Simulations Of Mixing Layers Research Articles

In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure.

Cloud atlas: navigating the multiphase landscape of tempestuous galactic winds

ABSTRACT Galaxies comprise intricate networks of interdependent processes which together govern their evolution. Central among these are the multiplicity of feedback channels, which remain incompletely understood. One outstanding problem is the understanding and modelling of the multiphase nature of galactic winds, which play a crucial role in galaxy formation and evolution. We present the results of three-dimensional magnetohydrodynamical simulations of tall–box interstellar medium (ISM) patches with clustered supernova-driven outflows. Dynamical fragmentation of the ISM during superbubble breakout seeds the resulting hot outflow with a population of cool clouds. We focus on analyzing and modelling the origin and properties of these clouds. Their presence induces large-scale turbulence, which, in turn, leads to complex cloud morphologies. Cloud sizes are well described by a power-law distribution and mass growth rates can be modelled using turbulent radiative mixing layer theory. Turbulence provides significant pressure support in the clouds, while magnetic fields only play a minor role. We conclude that many of the physical insights and analytic scalings derived from idealized small-scale simulations of turbulent radiative mixing layers and cloud–wind interactions are directly translatable and applicable to these larger scale cloud populations. This opens the door to developing effective subgrid recipes for their inclusion in global-scale galaxy models where they are unresolved.

Evaluating anisotropic minimum dissipation, sigma and modulated gradient subgrid-scale models in large-eddy simulation of compressible mixing layers

We evaluate three subgrid-scale (SGS) models in large eddy simulations (LES) of compressible mixing layers up to convective Mach number ( M c ) 2.0. The initial momentum-thickness based Reynolds number is 1000 to match recent high-resolution simulations of the same configuration. The simulations employ the Localised Artificial Diffusivity (LAD) shock-capturing scheme and evaluate constant-coefficient and dynamic versions of Anisotropic Minimum Dissipation (AMD), Sigma, and Modulated Gradient (MGM) SGS models. The results show that the LAD scheme is crucial for stability at higher convective Mach numbers, for M c > 1.2 . The SGS models improve the accuracy of the LES predictions, particularly for dissipation and Reynolds stresses. Dynamic versions of all three SGS models give accurate results. The AMD kernel is found to be most sensitive to the flow conditions since the dynamically obtained model coefficient varies the least with M c . Dynamic versions of the SGS models enhance the agreement with reference results compared to the constant-coefficient versions, particularly for the eddy-viscosity AMD and Sigma models, and to a lesser extent for the MGM model. The results also emphasise the importance of retaining a non-zero artificial-shear-viscosity term, even in the presence of explicit SGS models.

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Instability of mixing layers: Momentum and thermal transport in the continuum breakdown regime.

We examine the momentum and thermal transport in the continuum breakdown regime of a mixing layer flow, which exhibits Kelvin-Helmholtz instability under ideal continuum conditions. The Grad 13 moment model is used as it provides an adequate description of the flow physics (second-order accurate in Knudsen number) in the transition regime. Analytical solutions are developed under breakdown conditions for two-dimensional, compressible, parallel shear flows. It is shown that the deviation of viscous stress and heat flux from the Navier-Stokes-Fourier system follows two different scaling regimes depending upon the Mach number. At low Mach numbers, the departure of all stress and heat-flux components depends only upon the Knudsen number. At high Mach number, the scaling of shear stress and transverse heat flux depends on the product of the Knudsen and Mach numbers. The normal stresses depend individually on the Knudsen and Mach number. The scaling results are verified against numerical simulations of compressible mixing layers performed using the unified gas kinetic scheme for various degrees of rarefaction.

Magnetic fields in multiphase turbulence: impact on dynamics and structure

ABSTRACT Both multiphase gas and magnetic fields are ubiquitous in astrophysics. However, the influence of magnetic fields on mixing of the different phases is still largely unexplored. In this study, we use both turbulent radiative mixing layer (TRML) and turbulent box simulations to examine the effects of magnetic fields on cold gas growth rates, survival, and the morphology of the multiphase gas. Our findings indicate that, in general, magnetic fields suppress mixing in TRMLs, while turbulent box simulations show comparatively marginal differences in growth rates and survival of the cold gas. We reconcile these two seemingly contrasting results by demonstrating that similar turbulent properties result in comparable mixing, regardless of the presence or absence of magnetic fields. We, furthermore, find the cold gas clump size distribution to be independent of the magnetic fields, but the clumps are more filamentary in the MHD case. Synthetic Mg ii absorption lines support this picture being marginally different with and without magnetic fields; both cases align well with observations. We also examine the magnetic field strength and structure in turbulent boxes. We generally observe a higher mean magnetic field in the cold gas phase due to flux freezing and reveal fractal-like magnetic field lines in a turbulent environment.

Simulations of weakly magnetized turbulent mixing layers

ABSTRACT Radiative turbulent mixing layers (TMLs) are expected to form pervasively at the phase boundaries in multiphase astrophysical systems. This inherently small-scale structure is dynamically crucial because it directly regulates the mass, momentum, and energy exchanges between adjacent phases. Previous studies on hydrodynamic TMLs have revealed the interactions between cold and hot phases in the context of the circumgalactic medium, offering important insight into the fate of cold clouds traveling through hot galactic winds. However, the role of magnetic field has only been sparsely investigated. We perform a series of 3D magnetohydrodynamics simulations of such mixing layers in the presence of weak to modest background magnetic field. We find that due to field amplification, even relatively weak background magnetic fields can significantly reduce the surface brightness and inflow velocity of the hot gas in the mixing layer. This reduction is attributed to a combination of magnetic pressure support and direct suppression of turbulent mixing, both of which alter the phase structures. Our results are largely independent of thermal conduction and converged with resolution, offering insights on the survival of cold gas in multiphase systems.

The Impact of Cold-Air Outbreaks and Oceanic Lateral Fluxes on Dense-Water Formation in the Greenland Sea from a 10-Year Moored Record (1999–2009)

Abstract The Greenland Sea produces a significant portion of the dense water from the Nordic seas that supplies the lower limb of the Atlantic meridional overturning circulation. Here, we use a continuous 10-yr hydrographic record from moored profilers to examine dense-water formation in the central Greenland Sea between 1999 and 2009. Of primary importance for dense-water formation is air–sea heat exchange, and 60%–80% of the heat lost to the atmosphere during winter occurs during intense, short-lived events called cold-air outbreaks (CAOs). The long duration and high temporal resolution of the moored record has for the first time facilitated a statistical quantification of the direct impact of CAOs on the wintertime mixed layer in the Greenland Sea. The mixed layer development can be divided into two phases: a cooling phase and a deepening phase. During the cooling phase (typically between November and January), CAOs cooled the mixed layer by up to 0.08 K day−1, depending on the intensity of the events, while the mixed layer depth remained nearly constant. Later in winter (February–April), heat fluxes during CAOs primarily led to mixed layer deepening of up to 38 m day−1. Considerable variability was observed in the mixed layer response, indicating that lateral fluxes of heat and salt were also important. The magnitude and vertical distributions of these fluxes were quantified, and idealized mixed layer simulations suggest that their combined effect is a reduction in the mixed layer depth at the end of winter of up to several hundred meters.

DNS predictions of NOx production in developing turbulent mixing layers with non-premixed hydrogen–air combustion

ABSTRACT Direct numerical simulations of three-dimensional compressible mixing layers with non-premixed hydrogen–air combustion were performed using a detailed chemical reaction mechanism with production. Flow fields with three types of initial disturbances were simulated to investigate the relationship between developing vortical structures and formation. The amounts of and produced in the simple shear layer were smaller than those in the two- and three-dimensional mixing layers with vortical structures. In the mixing layers, the formation and expansion of the combustion region by the roller vortices and the baroclinic torque had a significant impact on production, while the relatively low-temperature combustion region formed by the three-dimensional developed rib vortices in the blade regions between the roller vortices had a large effect on the production. It was found that a two-dimensional simulation can estimate the production, while the information on a three-dimensional mixing layer is necessary to predict the production.

Study on post-processing method of supersonic mixing layer simulation results based on streamline tracking

On the time-average, the direction of the mixing layer midline remains essentially the same, with rich conclusions under the Cartesian coordinate system (CCS). However, the static pressure mismatch state of the jet leads to a strong coupling effect of expansion and compression in the mixing process. This causes the midline of the mixing layer to become irregularly curved in shape. It is not convenient to describe with fixed CCS anymore. Therefore, a post-processing method of the flow field is proposed based on streamline tracing using the Lagrangian viewpoint to establish a coordinate system for mixing layer evaluation based on the streamline as the coordinate axis, which is called the Followed Body Coordinate System (FBCS) in this study. The following conclusions are obtained for the velocity thickness, momentum thickness, and Pitot pressure thickness treated by FBCS, and they are in good agreement with each other. In addition, the correction of Pitot pressure thickness after two methods of processing is less than 0.08, and the scalar thickness is insensitive to the choice of coordinate system. The consistency of the corrected velocity thickness and momentum thickness is significantly enhanced. This is due to the fact that the processing in FBCS significantly reduces the effects of airflow velocity and density variations caused by flow expansion and compression. The problem of inaccurate vector thickness evaluation in this state is improved.

Direct numerical simulations of auto-igniting mixing layers in ammonia and ammonia-hydrogen combustion under engine-relevant conditions

This study investigated auto-ignition characteristics of ammonia-air and ammonia-hydrogen-air laminar and turbulent mixing layers by means of direct numerical simulations (DNS) under elevated pressure conditions. The results show that elevated pressure and hydrogen addition accelerate the auto-ignition process, reducing the auto-ignition delay time. Analysis of the heat release rate revealed that the first peak of the heat release rate corresponds to the increment of appearance in temperature (induction stage) and the second peak of the heat release rate corresponds to the steady maximum temperature regime (thermal runaway stage). The results found that both induction and thermal runaway stages are affected by turbulence for pure ammonia-air mixing layers, while only the thermal runaway stage is affected by turbulence for ammonia-hydrogen-air mixing layers. The auto-ignition occurs along the most reactive mixture fraction with lower scalar dissipation rate, being further reduced by elevated pressure and hydrogen addition. Three radicals (NH2, OH, HNO) distinguish the entire auto-ignition process very well for all cases.

Enhancement of thermal mixing under supercritical condition by increasing shear rate

The dynamical characteristics of the shear-driven mixing layer can be inhibited due to the variations in fluid density. In this work we expect to address this issue by increasing shear rate. Direct numerical simulations of mixing layer between two streams with different temperatures at supercritical pressure are conducted. We confirm that the turbulent characteristics of mixing layer are inhibited with increasing density ratio between the lower and upper streams, resulting in the destruction of large-scale vortex, especially at the high-density side. By increasing the velocity ratio between the two streams, however, the mixing performance is enhanced with regeneration of the hairpin vortex due to increase in mean shear. The enstrophy production thus increases due to enhancement of vortex stretching and the thermal mixing efficiency is enhanced due to the entrainment of vortical structures. Further, the streamwise spectra of the temperature fluctuations follow a slope of −3 in the viscous-diffusive range.

Radiative Turbulent Mixing Layers and the Survival of Magellanic Debris

The Magellanic Stream is sculpted by its infall through the Milky Way’s circumgalactic medium, but the rates and directions of mass, momentum, and energy exchange through the stream-halo interface are relative unknowns critical for determining the origin and fate of the Stream. Complementary to large-scale simulations of LMC-SMC interactions, we apply new insights derived from idealized, high-resolution cloud-crushing and radiative turbulent mixing layer simulations to the Leading Arm and Trailing Stream. Contrary to classical expectations of fast cloud breakup, we predict that the Leading Arm and much of the Trailing Stream should be surviving infall and even gaining mass due to strong radiative cooling. Provided a sufficiently supersonic tidal swing-out from the Clouds, the present-day Leading Arm could be a series of high-density clumps in the cooling tail behind the progenitor cloud. We back up our analytic framework with a suite of converged wind-tunnel simulations, finding that previous results on cloud survival and mass growth can be extended to high Mach number () flows with a modified drag time and longer growth time. We also simulate the Trailing Stream; we find that the growth time is long (approximately gigayears) compared to the infall time, and approximate Hα emission is low on average (∼ a few milliRayleigh) but can be up to tens of milliRayleigh in bright spots. Our findings also have broader extragalactic implications, e.g., galactic winds, which we discuss.

Large eddy simulation of supersonic mixing layers using a compressible filtered mass density function method

To verify the applicability and superiority of the compressible filtered mass density function method in real supersonic mixing flows, a classical experimental subsonic-supersonic spatial mixing layer is numerically investigated. In the present method, a transport equation for the scalar filtered mass density function is solved using the Lagrangian particle solver, while the filtered mass, momentum, and energy equations are fully coupled and solved by the large eddy simulation finite difference solver. First, a parametric study of the mixing model constant controlling the scalar mixing rate is conducted in the two-dimensional case. It is found that the mixing model constant has a significant effect on the root mean square profile of the mixture fraction. The appropriate mixing model constant for this supersonic mixing layer is given by comparing the root mean square results under three different mixing model constants. These results also show that the suitable mixing model constant used in compressible flows is much larger than that used in incompressible flows. Second, three-dimensional simulations are performed to verify the current method. For comparison, a traditional large eddy simulation with the gradient diffusion model is also conducted. The results show that the scalar mixing is better predicted by the filtered mass density function method than the gradient diffusion model. In particular, the mean and root mean square mixture fraction computed by the present method are in excellent agreement with the experimental data whereas the gradient diffusion model overestimates the peak root mean square mixture fraction by about 45%.

A methodology for modeling the interaction between turbulence and non-linearity of the equation of state

Computational fluid dynamics simulation of turbulent mixing layers with significant density variations may require a closure model for the interaction between the unresolved turbulence scales and the equation of state (EoS). Ideal gas flows with significant temperature variations and real gas flows near the critical pressure and temperature undergo non-linear density variations. Therefore, using the first moment closure to obtain the mean/filtered density field from the EoS in a pressure-based computational fluid dynamics approach may result in significant modeling errors. In this work, a methodology is formulated to determine whether or not a closure model is required in the context of low-Mach number mixing layers. The methodology is based on a presumed probability density function closure modeling approach to develop a regime diagram in terms of four non-dimensional variables: reduced pressure, normalized lower temperature, temperature ratio across the mixing layer, and normalized variance of temperature fluctuations. The regime diagram clearly outlines conditions requiring no closure model and is approximately universal for different working fluids in a mixing layer. A posteriori simulations of a turbulent jet flow at different thermodynamic conditions show that the regime diagram effectively determines the necessity of closure modeling for density.

On shear layer atomization within closed channels: Numerical simulations of a cough-replicating experiment

Aerosol generation during coughing and sneezing has gained major relevance due to the current COVID pandemic. The atomization involved in this process takes place in the complex context of the respiratory system and develops very rapidly. In order to get further insights on the early spray generation, we introduce a simplified model of physiological coughing or sneezing, in the form of a thin liquid layer subject to a rapid (30 m/s) air stream. The setup is simulated using the Volume-Of-Fluid method with octree mesh adaptation, the latter allowing grid sizes small enough to capture the Kolmogorov length scale. The results confirm the trend to an intermediate distribution between a Log-Normal and a Pareto distribution P(d)∝d−3.3 for the distribution of droplet sizes in agreement with a previous re-analysis of experimental results by one of the authors. The mechanism of atomization does not differ qualitatively from the multiphase mixing layer experiments and simulations. No mechanism for a bimodal distribution, also sometimes observed, is evidenced in these simulations.

Self-consistent, high-order spatial profiles in a model for two-fluid turbulent mixing.

A Reynolds-averaged Navier-Stokes model is presented with the property that it admits self-consistent, high-order spatial profiles in simulations of two-fluid turbulent mixing layers. Whereas previous models have been limited by the assumption of a linear mixing profile, the present paper relaxes this assumption and, as a result, is shown to achieve much better agreement with experimental profiles. Similarity analysis is presented to derive constraints on model coefficients to enforce desired self-similar growth rates that are fully consistent with the high-order spatial profiles. Through this similarity analysis, it is shown that care must be taken in model construction, as it is possible to construct certain terms in such a way as to leave growth rates unconstrained. This model, termed the k-ϕ-L-a-V model, is then applied in simulations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz mixing layers. These simulations confirm that the expected growth parameters are recovered and high-order spatial profiles are maintained.

Direct numerical simulations of temporal compressible mixing layers in a Bethe–Zel'dovich–Thompson dense gas: influence of the convective Mach number

Abstract

Numerical investigation of the effect of rotation on non-premixed hydrogen combustion in developing turbulent mixing layers

This study was aimed at examining the influence of the system rotation as an external action on the development of vortical structures and combustion. Specifically, three-dimensional direct numerical simulations of compressible mixing layers with non-premixed /air combustion were performed using a detailed chemical reaction scheme. The relationship between the developing vortical structures and chemical reactions in the flow field with the rotation was investigated. The development of combustion changed depending on the vortical structures, and the presence of roller vortices promoted the combustion phenomena. The influence of the vortical structures on the elementary reactions, which contribute to the heat release rate, was small. During the anticyclonic rotation, the roller vortices collapsed and suppressed the combustion. In contrast, the cyclonic rotation resulted in the generation of quasi-2D roller vortices, which enlarged the high-heat-release-rate regions and promoted the combustion. Overall, the vortical structures induced by the rotation can change the development of combustion even though the elementary reactions that contribute to the heat release rate remain unchanged. The presented findings can guide the prediction and control of turbulent combustion in practical situations involving fluid machinery.

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers.

Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the k-L-a-V Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)2470-004510.1103/PhysRevE.98.033111], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the k-L-a-V model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. It is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.