Similarity in swirling wakes and jets

1962 ◽  
Vol 14 (2) ◽  
pp. 241-243 ◽  
Author(s):  
A. J. Reynolds
Keyword(s):  
Angular Momentum ◽  
Swirling Flow ◽  
Turbulent Wake ◽  
Linear Momentum ◽  
Length Scale ◽  
Mean Velocity ◽  
Swirl Velocity ◽  
Velocity Scale ◽  
Zero Momentum ◽  
The Mean

Both the net linear momentum and the net angular momentum of a developing swirling flow can play important parts in determining its ultimate form. To illustrate this the turbulent wake with both axial and swirl components of mean velocity is discussed, in particular for the two limiting cases of domination by linear momentum and domination by angular momentum. The dual conservation of axial and angular momentum implies that in general the mean swirl component decreases more rapidly downstream than does the defect in the mean axial velocity. Hence wakes with non-zero momentum flux ultimately have the familiar length scale $\sim Z^{\frac{1}{3}$ and velocity defect scale $\sim Z^{-\frac{2}{3}$. But in the wake of a self-propelled body the net drag is negligible and a swirl-dominated development can persist with length scale $\sim Z^{\frac{1}{4}$ and swirl velocity scale $\sim Z^{-\frac{3}{4}$.

Application of an Angular Momentum Balance Method for Investigating Numerical Accuracy in Swirling Flow

2003 ◽  
Vol 125 (4) ◽  
pp. 723-730
Author(s):  
H. Nilsson ◽  
L. Davidson
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Angular Momentum ◽  
Swirling Flow ◽  
Linear Momentum ◽  
Correct Solution ◽  
Momentum Balance ◽  
Numerical Accuracy ◽  
Water Turbine ◽  
Water Turbines

This work derives and applies a method for the investigation of numerical accuracy in computational fluid dynamics. The method is used to investigate discretization errors in computations of swirling flow in water turbines. The work focuses on the conservation of a subset of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. However, the method can be used to investigate the effect of discretization on any equation that should be conserved in the correct solution, and the application is not limited to water turbines. Computations made for two Kaplan water turbine runners and a simplified geometry of one of the Kaplan runner ducts are investigated to highlight the general and simple applicability of the method.

Experimental Investigation of a Turbulent Boundary Layer Subjected to an Adverse Pressure Gradient

2011 ◽  
Author(s):  
Takanori Nakamura ◽  
Takatsugu Kameda ◽  
Shinsuke Mochizuki
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Adverse Pressure Gradient ◽  
Turbulent Intensity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Scale ◽  
The Mean ◽  
The Law

Experiments were performed to investigate the effect of an adverse pressure gradient on the mean velocity and turbulent intensity profiles for an equilibrium boundary layer. The equilibrium boundary layer, which makes self-similar profiles, was constructed using a power law distribution of free stream velocity. The exponent of the law was adjusted to −0.188. The wall shear stress was measured with a drag balance by a floating element. The investigation of the law of the wall and the similarity of the streamwise turbulent intensity profile was made using both a friction velocity and new proposed velocity scale. The velocity scale is derived from the boundary layer equation. The mean velocity gradient profile normalized with the height and the new velocity scale exists the region where the value is almost constant. The turbulent intensity profiles normalized with the friction velocity strongly depend on the nondimensional pressure gradient near the wall. However, by mean of the local velocity scale, the profiles might be achieved to be similar with that of a zero pressure gradient.

Stereo-PIV Measurements of Turbulent Swirling Flow Inside a Pipe

2020 ◽  
Author(s):  
Ayesha Almheiri ◽  
Lyes Khezzar ◽  
Mohamed Alshehhi ◽  
Saqib Salam ◽  
Afshin Goharzadeh
Keyword(s):  
Swirling Flow ◽  
Reverse Flow ◽  
Tangential Velocity ◽  
Circular Disk ◽  
Pipe Diameter ◽  
Working Fluid ◽  
Complex Flow ◽  
Mean Velocity ◽  
Radial Profiles ◽  
The Mean

Abstract Stereo-PIV is used to map turbulent strongly swirling flow inside a pipe connected to a closed recirculating system with a transparent test section of 0.6 m in length and a pipe diameter of 0.041 m. The Perspex pipe was immersed inside a water trough to reduce the effects of refraction. The working fluid was water and the Reynolds number based on the bulk average velocity inside the pipe and pipe diameter was equal to 14,450. The turbulent flow proceeds in the downstream direction and interacts with a circular disk. The measurements include instantaneous velocity vector fields and radial profiles of the mean axial, radial and tangential components of the velocity in the regions between the swirler exit and circular disk and around this later. The results for mean axial velocity show a symmetric behavior with a minimum reverse flow velocity along the centerline. As the flow developed along the pipe’s length, the intensity of the reversed flow was reduced and the intensity of the swirl decays. The mean tangential velocity exhibits a Rankine-vortex distribution and reached its maximum around half of the pipe’s radius. As the flow approaches the disk, the flow reaches stagnation and a complex flow pattern of vortices is formed. The PIV results are contrasted with LDV measurements of mean axial and tangential velocity. Good agreement is shown over the mean velocity profiles.

Experimental Investigation of Perforated Plate Turbulent Flow Past a Solid Sphere

2004 ◽  
Author(s):  
Himanshu Tyagi ◽  
Rui Liu ◽  
David S.-K. Ting ◽  
Clifton R. Johnston
Keyword(s):  
Perforated Plate ◽  
Solid Sphere ◽  
Length Scale ◽  
Freestream Turbulence ◽  
Comprehensive Investigation ◽  
Mean Velocity ◽  
Kolmogorov Length Scale ◽  
Turbulence Effect ◽  
Plastic Sphere ◽  
The Mean

As the first stage of a comprehensive investigation of turbulence effect on the aerodynamics of sphere, the effect of freestream turbulence on the wake generated behind a sphere is investigated in this study. A 10 cm (4 in) diameter plastic sphere was placed in a wind tunnel of cross section 75 cm by 75 cm. The freestream turbulence was generated by fixing a perforated plate to the entrance of the test section. The wake was characterized using a normal constant-temperature hotwire at 30D, 40D and 50D (11.25d, 15d & 18.75d respectively) downstream of the sphere (where D = 3.75 cm is the diameter of the perforated plate hole, and d is the diameter of the sphere). The Reynolds number of the flow, based on the mean velocity and the diameter of the sphere, was 6.6 × 104. Based on the instantaneous velocity measurement, Kolmogorov length scale, integral length scale and relative turbulence intensity in the wake were deduced.

Connections between the Ozmidov scale and mean velocity profile in stably stratified atmospheric surface layers

2016 ◽  
Vol 797 ◽  
Author(s):  
Dan Li ◽  
Scott T. Salesky ◽  
Tirtha Banerjee
Keyword(s):  
Velocity Profile ◽  
Atmospheric Stability ◽  
Length Scale ◽  
Surface Layers ◽  
Mean Velocity ◽  
Stable Conditions ◽  
Stringent Constraint ◽  
Ozmidov Scale ◽  
The Mean ◽  
Good Agreement

The mean velocity profile (MVP) in thermally stratified atmospheric surface layers (ASLs) deviates from the classic logarithmic form. A theoretical framework was recently proposed (Katulet al.Phys. Rev. Lett., vol. 107, 2011, 268502) to link the MVP to the spectrum of turbulence and was found to successfully predict the MVP for unstable stratification. However, the theory failed to reproduce the MVP in stable conditions (Saleskyet al.Phys. Fluids, vol. 25, 2013, 105101), especially when${\it\zeta}>0.2$(where${\it\zeta}$is the atmospheric stability parameter). In the present study, it is demonstrated that this shortcoming is due to the failure to identify the appropriate length scale that characterizes the size of momentum transporting eddies in the stable ASL. Beyond${\it\zeta}\approx 0.2$(near where the original theory fails), the Ozmidov length scale becomes smaller than the distance from the wall$z$and hence is a more stringent constraint for characterizing the size of turbulent eddies. An expression is derived to connect the Ozmidov length scale to the normalized MVP (${\it\phi}_{m}$), allowing${\it\phi}_{m}$to be solved numerically. It is found that the revised theory produces a prediction of${\it\phi}_{m}$in good agreement with the widely used empirical Businger–Dyer relation and two experimental datasets in the stable ASL. The results here demonstrate that the behaviour of${\it\phi}_{m}$in the stable ASL is closely linked to the size of momentum transporting eddies, which can be characterized by the Ozmidov scale under mildly to moderately stable conditions ($0.2<{\it\zeta}<1-2$).

Stratification Effects in a Bottom Ekman Layer

2008 ◽  
Vol 38 (11) ◽  
pp. 2535-2555 ◽  
Author(s):  
John R. Taylor ◽  
Sutanu Sarkar
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Outer Layer ◽  
Layer Structure ◽  
Wall Stress ◽  
Ekman Layer ◽  
Length Scale ◽  
Primary Role ◽  
Mean Velocity ◽  
The Mean

Abstract A stratified bottom Ekman layer over a nonsloping, rough surface is studied using a three-dimensional unsteady large eddy simulation to examine the effects of an outer layer stratification on the boundary layer structure. When the flow field is initialized with a linear temperature profile, a three-layer structure develops with a mixed layer near the wall separated from a uniformly stratified outer layer by a pycnocline. With the free-stream velocity fixed, the wall stress increases slightly with the imposed stratification, but the primary role of stratification is to limit the boundary layer height. Ekman transport is generally confined to the mixed layer, which leads to larger cross-stream velocities and a larger surface veering angle when the flow is stratified. The rate of turning in the mixed layer is nearly independent of stratification, so that when stratification is large and the boundary layer thickness is reduced, the rate of veering in the pycnocline becomes very large. In the pycnocline, the mean shear is larger than observed in an unstratified boundary layer, which is explained using a buoyancy length scale, u*/N(z). This length scale leads to an explicit buoyancy-related modification to the log law for the mean velocity profile. A new method for deducing the wall stress based on observed mean velocity and density profiles is proposed and shows significant improvement compared to the standard profile method. A streamwise jet is observed near the center of the pycnocline, and the shear at the top of the jet leads to local shear instabilities and enhanced mixing in that region, despite the fact that the Richardson number formed using the mean density and shear profiles is larger than unity.

The structure of the large eddies in fully developed turbulent shear flows. Part 2. The plane wake

1983 ◽  
Vol 137 ◽  
pp. 447-456 ◽  
Author(s):  
J. C. Mumford
Keyword(s):  
Large Scale ◽  
Turbulent Wake ◽  
Turbulent Shear ◽  
Spanwise Direction ◽  
Mean Velocity ◽  
Large Scale Structures ◽  
The Mean ◽  
Large Eddies ◽  
Stream Direction ◽  
Recognition Technique

A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the streamwise component of the velocity fields of the large eddies in the flow.The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction.

Investigation of Two-Equation Turbulence Models Applied to a Confined Axis-Symmetric Swirling Flow

2002 ◽  
Author(s):  
Ulf Engdar ◽  
Jens Klingmann
Keyword(s):  
Swirling Flow ◽  
Turbulence Models ◽  
Sudden Expansion ◽  
Center Line ◽  
Circulation Zone ◽  
Gas Turbine Combustor ◽  
Mean Velocity ◽  
Energy Field ◽  
The Mean ◽  
Almost All

The modeling of industrial combustion applications today is almost exclusively based on two-equation turbulence models. Despite its known limitations, the most the widely used model is still the standard k-ε model. The objective of this paper is to investigate the performance of two-equation turbulence models applied to a confined swirling flow. Numerical modeling of an axis-symmetric confined sudden expansion, followed by a contraction with the assumption of steady flow and an incompressible fluid, has been conducted. The flow field is what can be expected in simplified dump gas turbine combustor geometry. In this investigation, three different swirl cases were considered: no swirl, moderate swirl (no central re-circulation zone) and strong swirl (a central re-circulation zone occurring). The models investigated were: the standard k-ε model, a curvature-modified k-ε model, Chen’s k-ε model, a cubic non-linear k-ε model, the standard k-ω model and the Shear Stress Transport (SST) k-ω) model. The results show that almost all models were able to predict the major impact of the moderate swirl: reduced outer re-circulation lengths and retardation of the axial velocity on the center-line. However, the Chen k-ε model and the SST k-ω) model were found to better reproduce the mean velocity field and the turbulent kinetic energy field from the measurements. For a strong swirl, a large re-circulation zone is formed along the center-line, which the standard k-ε model and the modified k-ε model fail to predict. However, the shape and size of the re-circulation zone differ strongly between the models. At this swirl number, the performances of all models were, without exception, worse than for the lower swirl numbers. The SST k-ω model achieved the best agreement between computations and experimental data.

Mean-flow scaling of turbulent pipe flow

1998 ◽  
Vol 373 ◽  
pp. 33-79 ◽  
Author(s):  
MARK V. ZAGAROLA ◽  
ALEXANDER J. SMITS
Keyword(s):  
Friction Factor ◽  
Friction Velocity ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Mean Velocity ◽  
Velocity Scale ◽  
The Mean ◽  
Log Law ◽  
High Reynolds

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

Experimental Investigation and Similarity Solution of the Axisymmetric Turbulent Wake With Rotation

2013 ◽  
Author(s):  
Martin Wosnik ◽  
Nathaniel Dufresne
Keyword(s):  
Free Stream ◽  
Scaling Function ◽  
Similarity Theory ◽  
Analytical Investigation ◽  
Turbulent Wake ◽  
Velocity Fields ◽  
Hot Wire ◽  
Swirl Velocity ◽  
Blade Tip ◽  
The Mean

An experimental and analytical investigation of an axisymmetric turbulent wake with rotation was carried out. The axial and azimuthal (swirl) velocity fields were measured in the wake of a single 3-bladed model wind turbine with rotor diameter of 0.91m, up to 20 diameters downstream. The turbine was positioned in the free stream, near the entrance of the 6 m × 2.7 m cross section of the UNH Flow Physics Facility. Measurements were conducted at different rotor loading conditions with blade tip-speed ratios from 2.0 to 2.8. A pitot-static tube and constant temperature hot-wire anemometry with a multi-wire sensor were used to measure velocity fields. An equilibrium similarity theory for the turbulent axisymmetric wake with rotation was outlined, and first evidence for a new scaling function for the decay of the mean swirling velocity component, Wmax ∝ x−1 ∝ Uo3/2, was found.

Sign in / Sign up

Export Citation Format

Share Document