scholarly journals Investigation of the influence of narrowing annular channel and Reynolds number on formation of Tayler-Gortler vortexes

2021 ◽  
Vol 2039 (1) ◽  
pp. 012025
Author(s):  
E V Pankratov
Keyword(s):  
Reynolds Number ◽  
Swirling Flow ◽  
Outer Cylinder ◽  
Cone Angle ◽  
Annular Channel ◽  
Reynolds Numbers ◽  
Görtler Vortices ◽  
First Case ◽  
Constant Diameter ◽  
Secondary Vortices

Abstract Abstract. The article investigates the Taylor-Gortler vortices arising in a swirling flow when the annular channel narrows. Several options for the geometry of the narrowed annular channel are researched. In the first case, the outer cylinder with a constant diameter and the inner cone with a variable cone angle are considered. In the second case, on the contrary an inner cylinder with a constant diameter and an outer cone with a variable cone angle are considered. All geometries were tested at different Reynolds numbers Re. = 8.3-103…21•103. As a result, the analysis of the propagation of secondary vortices along the length of the annular channel is presented.

Admissible Reynolds numbers for Poiseuille flow in jet viscometer orifices

1975 ◽  
Vol 347 (1648) ◽  
pp. 47-60 ◽  
Keyword(s):  
Reynolds Number ◽  
Shear Viscosity ◽  
Reynolds Numbers ◽  
Viscosity Reduction ◽  
Fully Developed Flow ◽  
Low Reynolds Numbers ◽  
Constant Diameter ◽  
Low Reynolds ◽  
Low Rate ◽  
Poiseuille Equation

At low Reynolds numbers for which the flow through a jet viscometer orifice strictly obeys the Poiseuille equation, the effective hydrodynamic length L 0 which may be calculated from the volume flow rate, the applied pressure difference, the radius of the orifice, and the density and low rate of shear viscosity of the liquid is much larger than the length L of ‘constant diameter’ of the orifice. It was shown before that a close approach, say 95%, to fully developed flow in the ‘constant diameter’ section of these short orifices is possible at sufficiently low Reynolds numbers, but it is shown now that L 0 may be used to calculate the largest admissible Reynolds number for 95% approach to fully developed flow. The flow in jet visco-meter orifices may be described by the Poiseuille–Hagenbach equation. At very low Reynolds numbers there is strict Poiseuille flow. This is followed by a short range of Reynolds numbers in which the inertia force correction factor m ( see equation (1)) increases steeply with the Reynolds number to reach a plateau value at a diameter Reynolds number of about 20. Although L 0 is not constant over the whole range of admissible Reynolds numbers, it satisfies the Poiseuille-Hagenbach equation if it is used with the appropriate m -value for each orifice and flow condition. For quantitative measurements of the temporary viscosity reduction of a liquid by an applied shear stress, care must be taken to avoid the transition region in which m varies with Re , because the Reynolds number Re can only be calculated with the low rate of shear viscosity of the liquid. It is important to find the mean rate of shear for any particular temporary viscosity reduction. Within the admissible range of Reynolds numbers, this may be derived from the Poiseuille equation. It is shown that the temporary viscosity reduction curve of one liquid which was measured with three jet orifices of different m-Re characteristics was a unique curve.

Development of a Tip-Leakage Flow—Part 1: The Flow Over a Range of Reynolds Numbers

2006 ◽  
Vol 128 (4) ◽  
pp. 751-764 ◽  
Author(s):  
Ghanem F. Oweis ◽  
David Fry ◽  
Chris J. Chesnakas ◽  
Stuart D. Jessup ◽  
Steven L. Ceccio
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Leakage Flow ◽  
Core Size ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Downstream Distance ◽  
Secondary Vortices

An extensive experimental investigation was carried out to examine the tip-leakage flow on ducted propulsors. The flow field around three-bladed, ducted rotors operating in uniform inflow was measured in detail with three-dimensional laser Doppler velocimetry and planar particle imaging velocimetry. Two geometrically similar, ducted rotors were tested over a Reynolds number range from 0.7×106 to 9.2×106 in order to determine how the tip-leakage flow varied with Reynolds number. An identification procedure was used to discern and quantify regions of concentrated vorticity in instantaneous flow fields. Multiple vortices were identified in the wake of the blade tip, with the largest vortex being associated with the tip-leakage flow, and the secondary vortices being associated with the trailing edge vortex and other blade-wake vortices. The evolution of identified vortex quantities with downstream distance is examined. It was found that the strength and core size of the vortices are weakly dependent on Reynolds number, but there are indications that they are affected by variations in the inflowing wall boundary layer on the duct. The core size of the tip-leakage vortex does not vary strongly with varying boundary layer thickness on the blades. Instead, its dimension is on the order of the tip clearance. There is significant flow variability for all Reynolds numbers and rotor configurations. Scaled velocity fluctuations near the axis of the primary vortex increase significantly with downstream distance, suggesting the presence of spatially uncorrelated fine scale secondary vortices and the possible existence of three-dimensional vortex-vortex interactions.

Poiseuille flow in jet viscometer orifices

1968 ◽  
Vol 303 (1475) ◽  
pp. 429-451 ◽  
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Velocity Profile ◽  
Reynolds Numbers ◽  
Correction Coefficient ◽  
Geometrical Shape ◽  
Energy Correction ◽  
Constant Diameter ◽  
Rate Of Increase ◽  
Parabolic Velocity Profile

A photomicrographic technique is described for determining the geometrical shape of glass jet viscometer orifices. These orifices are composed of a radiused entrance, a short constant diameter section, and a ‘diffuser type’ exit in which pressure recovery takes place. The length/diameter ratio of the constant diameter section of these orifices governs the highest Reynolds number for attaining 95% parabolic velocity profile, as calculated on the basis of Sparrow, Lin & Lundgren’s (1964) theoretical analysis of the development of parabolic velocity profile in the entrance region of tubes. Thirteen orifices were examined, and for these the highest admissible diameter Reynolds numbers were between 12 and 81. Thus, rates of shear, which can be calculated from the Poiseuille equation with an error of less than 1.5%, can amount to 6 x 10 5 s -1 without the liquid passing through the orifice suffering a temperature rise by viscous heating of more than 0.05°C. No kinetic energy correction is required for Reynolds numbers less than 10. For larger Reynolds numbers a correction should be made. The kinetic energy correction coefficient increases steeply with the Reynolds number, but the rate of increase depends upon the shape of the orifice profile. The largest kinetic energy correction coefficients of the thirteen orifices have values between 0.55 and 0.84. Within the range of Reynolds numbers admissible for 95% development of parabolic velocity profile, substantial temporary viscosity reductions were found. Neither surface tension nor elastic properties of the liquid affect the flow behaviour under the described experimental conditions.

scholarly journals Fluid friction between rotating cylinders I—Torque measurements

1936 ◽  
Vol 157 (892) ◽  
pp. 546-564 ◽  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Centrifugal Force ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Stream Line ◽  
Rotating Cylinders ◽  
Torque Measurements ◽  
Critical Reynolds Numbers ◽  
The Stability

The stability of fluid contained between concentric rotating cylinders has been investigated and it has been shown that, when only the inner cylinder rotates, the flow becomes unstable when a certain Reynolds number of the flow is exceeded. When the outer cylinder only is rotated, the flow is stable so far as disturbances of the type produced in the former case are concerned, but provided the Reynolds number of the flow exceeds a certain value, turbulence sets in. The object of the present experiments was partly to measure the torque reaction between two cylinders in the two cases in order to find the effect of centrifugal force on the turbulence, and partly to find the critical Reynolds numbers for the transition from stream-line to turbulent flow. The apparatus is shown diagrammatically in fig. 1.

Low Pressure Turbine Secondary Vortices: Reynolds Lapse

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Matthias Kuerner ◽  
Georg A. Reichstein ◽  
Daniel Schrack ◽  
Martin G. Rose ◽  
Stephan Staudacher ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Reynolds Numbers ◽  
Test Facility ◽  
Low Pressure Turbine ◽  
Small Reynolds Numbers ◽  
Unsteady Simulation ◽  
Aero Engines ◽  
Secondary Vortices ◽  
The Impact

A two-stage turbine is tested in a cooperation between the Institute of Aircraft Propulsion Systems (ILA) and MTU Aero Engines GmbH (MTU). The experimental results taken in the Altitude Test Facility (ATF) are used to assess the impact of cavity flow and leakage on vortex structures. The analysis focuses on a range of small Reynolds numbers, from as low as 35,000 up to 88,000. The five hole probe area traverse data is compared to steady multistage CFD predictions behind the second vane. The numerical model compares computations without and with cavities modeled. The simulation with cavities is superior to the approach without cavities. The vortex induced blockage is found to be inversely proportional to the Reynolds number. The circulation of the vortices is dependent on the Reynolds number showing a reversing trend to the smallest Reynolds numbers. The steady numerical model as of yet is unsuitable to predict these trends. A first unsteady simulation suggests major improvements.

LP Turbine Secondary Vortices: Reynolds Lapse

2011 ◽  
Author(s):  
Matthias Kuerner ◽  
Georg A. Reichstein ◽  
Daniel Schrack ◽  
Martin G. Rose ◽  
Stephan Staudacher ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Reynolds Numbers ◽  
Test Facility ◽  
Small Reynolds Numbers ◽  
Unsteady Simulation ◽  
Aero Engines ◽  
Lp Turbine ◽  
Secondary Vortices ◽  
The Impact

A two-stage turbine is tested in a cooperation between the Institute of Aircraft Propulsion Systems (ILA) and MTU Aero Engines GmbH (MTU). The experimental results taken in the Altitude Test Facility (ATF) are used to assess the impact of cavity flow and leakage on vortex structures. The analysis focuses on a range of small Reynolds numbers, from as low as 35,000 up to 88,000. The five hole probe area traverse data is compared to steady multistage CFD predictions behind the second vane. The numerical model compares computations without and with cavities modeled. The simulation with cavities is superior to the approach without cavities. The vortex induced blockage is found to be inversely proportional to Reynolds number. The circulation of the vortices is dependent on the Reynolds number showing a reversing trend to smallest Reynolds numbers. The steady numerical model as of yet is unsuitable to predict these trends. A first unsteady simulation suggests major improvements.

scholarly journals Turbulent Swirling Flow in Short Cylindrical Chambers

1993 ◽  
Vol 115 (3) ◽  
pp. 444-451 ◽  
Author(s):  
A. Riahi ◽  
P. G. Hill
Keyword(s):  
Reynolds Number ◽  
Swirling Flow ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Cylindrical Chamber ◽  
Transient Conditions ◽  
Chamber Length ◽  
Smooth Disk ◽  
Length To Diameter Ratio

Turbulent swirling flow in a short closed cylindrical chamber has been measured with laser Doppler anemometry. The swirl was generated by a rotating roughened disk and measured during steady and transient conditions with a smooth disk. The velocity and turbulence fields were found to be strongly dependent on swirl Reynolds numbers (in the range 0.3 × 106 < ΩR2/v < 0.6 × 106) and on chamber length-to-diameter ratio (in the range 0.1 ≤ L/D ≤ 0.5). With a roughened disk the flow was nearly independent of Reynolds number though still strongly dependent on chamber length-to-diameter ratio.

scholarly journals Simulation of Lid-Driven Cavity Flow with Internal Circular Obstacles

2020 ◽  
Vol 10 (13) ◽  
pp. 4583 ◽  
Author(s):  
Tingting Huang ◽  
Hee-Chang Lim
Keyword(s):  
Reynolds Number ◽  
Solid Wall ◽  
Vortex Formation ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Time Model ◽  
Cross Sectional ◽  
Driven Cavity ◽  
Secondary Vortices ◽  
Boltzmann Method

The Lattice Boltzmann method (LBM) has been applied for the simulation of lid-driven flows inside cavities with internal two-dimensional circular obstacles of various diameters under Reynolds numbers ranging from 100 to 5000. With the LBM, a simplified square cross-sectional cavity was used and a single relaxation time model was employed to simulate complex fluid flow around the obstacles inside the cavity. In order to made better convergence, well-posed boundary conditions should be defined in the domain, such as no-slip conditions on the side and bottom solid-wall surfaces as well as the surface of obstacles and uniform horizontal velocity at the top of the cavity. This study focused on the flow inside a square cavity with internal obstacles with the objective of observing the effect of the Reynolds number and size of the internal obstacles on the flow characteristics and primary/secondary vortex formation. The current LBM has been successfully used to precisely simulate and visualize the primary and secondary vortices inside the cavity. In order to validate the results of this study, the results were compared with existing data. In the case of a cavity without any obstacles, as the Reynolds number increases, the primary vortices move toward the center of the cavity, and the secondary vortices at the bottom corners increase in size. In the case of the cavity with internal obstacles, as the Reynolds number increases, the secondary vortices close to the internal obstacle become smaller owing to the strong primary vortices. In contrast, depending on the sizes of the obstacles ( R / L = 1/16, 1/6, 1/4, and 2/5), secondary vortices are induced at each corner of the cavity and remain stationary, but the secondary vortices close to the top of the obstacle become larger as the size of the obstacle increases.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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