The Swirling Turbulent Jet

1972 ◽  
Vol 94 (4) ◽  
pp. 739-747 ◽  
Author(s):  
B. D. Pratte ◽  
J. F. Keffer
Keyword(s):  
Experimental Investigation ◽  
Static Pressure ◽  
Decay Rates ◽  
Turbulent Jet ◽  
Entrainment Rate ◽  
Self Similarity ◽  
Free Jet ◽  
Swirling Jet ◽  
Self Similar ◽  
The Mean

An experimental investigation has been made of a swirling jet having a moderate ratio of swirling to axial momentum. Measurements showed that the flow achieved a self-similarity for the mean velocities rather quickly while the normal turbulent intensities reached a self-similar state after a longer period of jet development. Conservation arguments were used to predict streamwise decay rates for the mean quantities. The analysis showed that the maximum axial and swirling velocity components should vary asymptotically as (x − x0)−1 and (x − x0)−2, respectively. The experimental results confirmed this satisfactorily. The minimum static pressure was predicted to vary at a rate proportional to (x − x0)−4. Measurements indicated, however, that the relation was closer to (x − x0)−2. Better agreement with the data was achieved when the analytical expression was adjusted for the effect of the turbulence terms. The entrainment rate and angle of spread for the swirling jet were found to be nearly twice that of the non-swirling free jet.

Direct numerical simulation of axisymmetric wakes embedded in turbulence

2012 ◽  
Vol 710 ◽  
pp. 482-504 ◽  
Author(s):  
Elad Rind ◽  
Ian P. Castro
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Decay Rate ◽  
Relative Strength ◽  
Decay Rates ◽  
The Self ◽  
Self Similarity ◽  
Self Similar ◽  
External Turbulence ◽  
Different Levels

AbstractDirect numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the former.

Coherent Structures and Correlation Fields in the Mixing Transition of a Turbulent Round Free Jet

2018 ◽  
Author(s):  
Benedikt Krohn ◽  
Sunming Qin ◽  
Victor Petrov ◽  
Annalisa Manera
Keyword(s):  
Coherent Structures ◽  
High Speed ◽  
Near Field ◽  
The Self ◽  
Turbulent Shear ◽  
Past Century ◽  
Self Similarity ◽  
Free Jet ◽  
Similar Region ◽  
Self Similar

Turbulent free jets attracted the focus of many scientists within the past century regarding the understanding of mass- and momentum transport in the turbulent shear field, especially in the near-field and the self-similar region. Recent investigations attempt to understand the intermediate fields, called the mixing transition or ‘the route to self-similarity’. An apparent gap is recognized in light of this mixing transition, with two main conjectures being put forth. Firstly the flow will always asymptotically reach a fully self-similar state if boundary conditions permit. The second proposes partial and local self-similarity within the mixing transition. We address the later with an experimental investigation of the intermediate field turbulence dynamics in a non-confined free jet with a nozzle diameter of 12.7 mm and an outer scale Reynolds number of 15,000. High speed Particle Image Velocimetry (PIV) is used to record the velocity fields with a final spatial resolution of 194 × 194 μm2. The analysis focuses on higher order moments and two-point correlations of velocity variances in space and time. We observed local self-similarity in the measured correlation fields. Coherent structures are present within the near-field where the turbulent energy spectrum cascades along a dissipative slope. Towards the transition region, the spectrum smoothly transforms to a viscous cascade, as it is commonly observed in the self-similar region.

scholarly journals Self-similar properties of decelerating turbulent jets

2017 ◽  
Vol 833 ◽  
Author(s):  
Dong-hyuk Shin ◽  
A. J. Aspden ◽  
Edward S. Richardson
Keyword(s):  
Velocity Profile ◽  
Axial Velocity ◽  
Turbulent Jets ◽  
Entrainment Rate ◽  
Velocity Statistics ◽  
Radial Profiles ◽  
Axial Velocity Profile ◽  
Self Similar ◽  
The Mean ◽  
Analytical Relations

The flow in a decelerating turbulent round jet is investigated using direct numerical simulation. The simulations are initialised with a flow field from a statistically stationary turbulent jet. Upon stopping the inflow, a deceleration wave passes through the jet, behind which the velocity field evolves towards a new statistically unsteady self-similar state. Assumption of unsteady self-similar behaviour leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics. Consistency between these predictions and the simulation data supports the use of the assumption of self-similarity. The mean radial velocity is predicted to reverse in direction near to the jet centreline as the deceleration wave passes, contributing to an approximately threefold increase in the normalised mass entrainment rate. The shape of the mean axial velocity profile undergoes a relatively small change across the deceleration transient, and this observation provides direct evidence in support of previous models that have assumed that the mean axial velocity profile, and in some cases also the jet spreading angle, remain approximately constant within unsteady jets.

Passive Control of the Two-Dimensional Jet Using a Rectangular Notch

2002 ◽  
Author(s):  
Shigetaka Fujita ◽  
Takashi Harima ◽  
Hideo Osaka
Keyword(s):  
Passive Control ◽  
Core Region ◽  
Turbulent Jet ◽  
Upstream Region ◽  
Entrainment Rate ◽  
Two Dimensional ◽  
Flow Properties ◽  
Potential Core ◽  
The Mean ◽  
Rectangular Notch

The mean and turbulent flow properties of turbulent jet issuing from a quasi two-dimensional (2-D) nozzle with a rectangular notch (aspect ratio: AR=12.5) perpendicular to the two-dimensional nozzle at the midspan, have been measured. The exit Reynolds number was kept constant 13000. The aim of this study is to examine the effects of the rectangular notch on the mean and turbulent flowfields of the two-dimensional jet, and to clarify a possibility of a passive control of the two-dimensional jet using a rectangular notch. From the experiments, it was revealed that the potential core region existed until the section of x/d=25. In the upstream region, the entrainment rate was smaller than that of the two-dimensional jet due to the inward secondary flow on the y and z axes. Furthermore, the streamwise development of the turbulent intensity was delayed.

scholarly journals Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows

2019 ◽  
Vol 871 ◽  
pp. 377-400 ◽  
Author(s):  
R. Baidya ◽  
W. J. Baars ◽  
S. Zimmerman ◽  
M. Samie ◽  
R. J. Hearst ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Momentum Equation ◽  
The Self ◽  
Self Similarity ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baarset al.(J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of$7:1:1$in the streamwise, spanwise and wall-normal directions, respectively.

scholarly journals Anisotropic 𝑝-Laplacian Evolution of Fast Diffusion Type

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Filomena Feo ◽  
Juan Luis Vázquez ◽  
Bruno Volzone
Keyword(s):  
Decay Rates ◽  
The Self ◽  
Fast Diffusion ◽  
Finite Mass ◽  
Self Similarity ◽  
Diffusion Type ◽  
Laplacian Equation ◽  
Self Similar Solution ◽  
Self Similar ◽  
Mathematical Difficulties

Abstract We study an anisotropic, possibly non-homogeneous version of the evolution 𝑝-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive sharp L 1 L^{1} - L ∞ L^{\infty} estimates. We prove the existence of a self-similar fundamental solution of this equation in the appropriate exponent range, and uniqueness in a smaller range. We also obtain the asymptotic behaviour of finite mass solutions in terms of the self-similar solution. Positivity, decay rates as well as other properties of the solutions are derived. The combination of self-similarity and anisotropy is not common in the related literature. It is however essential in our analysis and creates mathematical difficulties that are solved for fast diffusions.

Design and Performance of Vaneless Volutes for Radial Inflow Turbines: Part 2: Experimental Investigation of the Mean Line Performance—Assessment of Empirical Design Parameters

1994 ◽  
Vol 208 (3) ◽  
pp. 213-224 ◽  
Author(s):  
A Whitfield ◽  
S A MacGregor ◽  
A B Mohd Noor
Keyword(s):  
Experimental Investigation ◽  
Static Pressure ◽  
Swirling Flow ◽  
Design Procedure ◽  
Design Parameters ◽  
Flow Angle ◽  
One Dimensional ◽  
Specific Objective ◽  
The Mean ◽  
And Performance

The non-dimensional design procedure described in Part 1 assumed a one-dimensional compressible flow and as such relied on the empirical specification of the dissipation of angular momentum, the dissipation of energy and the deviation of the swirling flow from that of a free vortex. This was based largely on data available in the published literature. In order to develop and substantiate the empirical procedures further an experimental study was carried out in parallel with the development of the design procedure. The experimental investigation described here had the specific objective of assessing and developing appropriate empirical models and coefficients for application to the design procedure. The study concentrated on the application of a five-hole probe located in the centre of the volute passage and at a series of azimuth angles around the discharge. The probe provided stagnation and static pressure measurements, from which the gas velocity was derived, together with the flow angle. When taking measurements at the volute discharge a stationary dummy rotor was used to carry the five-hole probe.

scholarly journals Controlled Excitation of a Cold Turbulent Swirling Free Jet

1988 ◽  
Vol 110 (2) ◽  
pp. 234-237 ◽  
Author(s):  
R. Taghavi ◽  
E. J. Rice ◽  
S. Farokhi
Keyword(s):  
Acoustic Waves ◽  
Plane Waves ◽  
Acoustic Excitation ◽  
Mean Velocity ◽  
Instability Waves ◽  
Free Jet ◽  
Swirling Jet ◽  
Axial Mass ◽  
Change In The Mean ◽  
The Mean

Experimental results from acoustic excitation of a cold free turbulent jet with and without swirl are presented. A flow with a swirl number of 0.35 (i.e., moderate swirl) is excited internally by plane acoustic waves at a constant sound pressure level and at various frequencies. It is observed that the cold swirling jet is excitable by plane waves, and that the instability waves grow about 50 percent less in peak r.m.s. amplitude, and saturate further upstream compared to corresponding waves in a jet without swirl having the same axial mass flux. The preferred Strouhal number based on the mass-averaged axial velocity and nozzle exit diameter for both swirling and nonswirling flows is 0.4. So far no change in the mean velocity components of the swirling jet is observed as a result of excitation.

scholarly journals Effect of nozzle geometry on the dynamics and mixing of self-similar turbulent jets

2021 ◽  
Author(s):  
Pourya Nejatipour ◽  
Babak Khorsandi
Keyword(s):  
Mass Flow ◽  
Cross Sections ◽  
Turbulent Jets ◽  
Nozzle Geometry ◽  
Entrainment Rate ◽  
Radial Profiles ◽  
Self Similar ◽  
The Mean ◽  
Elliptical Jet ◽  
Velocity Variances

Abstract The effect of nozzle geometry on the dynamics and mixing of turbulent jets is experimentally investigated. The jets with a Reynolds number of 13,000 were issued from four different pipes with circular, elliptical, square and triangular cross sections. The velocity field was measured in the self-similar region of the jets using an acoustic Doppler velocimeter. Statistical parameters, such as the mean velocities, velocity variances, spreading rates, mass flow rates, and entrainment rates are presented. The results show that despite having approximately similar decay rates for the mean centerline velocities, the radial profiles of the axial mean velocity varied in jets with different nozzle cross sections and were widest for elliptical jets and narrowest for the triangular ones. On the other hand, velocity variances were greatest for the triangular jet when compared to the jets released from cross sections of other geometries. Furthermore, the spreading rate, mass flow rate, and entrainment rate were highest for the elliptical jet, and lowest for the triangular jet. From this it can be inferred that the elliptical jet has the highest mixing and dilution. The results of this study could help to improve the initial mixing of pollutants by optimizing the initial conditions.

Self-similar mean dynamics in turbulent wall flows

2013 ◽  
Vol 718 ◽  
pp. 596-621 ◽  
Author(s):  
J. C. Klewicki
Keyword(s):  
Boundary Layer ◽  
Similarity Solution ◽  
Reynolds Numbers ◽  
Channel Height ◽  
Self Similarity ◽  
Mean Velocity ◽  
Wall Flows ◽  
Self Similar ◽  
The Mean ◽  
Turbulent Wall

AbstractThis study investigates how and why dynamical self-similarities emerge with increasing Reynolds number within the canonical wall flows beyond the transitional regime. An overarching aim is to advance a mechanistically coherent description of turbulent wall-flow dynamics that is mathematically tractable and grounded in the mean dynamical equations. As revealed by the analysis of Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst.A, vol. 24, 2009, pp. 781–807), the equations that respectively describe the mean dynamics of turbulent channel, pipe and boundary layer flows formally admit invariant forms. These expose an underlying self-similar structure. In all cases, two kinds of dynamical self-similarity are shown to exist on an internal domain that, for all Reynolds numbers, extends from$O(\nu / {u}_{\tau } )$to$O(\delta )$, where$\nu $is the kinematic viscosity,${u}_{\tau } $is the friction velocity and$\delta $is the half-channel height, pipe radius, or boundary layer thickness. The simpler of the two self-similarities is operative on a large outer portion of the relevant domain. This self-similarity leads to an explicit analytical closure of the mean momentum equation. This self-similarity also underlies the emergence of a logarithmic mean velocity profile. A more complicated kind a self-similarity emerges asymptotically over a smaller domain closer to the wall. The simpler self-similarity allows the mean dynamical equation to be written as a closed system of nonlinear ordinary differential equations that, like the similarity solution for the laminar flat-plate boundary layer, can be numerically integrated. The resulting similarity solutions are demonstrated to exhibit nearly exact agreement with direct numerical simulations over the solution domain specified by the theory. At the Reynolds numbers investigated, the outer similarity solution is shown to be operative over a domain that encompasses${\sim }40\hspace{0.167em} \% $of the overall width of the flow. Other properties predicted by the theory are also shown to be well supported by existing data.

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