Effect of viscosity, eddy viscosity and velocity profile on the unstable mode in a lined duct with flow

2016 ◽  
Author(s):  
Bo Xin ◽  
Xiaodong Jing ◽  
Xiaofeng Sun
Keyword(s):  
Velocity Profile ◽  
Eddy Viscosity ◽  
Unstable Mode

scholarly journals Reinvestigating the Parabolic-Shaped Eddy Viscosity Profile for Free Surface Flows

Hydrology ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 126
Author(s):  
Rafik Absi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Velocity Profile ◽  
Eddy Viscosity ◽  
Velocity Profiles ◽  
Free Surface Flows ◽  
Analytical Models ◽  
Surface Flows ◽  
Viscosity Models ◽  
Viscosity Profile

The flow in rivers is turbulent. The main parameter related to turbulence in rivers is the eddy viscosity, which is used to model a turbulent flow and is involved in the determination of both velocities and sediment concentrations. A well-known and largely used vertical distribution of eddy viscosity in free surface flows (open channels and rivers) is given by the parabolic profile that is based on the logarithmic velocity profile assumption and is valid therefore only in the log-law layer. It was improved thanks to the log-wake law velocity profile. These two eddy viscosities are obtained from velocity profiles, and the main shortcoming of the log-wake profile is the empirical Coles’ parameter. A more rigorous and reliable analytical eddy viscosity model is needed. In this study, we present two analytical eddy viscosity models based on the concepts of velocity and length scales, which are related to the exponentially decreasing turbulent kinetic energy (TKE) function and mixing length, namely, (1) the exponential-type profile of eddy viscosity and (2) an eddy viscosity based on an extension of von Karman’s similarity hypothesis. The eddy viscosity from the second model is -independent, while the eddy viscosity from the first model is -dependent (where is the friction Reynolds number). The proposed analytical models were validated through computation of velocity profiles, obtained from the resolution of the momentum equation and comparisons to experimental data. With an additional correction function related to the damping effect of turbulence near the free surface, both models are similar to the log-wake-modified eddy viscosity profile but with different values of the Coles’ parameter, i.e., for the first model and for the second model. These values are similar to those found in open-channel flow experiments. This provides an explanation about the accuracy of these two analytical models in the outer part of free surface flows. For large values of ( > 2000), the first model becomes independent, and the two coefficients reach asymptotic values. Finally, the two proposed eddy viscosity models are validated by experimental data of eddy viscosity.

scholarly journals Generation of Gravity-Capillary Wind Waves by Instability of a Coupled Shear-Flow

2022 ◽  
Vol 10 (1) ◽  
pp. 46
Author(s):  
Malek Abid ◽  
Christian Kharif ◽  
Hung-Chu Hsu ◽  
Yang-Yih Chen
Keyword(s):  
Velocity Profile ◽  
Unstable Mode ◽  
Wind Waves ◽  
Surface Current ◽  
Viscous Flows ◽  
Shear Velocity ◽  
Threshold Value ◽  
Surface Velocity ◽  
Mixing Length ◽  
Flow Turbulence

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

The two-dimensional mixing region

1970 ◽  
Vol 41 (2) ◽  
pp. 327-361 ◽  
Author(s):  
I. Wygnanski ◽  
H. E. Fiedler
Keyword(s):  
Velocity Profile ◽  
Eddy Viscosity ◽  
Mixing Layer ◽  
Outer Part ◽  
Eddy Diffusivity ◽  
Turbulent Energy ◽  
Two Dimensional ◽  
Low Velocity ◽  
Mean Velocity ◽  
Axial Velocity Profile

The two-dimensional incompressible mixing layer was investigated by using constant-temperature, linearized hot wire anemometers. The measurements were divided into three categories: (1) the conventional average measurements; (2) time-average measurements in the turbulent and the non-turbulent zones; (3) ensemble average measurements conditioned to a specific location of the interface. The turbulent energy balance was constructed twice, once using the conventional results and again using the turbulent zone results. Some differences emerged between the two sets of results. It appears that the mixing region can be divided into two regions, one on the high velocity side which resembles the outer part of a wake and the other on the low velocity side which resembles a jet. The binding turbulent–non-turbulent interfaces seem to move independently of each other. There is a strong connexion between the instantaneous location of the interface and the axial velocity profile. Indeed the well known exponential mean velocity profile never actually exists at any given instant. In spite of the complexity of the flow the simple concepts of eddy viscosity and eddy diffusivity appear to be valid within the turbulent zone.

Dependence of the Smagorinsky-Lilly's Constant on Inertia, Wind Stress, and Bed Roughness for Large Eddy Simulations

2006 ◽  
Vol 22 (2) ◽  
pp. 125-136
Author(s):  
W.-H. Chung
Keyword(s):  
Velocity Profile ◽  
Wind Stress ◽  
Eddy Viscosity ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Large Eddy Simulations ◽  
Closed Form Expression ◽  
Large Eddy ◽  
Flow Motion ◽  
Bed Roughness

AbstractEquations governing large eddy simulations are usually closed by incorporating with the Smagorinsky-Lilly's turbulence model of eddy viscosity. The model contains a so-called filtering length and a Smagorinsky-Lilly “constant” that changes among different researchers. The variation range of the constant is wide and its value is usually determined in a sense of “guessing”. Since the constant is closely related to the magnitude of eddy viscosity, hence to our numerical solutions eventually, setting a more precise and determinate procedure for prescribing the constant seems to be worthy it. The constant,CSL, is first estimated in use of the properties of fluid flow within the inertia subrange. Then, along with a general derivation, the explicit closed-form expression for the constant is presented for steady uniform flows. It is found that, with the analogy between the filtering technique and Reynolds average,CSLmay not necessarily be constant but proportional to the Manning n and water depth. Other than the determination ofCSL, the vertical flow velocity profile in an infinitely long wide rectangular channel without spiral flow motion is obtained through the use of the Smagorinsky-Lilly's turbulence closure model. It is shown analytically that the velocity profile in unsteady open channel flow can be expressed as a function of an integration functionJn(z)that accounts for wind stress and inertia terms. With the velocity profile, effects of inertia terms, wind stress, and channel bed roughness onCSLare deeply explored in response to the dependence ofCSLonJn(z).

Nonlinear aspects of an internal gravity wave co-existing with an unstable mode associated with a Helmholtz velocity profile

1976 ◽  
Vol 76 (1) ◽  
pp. 65-84 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Wave ◽  
Unstable Mode ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Jump Discontinuity ◽  
Weakly Nonlinear ◽  
Boussinesq Fluid

Recently Lindzen (1974) has proposed a model of a shear-layer instability which allows unstable modes to co-exist with radiating internal gravity waves. The model is an infinite, continuously stratified, Boussinesq fluid, with a simple jump discontinuity in the velocity profile. Linear stability theory shows that the model is stable for wavenumbers k such that k2 < N2/2U2, where N is the Brunt—Väisälä frequency and 2U is the change in velocity across the discontinuity. For N2/2U2 < k2 < N2/U2 an unstable mode may co-exist with an internal gravity wave. This paper examines the weakly nonlinear aspects of this model for wavenumbers k close to the critical wavenumber N/2½U. An equation governing the evolution of the amplitude of the interfacial displacement is derived. It is shown that the interface may support a stable finite amplitude internal gravity wave.

Assessment of turbulence model performance for transonic flow over an axisymmetric bump

2001 ◽  
Vol 105 (1043) ◽  
pp. 17-32 ◽  
Author(s):  
R. G. M. Hasan ◽  
J. J. McGuirk
Keyword(s):  
Velocity Profile ◽  
Eddy Viscosity ◽  
Computational Study ◽  
Model Performance ◽  
Turbulence Models ◽  
Research Programme ◽  
Wall Functions ◽  
Viscosity Models ◽  
Non Linear ◽  
Shock Location

Abstract A computational study has been performed to evaluate the predictive capabilities of some existing eddy-viscosity (both linear, LEVM, and non-linear, NLEVM) and Reynolds stress transport turbulence models (RSTM) by reference to a transonic shock-induced separated flow over a 10% axisymmetric bump. The calculations have been carried out during the course of a collaborative research programme including both UK universities and industry. The findings of the project demonstrate that improved results can be obtained for such flows by using more advanced turbulence models. For linear eddy-viscosity models, only the SST approach gave good predictions of shock location, recirculation size and pressure recovery, although this was accompanied by deficiencies in the prediction of post-shock velocity profile shape. Non-linear eddy-viscosity models, particularly at the cubic level, provided a more consistent level of agreement with experiments over the range of shock location, wall pressure and velocity profile parameters. Some improvement was also seen in the prediction of turbulence quantities, although only a move to an RSTM closure model reproduced the measured peak stress levels accurately. It was notable that the use of low-Re variants of the models (instead of wall functions) produced no significant improvement in predictions. There are, however, some shortcomings in all models, particularly in the development of flow after reattachment, which was always predicted to be too slow.

Rotational channel flow over small three-dimensional bottom irregularities

1974 ◽  
Vol 66 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Jørgen Fredsøe
Keyword(s):  
Velocity Profile ◽  
Eddy Viscosity ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Wall Slip ◽  
Inviscid Fluid ◽  
Rotational Flow ◽  
Arbitrary Angle ◽  
Unidirectional Flow ◽  
Transverse Movement

Rotational flow of an inviscid fluid over an irregularity in the bottom is investigated. The flow is regarded as a perturbed unidirectional flow, and the shape of the irregularity is described using Fourier transforms. The velocity profile in the unidirectional flow is determined using the eddy-viscosity concept and a finite wall slip velocity.Two different examples of irregularities are considered: (a) an infinitely long straight irregularity which forms an arbitrary angle with the direction of the basic flow and (b) a hump in a channel with impermeable walls. The influence of rotation on the two- and three-dimensional waves which are formed downstream of these irregularities is analysed and experimentally verified. Further, it is shown that the gradient of the basic velocity profile increases the transverse movement of the fluid particles at the bottom, while at the surface this transverse movement is decreased.

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