The mixing region in freely decaying variable-density turbulence

2015 ◽  
Vol 772 ◽  
pp. 386-426 ◽  
Author(s):  
Pooya Movahed ◽  
Eric Johnsen
Keyword(s):  
Kinetic Energy ◽  
Density Gradient ◽  
Kinematic Viscosity ◽  
Density Ratio ◽  
Variable Density ◽  
Unit Mass ◽  
Material Interface ◽  
Variable Density Turbulence ◽  
Set Up ◽  
Density Ratios

A novel set-up is proposed to numerically study turbulent multimaterial mixing, starting from an unperturbed material interface between a light and a heavy fluid. We conduct direct numerical simulation (DNS) to better understand the role of density gradient alone on the turbulence, specifically with regard to the mixing region dynamics and anisotropy across scales. Freely decaying isotropic turbulent fields of different densities but identical kinematic viscosities are juxtaposed. The rationale for this strategy is that conventional turbulence scalings are based on kinetic energy per unit mass and kinematic viscosity. Thus, by matching the initial kinematics (root-mean-square velocity) and the dissipation (kinematic viscosity), the turbulence (kinetic energy per unit mass) decays at the same rate in both fluids. With this set-up, the effect of the density gradient alone on the turbulence can be considered, independently from other contributions (e.g. mismatch in kinetic energy per unit mass, acceleration field, etc.). We examine the mixing region dynamics at large and small scales for different density ratios and Reynolds numbers. After an initial transient, we observe a self-similar growth of the mixing region, which we explain via theoretical arguments verified by the DNS results. Inside the mixing region, the momentum of the heavier eddies causes the mean interface location to shift toward the light fluid. A higher density ratio leads to a wider, less molecularly mixed mixing region. Although anisotropy is evident at the large scales, the dissipation scales remain essentially isotropic, even at the highest density ratio under consideration (12:1). The intermittency of the velocity field exhibits isotropy, while the mass fraction field is more intermittent in the direction of the density gradient.

scholarly journals Nonlinear effects in buoyancy-driven variable-density turbulence

2016 ◽  
Vol 810 ◽  
pp. 362-377 ◽  
Author(s):  
P. Rao ◽  
C. P. Caulfield ◽  
J. D. Gibbon
Keyword(s):  
Density Gradient ◽  
Blow Up ◽  
Nonlinear Effects ◽  
Variable Density ◽  
Density Field ◽  
Strong Mixing ◽  
Spatial Average ◽  
Large Growth ◽  
Variable Density Turbulence ◽  
Using Data

We consider the time dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\unicode[STIX]{x1D714}}$ and $D_{m,\unicode[STIX]{x1D703}}$ of the vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ and the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D703}=\log (\unicode[STIX]{x1D70C}^{\ast }/\unicode[STIX]{x1D70C}_{0}^{\ast })$, in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, $\unicode[STIX]{x1D70C}^{\ast }(\boldsymbol{x},t)$ is the composition density of a mixture of two incompressible miscible fluids with fluid densities $\unicode[STIX]{x1D70C}_{2}^{\ast }>\unicode[STIX]{x1D70C}_{1}^{\ast }$, and $\unicode[STIX]{x1D70C}_{0}^{\ast }$ is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the $L^{2}$-spatial average of the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ can reach extremely large values at intermediate times, even in flows with low Atwood number $At=(\unicode[STIX]{x1D70C}_{2}^{\ast }-\unicode[STIX]{x1D70C}_{1}^{\ast })/(\unicode[STIX]{x1D70C}_{2}^{\ast }+\unicode[STIX]{x1D70C}_{1}^{\ast })=0.05$, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ might blow up in a finite time.

A Kármán–Howarth–Monin equation for variable-density turbulence

2018 ◽  
Vol 843 ◽  
pp. 382-418 ◽  
Author(s):  
Chris C. K. Lai ◽  
John J. Charonko ◽  
Katherine Prestridge
Keyword(s):  
Energy Transfer ◽  
Initial Density ◽  
Density Ratio ◽  
Variable Density ◽  
Navier Stokes ◽  
Mean Flow ◽  
Development Region ◽  
The Mean ◽  
Variable Density Turbulence ◽  
Transfer Term

We present a generalisation of the Kármán–Howarth–Monin (K–H–M) equation to include variable-density (VD) effects. The derived equation (i) reduces to the original K–H–M equation when density is a constant and (ii) leads to a VD analogue of the $4/5$-law with the same value of constant ($=4/5$) appearing as the prefactor of the dissipation rate. The equation is employed to understand negative turbulent kinetic energy production in a $\text{SF}_{6}$ turbulent round jet with an initial density ratio of 4.2. From a Reynolds-averaged Navier–Stokes (RANS) perspective, negative production means that the mean flow is strengthened at the expense of the energy of turbulent fluctuations. We show that the associated energy transfer is accomplished by the deformation of smaller turbulent eddies into large ones in the development region of the jet and is captured by the linear scale-by-scale energy transfer term in the VD K–H–M equation. The nonlinear transfer term of the VD K–H–M equation depicts a conventional forward cascade for all eddies having a size less than the Eulerian integral length scale, regardless of their orientation. The net effect is a retarded energy cascade in the non-Boussinesq jet that has not been accounted for by existing turbulence theories. Implications of this observation for turbulence modelling are discussed.

Study of Turbulent Variable Density Jets With Different Asymmetric Geometries

Volume 1 ◽  
2004 ◽  
Author(s):  
Bachir Imine ◽  
Miloud Abidat ◽  
Omar Imine ◽  
Hichem Gazzah ◽  
Iskender Go¨kalp
Keyword(s):  
Kinetic Energy ◽  
Aspect Ratio ◽  
Turbulent Kinetic Energy ◽  
Comparative Studies ◽  
Longitudinal Velocity ◽  
Turbulent Jets ◽  
Reynolds Stress Model ◽  
Variable Density ◽  
Stress Model ◽  
Density Ratios

In the present study, the effects of inlet jet geometry on the process of mixture with variable density have been investigated numerically. Three density ratios were considered, namely 1.0, 1.8 and 0.66 for Air-air, CH4-Air and CO2-Air mixtures respectively. The jets are produced through rectangular, elliptic and triangular tubes with aspect ratio 1.33. A second-order Reynolds stress model (RSM) is used to investigate variable density effects in asymmetric turbulent jets. Comparative studies are presented in the case of the calculations of the average variables such as the longitudinal velocity, species and the turbulent kinetic energy. The results obtained show that the asymmetric geometry noticeably enhances mixture in comparison with the axisymmetric case. Typical phenomenon of 3D jets are observed.

Effects on Momentum Thickness and Density Ratio for Side-Jet Formation in Round Jets With Variable-Density

2011 ◽  
Author(s):  
Yasuhiro Kaneda ◽  
Akinori Muramatsu
Keyword(s):  
Nozzle Exit ◽  
Mass Density ◽  
Laser Sheet ◽  
Density Ratio ◽  
Variable Density ◽  
Momentum Thickness ◽  
Hot Wire ◽  
Jet Formation ◽  
Ambient Gas ◽  
Density Ratios

If the mass density of an issuing gas is sufficiently lower than that of the ambient gas, radial ejections of the jet gas may be generated near the nozzle exit. These radial ejections are referred to as side jets. The parameters for side-jet formation have been reported to be the density ratio of the jet gas and the ambient gas and the momentum thickness at the nozzle exit. In the present experimental study, gases with variable density were discharged into still air. Two round nozzles having different area contraction ratios were used in order to vary the momentum thickness. The momentum thicknesses were obtained after the velocity profiles at the nozzle exit were measured by a hot-wire probe and a hot-wire concentration probe for jets with various density ratios and issuing velocities. The existence of side jets was confirmed by flow visualization of the jets using a laser sheet. The domain for side-jet formation is illustrated using the non-dimensional momentum thickness and the density ratio.

A semi-Lagrangian direct-interaction closure of the spectra of isotropic variable-density turbulence

2019 ◽  
Vol 876 ◽  
pp. 186-236 ◽  
Author(s):  
David J. Petty ◽  
C. Pantano
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Density Ratio ◽  
Direct Interaction ◽  
Variable Density ◽  
Constant Density ◽  
Velocity Spectrum ◽  
Variable Density Flow ◽  
Density Flow ◽  
Variable Density Turbulence

A study of variable-density homogeneous stationary isotropic turbulence based on the sparse direct-interaction perturbation (SDIP) and supporting direct numerical simulations (DNS) is presented. The non-solenoidal flow considered here is an example of turbulent mixing of gases with different densities. The spectral statistics of this type of flow are substantially more difficult to understand theoretically than those of the similar solenoidal flows. In the approach described here, the nonlinearly coupled velocity and scalar (which determine the density of the fluid) equations are expanded in terms of a normalised density ratio parameter. A new set of coupled integro-differential SDIP equations are derived and then solved numerically for the first-order correction to the incompressible equations in the variable-density expansion parameter. By adopting a regular expansion approach, one obtains leading-order corrections that are universal and therefore interesting in their own right. The predictions are then compared with DNS of forced variable-density flow with different density contrasts. It is found that the velocity spectrum owing to variable density is indistinguishable from that of constant-density turbulence, as it is supported by a wealth of indirect experimental evidence, but the scalar spectra show significant deviations, and even loss of monotonicity, as a function of the type and strength of the large-scale source of the mixing. Furthermore, the analysis helps clarify what may be the proper approach to interpret the power spectrum of variable-density turbulence.

scholarly journals Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

2014 ◽  
Vol 44 (10) ◽  
pp. 2661-2680 ◽  
Author(s):  
P. Ryan Jackson ◽  
Chris R. Rehmann
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Kinematic Viscosity ◽  
Laboratory Experiments ◽  
Density Ratio ◽  
Eddy Diffusivity ◽  
Buoyancy Frequency ◽  
Differential Diffusion ◽  
Rate Of Dissipation ◽  
Diffusivity Ratio

Abstract Laboratory experiments were performed to measure differential diffusion of temperature and salinity across a sheared density interface. The eddy diffusivity of temperature KT exceeded the eddy diffusivity of salinity KS by as much as 1.5 orders of magnitude at low ε/νN2, where ε is the rate of dissipation of turbulent kinetic energy, ν is the kinematic viscosity, and N is the buoyancy frequency in the pycnocline. The diffusivity ratio d = KS/KT increased from about 0.05 to 1 over the range 0.1 < ε/νN2 < 40. These differences made the eddy diffusivity of density depend on the density ratio. The trend of d with ε/νN2 was consistent with trends found in other experiments, simulations, and theory, and the collapse of several datasets allowed the diffusivity ratio to be expressed as a function of ε/νN2. However, shear decreased differential diffusion less in the experiments than predicted by theory for homogeneous turbulence subjected to constant shear and stratification. No strong effect of the density ratio on the diffusivity ratio was apparent. Because many flows in oceanography and limnology have values of ε/νN2 low enough to exhibit significant differential diffusion, accounting for differential diffusion in interpreting measurements and modeling stratified water bodies is recommended.

Buoyancy-driven variable-density turbulence

2007 ◽  
Vol 591 ◽  
pp. 43-71 ◽  
Author(s):  
D. LIVESCU ◽  
J. R. RISTORCELLI
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Mass Flux ◽  
Variable Density ◽  
Projection Algorithm ◽  
Stratified Medium ◽  
Mean Pressure ◽  
The Mean ◽  
Variable Density Turbulence ◽  
Non Equilibrium

Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

Equation of State’s Crossover Enhancement of Pseudopotential Lattice Boltzmann Modeling of CO2 Flow in Homogeneous Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 434
Author(s):  
Assetbek Ashirbekov ◽  
Bagdagul Kabdenova ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Equations Of State ◽  
Density Ratio ◽  
Narrow Channel ◽  
Lattice Boltzmann Model ◽  
High Density Ratio ◽  
Homogeneous Porous Medium ◽  
Density Ratios

The original Shan-Chen’s pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile.

scholarly journals Incompressible variable-density turbulence in an external acceleration field

2017 ◽  
Vol 827 ◽  
pp. 506-535 ◽  
Author(s):  
Ilana Gat ◽  
Georgios Matheou ◽  
Daniel Chung ◽  
Paul E. Dimotakis
Keyword(s):  
Growth Rate ◽  
Turbulent Flow ◽  
Shear Layers ◽  
Variable Density ◽  
Fluid Composition ◽  
Turbulent Regime ◽  
Low Density ◽  
Acceleration Field ◽  
Density Ratios ◽  
Mixed Fluid

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

A Numerical Study of Flow and Heat Transfer in Rotating Rectangular Channels AR=4 With 45 deg Rib Turbulators by Reynolds Stress Turbulence Model

2003 ◽  
Vol 125 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Mohammad Al-Qahtani ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Density Ratio ◽  
Convective Transport ◽  
High Density ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Rectangular Channels ◽  
Density Ratios

Computations were performed to study three-dimensional turbulent flow and heat transfer in stationary and rotating 45 deg ribbed rectangular channels for which experimental heat transfer data were available. The channel aspect ratio (AR) is 4:1, the rib height-to-hydraulic diameter ratio e/Dh is 0.078 and the rib-pitch-to-height ratio P/e is 10. The rotation number and inlet coolant-to-wall density ratios, Δρ/ρ, were varied from 0.0 to 0.28 and from 0.122 to 0.40, respectively, while the Reynolds number was fixed at 10,000. Also, two channel orientations (β=90deg and 135 deg from the rotation direction) were investigated with focus on the high rotation and high density ratios effects on the heat transfer characteristics of the 135 deg orientation. These results show that, for high rotation and high density ratio, the rotation induced secondary flow overpowered the rib induced secondary flow and thus change significantly the heat transfer characteristics compared to the low rotation low density ratio case. A multi-block Reynolds-Averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure. In the present method, the convective transport equations for momentum, energy, and turbulence quantities are solved in curvilinear, body-fitted coordinates using the finite-analytic method.

Sign in / Sign up

Export Citation Format

Share Document