Velocity Profile for Developing Flow over Stepped Spillway

2011 ◽  
Author(s):  
X. J. Cheng ◽  
J. S. Gulliver ◽  
Jiachun Li ◽  
Song Fu
Keyword(s):  
Velocity Profile ◽  
Stepped Spillway ◽  
Developing Flow

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Linear Spatial Stability of Developing Flow in a Parallel Plate Channel

1981 ◽  
Vol 48 (1) ◽  
pp. 192-194 ◽  
Author(s):  
S. C. Gupta ◽  
V. K. Garg
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Parallel Plate ◽  
Critical Reynolds Number ◽  
Two Dimensional ◽  
Spatial Stability ◽  
Percent Change ◽  
Developing Flow ◽  
The Stability ◽  
Plate Channel

It is found that even a 5 percent change in the velocity profile produces a 100 percent change in the critical Reynolds number for the stability of developing flow very close to the entrance of a two-dimensional channel.

Tangential flow development for laminar axial flow in an annulus with a rotating inner cylinder

1972 ◽  
Vol 328 (1572) ◽  
pp. 123-141 ◽  
Keyword(s):  
Velocity Profile ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Axial Distance ◽  
Taylor Vortices ◽  
Developing Flow ◽  
Axial Velocity Profile ◽  
Displacement Thickness ◽  
Core Rotation ◽  
Tangential Velocity Profile

The numerical finite-difference procedure of Gosman et al. (1969) is used to predict the growth of the tangential velocity profile and boundary-layer displacement thickness across an isothermal laminar axial flow through a concentric annulus when the inner cylinder is rotated at speeds which are insufficient to generate Taylor vortices. Solutions are obtained for fully developed and for developing axial flow over the ranges 0.05 < R 1 /R 2 < 0.98, 0.0002 < l < 1.0 and 100 < Re < 1700. The axial velocity profile is predicted to be insensitive to core rotation and, if varied, to influence only marginally the development of the tangential velocity profile; this is such that its dimensionless displacement thickness is related to dimensionless axial distance by a power law except near full development and at very low Reynolds number. Predictions at high Re accord extremely well with measurements. Astill’s (1964) stability criterion for the onset of vortices in tangential developing flow is accordingly presented afresh in terms of system parameters readily available to the designer.

Stability of developing flow in a pipe: non-axisymmetric disturbances

1981 ◽  
Vol 110 ◽  
pp. 209-216 ◽  
Author(s):  
Vijay K. Garg
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Critical Reynolds Number ◽  
Temporal Stability ◽  
Developing Flow ◽  
The Stability ◽  
Axisymmetric Disturbances ◽  
Stability Results ◽  
Boundary Layer Edge ◽  
Critical Wavenumber

Spatial stability results for the developing flow in a rigid circular pipe are presented for the velocity profile obtained by the Hornbeck (1963) method and compared with the available temporal stability results for the velocity profile obtained by Sparrow, Lin & Lundgren (1964). The disturbance is taken to be non-axisymmetric, and Gram–Schmidt orthonormalization is used to remove the parasitic errors during numerical integration.It is found that the stability characteristics are very sensitive to the velocity field in the inlet region. At all axial locations investigated the critical frequency and critical wavenumber for the Hornbeck profile are larger than the corresponding values for the Sparrow profile while the critical Reynolds number is smaller. The minimum critical Reynolds number for the Hornbeck profile is only 13250 and occurs at $\overline{X} = 0.0032$ compared with 19780 at $\overline{X} = 0.0049$ for the Sparrow profile. The maximum difference between the two velocity profiles occurs near the boundary-layer edge but is within 5%. Results for the Hornbeck profile are found to be closer to the experimental data of Sarpkaya (1975).

Investigation of the influence of the flow structure on the accuracy of flow measurement before a hydrometric structure in an open channel

2020 ◽  
pp. 41-44
Author(s):  
Anatoly Kusher
Keyword(s):  
Velocity Profile ◽  
Flow Velocity ◽  
Water Flow ◽  
Flow Measurement ◽  
Water Discharge ◽  
Critical Depth ◽  
Flow Measurements ◽  
Study Results ◽  
Flow Velocity Profile ◽  
Upstream Flow

The reliability of water flow measurement in irrigational canals depends on the measurement method and design features of the flow-measuring structure and the upstream flow velocity profile. The flow velocity profile is a function of the channel geometry and wall roughness. The article presents the study results of the influence of the upstream flow velocity profile on the discharge measurement accuracy. For this, the physical and numerical modeling of two structures was carried out: a critical depth flume and a hydrometric overfall in a rectangular channel. According to the data of numerical simulation of the critical depth flume with a uniform and parabolic (1/7) velocity profile in the upstream channel, the values of water discharge differ very little from the experimental values in the laboratory model with a similar geometry (δ < 2 %). In contrast to the critical depth flume, a change in the velocity profile only due to an increase in the height of the bottom roughness by 3 mm causes a decrease of the overfall discharge coefficient by 4…5 %. According to the results of the numerical and physical modeling, it was found that an increase of backwater by hydrometric structure reduces the influence of the upstream flow velocity profile and increases the reliability of water flow measurements.

Sign in / Sign up

Export Citation Format

Share Document