scholarly journals Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth

2014 ◽  
Vol 748 ◽  
pp. 85-112 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Density Ratio ◽  
Mixing Layer ◽  
Layer Growth ◽  
Planar Geometry ◽  
Rarefaction Waves ◽  
Mean Flow ◽  
Symmetric Flow ◽  
Turbulent Statistics ◽  
The Mean

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ${\approx }1.2$, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of $3\, \%$): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. Turbulent statistics are developed in Part 2 (Lombardini, M., Pullin, D. I. & Meiron, D. I. J. Fluid Mech., vol. 748, 2014, pp. 113–142). A wave-diagram analysis of the radially symmetric flow highlights that the light–heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy–light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer–Meshkov (RM) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh–Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different. A small-amplitude stability analysis along the lines of Bell (Los Alamos Scientific Laboratory Report, LA-1321, 1951) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96–98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Bell–Plesset effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (${\approx } 2$) and rather high ($\ell >10$) mode numbers considered.

scholarly journals Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics

2014 ◽  
Vol 748 ◽  
pp. 113-142 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Spherical Surface ◽  
Density Ratio ◽  
Mixing Layer ◽  
Inertial Subrange ◽  
Planar Geometry ◽  
Late Time ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Decaying Turbulence

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

On the periodically excited plane turbulent mixing layer, emanating from a jagged partition

2007 ◽  
Vol 589 ◽  
pp. 479-507 ◽  
Author(s):  
E. KIT ◽  
I. WYGNANSKI ◽  
D. FRIEDMAN ◽  
O. KRIVONOSOVA ◽  
D. ZHILENKO
Keyword(s):  
Turbulent Mixing ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Mean Flow ◽  
Trailing Edge ◽  
Mean Velocity ◽  
Turbulent Mixing Layer ◽  
Arithmetic Average ◽  
The Mean

The flow in a turbulent mixing layer resulting from two parallel different velocity streams, that were brought together downstream of a jagged partition was investigated experimentally. The trailing edge of the partition had a short triangular ‘chevron’ shape that could also oscillate up and down at a prescribed frequency, because it was hinged to the stationary part of the partition to form a flap (fliperon). The results obtained from this excitation were compared to the traditional results obtained by oscillating a two-dimensional fliperon. Detailed measurements of the mean flow and the coherent structures, in the periodically excited and spatially developing mixing layer, and its random constituents were carried out using hot-wire anemometry and stereo particle image velocimetry.The prescribed spanwise wavelength of the chevron trailing edge generated coherent streamwise vortices while the periodic oscillation of this fliperon locked in-phase the large spanwise Kelvin–Helmholtz (K-H) rolls, therefore enabling the study of the inter- action between the two. The two-dimensional periodic excitation increases the strength of the spanwise rolls by increasing their size and their circulation, which depends on the input amplitude and frequency. The streamwise vortices generated by the jagged trailing edge distort and bend the primary K-H rolls. The present investigation endeavours to study the distortions of each mode as a consequence of their mutual interaction. Even the mean flow provides evidence for the local bulging of the large spanwise rolls because the integral width (the momentum thickness, θ), undulates along the span. The lateral location of the centre of the ensuing mixing layer (the location where the mean velocity is the arithmetic average of the two streams,y0), also suggests that these vortices are bent. Phase-locked and ensemble-averaged measurements provide more detailed information about the bending and bulging of the large eddies that ensue downstream of the oscillating chevron fliperon. The experiments were carried out at low speeds, but at sufficiently high Reynolds number to ensure naturally turbulent flow.

The interaction between the mean flow and coherent structures in turbulent mixing layers

1994 ◽  
Vol 260 ◽  
pp. 81-94 ◽  
Author(s):  
J. Cohen ◽  
B. Marasli ◽  
V. Levinski
Keyword(s):  
Velocity Profile ◽  
Coherent Structures ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Mean Flow ◽  
Mean Velocity ◽  
Turbulent Mixing Layer ◽  
Self Similar ◽  
The Mean

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional turbulent mixing layer is addressed. Based on considerations from stability theory, previous experimental results, in particular the modification of the mean velocity profile, the peculiar growth of the forced shear-layer thickness and the spatial growth of the disturbance amplitude, are explained. A model that assumes a quasi-parallel mean flow having a self-similar mean velocity profile is developed. The model is capable of predicting the downstream evolution of turbulent mixing layers subjected to external excitations.

Measurement of the Mean Flow Field in a Smooth Rotating Channel With Coriolis and Buoyancy Effects

2017 ◽  
Author(s):  
Ruquan You ◽  
Haiwang Li ◽  
Zhi Tao ◽  
Kuan Wei
Keyword(s):  
Flow Field ◽  
Coriolis Force ◽  
Indium Tin Oxide ◽  
Buoyancy Force ◽  
Flow Direction ◽  
Density Ratio ◽  
Mean Flow ◽  
The Mean ◽  
Static Conditions ◽  
Rotating Channel

The mean flow field in a smooth rotating channel was measured by particle image velocimetry under the effect of buoyancy force. In the experiments, the Reynolds number, based on the channel hydraulic diameter (D) and the bulk mean velocity (Um), is 10000, and the rotation numbers are 0, 0.13, 0.26, 0.39, 0.52, respectively. The four channel walls are heated with Indium Tin Oxide (ITO) heater glass, making the density ratio (d.r.) about 0.1 and the maximum value of buoyancy number up to 0.27. The mean flow field was simulated on a 3D reconstruction at the position of 3.5<X/D<6.5, where X is along the mean flow direction. The effect of Coriolis force and buoyancy force on the mean flow was taken into consideration in the current work. The results show that the Coriolis force pushes the mean flow to the trailing side, making the asymmetry of the mean flow with that in the static conditions. On the leading surface, due to the effect of buoyancy force, the mean flow field changes considerably. Comparing with the case without buoyancy force, separated flow was captured by PIV on the leading side in the case with buoyancy force. More details of the flow field will be presented in this work.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

scholarly journals Experimental study into the Rayleigh–Taylor turbulent mixing zone heterogeneous structure

2003 ◽  
Vol 21 (3) ◽  
pp. 375-379 ◽  
Author(s):  
Yu.A. KUCHERENKO ◽  
A.P. PYLAEV ◽  
V.D. MURZAKOV ◽  
A.V. BELOMESTNIH ◽  
V.N. POPOV ◽  
...  
Keyword(s):  
Turbulent Mixing ◽  
Measurement Errors ◽  
Density Ratio ◽  
Mixing Layer ◽  
Light Sheet ◽  
Immiscible Fluids ◽  
Heterogeneous Structure ◽  
Layer System ◽  
Glycerin Solution ◽  
Refractive Index Matching

Experiments conducted on the SOM facility at the Russian Federal Nuclear Center–VNIITF, concerning the turbulent mixing induced by the Rayleigh–Taylor instability in a three-layer system of immiscible liquids are described. The fluids are contained in a small tank 6.4 cm × 5.4 cm × 12 cm, which is accelerated vertically downward by a gas gun. The mixing layer evolution was imaged by seeding one of the fluids with particles and using a bidirectional light sheet method (refractive index matching was used to minimize measurement errors). Experiments were performed for two different accelerations (g = 350 g0 and g = 100 g0, where g0 = 980 cm/s2, and the acceleration decreases with distance traveled), and with aqueous solutions of glycerin and benzene (with density ratio 1.6). The lower, middle, and upper layers were a sodium hyposulfite–glycerin solution, a water–glycerin solution, and benzene, respectively. The glycerin solution was seeded with particles. The principal objective of the experiments was to obtain the distribution of fluid particle sizes arising from the mixing of the immiscible fluids.

scholarly journals Effects of Rear Angle on the Turbulent Wake Flow between Two in-Line Ahmed Bodies

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 328
Author(s):  
Ebenezer Essel ◽  
Subhadip Das ◽  
Ram Balachandar
Keyword(s):  
Wake Flow ◽  
Recirculation Region ◽  
Wake Region ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Slant Angle ◽  
The Road ◽  
Rear Angle ◽  
Turbulent Statistics ◽  
The Mean

Understanding the wake characteristics between two in-line vehicles is essential for improving and developing new strategies for reducing in-cabin air pollution. In this study, Ahmed bodies are used to investigate the effects of the rear slant angle of a leading vehicle on the mean flow and turbulent statistics between two vehicles. The experiments were conducted with a particle image velocimetry at a fixed Reynolds number, R e H = 1.7 × 10 4 , and inter-vehicle spacing distance of 0.75 L , where H and L are the height and length of the model. The rear slant angles investigated were a reference square back, high-drag angle ( α = 25 ° ) and low-drag angle ( α = 35 ° ). The mean velocities, Reynolds stresses, production of turbulent kinetic energy and instantaneous swirling strength are used to provide physical insight into the wake dynamics between the two bodies. The results indicate that the recirculation region behind the square back Ahmed body increases while those behind the slant rear-end bodies decreases in the presence of a follower. For the square back models, the dominant motion in the wake region is a strong upwash of jet-like flow away from the road but increasing the rear slant angle induces a stronger downwash flow that suppresses the upwash and dominates the wake region.

Fully coupled resonant-triad interactions in a free shear layer

1994 ◽  
Vol 278 ◽  
pp. 101-121 ◽  
Author(s):  
R. Mallier ◽  
S. A. Maslowe
Keyword(s):  
Flow Direction ◽  
Mixing Layer ◽  
Adverse Pressure Gradient ◽  
Critical Layer ◽  
Free Shear Layer ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Initial Interaction ◽  
The Mean ◽  
Fully Coupled

We report the results of an investigation of the weakly nonlinear evolution of a triad of waves, each slightly amplified on a linear basis, that are superimposed on a tanh y mixing layer. The triad consists of a plane wave and a pair of oblique modes that act as a subharmonic of order 1/2. The oblique modes are inclined at approximately ±60°. to the mean flow direction and because the resonance conditions are satisfied exactly the analysis is entirely self-consistent as an asymptotic theory. The nonlinearity first occurs within the critical layer and the initial interaction is of the parametric resonance type. This produces faster than exponential growth of the oblique waves, behaviour observed recently in the experiments of Corke & Kusek (1993). The critical-layer dynamics lead subsequently to coupled integro-differential equations governing the amplitude evolution and, as first shown in related work by Goldstein & Lee (1992) on boundary layers in an adverse pressure gradient, these equations develop singularities in a finite time.

Large-scale structures in a forced turbulent mixing layer

1985 ◽  
Vol 150 ◽  
pp. 23-39 ◽  
Author(s):  
M. Gaster ◽  
E. Kit ◽  
I. Wygnanski
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Phase Distribution ◽  
Mixing Layer ◽  
Global Scale ◽  
Travelling Wave ◽  
Mean Flow ◽  
Turbulent Mixing Layer ◽  
Large Scale Structures ◽  
Scale Structures

The large-scale structures that occur in a forced turbulent mixing layer at moderately high Reynolds numbers have been modelled by linear inviscid stability theory incorporating first-order corrections for slow spatial variations of the mean flow. The perturbation stream function for a spatially growing time-periodic travelling wave has been numerically evaluated for the measured linearly diverging mean flow. In an accompanying experiment periodic oscillations were imposed on the turbulent mixing layer by the motion of a small flap at the trailing edge of the splitter plate that separated the two uniform streams of different velocity. The results of the numerical computations are compared with experimental measurements.When the comparison between experimental data and the computational model was made on a purely local basis, agreement in both the amplitude and phase distribution across the mixing layer was excellent. Comparisons on a global scale revealed, not unexpectedly, less good accuracy in predicting the overall amplification.

PIV Study of Shallow Open Channel Flow Over d- and k-Type Transverse Ribs

2007 ◽  
Vol 129 (8) ◽  
pp. 1058-1072 ◽  
Author(s):  
M. F. Tachie ◽  
K. K. Adane
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Cross Section ◽  
Open Channel ◽  
Skin Friction Coefficient ◽  
Mixing Length ◽  
Mean Flow ◽  
Turbulent Statistics ◽  
The Mean

A particle image velocimetry was used to study shallow open channel turbulent flow over d-type and k-type transverse ribs of square, circular, and semi-circular cross sections. The ratio of boundary layer thickness to depth of flow varied from 50% to 90%. The mean velocities and turbulent quantities were evaluated at the top plane of the ribs to characterize interaction between the cavities and overlying boundary layer. It was found that the overlying boundary layer interacts more strongly with k-type cavities than observed for d-type cavities. The profiles of the mean velocities and turbulent statistics were then spatially averaged over a pitch, and these profiles were used to study the effects of rib type and cross section on the flow field. The mean velocity gradients were found to be non-negligible across the boundary layer, and the implications of this observation for momentum transport, eddy viscosity, and mixing length distributions are discussed. The results show that the skin friction coefficient, Reynolds stresses and mixing length distributions are independent of rib cross section for d-type. For the k-type ribs, significant variations in skin friction coefficient values, mean flow, and turbulence fields are observed between square ribs and circular/semi-circular ribs.

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