Instantaneous three-dimensional concentration measurements in the self-similar region of a round high-Schmidt-number jet

1994 ◽  
Vol 279 ◽  
pp. 313-350 ◽  
Author(s):  
M. Yoda ◽  
L. Hesselink ◽  
M. G. Mungal
Keyword(s):  
Concentration Gradient ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Concentration Field ◽  
The Self ◽  
Gradient Field ◽  
Geometrical Parameters ◽  
Similar Region ◽  
Self Similar ◽  
Local Topology

The virtually instantaneous three-dimensional concentration fields in the self-similar region of natural or unexcited, circularly excited and weakly buoyant round jets of Reynolds number based on nozzle diameter of 1000 to 4000 are measured experimentally at a spatial resolution of the order of the Kolmogorov length scale. Isoconcentration surfaces are extracted from the concentration field. These surfaces along with their geometrical parameters are used to deduce the structure and modal composition of the jet. The concentration gradient field is calculated, and its local topology is classified using critical-point concepts.Large-scale structure is evident in the form of ‘clumps’ of higher-concentration jet fluid. The structure, which has a downstream extent of about the local jet diameter, is roughly axisymmetric with a conical downstream end. This structure appears to be present only in fully turbulent jets. The antisymmetric two-dimensional images previously thought to be axial slices of an expanding spiral turn out in our data to instead be slices of a simple sinusoid in three dimensions. This result suggests that the helical mode, when present, is in the form of a pair of counter-rotating spirals, or that the +1 and −1 modes are simultaneously present in the flow, with their relative phase set by initial conditions.In terms of local structure, regions with a large magnitude in concentration gradient are shown to have a local topology which is roughly axisymmetric and compressed along the axis of symmetry. Such regions, which would be locally planar and sheet-like, may correspond to the superposition of several of the layer-like structures which are the basic structure of the fine-scale passive scalar field (Buch & Dahm 1991; Ruetsch & Maxey 1991).

Characteristics of Turbulent Three-Dimensional Wall Jets

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
M. Agelin-Chaab ◽  
M. F. Tachie
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Orthogonal Decomposition ◽  
The Self ◽  
Shear Stresses ◽  
Spread Rate ◽  
Similar Region ◽  
Self Similar ◽  
Proper Orthogonal

Three-dimensional turbulent wall jet was investigated using a particle image velocimetry technique. Three Reynolds numbers based on the jet exit velocity and diameter of 5000, 10,000, and 20,000 were studied. Profiles of the mean velocities, turbulence intensities, and Reynolds shear stresses as well as two-point velocity correlations and proper orthogonal decomposition analyses were used to document the salient features of the wall jets. The decay and spread rates are independent of Reynolds numbers in the self-similar region. The estimated values of 1.15, 0.054, and 0.255 for the decay rate, wall-normal spread rate, and lateral spread rate, respectively, are within the range of values reported in the literature. The two-point correlation analysis showed that the inclination of the streamwise velocity correlation contours in the inner layer is 11±3 deg in the wall region, which is similar to those of canonical turbulent boundary layers. The results from the proper orthogonal decomposition indicate that low-order modes contribute more to the turbulence statistics in the self-similar region than in the developing region. The Reynolds shear stresses are the biggest benefactors of the low-order mode contribution while the wall-normal turbulence intensities are the least.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

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 Bubble pinch-off in turbulence

2019 ◽  
Vol 116 (51) ◽  
pp. 25412-25417 ◽  
Author(s):  
Daniel J. Ruth ◽  
Wouter Mostert ◽  
Stéphane Perrard ◽  
Luc Deike
Keyword(s):  
Flow Field ◽  
Initial Conditions ◽  
The Self ◽  
Similar Process ◽  
Linear Perturbation ◽  
Bubble Shape ◽  
Complex Flow ◽  
Experimental Conditions ◽  
Initial Flow ◽  
Self Similar

Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size,d¯, can be described byd¯∼(t−t0)α, wheret0is the pinch-off or singularity time andα≈0.5, in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi–2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causingd¯to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.

Intermittency caused by compressibility: a Lagrangian study

2015 ◽  
Vol 786 ◽  
Author(s):  
Yantao Yang ◽  
Jianchun Wang ◽  
Yipeng Shi ◽  
Zuoli Xiao ◽  
X. T. He ◽  
...  
Keyword(s):  
Mach Number ◽  
Time Scales ◽  
Time Scale ◽  
Driving Force ◽  
Three Dimensional ◽  
Point Of View ◽  
Scaling Exponent ◽  
Similar Region ◽  
Turbulent Statistics ◽  
Self Similar

We investigate how compressibility affects the turbulent statistics from a Lagrangian point of view, particularly in the parameter range where the flow transits from the incompressible type to a state dominated by shocklets. A series of three-dimensional simulations were conducted for different types of driving and several Mach numbers. For purely solenoidal driving, as the Mach number increases a new self-similar region first emerges in the Lagrangian structure functions at sub-Kolmogorov time scale and gradually extends to larger time scale. In this region the relative scaling exponent saturates and the saturated value decreases as the compressibility becomes stronger, which can be attributed to the shocklets. The scaling exponent for the inertial range is still very close to that of incompressible turbulence for small Mach number, and discrepancy becomes visible when the Mach number is high enough. When the driving force is dominated by the compressive component the shocklet-induced self-similar region occupies a much wider range of time scales than that in the purely solenoidal driving case. Regardless of the type of driving force, the probability density functions of the velocity increment collapse onto one another for the time scales in the new self-similar region after proper normalization.

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Application of nonstationary self-similar variables for solving the three-dimensional problem of the decay of a special discontinuity

2021 ◽  
pp. 52-64
Author(s):  
Сергей Петрович Баутин ◽  
Сергей Львович Дерябин
Keyword(s):  
Cauchy Problem ◽  
Power Series ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Physical Space ◽  
Initial Moment ◽  
Algebraic Equations ◽  
Gas Dynamics Equations ◽  
Self Similar ◽  
Isentropic Flows

Построение в физическом пространстве решения задачи о распаде специального разрыва, т.е. трехмерных изэнтропических течений политропного газа, возникающих после мгновенного разрушения в начальный момент времени непроницаемой стенки, отделяющей неоднородный движущийся газ от вакуума. В задаче учитывается действие силы тяжести и силы Кориолиса. В систему уравнений газовой динамики введена автомодельная особенность в переменную, которая выводит с поверхности раздела. Для полученной системы поставлена задача Коши с данными на звуковой характеристике. Решение задачи строилось в виде степенных рядов. Часть коэффициентов рядов определялась при решении алгебраических уравнений, а часть из решений - обыкновенных дифференциальных уравнений. Методом мажорант доказана сходимость построенных рядов. Построенное решение позволяет задавать начальные условия для разностной схемы при численном моделировании решений данной характеристической задачи Коши The aim of this study is to construct a solution to the problem of the decay of a special discontinuity in physical space. The problem reduces to finding of three-dimensional isentropic flows of a polytropic gas that occur after the instantaneous destruction of an impermeable wall separating an inhomogeneous moving gas from a vacuum at the initial moment of time. The problem takes into account the forces of gravity and Coriolis. Research methods. In the system of gas dynamics equations, a self-similar feature is introduced in a variable that outputs from the initial interface. For the resulting system, the Cauchy problem is formulated using conditions on the sound characteristic. The solution to this problem is constructed in the form of power series. The coefficients of the series are partly determined by solving algebraic equations, another part can be found as solutions of ordinary differential equations. The convergence of the constructed series is proved by the Majorant method The results obtained in the work. In the form of a convergent power series, solutions to the problem of the decay of a special discontinuity in physical space are constructed. Conclusions. The solution constructed in physical space allows setting the initial conditions for the numerical simulation of this characteristic Cauchy problem using a difference scheme.

Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

1983 ◽  
Vol 29 (1) ◽  
pp. 139-142 ◽  
Author(s):  
J. R. Burgan ◽  
M. R. Feix ◽  
E. Fijalkow ◽  
A. Munier
Keyword(s):  
Asymptotic Solution ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Asymptotic Solutions ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
New Equation

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

Tomographic Reconstruction of Unsteady Fields Using Proper Orthogonal Decomposition

2008 ◽  
Author(s):  
Dhruv Singh ◽  
Atul Srivastava ◽  
K. Muralidhar
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
Concentration Field ◽  
Orthogonal Decomposition ◽  
Gradient Field ◽  
Data Set ◽  
Cylindrical Annulus ◽  
Typical Experiment ◽  
Proper Orthogonal

An algorithm for the reconstruction of unsteady three dimensional concentration field from path-integrated data has been discussed. We propose the use of Proper Orthogonal Decomposition (Karhunen Loe´ve Expansion) to completely decouple the spatial and temporal components of the image sequence (projections) obtained from a typical experiment enabling the analysis of an asynchoronous time-dependent data set. We apply the algorithm to experimental data from a Laser Interferometric study of convection in a cylindrical annulus to capture transients that are invariably faster than the camera speed. The strength of the technique is demonstrated in the reconstruction of the flow field (related to concentration gradients) from model (simulated) Schlieren projections. Tomographic reconstruction based on Convolution Back Projection (CBP) has been coupled with Proper Orthogonal Decomposition to enable the reconstruction of unsteady concentration gradient field from asynchronous projections.

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