  
Mean Velocity ◽  
Round Jet ◽  
The Mean

Self-preservation (SP) solutions on the axis of a turbulent round jet are derived for the transport equation of the second-order structure function of the turbulent kinetic energy ($k$), which may be interpreted as a scale-by-scale (s.b.s.) energy budget. The analysis shows that the mean turbulent energy dissipation rate, $\overline{{\it\epsilon}}$, evolves like $x^{-4}$ ($x$ is the streamwise direction). It is important to stress that this derivation does not use the constancy of the non-dimensional dissipation rate parameter $C_{{\it\epsilon}}=\overline{{\it\epsilon}}u^{\prime 3}/L_{u}$ ($L_{u}$ and $u^{\prime }$ are the integral length scale and root mean square of the longitudinal velocity fluctuation respectively). We show, in fact, that the constancy of $C_{{\it\epsilon}}$ is simply a consequence of complete SP (i.e. SP at all scales of motion). The significance of the analysis relates to the fact that the SP requirements for the mean velocity and mean turbulent kinetic energy (i.e. $U\sim x^{-1}$ and $k\sim x^{-2}$ respectively) are derived without invoking the transport equations for $U$ and $k$. Experimental hot-wire data along the axis of a turbulent round jet show that, after a transient downstream distance which increases with Reynolds number, the turbulence statistics comply with complete SP. For example, the measured $\overline{{\it\epsilon}}$ agrees well with the SP prediction, i.e. $\overline{{\it\epsilon}}\sim x^{-4}$, while the Taylor microscale Reynolds number $Re_{{\it\lambda}}$ remains constant. The analytical expression for the prefactor $A_{{\it\epsilon}}$ for $\overline{{\it\epsilon}}\sim (x-x_{o})^{-4}$ (where $x_{o}$ is a virtual origin), first developed by Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) and rederived here solely from the SP analysis of the s.b.s. energy budget, is validated and provides a relatively simple and accurate method for estimating $\overline{{\it\epsilon}}$ along the axis of a turbulent round jet.

On the normalized dissipation parameter in decaying turbulence

2017 ◽  
Vol 817 ◽  
pp. 61-79 ◽  
Author(s):  
L. Djenidi ◽  
N. Lefeuvre ◽  
M. Kamruzzaman ◽  
R. A. Antonia
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Far Field ◽  
Round Jet ◽  
Decaying Turbulence

The Reynolds number dependence of the non-dimensional mean turbulent kinetic energy dissipation rate$C_{\unicode[STIX]{x1D716}}=\overline{\unicode[STIX]{x1D716}}L/u^{\prime 3}$(where$\unicode[STIX]{x1D716}$is the mean turbulent kinetic energy dissipation rate,$L$is an integral length scale and$u^{\prime }$is the velocity root-mean-square) is investigated in decaying turbulence. Expressions for$C_{\unicode[STIX]{x1D716}}$in homogeneous isotropic turbulent (HIT), as approximated by grid turbulence, and in local HIT, as on the axis of the far field of a turbulent round jet, are developed from the Navier–Stokes equations within the framework of a scale-by-scale energy budget. The analysis shows that when turbulence decays/evolves in compliance with self-preservation (SP),$C_{\unicode[STIX]{x1D716}}$remains constant for a given flow condition, e.g. a given initial Reynolds number. Measurements in grid turbulence, which does not satisfy SP, and on the axis in the far field of a round jet, which does comply with SP, show that$C_{\unicode[STIX]{x1D716}}$decreases in the former case and remains constant in the latter, thus supporting the theoretical results. Further, while$C_{\unicode[STIX]{x1D716}}$can remain constant during the decay for a given initial Reynolds number, both the theory and measurements show that it decreases towards a constant,$C_{\unicode[STIX]{x1D716},\infty }$, as$Re_{\unicode[STIX]{x1D706}}$increases. This trend, in agreement with existing data, is not inconsistent with the possibility that$C_{\unicode[STIX]{x1D716}}$tends to a universal constant.

Numerical Modelling of Multi-Step Energy Dissipation Facility in Rushing Trough

2011 ◽  
Vol 94-96 ◽  
pp. 606-612
Author(s):  
Yan Wei Li ◽  
Zhi Yong Li
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Numerical Modelling ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Steep Slope ◽  
Turbulent Dissipation ◽  
Turbulent Dissipation Rate ◽  
Energy Facility ◽  
Cfd Method

Abstract：Rushing trough is often used as drainage in steep slope section, velocity of flow can be reduced and water-damage of road can also be prevented furtherly if multi-step energy dissipation facility is placed in rushing trough. In this paper, CFD method is adopted and VOF calculating model is established and turbulent kinetic energy and turbulent dissipation rate are introduced as standard to analyse energy dissipation mechanics of the facility. The factors such as height of embankment, gradient of trough, size of step and velocity of flow in inlet, which can influence efficiency of energy dissipation, are also discussed in the paper and regression formula about efficency of energy dissipation is presented. All the conclusion can guide the design of consumed energy facility.

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