Nicholas J. Mueschke

Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data

A 1152×760×1280 direct numerical simulation (DNS) using initial conditions, geometry, and physical parameters chosen to approximate those of a transitional, small Atwood number Rayleigh–Taylor mixing experiment [Mueschke et al., J. Fluid Mech. 567, 27 (2006)] is presented. In particular, the Atwood number is 7.5×10−4, and temperature diffusion is modeled by mass diffusion with an equivalent Schmidt number of 7. The density and velocity fluctuations measured just off of the splitter plate in this buoyantly unstable water channel experiment were parametrized to provide physically realistic, anisotropic initial conditions for the DNS. The methodology for parametrizing the measured data and numerically implementing the resulting perturbation spectra in the simulation is discussed in detail. The DNS is then validated by comparing quantities from the simulation to experimental measurements. In particular, large-scale quantities (such as the bubble front penetration hb and the mixing layer growth parameter αb), ...

Measurements of molecular mixing in a high-Schmidt-number Rayleigh-Taylor mixing layer

Molecular mixing measurements are reported for a high-Schmidt-number ( Sc ~ 10 3 ), small-Atwood-number ( A ≈ 7.5 × 10 −4 ) buoyancy-driven turbulent Rayleigh–Taylor (RT) mixing layer in a water channel facility. Salt was added to the top water stream to create the desired density difference. The degree of molecular mixing was measured as a function of time by monitoring a diffusion-limited chemical reaction between the two fluid streams. The pH of each stream was modified by the addition of acid or alkali such that a local neutralization reaction occurred as the two fluids molecularly mixed. The progress of this neutralization reaction was tracked by the addition of phenolphthalein – a pH-sensitive chemical indicator – to the acidic stream. Accurately calibrated backlit optical techniques were used to measure the average concentration of the coloured chemical indicator. Comparisons of chemical product formation for pre-transitional buoyancy- and shear-driven mixing layers are given. It is also shown that experiments performed at different equivalence ratios (acid/alkali concentrations) can be combined to obtain a mathematical relationship between the coloured product formed and the density variance. This relationship was used to obtain high-fidelity quantitative measures of the degree of molecular mixing which are independent of probe resolution constraints. The dependence of molecular mixing on the Schmidt and Reynolds numbers is examined by comparing the current Sc ~ 10 3 measurements with previous Sc = 0.7 gas-phase and Pr = 7 (where Pr is the Prandtl number) liquid-phase measurements. This comparison indicates that the Schmidt number has a large effect on the quantity of mixed fluid at small Reynolds numbers Re h 3 . At larger Reynolds numbers, corresponding to later times in this experiment, all mixing parameters indicated a greater degree of molecular mixing and a decreased Schmidt number dependence. Implications for the development and quantitative assessment of turbulent transport and mixing models appropriate for RT instability-induced mixing are discussed.

Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. II. Dynamics of transitional flow and mixing statistics

A 1152×760×1280 direct numerical simulation (DNS) using initial conditions, geometry, and physical parameters chosen to approximate those of a transitional, small Atwood number, nonreacting Rayleigh–Taylor mixing experiment was presented in Paper I [Mueschke and Schilling, Phys. Fluids 21, 014106 (2009)]. In addition, the DNS model of the experiment was validated by comparing quantities from the simulation to experimental measurements, including large-scale quantities, higher-order statistics, and vertical velocity and density variance spectra. In Paper II of this study, other quantities not measured in the experiment are obtained from the DNS and discussed, such as the integral- and Taylor-scale Reynolds numbers, Reynolds stress and dissipation anisotropy, two-dimensional density and velocity variance spectra, hypothetical chemical product formation measures (similar to those used in reacting shear flow experiments), other local and global mixing parameters, and the statistical composition of mixed fluid...

Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data

Data from a 1152×760×1280 direct numerical simulation (DNS) [N. J. Mueschke and O. Schilling, “Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data,” Phys. Fluids 21, 014106 (2009)] of a transitional Rayleigh–Taylor mixing layer modeled after a small Atwood number water channel experiment is used to comprehensively investigate the structure of mean and turbulent transport and mixing. The simulation had physical parameters and initial conditions approximating those in the experiment. The budgets of the mean vertical momentum, heavy-fluid mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate equations are constructed using Reynolds averaging applied to the DNS data. The relative importance of mean and turbulent production, turbulent dissipation and destruction, and turb...

Numerical Investigation of Single-Mode Richtmyer-Meshkov Instability

The Richtmyer-Meshkov (RM) instability occurs when a shock passes through a perturbed interface separating fluids of different densities. Similarly, RM instabilities may also occur when a perturbed interface between two incompressible fluids of different density is impulsively accelerated. We report work that investigates RM instabilities between incompressible media by way of numerical simulations that are matched to experiments reported by Niederhaus & Jacobs [1]. We also describe a compact, fractional time-step, two-dimensional, finite-volume numerical algorithm that solves the non-Bousinesq Euler equations explicitly on a Cartesian, co-located grid. Numerical advection of volume fractions and momentum is second-order accurate in space and unphysical oscillations are prevented by using Van Leer flux limiters [2,3]. An initial velocity impulse has been used to model the impulsive acceleration history found in the experiments [1]. We report accurate simulation of the experimentally measured early-, intermediate-, and late-time penetrations of one fluid into another.Copyright

Numerical investigation of internal vortex structure in two dimensional, incompressible Richtmyer-Meshkov flows

Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ1 ≠ ρ2 . This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs [1]. A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs [1] and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse [2] has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs [1]. Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.Copyright