The Elliptic Solution of the Secondary Flow Problem

1983 ◽  
Vol 105 (3) ◽  
pp. 530-535 ◽  
Author(s):  
S. Abdallah ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Elliptic Solution ◽  
Dimensional Flow ◽  
Flow Vorticity ◽  
Dependent Variables ◽  
Two Dimensional Flow ◽  
Uniqueness Of The Solution

This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the streamlike function formulation. A new mechanism is implemented to exchange information between the solutions on the three family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

The Elliptic Solution of the Secondary Flow Problem

1982 ◽  
Author(s):  
S. Abdallah ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Elliptic Solution ◽  
Dimensional Flow ◽  
Flow Vorticity ◽  
Dependent Variables ◽  
Two Dimensional Flow ◽  
Uniqueness Of The Solution

This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the stream-like function formulation. A new mechanism is implemented to exchange information between the solutions on the 3 family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

On two-dimensional inviscid flow in a waterfall

1965 ◽  
Vol 22 (2) ◽  
pp. 359-369 ◽  
Author(s):  
N. S. Clarke
Keyword(s):  
Asymptotic Expansion ◽  
Flow Field ◽  
Froude Number ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Free Streamlines ◽  
Two Dimensional Flow ◽  
Boundary Geometry

This paper is concerned with the two-dimensional flow in a free waterfall, falling under the influence of gravity, the fluid being considered to be incompressible and inviscid. A parameter ε, such that 2/ε is the Froude number based on conditions far upstream, is defined and considered to be small. A flowline co-ordinate system is used to overcome the difficulty that the boundary geometry is not known in advance. An asymptotic expansion based on ε is constructed as an approximation valid upstream and near the edge, but singular far downstream. Another asymptotic expansion, based upon the thinness of the fall, is constructed as an approximation valid far downstream, but failing to satisfy the conditions upstream. The two expansions are then matched to give a solution covering the whole flow field. The shapes of the free streamlines are shown for a number of values of ε for which the solutions are seemingly valid.

Simulation of Three-Dimensional Flow Field Around Unconventional Bridge Piers

2017 ◽  
Author(s):  
Adnan Ismael ◽  
Hamid Hussein ◽  
Mohammed Tareq ◽  
Mustafa Gunal
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Bridge Piers ◽  
Three Dimensional Flow ◽  
Dimensional Flow

scholarly journals Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 139-148
Author(s):  
Shiyang Liu ◽  
Xuefu Zhang ◽  
Feng Gao ◽  
Liangwen Wei ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Field Distribution ◽  
Rapid Development ◽  
Maximum Velocity ◽  
Distribution Characteristics ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Laboratory Test Results ◽  
Transverse Distance ◽  
Two Dimensional Flow

AbstractWith the rapid development of traffic infrastructure in China, the problem of crystal plugging of tunnel drainage pipes becomes increasingly salient. In order to build a mechanism that is resilient to the crystal plugging of flocking drainage pipes, the present study used the numerical simulation to analyze the two-dimensional flow field distribution characteristics of flocking drainage pipes under different flocking spacings. Then, the results were compared with the laboratory test results. According to the results, the maximum velocity distribution in the flow field of flocking drainage pipes is closely related to the transverse distance h of the fluff, while the longitudinal distance h of the fluff causes little effect; when the transverse distance h of the fluff is less than 6.25D (D refers to the diameter of the fluff), the velocity between the adjacent transverse fluffs will be increased by more than 10%. Moreover, the velocity of the upstream and downstream fluffs will be decreased by 90% compared with that of the inlet; the crystal distribution can be more obvious in the place with larger velocity while it is less at the lower flow rate. The results can provide theoretical support for building a mechanism to deal with and remove the crystallization of flocking drainage pipes.

Experimental investigation on the three-dimensional flow field from a meltblowing slot die

e-Polymers ◽  
2020 ◽  
Vol 20 (1) ◽  
pp. 724-732
Author(s):  
Changchun Ji ◽  
Yudong Wang
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Great Influence ◽  
Distribution Characteristics ◽  
Air Velocity ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Airflow Distribution ◽  
Slot Die ◽  
Center Area

AbstractTo investigate the distribution characteristics of the three-dimensional flow field under the slot die, an online measurement of the airflow velocity was performed using a hot wire anemometer. The experimental results show that the air-slot end faces have a great influence on the airflow distribution in its vicinity. Compared with the air velocity in the center area, the velocity below the slot end face is much lower. The distribution characteristics of the three-dimensional flow field under the slot die would cause the fibers at different positions to bear inconsistent air force. The air velocity of the spinning centerline is higher than that around it, which is more conducive to fiber diameter attenuation. The violent fluctuation of the instantaneous velocity of the airflow could easily cause the meltblowing fiber to whip in the area close to the die.

scholarly journals Transient Three-Dimensional Flow Field Measurements by Means of 3D µPTV in Drying Poly(Vinyl Acetate)-Methanol Thin Films Subject to Short-Scale Marangoni Instabilities

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1223
Author(s):  
Max Tönsmann ◽  
Philip Scharfer ◽  
Wilhelm Schabel
Keyword(s):  
Flow Field ◽  
Vinyl Acetate ◽  
Three Dimensional ◽  
Field Measurements ◽  
Initial Assessment ◽  
Ambient Conditions ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Short Scale ◽  
Dry Film

Convective Marangoni instabilities in drying polymer films may induce surface deformations, which persist in the dry film, deteriorating product performance. While theoretic stability analyses are abundantly available, experimental data are scarce. We report transient three-dimensional flow field measurements in thin poly(vinyl acetate)-methanol films, drying under ambient conditions with several films exhibiting short-scale Marangoni convection cells. An initial assessment of the upper limit of thermal and solutal Marangoni numbers reveals that the solutal effect is likely to be the dominant cause for the observed instabilities.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Sign in / Sign up

Export Citation Format

Share Document