Oscillatory Flow and Gas Transport Through a Symmetrical Bifurcation

2000 ◽  
Vol 123 (2) ◽  
pp. 145-153 ◽  
Author(s):  
Hideki Fujioka ◽  
Kotaro Oka ◽  
Kazuo Tanishita
Keyword(s):  
Secondary Flow ◽  
Oscillatory Flow ◽  
Gas Transport ◽  
Three Dimensional ◽  
Effective Diffusivity ◽  
Navier Stokes ◽  
Dean Number ◽  
Curved Tube ◽  
Simpler Algorithm ◽  
Flow Divider

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, α=9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/α4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/α4⩽10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/α4⩾20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.

Experimental and Numerical Investigation of Stator Exit Flow Field of an Automotive Torque Converter

1996 ◽  
Vol 118 (4) ◽  
pp. 835-843 ◽  
Author(s):  
B. V. Marathe ◽  
B. Lakshminarayana ◽  
Y. Dong
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Numerical Investigation ◽  
Three Dimensional ◽  
Axial Flow ◽  
Torque Converter ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Complex Flow ◽  
Rate Of Decay

The objective of this investigation is to understand the nature of the complex flow field inside each element of the torque converter through a systematic experimental and numerical investigation of the flow field. A miniature five-hole probe was used to acquire the data at the exit of the stator at several operating conditions. The flow field is found to be highly three dimensional with substantial flow deviations, and secondary flow at the exit of the stator. The secondary flow structure, caused by the upstream radial variation of the through flow, induces flow overturning near the core. Flow separation near the shell causes flow underturning in this region. The rate of decay of stator wake is found to be slower than that observed in the wakes of axial flow turbine nozzles. The flow predictions by a Navier–Stokes code are in good agreement with the pressure and the flow field measured at the exit of the stator at the design and the off-design conditions.

scholarly journals Effect of the Radial Pressure Gradient on the Secondary Flow Generated in an Annular Turbine Cascade

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hesham M. El-Batsh
Keyword(s):  
Pressure Gradient ◽  
Secondary Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Navier Stokes ◽  
Pressure Probe ◽  
Passage Vortex ◽  
Flow Loss ◽  
Radial Pressure Gradient

This paper introduces an investigation of the effect of radial pressure gradient on the secondary flow generated in turbine cascades. Laboratory measurements were performed using an annular sector cascade which allowed the investigation using relatively small number of blades. The flow was measured upstream and downstream of the cascade using a calibrated five-hole pressure probe. The three-dimensional Reynolds Averaged Navier Stokes equations were solved to understand flow physics. Turbulence was modeled using eddy-viscosity assumption and the two-equation Shear Stress Transport (SST)k-ωmodel. The results obtained through this study showed that the secondary flow is significantly affected by the pressure gradient along blade span. The experimental measurements and the numerical calculations predicted passage vortex near blade hub which had larger and stronger values than that predicted near blade tip. The loss distribution revealed that secondary flow loss was concentrated near blade hub. It is recommended that attempts of reducing secondary flow in annular cascade should put emphasis on the passage vortex near the hub.

Experimental and Numerical Investigation Into the Unsteady Interaction of Labyrinth Seal Leakage Flow and Main Flow in a 1.5-Stage Axial Turbine

2004 ◽  
Author(s):  
A. Giboni ◽  
K. Wolter ◽  
J. R. Menter ◽  
H. Pfost
Keyword(s):  
Secondary Flow ◽  
Three Dimensional ◽  
Labyrinth Seal ◽  
Main Flow ◽  
Navier Stokes ◽  
Experimental Program ◽  
Leakage Flow ◽  
Axial Turbine ◽  
Flow Phenomena ◽  
Grid Points

This paper presents the results of experimental and numerical investigations into the flow in a 1.5-stage low-speed axial turbine with a straight labyrinth seal on the rotor shroud. The paper focuses on the time dependent interaction between the leakage flow and the main flow. The experimental program consists of time accurate measurements of the three-dimensional properties of the main flow. The region of the entering leakage flow downstream of the rotor trailing edge was of special interest. The measurements were carried out using pneumatic five-hole probes and three dimensional hot-wire probes at the design operating point of the turbine. The measurement planes behind the three blade rows extend over one pitch from the shroud to the casing. The complex three-dimensional flow field is mapped in great detail by 1,008 points per measurement plane. The time-accurate experimental data of the three measurement planes was compared with the results of unsteady, numerical simulations of the turbine flow. The 3D-Navier-Stokes Solver CFX-TASCflow was used. The experimental and numerical results correspond well and allow detailed analysis of the mixing process. As demonstrated in this paper, the leakage flow causes strong fluctuations of the secondary flow behind the rotor and the second stator. Above all, the high number of numerical grid points reveals both the secondary flow phenomena and the vortex structures of the mixing zone. The time-dependence of both position and intensity of the vortices is shown. The development of the important leakage vortex is illustrated and explained. The paper shows that even at realistic clearance heights the leakage flow gives rise to negative incidence of considerable parts of the downstream stator which causes the flow to separate. Thus, labyrinth seal leakage flow should be taken properly into account in the design or optimization process of turbomachinery.

Instability and transitions of flow in a curved square duct: the development of two pairs of Dean vortices

1996 ◽  
Vol 314 ◽  
pp. 227-246 ◽  
Author(s):  
Philip A. J. Mees ◽  
K. Nandakumar ◽  
J. H. Masliyah
Keyword(s):  
Secondary Flow ◽  
Flow Pattern ◽  
Stokes Equations ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Flow State ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Measured Velocity ◽  
Dean Vortices

Steady developing flow of an incompressible Newtonian fluid in a curved duct of square cross-section (the Dean problem) is investigated both experimentally and numerically. This study is a continuation of the work by Bara, Nandakumar & Masliyah (1992) and is focused on flow rates between Dn = 200 and Dn = 600 (Dn = Re/(R/a)1/2, where Re is the Reynolds number, R is the radius of curvature of the duct and a is the duct dimension; the curvature ratio, R/a, is 15.1).Numerical simulations based on the steady three-dimensional Navier – Stokes equations predict the development of a 6-cell secondary flow pattern above a Dean number of 350. The 6-cell state consists of two large Ekman vortices and two pairs of small Dean vortices near the outer wall that result from the primary instability that is of centrifugal nature. The 6-cell flow state develops near θ = 80° and breaks down symmetrically into a 2-cell flow pattern.The apparatus used to verify the simulations had a duct dimension of 1.27 cm and a streamwise length of 270°. At a Dean number of 453, different velocity profiles of the 6-cell flow state at θ = 90° and spanwise profiles of the streamwise velocity at every 20° were measured using a laser-Doppler anemometer. All measured velocity profiles, as well as flow visualization of secondary flow patterns, are in very good agreement with the simulations, indicating that the parabolized Navier – Stokes equations give an accurate description of the flow.Based on the similarity with boundary layer flow over a concave wall (the Görtler problem), it is suggested that the transition to the 6-cell flow state is the result of a decreasing spanwise wavelength of the Dean vortices with increasing flow rate. A numerical stability analysis shows that the 6-cell flow state is unconditionally unstable. This is the first time that detailed experiments and simulations of the development of a 6-cell flow state are reported.

Numerical Simulation Study on the Concentration Field in an Oscillatory Flow Reactor with Conic Ring Baffles

2013 ◽  
Vol 378 ◽  
pp. 418-423
Author(s):  
Gang Liu ◽  
Jia Wu ◽  
Wei Li
Keyword(s):  
Numerical Simulation ◽  
Oscillatory Flow ◽  
Flow Reactor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Concentration Field ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Diffusion Coefficient ◽  
Simulation Results

The three-dimensional construct of concentration field in an oscillatory flow reactor (OFR) containing periodically spaced conic ring baffles was investigated by numerical simulation employing Reynolds-averaged Navier-Stokes equations. The computation covered a range of Oscillatory Reynolds number (Reo) from 623.32 to 3116.58 at Strouhal number (St) 0.995 and 1.99. The contour of concentration field showed that the concentration in the most part of the channel is relative uniform and a small retention area is found below the conic ring baffles, which means a region of relative poor mixing. In addition, the turbulent diffusion coefficient calculated from the simulation results implied the greater oscillatory amplitude and oscillatory frequency superimposed to the fluid, the stronger is the turbulence intensity.

Direct Numerical Simulation of Effects of Small Angle of Incidence on Honji Instability

2011 ◽  
Author(s):  
Kun Yang ◽  
Liang Cheng ◽  
Hongwei An ◽  
Ming Zhao
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Navier Stokes Equations ◽  
Small Incidence ◽  
Inclination Angles

This paper concerns Honji instability generated around a circular cylinder in an oscillatory flow with a small oblique angle. In this study, direct numerical simulation has been conducted for an oscillatory flow past a stationary cylinder with small incidence angles (α) of 5° and 10° at KC number of 2 and β number of 200. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin finite element method. Flow structures around the cylinder are visualized through using streamlines, velocity vectors and vorticity contours. Honji instability has been captured at both chosen inclination angles. However Honji vortex pairs are asymmetric at α = 5° and 10° due to the inclination of the oscillation direction and can only be observed during the flow reversal. It is also found that the flow inclination appears to suppress the three-dimensional instability.

Calculation of the steady flow through a curved tube using a new finite-difference method

1980 ◽  
Vol 99 (3) ◽  
pp. 449-467 ◽  
Author(s):  
S. C. R. Dennis
Keyword(s):  
Finite Difference ◽  
Steady Flow ◽  
Stokes Equations ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Dean Number ◽  
Numerical Work ◽  
Curved Tube ◽  
Flow Through

A numerical method is described which is suitable for solving the equations governing the steady motion of a viscous fluid through a slightly curved tube of circular cross-section but which is also applicable to the solution of any problem governed by the steady two-dimensional Navier–Stokes equations in the plane polar co-ordinate system. The governing equations are approximated by a scheme which yields finite-difference equations which are of second-order accuracy with respect to the grid sizes but which have associated matrices which are diagonally dominant. This makes them generally more amenable to solution by iterative techniques than the approximations obtained using standard central differences, while preserving the same order of accuracy.The main object of the investigation is to obtain numerical results for the problem of steady flow through a curved tube which corroborate previous numerical work on this problem in view of a recent paper (Van Dyke 1978) which tends to cast doubt on the accuracy of previous calculations at moderately high values of the Dean number; this is the appropriate Reynolds-number parameter in this problem. The present calculations tend to verify the accuracy of previous results for Dean numbers up to 5000, beyond which it is difficult to obtain accurate results. Calculated properties of the flow are compared with those obtained in previous numerical work, with the predictions of boundary-layer theory for large Dean numbers and with the predictions of Van Dyke (1978).

Fully developed intermittent flow in a curved tube

1997 ◽  
Vol 347 ◽  
pp. 263-287 ◽  
Author(s):  
YUTAKA KOMAI ◽  
KAZUO TANISHITA
Keyword(s):  
Secondary Flow ◽  
Axial Velocity ◽  
Axial Flow ◽  
Outer Wall ◽  
Intermittent Flow ◽  
Cycle Period ◽  
Straight Tube ◽  
Flow Profile ◽  
Dean Number ◽  
Curved Tube

Fully developed intermittent flow in a strongly curved tube was numerically simulated using a numerical scheme based on the simpler method. Physiological pulsatile flow in the aorta was simulated as intermittent flow, with a waveform consisting of a pulse-like systolic flow period followed by a stationary diastolic period. Numerical simulations were carried out for the following conditions: Dean number κ=393, frequency parameter α=4–27, curvature ratio δ=1/2, 1/3 and 1/7, and intermittency parameter η=0–1/2, where η is the ratio of a systolic time to the cycle period. For α=18 and 27 the axial-flow profile in a systolic period becomes close to that of a sinusoidally oscillatory flow. At the end of the systole, a region of reversed axial velocity appears in the vicinity of the tube wall, which is caused by the blocking of the flow, similar to blocked flow in a straight tube. This area is enlarged near the inner wall of the bend by the curvature effect. Circumferential flow accelerated in a systole streams into the inner corner and collides at the symmetry line, which creates a jet-like secondary flow towards the outer wall. The region of reversed axial velocity is extended to the tube centre by the secondary flow. The development of the flow continues during the diastolic period for α higher than 8, and the flow does not completely dissipate, so that a residual secondary vortex persists until the next systole. Accordingly, the development of secondary flow in the following systolic phase is strongly affected by the residual vortex at the end of the previous diastolic phase, especially by stationary diastolic periods. Therefore, intermittent flow in a curved tube is strongly affected by the stationary diastolic period. For η=0 and 1/5, the induced secondary flow in a systole forms additional vortices near the inner wall, whereas for η=1/3 and 1/2 additional vortices do not appear. The characteristics of intermittent flow in a curved tube are also strongly affected by the length of the diastolic period, which represents a period of zero flow.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

scholarly journals Simulation and Validation of Mach Number Effects on Secondary Flow in a Transonic Turbine Using a Multigrid, k-ε Solver

1996 ◽  
Author(s):  
M. Koiro ◽  
B. Lakshminarayana
Keyword(s):  
Secondary Flow ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Test Case ◽  
Efficient Manner ◽  
Transonic Turbine ◽  
Mach Numbers ◽  
High Mach

An existing three dimensional Navier-Stokes flow solver with an explicit Runge-Kutta algorithm and a low Reynolds number k-ε turbulence model has been modified in order to simulate turbomachinery flows in a more efficient manner. The solver has been made to converge more rapidly through use of the mutligrid technique. Stability problems associated with use of multigrid in conjunction with two equation turbulence models are addressed and techniques to alleviate instability are investigated. Validation for the new code was performed with a transonic turbine cascade tested by Perdichizzi. In the fully three dimensional turbulent cascade, real convergence (i.e. CPU time) was improved nearly two times the original code. Robustness was enhanced with the full multigrid initialization procedure. The same test case was then used to perform a series of simulations that investigated the effect of different exit Mach numbers on secondary flow features. This permitted an in depth study into the mechanisms of secondary flow formation and secondary losses at high Mach numbers. In this cascade, it was found that secondary losses and secondary flow deviation, which are fairly constant in incompressible flows with similar geometries, underwent a large reduction in the compressible flow range. The structure of the trailing edge shock system and the reduced endwall boundary layer at supersonic exit conditions were shown to be very significant in reducing the amount of secondary flow and losses.

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