scholarly journals A numerical study of a variable-density low-speed turbulent mixing layer

2017 ◽  
Vol 830 ◽  
pp. 569-601 ◽  
Author(s):  
Antonio Almagro ◽  
Manuel García-Villalba ◽  
Oscar Flores
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Incompressible Flows ◽  
Numerical Study ◽  
Density Ratio ◽  
Mixing Layer ◽  
Variable Density ◽  
The Self ◽  
Low Speed ◽  
Self Similar

Direct numerical simulations of a temporally developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier–Stokes equations in the low-Mach-number approximation are solved using a novel algorithm based on an extended version of the velocity–vorticity formulation used by Kim et al. (J. Fluid Mech., vol 177, 1987, 133–166) for incompressible flows. Four cases with density ratios $s=1,2,4$ and 8 are considered. The simulations are run with a Prandtl number of 0.7, and achieve a $Re_{\unicode[STIX]{x1D706}}$ up to 150 during the self-similar evolution of the mixing layer. It is found that the growth rate of the mixing layer decreases with increasing density ratio, in agreement with theoretical models of this phenomenon. Comparison with high-speed data shows that the reduction of the growth rates with increasing density ratio has a weak dependence with the Mach number. In addition, the shifting of the mixing layer to the low-density stream has been characterized by analysing one-point statistics within the self-similar interval. This shifting has been quantified, and related to the growth rate of the mixing layer under the assumption that the shape of the mean velocity and density profiles do not change with the density ratio. This leads to a predictive model for the reduction of the growth rate of the momentum thickness, which agrees reasonably well with the available data. Finally, the effect of the density ratio on the turbulent structure has been analysed using flow visualizations and spectra. It is found that with increasing density ratio the longest scales in the high-density side are gradually inhibited. A gradual reduction of the energy in small scales with increasing density ratio is also observed.

Density and Compressibility Effects on the Structure of Supersonic Mixing Layer: Experimental Results and Similarity Analysis

2003 ◽  
Author(s):  
M. Menaa ◽  
J. P. Dussauge
Keyword(s):  
Mach Number ◽  
Velocity Profile ◽  
Mixing Layer ◽  
Variable Density ◽  
Turbulent Shear ◽  
Turbulent Friction ◽  
Low Speed ◽  
Rate Of Spread ◽  
Supersonic Mixing ◽  
Supersonic Mixing Layer

Self-similar solutions for mixing layers in supersonic flow and in subsonic flow with variable density are examined. The equation for the velocity profile is derived for a unity turbulent Prandtl number and/or prescribed density distributions. It is found that the shape of the velocity profile is not sensitive to Mach number and is nearly the same for supersonic layers with moderate convective Mach numbers and in low speed flows with variable density: in such conditions, the only compressibility effect is found on the rate of spread. It is also found that turbulent friction is a function of Mach number and of velocity and density ratios. The effect of these last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear stress last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear strees in supersonic mixing layer is discussed. A simple formulation is proposed, in which the effects of density ratio and convective Mach number can be sepearated, as it is usually done for the rate of spread.

Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties

2012 ◽  
Vol 711 ◽  
pp. 437-468 ◽  
Author(s):  
Qiang Zhou ◽  
Feng He ◽  
M. Y. Shen
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Mixing Layer ◽  
The Self ◽  
Streamwise Vortices ◽  
Hairpin Vortices ◽  
Self Similar ◽  
Flower Structures ◽  
Convective Mach Number

AbstractThe spatially developing compressible plane mixing layer with a convective Mach number of 0.7 is investigated by direct numerical simulation. A pair of equal and opposite oblique instability waves is introduced to perturb the mixing layer at the inlet. The full evolution process of instability, including formation of $ \mrm{\Lambda} $-vortices and hairpin vortices, breakdown of large structures and establishment of self-similar turbulence, is presented clearly in the simulation. In the transition process, the flow fields are populated sequentially by $ \mrm{\Lambda} $-vortices, hairpin vortices and ‘flower’ structures. This is the first direct evidence showing the dominance of these structures in the spatially developing mixing layer. Hairpin vortices are found to play an important role in the breakdown of the flow. The legs of hairpin vortices first evolve into sheaths with intense vorticity then break up into small slender vortices. The later flower structures are produced by the instability of the heads of the hairpin vortices. They prevail for a long distance in the mixing layer until the flow starts to settle down into its self-similar state. The preponderance of slender inclined streamwise vortices is observed in the transversal middle zone of the transition region after the breakup of the hairpin legs. This predominance of streamwise vortices also persists in the self-similar turbulent region, though the vortices there are found to be relatively very weak. The evolution of both the mean streamwise velocity profile and the Reynolds stresses is found to have close connection to the behaviour of the large vortex structures. High growth rates of the momentum and vorticity thicknesses are observed in the transition region of the flow. The growth rates in the self-similar turbulence region decay to a value that agrees well with previous experimental and numerical studies. Shocklets occur in the simulation, and their formation mechanisms are elaborated and categorized. This is the first three-dimensional simulation that captures shocklets at this low convective Mach number.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

scholarly journals Computing multi-mode shock-induced compressible turbulent mixing at late times

2015 ◽  
Vol 779 ◽  
pp. 411-431 ◽  
Author(s):  
T. Oggian ◽  
D. Drikakis ◽  
D. L. Youngs ◽  
R. J. R. Williams
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Suitable Model ◽  
Late Time ◽  
Flow Equations ◽  
Multi Mode

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

A Numerical Study of the Self-Similar Solutions of the Schrödinger Map

2009 ◽  
Vol 70 (4) ◽  
pp. 1047-1077 ◽  
Author(s):  
F. de la Hoz ◽  
C. J. García-Cervera ◽  
L. Vega
Keyword(s):  
Numerical Study ◽  
The Self ◽  
Self Similar ◽  
Similar Solutions ◽  
Schrödinger Map

Numerical Study on the Response of Tip Leakage Flow Unsteadiness to Micro Tip Injection in a Low-Speed Isolated Compressor Rotor

2007 ◽  
Author(s):  
Shaojuan Geng ◽  
Hongwu Zhang ◽  
Jingyi Chen ◽  
Weiguang Huang
Keyword(s):  
Numerical Study ◽  
The Self ◽  
Axial Position ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Low Speed ◽  
Tip Leakage ◽  
Flow Unsteadiness ◽  
Compressor Rotor ◽  
Tip Injection

A numerical study on the unsteady tip leakage flow with discrete micro tip injection from casing shroud in a low-speed isolated axial compressor rotor is presented. The main target is to clarify the flow mechanism of how the stall control measures act on the tip leakage flow typified by its self-induced unsteady flow characteristics. At operating condition near stall point, a series of calculations have been carried out for different axial position of injector and different injected mass flow rate. The computation results of flow field near rotor tip region show that under the influence of injected flow, the transient pressure distribution fluctuates along blade chord on both pressure and suction sides with respect to the relative position of injector and rotor. The pressure difference across the pressure and suction sides of compressor blade changes correspondingly, thus introduces a forced flow unsteadiness interacting with the unsteady tip leakage flow. When the injection is relatively strong and able to meet the tip leakage flow at its origination, the self-induced unsteadiness of tip leakage flow can be suppressed completely. In most cases, both frequency components of the self-induced unsteadiness and forced-induced unsteadiness are co-existing. The corresponding transient flow contours show that a local high pressure spot appears near blade pressure side, which moves downstream and shifts the tip leakage flow trajectory with less or without touching the neighboring pressure surface of the blade. Based on this understanding of discrete tip injection as force-induced flow unsteadiness, the numerical results are also analyzed to optimize the effect of injection in changing the route of tip leakage flow trajectories and therefore the chance of stability improvement of the compressor rotor.

A Numerical Study of Flow and Heat Transfer in a Smooth and Ribbed U-Duct With and Without Rotation

2000 ◽  
Vol 123 (2) ◽  
pp. 219-232 ◽  
Author(s):  
Y.-L. Lin ◽  
T. I.-P. Shih ◽  
M. A. Stephens ◽  
M. K. Chyu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Mach Number ◽  
Vector Fields ◽  
Numerical Study ◽  
Density Ratio ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Flow And Heat Transfer

Computations were performed to study the three-dimensional flow and heat transfer in a U-shaped duct of square cross section under rotating and non-rotating conditions. The parameters investigated were two rotation numbers (0, 0.24) and smooth versus ribbed walls at a Reynolds number of 25,000, a density ratio of 0.13, and an inlet Mach number of 0.05. Results are presented for streamlines, velocity vector fields, and contours of Mach number, pressure, temperature, and Nusselt numbers. These results show how fluid flow in a U-duct evolves from a unidirectional one to one with convoluted secondary flows because of Coriolis force, centrifugal buoyancy, staggered inclined ribs, and a 180 deg bend. These results also show how the nature of the fluid flow affects surface heat transfer. The computations are based on the ensemble-averaged conservation equations of mass, momentum (compressible Navier-Stokes), and energy closed by the low Reynolds number SST turbulence model. Solutions were generated by a cell-centered finite-volume method that uses second-order flux-difference splitting and a diagonalized alternating-direction implicit scheme with local time stepping and V-cycle multigrid.

Density Ratio and Entrainment Effects on Asymptotic Rayleigh–Taylor Instability

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Assaf Shimony ◽  
Guy Malamud ◽  
Dov Shvarts
Keyword(s):  
Numerical Study ◽  
Density Ratio ◽  
Three Dimensional ◽  
Growth Parameter ◽  
Taylor Instability ◽  
Mixing Zone ◽  
Mixing Process ◽  
Mixing Parameters ◽  
Rayleigh Taylor Instability ◽  
Self Similar

A comprehensive numerical study was performed in order to examine the effect of density ratio on the mixing process inside the mixing zone formed by Rayleigh–Taylor instability (RTI). This effect exhibits itself in the mixing parameters and increase of the density of the bubbles. The motivation of this work is to relate the density of the bubbles to the growth parameter for the self-similar evolution, α, we suggest an effective Atwood formulation, found to be approximately half of the original Atwood number. We also examine the sensitivity of the parameters above to the dimensionality (two-dimensional (2D)/three-dimensional (3D)) and to numerical miscibility.

Vorticity and mixing in Rayleigh–Taylor Boussinesq turbulence

2016 ◽  
Vol 802 ◽  
pp. 395-436 ◽  
Author(s):  
Nicolas Schneider ◽  
Serge Gauthier
Keyword(s):  
Large Scale ◽  
Mixing Layer ◽  
Boussinesq Approximation ◽  
The Self ◽  
Small Scale ◽  
Nonlinear Growth ◽  
Small Scales ◽  
Self Similar ◽  
Order Quantities ◽  
Non Gaussian

The Rayleigh–Taylor instability induced turbulence is studied under the Boussinesq approximation focusing on vorticity and mixing. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to $(24\times 40)\times 940^{2}=848\,M$ collocation points. The Taylor Reynolds number is $\mathit{Re}_{\unicode[STIX]{x1D706}_{zz}}\approx 142$ and a short inertial range is observed. The nonlinear growth rate of the turbulent mixing layer is found to be close to $\unicode[STIX]{x1D6FC}_{b}=0.021$. Our conclusions may be summarized as follows.(i) The simulation data are in agreement with the scalings for the pressure ($k^{-7/3}$) and the vertical mass flux ($k^{-7/3}$).(ii) Mean quantities have a self-similar behaviour, but some inhomogeneity is still present. For higher-order quantities the self-similar regime is not fully achieved.(iii) In the self-similar regime, the mean dissipation rate and the enstrophy behave as $\langle \overline{\unicode[STIX]{x1D700}}\rangle \propto t$ and $\langle \overline{\unicode[STIX]{x1D714}_{i}\,\unicode[STIX]{x1D714}_{i}}^{1/2}\rangle \propto t^{1/2}$, respectively.(iv) The large-scale velocity fluctuation probability density function (PDF) is Gaussian, while vorticity and dissipation PDFs show large departures from Gaussianity.(v) The pressure PDF exhibits strong departures from Gaussianity and is skewed. This is related to vortex coherent structures.(vi) The intermediate scales of the mixing are isotropic, while small scales remain anisotropic. This leaves open the possibility of a small-scale buoyancy. Velocity intermediate scales are also isotropic, while small scales remain anisotropic. Mixing and dynamics are therefore consistent.(vii) Properties and behaviours of vorticity and enstrophy are detailed. In particular, equations for these quantities are written down under the Boussinesq approximation.(viii) The concentration PDF is quasi-Gaussian. The vertical concentration gradient is both non-Gaussian and strongly skewed.

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