Similarity behaviour of momentumless turbulent wakes

1975 ◽  
Vol 71 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Michael L. Finson
Keyword(s):  
Initial Conditions ◽  
Turbulent Energy ◽  
Similarity Solutions ◽  
Decay Rates ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Radial Profiles ◽  
The Mean ◽  
Momentumless Wake ◽  
Far Wake

Similarity solutions are determined for the turbulent wake of a self-propelled body (thrust = drag). The momentumless wake is shown to behave in a manner intermediate to homogeneous grid turbulence and more familiar free-shear flows such as the drag wake or jet. In essence the decay of momentumless-wake turbulence is similar to that of grid turbulence, but proceeds at a somewhat greater rate owing to lateral diffusion. The mean velocity difference is coupled to the difference $\overline{u^2}-\overline{v^2}$ between the axial and radial components of the mean-square fluctuating velocity. It is necessary to consider governing relations for various second-order turbulence quantities. Previously developed closure approximations yield far-wake decay rates that agree well with available measurements. Production of turbulent energy is negligible asymptotically; thus there is no balance between production and dissipation, and the far-wake behaviour does not become independent of the initial (near-wake) conditions. Even the radial profiles depend on the initial conditions, and there is no natural length scale with which to characterize the far wake.

The effect of jet injection geometry on two-dimensional momentumless wakes

1991 ◽  
Vol 224 ◽  
pp. 29-47 ◽  
Author(s):  
W. J. Park ◽  
J. M. Cimbala
Keyword(s):  
Turbulence Intensity ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Spreading Rate ◽  
Two Dimensional ◽  
Jet Injection ◽  
Mean Velocity ◽  
Rate Of Decay ◽  
The Mean ◽  
Momentumless Wake

It is shown experimentally that a two-dimensional momentumless wake is strongly dependent on the jet injection configuration of the model. Namely, the decay rate of mean velocity overshoot ranged from x−0.92 to x−2.0 for three different configurations, while the spreading rate ranged from x0.3 to x0.46 for those same configurations. The magnitude of axial turbulence intensity was also found to depend on model configuration. On the other hand, the rate of decay of axial turbulence intensity was the same (x−0.81) for all three models. In all cases the mean shear and Reynolds stress decayed rapidly, leaving nearly isotropic turbulence beyond 30 or 40 model diameters.Appropriate length- and velocity scales are identified which normalize the mean velocity profiles into self-similar form. The shape of the normalized profile, however, was different for each configuration, indicating again that the initial conditions are felt very far downstream.

Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet

1993 ◽  
Vol 246 ◽  
pp. 225-247 ◽  
Author(s):  
N. R. Panchapakesan ◽  
J. L. Lumley
Keyword(s):  
Density Ratio ◽  
Effective Diameter ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Air Jet ◽  
Plume Region ◽  
Turbulent Schmidt Number ◽  
Radial Profiles ◽  
The Mean ◽  
Mean Concentration

A turbulent round jet of helium was studied experimentally using a composite probe consisting of an interference probe of the Way–Libby type and an × -probe. Simultaneous measurements of two velocity components and helium mass fraction concentration were made in the x/d range 50–120. These measurements are compared with measurements in an air jet of the same momentum flux reported in Part 1. The jet discharge Froude number was 14000 and the measurement range was in the intermediate region between the non-buoyant jet region and the plume region. The measurements are consistent with earlier studies on helium jets. The mass flux of helium across the jet is within ±10% of the nozzle input. The mean velocity field along the axis of the jet is consistent with the scaling expressed by the effective diameter but the mean concentration decay constant exhibits a density-ratio dependence. The radial profiles of mean velocity and mean concentration agree with earlier measurements, with the half-widths indicating a turbulent Schmidt number of 0.7. Significantly higher intensities of axial velocity fluctuations are observed in comparison with the air jet, while the intensities of radial and azimuthal velocity fluctuations are virtually identical with the air jet when scaled with the half-widths. Approximate budgets for the turbulent kinetic energy, scalar variance and scalar fluxes are presented. The ratio of mechanical to scalar timescales is found to be close to 1.5 across most of the jet. Current models for triple moments involving scalar fluctuations are compared with measurements. As was observed with the velocity triple moments in Part 1, the performance of the Full model that includes all terms except advection was found to be very good in the fully turbulent region of the jet.

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

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.

Spectral analogues of the law of the wall, the defect law and the log law

2014 ◽  
Vol 757 ◽  
pp. 498-513 ◽  
Author(s):  
Carlo Zúñiga Zamalloa ◽  
Henry Chi-Hin Ng ◽  
Pinaki Chakraborty ◽  
Gustavo Gioia
Keyword(s):  
Turbulent Energy ◽  
Wall Turbulence ◽  
Spectral Domain ◽  
Energy Spectra ◽  
Scaling Relations ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean ◽  
Log Law ◽  
The Law

AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defect law and the log law. By design, each spectral analogue applies in the same spatial domain as the attendant scaling relation for the mean-velocity profiles: the spectral analogue of the law of the wall in the inner layer, the spectral analogue of the defect law in the outer layer and the spectral analogue of the log law in the overlap layer. In addition, as we are able to show without invoking any model of wall turbulence, each spectral analogue applies in a specific spectral domain (the spectral analogue of the law of the wall in the high-wavenumber spectral domain, where viscosity is active, the spectral analogue of the defect law in the low-wavenumber spectral domain, where viscosity is negligible, and the spectral analogue of the log law in a transitional intermediate-wavenumber spectral domain, which may become sizable only at ultra-high$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }$), with the implication that there exist model-independent one-to-one links between the spatial domains and the spectral domains. We test the spectral analogues using experimental and computational data on pipe flow and channel flow.

Transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow

2015 ◽  
Vol 777 ◽  
pp. 151-177 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
H. Abe ◽  
T. Zhou ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Transport Equation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Normal Velocity ◽  
Turbulent Energy Dissipation Rate ◽  
The Mean

The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.

scholarly journals Tidal disruption events on to stellar black holes in triples

2019 ◽  
Vol 489 (1) ◽  
pp. 727-737 ◽  
Author(s):  
Giacomo Fragione ◽  
Nathan W C Leigh ◽  
Rosalba Perna ◽  
Bence Kocsis
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Force ◽  
Main Sequence ◽  
Initial Conditions ◽  
Main Sequence Stars ◽  
Tidal Disruption ◽  
Mean Velocity ◽  
Massive Black Holes ◽  
The Mean

ABSTRACT Stars passing too close to a black hole can produce tidal disruption events (TDEs), when the tidal force across the star exceeds the gravitational force that binds it. TDEs have usually been discussed in relation to massive black holes that reside in the centres of galaxies or lurk in star clusters. We investigate the possibility that triple stars hosting a stellar black hole (SBH) may be sources of TDEs. We start from a triple system made up of three main-sequence stars and model the supernova (SN) kick event that led to the production of an inner binary comprised of an SBH. We evolve these triples with a high-precision N-body code and study their TDEs as a result of Kozai–Lidov oscillations. We explore a variety of distributions of natal kicks imparted during the SN event, various maximum initial separations for the triples, and different distributions of eccentricities. We show that the main parameter that governs the properties of the SBH–MS binaries that produce a TDE in triples is the mean velocity of the natal kick distribution. Smaller σ’s lead to larger inner and outer semimajor axes of the systems that undergo a TDE, smaller SBH masses, and longer time-scales. We find that the fraction of systems that produce a TDE is roughly independent of the initial conditions, while estimate a TDE rate of $2.1\times 10^{-4}{\!-\!}4.7 \, \mathrm{yr}^{-1}$, depending on the prescriptions for the SBH natal kicks. This rate is almost comparable to the expected TDE rate for massive black holes.

Evolution of flat-plate wakes in sink flow

2009 ◽  
Vol 626 ◽  
pp. 241-262 ◽  
Author(s):  
MEHRAN PARSHEH ◽  
ANDERS A. DAHLKILD
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Initial Conditions ◽  
Plate Boundary ◽  
Similarity Solutions ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Plate Edge ◽  
Flow Acceleration ◽  
Self Similar

Evolution of flat-plate wakes in sink flow has been studied both analytically and experimentally. For such wakes, a similarity solution is derived which considers simultaneous presence of both laminar and turbulent stresses inside the wake. This solution utilizes an additional Reynolds-stress term which represents the fluctuations similar to those in wall-bounded flows, accounting for the fluctuations originating from the plate boundary layer. In this solution, it is shown that the total stress, the sum of laminar and Reynolds shear stresses, becomes self-similar. To investigate the accuracy of the analytical results, the wake of a flat plate located at the centreline of a planar contraction is studied using hot-wire anemometry. Wakes of both tapered and blunt edges are considered. The length of the plates and the flow acceleration number K = 6.25 × 10−6 are chosen such that the boundary-layer profiles at the plate edge approach the self-similar laminar solution of Pohlhausen (Z. Angew. Math. Mech., vol. 1, 1921, p. 252). A short plate in which the boundary layer at the edge does not fully relaminarize is also considered. The development of the turbulent diffusivity used in the analysis is determined empirically for each experimental case. We have shown that the obtained similarity solutions, accounting also for the initial conditions in each case, generally agree well with the experimental results even in the near field. The results also show that the mean velocity of the transitional wake behind a tapered edge becomes self-similar almost immediately downstream of the edge.

Liquid Fuel Flameless Combustion RANS Simulation

2008 ◽  
Author(s):  
Patrick Le Clercq ◽  
Mark Schlieper ◽  
Berthold Noll ◽  
Manfred Aigner
Keyword(s):  
Boundary Conditions ◽  
Turbulence Modeling ◽  
Initial Conditions ◽  
Liquid Fuels ◽  
Inlet Temperature ◽  
Flameless Combustion ◽  
Two Phase ◽  
Mean Velocity ◽  
Radial Profiles ◽  
Global Reaction

The numerical simulation of flameless combustion with liquid fuels is presented. Computations follow a RANS approach for turbulence modeling with a global reaction mechanism and the eddy dissipation concept for the combustion. Several approaches were tested for defining spray boundary conditions. A phenomenological analysis of the two-phase mixing and heat transfer that follow the injection enabled us to derive the spray boundary conditions that would eventually lead to our main goal; the simulation of flameless combustion. Computation results are compared to experimental measurements. First the isothermal mean velocity field computation is validated using LDA measurements. Then, temperature and CO2 radial-profiles at different axial positions and CO and NOx concentration levels at the outlet are compared to experimental data. The effect of spray initial conditions, inlet temperature, mixture properties and chemistry are analyzed.

Transport equations for the normalized nth-order moments of velocity derivatives in grid turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
S.L. Tang ◽  
R.A. Antonia ◽  
L. Djenidi
Keyword(s):  
Large Scale ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Transport Equations ◽  
Small Scale ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Local Isotropy ◽  
Advection Term ◽  
The Mean

Transport equations for the normalized moments of the longitudinal velocity derivative ${F_{n + 1}}$ (here, $n$ is $1, 2, 3\ldots$ ) are derived from the Navier–Stokes (N–S) equations for shearless grid turbulence. The effect of the (large-scale) streamwise advection of ${F_{n + 1}}$ by the mean velocity on the normalized moments of the velocity derivatives can be expressed as $C_1 {F_{n + 1}}/Re_\lambda$ , where $C_1$ is a constant and $Re_\lambda$ is the Taylor microscale Reynolds number. Transport equations for the normalized odd moments of the transverse velocity derivatives ${F_{y,n + 1}}$ (here, $n$ is 2, 4, 6), which should be zero if local isotropy is satisfied, are also derived and discussed in sheared and shearless grid turbulence. The effect of the (large-scale) streamwise advection term on the normalized moments of the velocity derivatives can also be expressed in the form $C_2 {F_{y,n + 1}}/Re_\lambda$ , where $C_2$ is a constant. Finally, the contribution of the mean shear in the transport equation for ${F_{n + 1}}$ can be modelled as $15 B/Re_\lambda$ , where $B$ ( $=S^*{S_{s,n + 1}}$ ) is the product of the non-dimensional shear parameter $S^*$ and the normalized mixed longitudinal-transverse velocity derivatives ${{S_{s,n + 1}}}$ ; if local isotropy is satisfied, $S_{s,n + 1}$ should be zero. These results indicate that if ${F_{n + 1}}$ , ${F_{y,n + 1}}$ and $B$ do not increase as rapidly as $Re_\lambda$ , then the effect of the large-scale structures on small-scale turbulence will disappear when $Re_\lambda$ becomes sufficiently large.

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