scholarly journals On the Flow Instabilities and Turbulent Kinetic Energy of Large-Scale Francis Hydroturbine Model at Low Flow Rate Conditions

2014 ◽  
Vol 6 ◽  
pp. 786891
Author(s):  
Wen-Tao Su ◽  
Xiao-Bin Li ◽  
Feng-Chen Li ◽  
Xian-Zhu Wei ◽  
Jin-Tao Liu ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Phase Difference ◽  
Large Scale ◽  
Pressure Oscillation ◽  
Curvilinear Coordinates ◽  
Flow Instabilities ◽  
Experimental Result ◽  
Production Term ◽  
Francis Hydroturbine

This paper is to make a better understanding of the flow instabilities and turbulent kinetic energy (TKE) features in a large-scale Francis hydroturbine model. The flow instability with aspect of pressure oscillation and pressure-velocity correlation was investigated using large eddy simulation (LES) method along with two-phase cavitation model. The numerical simulation procedures were validated by the existing experimental result, and further the TKE evolution was analyzed in a curvilinear coordinates. By monitoring the fluctuating pressure and velocities in the vanes’ wake region, the local pressure and velocity variations were proven to have a phase difference approaching π/2, with a reasonable cross-correlation coefficient. Also the simultaneous evolution of pressure fluctuations at the opposite locations possessed a clear phase difference of π, indicating the stresses variations on the runner induced by pressure oscillation were in an odd number of nodal diameter. Considering the TKE generation, the streamwise velocity component u s′2 contributed the most to the TKE, and thus the normal stress production term and shear stress production term imparted more instability to the flow than other production terms.

scholarly journals Discussion on improved method of turbulence model for supercritical water flow and heat transfer

2020 ◽  
Vol 24 (5 Part A) ◽  
pp. 2729-2741
Author(s):  
Zhenchuan Wang ◽  
Guoli Qi ◽  
Meijun Li
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Buoyancy Effect ◽  
Improved Method ◽  
Production Term ◽  
Flow And Heat Transfer ◽  
Effect Model

The turbulence model fails in supercritical fluid-flow and heat transfer simulation, owing to the drastic change of thermal properties. The inappropriate buoyancy effect model and the improper turbulent Prandtl number model are several of these factors lead to the original low-Reynolds number turbulence model unable to predict the wall temperature for vertically heated tubes under the deteriorate heat transfer conditions. This paper proposed a simplified improved method to modify the turbulence model, using the generalized gradient diffusion hypothesis approximation model for the production term of the turbulent kinetic energy due to the buoyancy effect, using a turbulence Prandtl number model for the turbulent thermal diffusivity instead of the constant number. A better agreement was accomplished by the improved turbulence model compared with the experimental data. The main reason for the over-predicted wall temperature by the original turbulence model is the misuse of the buoyancy effect model. In the improved model, the production term of the turbulent kinetic energy is much higher than the results calculated by the original turbulence model, especially in the boundary-layer. A more accurate model for the production term of the turbulent kinetic energy is the main direction of further modification for the low Reynolds number turbulence model.

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

2021 ◽  
Author(s):  
Ewa Jarosz ◽  
Hemantha W. Wijesekera ◽  
David W. Wang
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Vertical Velocity ◽  
Mixed Layer Depth ◽  
Vertical Transport ◽  
Rate Of Change ◽  
Production Term ◽  
Forcing Mechanisms ◽  
Surface Buoyancy

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downweling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 min to 40 min and estimated lateral scales ranged from 90 m to 430 m, which were 1.5 – 6 times larger than the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high wind, and high-sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

Turbulent Jet Mixing Enhancement and Control Using Self-Excited Nozzles

2007 ◽  
Vol 129 (7) ◽  
pp. 842-851 ◽  
Author(s):  
Uri Vandsburger ◽  
Yiqing Yuan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Nozzle Exit ◽  
Large Scale ◽  
Rectangular Cross Section ◽  
Near Field ◽  
Excitation Frequency ◽  
Mixing Enhancement ◽  
Mixing Rate ◽  
Jet Mixing

A new self-excited jet methodology was developed for the mixing enhancement of jet fluid with its surrounding, quiescent, stagnant, or coflowing fluid. The nozzles, of a square or rectangular cross section, featured two flexible side walls that could go into aerodynamically-induced vibration. The mixing of nozzle fluid was measured using planar laser-induced fluorescence (PLIF) from acetone seeded into the nozzle fluid. Overall, the self-excited jet showed enhanced mixing with the ambient fluid; for example, at 390Hz excitation a mixing rate enhancement of 400% at x∕D=4 and 200% at x∕D=20 over the unexcited jet. The mixing rate was sensitive to the excitation frequency, increasing by 60% with the frequency changing from 200 to 390Hz (corresponding to a Strouhal number from 0.052 to 0.1). It was also observed that the mixing rate increased with the coflow velocity. To explain the observed mixing enhancement, the flow field was studied in detail using four-element hot wire probes. This led to the observation of two pairs of counter rotating large-scale streamwise vortices as the dominant structures in the excited flow. Shedding right from the nozzle exit, these inviscid vortices provided a rapid transport of the momentum and mass between the jet and the surrounding fluid at a length scale comparable to half-nozzle diameter. Moreover, the excited jet gained as much as six times the turbulent kinetic energy at the nozzle exit over the unexcited jet. Most of the turbulent kinetic energy is concentrated within five diameters from the nozzle exit, distributed across the entire jet width, explaining the increased mixing in the near field.

scholarly journals Experimental Analysis of Horizontal Turbulence of Flow over Flat and Deformed Beds

2015 ◽  
Vol 62 (3-4) ◽  
pp. 77-99 ◽  
Author(s):  
Donatella Termini
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Experimental Analysis ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Reynolds Shear Stress ◽  
Turbulent Structures ◽  
Quadrant Method ◽  
Initial Sequence

AbstractLaboratory experiments in a straight flume were carried out to examine the evolution of large-scale horizontal turbulent structures under flat-bed and deformed-bed conditions. In this paper, the horizontal turbulence of flow under these conditions is analyzed and compared. The conditioned quadrant method is applied to verify the occurrence of turbulent events. The distributions of horizontal Reynolds shear stress and turbulent kinetic energy are also presented and discussed. Results show the occurrence of an “initial” sequence of horizontal vortices whose average spatial length scales with the channel width. Under deformed-bed conditions, this spatial length does not change.

scholarly journals The Microscale Obstacle Resolving Meteorological Model MITRAS: Model Theory

2017 ◽  
Author(s):  
Mohamed H. Salim ◽  
K. Heinke Schlünzen ◽  
David Grawe ◽  
Marita Boettcher ◽  
Andrea M. U. Gierisch ◽  
...  
Keyword(s):  
Wind Speed ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Radiation Absorption ◽  
Grid Cells ◽  
Meteorological Model ◽  
Production Term ◽  
Wall Functions ◽  
Radiative Processes ◽  
Microscale Model

Abstract. This paper describes the developing theory and the underlying processes of the microscale obstacle resolving model MITRAS Version 2. MITRAS calculates wind, temperature, humidity and precipitation fields as well as transport within the obstacles layer using Reynolds averaging. It explicitly resolves obstacles, including buildings and overhanging obstacles, to consider their aerodynamic and thermodynamic effects. Buildings are represented by impermeable grid cells at the building positions so that the wind speed vanishes and zero turbulent kinetic energy is assumed in these grid cells. Wall functions are used to calculate appropriate turbulent fluxes. Most exchange processes at the obstacle surfaces are considered in MITRAS, including convective and radiative processes in order to obtain an accurate surface temperature. MITRAS is also able to simulate the effect of wind turbines. They are parameterized using the actuator-disk concept to account for the reduction in wind speed. The turbulence generation in the wake of a wind turbine is parameterized by adding an additional part to the turbulence mechanical production term in the turbulent kinetic energy equation. Effects of trees are considered explicitly, including the wind speed reduction, turbulence production, and dissipation due to drag forces from plant foliage elements as well as the radiation absorption and shading. The paper is providing not only a documentation of the model dynamics and numerical framework but also a solid foundation for future microscale model extensions.

LDV Measurements of Periodic Fully Developed Main and Secondary Flows in a Channel With Rib-Disturbed Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 109-114 ◽  
Author(s):  
T.-M. Liou ◽  
Y.-Y. Wu ◽  
Y. Chang
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Secondary Flows ◽  
Laser Doppler Velocimeter ◽  
Parameter Distribution ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Production Term ◽  
Basic Assumptions

Laser-Doppler velocimeter measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for periodic fully developed flows in a channel with square rib-disturbed walls on two opposite sides. Quantities such as the vorticity thickness and turbulent kinetic energy are used to characterize the flow. The investigated flow was periodic in space. The Reynolds number based on the channel hydraulic diameter was 3.3×104. The ratios of pitch to rib-height and rib-height to chamber-height were 10 and 0.133, respectively. Regions where maximum and minimum Reynolds stress and turbulent kinetic energy occurred were identified from the results. The growth rate of the shear layers of the present study was compared with that of a backward-facing step. The measured turbulence anisotropy and structure parameter distribution were used to examine the basic assumptions embedded in the k–ε and k–ε–A models. For a given axial station, the peak axial mean-velocity was found not to occur at the center point. The secondary flow was determined to be Prandtl’s secondary flow of the second kind according to the measured streamwise mean vorticity and its production term.

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