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arXiv2018

Fractal mesh refinement, rare events and type Ia supenova

Fractal mesh refinement enables mesh refinement regimes to the Gibson scale and beyond. Conventional multifractal subgrid models have cost considerations which also lead to local mesh refinement, but more importantly, the application of these models to compressible turbulent deflagration fronts is a topic for future research, while subgrid models tuned to this complex physics lack a multifractal search focus, and for cost reasons do not allow the large search volumes required to find the sought for rare event to trigger a DDT. Here we propose methods to resolve fine scales and locate rare possible DDT trigger events within large volumes while addressing multifractal issues at a feasible computational cost. We are motivated by the goal of confirming or assessing the hypothesis of a delayed detonation in type Ia supernova and to assessing the delay in this event if it is found to occur.

physics.comp-ph↗

arXiv2018

Stability of boundary layer flow based on energy gradient theory

The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

physics.flu-dyn↗

arXiv2018

Global instability of wing shock buffet

Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. The question of global instability leading to flow unsteadiness is addressed herein. It is shown for the first time that incipient three-dimensional shock buffet is governed by the dynamics of a single unstable linear eigenmode with its spatial structure describing previously reported buffet cells. An inner-outer Krylov approach is proposed to solve the arising large-scale eigenvalue problem iteratively using shift-and-invert spectral transformation and sparse iterative linear solver. The established numerical strategy with an industrial flow solver means that a practical non-canonical test case at high-$Re$ flow condition can be investigated. A modern wing design with publicly available geometry and experimental data for code validation is studied. The numerical findings can be exploited for routes to flow control and model reduction.

physics.flu-dyn↗

arXiv2018

Effect of secondary swirl in supersonic gas and plasma flows in self-vacuuming vortex tube

This article presents the results of simulation for a special type of vortex tubes - self-vacuuming vortex tube (SVVT), for which extreme values of temperature separation and vacuum are realized. The main results of this study are the flow structure in the SVVT and energy loss estimations on oblique shock waves, gas friction, instant expansion and organization of vortex bundles in SVVT.

physics.flu-dyn↗

arXiv2018

A systematic study of turbulent heat transfer over rough walls

Direct Numerical Simulations are used to solve turbulent flow and heat transfer over a variety of rough walls in a channel. The wall geometries are exactly resolved in the simulations. The aim is to understand the effect of roughness morphology and its scaling on the augmentation of heat transfer relative to that of skin friction. A number of realistic rough surface maps obtained from the scanning of gas turbine blades and internal combustion engines as well as several artificially generated rough surfaces are examined. In the first part of the paper, effects of statistical surface properties, namely surface slope and roughness density, at constant roughness height are systematically investigated, and it is shown that Reynolds analogy factor (two times Stanton number divided by skin friction coefficient) varies meaningfully but moderately with the surface parameters except for the case with extremely low slope or density where the Reynolds analogy factor grows significantly and tends to that of a smooth wall. In the second part of the paper, the roughness height is varied (independently in both inner and outer units) while the geometrical similarity is maintained. Considering all the simulated cases, it is concluded that Reynolds analogy factor correlates fairly well with the equivalent sand roughness scaled in inner units and asymptotically tends to a plateau.

physics.flu-dyn↗

arXiv2018

Input-output analysis of Mach 0.9 jet noise

We examine amplifying behavior of small perturbations about Reynolds-averaged Navier-Stokes solutions (RANS) of a $M_j = 0.9$ subsonic turbulent jet using input-output (I/O) analysis. Singular value decomposition (SVD) of the resolvent of the linearized Navier-Stokes (LNS) equations forms an orthonormal set of I/O mode pairs, sorted in descending order by the magnitude of the corresponding singular values. In this study we design a filter to restrict input forcings to be active only in regions where turbulent kinetic energy (TKE) of jet turbulence is high. For an output domain, we directly implement the Ffowcs Williams-Hawkings (FWH) method within I/O analysis framework to measure far-field sound of observers distributed along an arc. In this way we find that the resulting TKE-weighted input modes captures coherent structures in the near-field of turbulent jets. Optimal input modes correspond to wavepackets represented by asymmetric pseudo-Gaussian envelope functions at a given forcing frequency. These wavepackets remain similar in shape over a range of frequencies for $St > 0.5$, and scale as $St^{-0.5}$. While the optimal mode is a wavepacket, sub-optimal modes represent decoherence of the optimal input mode. By projecting high-fidelity large eddy simulation (LES) data onto the basis of input modes, we find that input modes do indeed capture the acoustically relevant dynamics in the jet. The far-field acoustics predicted by the LES are recovered using only a few number of I/O modes.

physics.flu-dyn↗

arXiv2018

Second Newtonian branch of salt-free aqueous xanthan solutions

We study aqueous xanthan solutions at shear rates up to about 105 s-1. At these shear rates, the salt-free solutions show a second Newtonian branch. Depending on the xanthan concentration, we find two different regimes with scaling laws well-known for the zero viscosity of dilute and semidilute particle solutions: The crossover concentration is considerably higher than in the first Newtonian branch, which can be related to the orientation of the polyelectrolytes. In the second regime, the normal stress differences increase with an exponent of about 1, indicating that the polymer solution behaves like nematic liquid crystals or rigid fiber suspensions. In the first regime, the exponent is smaller suggesting that the polyelectrolytes behave more flexible

physics.flu-dyn↗

arXiv2018

On the Rheology of Newtonian Single-Phase Multicomponent Mixtures

In the turbulent boundary layer of multicomponent fluid mixtures, the species-specific mass flux is determined by the combination of turbulent-diffusiophoretic diffusion and diffusion due to gradients in supplementary fields (e.g. temperature). For inert mixtures, a balance must exist between all the diffusive transport mechanisms so that the net diffusive mass flux normal to the wall is zero everywhere. This may require non-constant composition profiles. Implications are discussed, and mathematical modelling is employed to demonstrate how this may affect fluid property profiles, wall heat flux, and wall shear stress in a Newtonian ternary gas mixture ($H_2 + N_2 + CO_2$) subject to a temperature gradient.

physics.flu-dyn↗

arXiv2018

Local Well-posedness of Strong Solutions to the Three-dimensional Compressible Primitive Equations

This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity. We also introduce the free boundary problem for the compressible primitive equations.

math.AP↗

arXiv2018

Early Transient Period in the Evolution of the Area of a Passive Front Propagating in a Strong Turbulence

Influence of statistically stationary, homogeneous, and isotropic turbulence on the mean area of a passive self-propagating front and, hence, on the rate of fluid consumption by the front is analysed in the case of asymptotically high turbulent Reynolds number $Re_L$ and asymptotically high ratio of the Kolmogorov velocity to a constant speed $u_0$ of the front. By considering an early stage of the front evolution, the mean (over the studied early stage) front area and consumption velocity $\bar{u}_T$ are analytically determined. The analysis shows that the mean $\bar{u}_T$ is proportional to the rms turbulent velocity, which characterizes large-scale turbulent eddies, even if the instantaneous rate of an increase in the front area is mainly controlled by the smallest Kolmogorov eddies. A straightforward dependence of the mean area or $\bar{u}_T$ on the Kolmogorov velocity, length, and time scales vanishes due to the following physical mechanism. At high $Re_L$, turbulent stretching created by small-scale eddies increases the front area exponentially with time, whereas a volume bounded by the leading and trailing edges of the front grows significantly slower. Therefore, after a short time, the volume is tightly filled by the front and the mean distance between opposed front elements becomes small with respect to Kolmogorov length scale. Subsequently, such front elements collide, thus, reducing the front area and limiting the mean $\bar{u}_T$.

physics.flu-dyn↗

arXiv2018

Instabilities of MHD flows driven by traveling magnetic fields

The flow of an electrically conducting fluid driven by a traveling magnetic field imposed at the endcaps of a cylindrical annulus is numerically studied. At sufficiently large magnetic Reynolds number, the system undergoes a transition from synchronism with the traveling field to a stalled flow, similar to the one observed in electromagnetic pumps. A new type of boundary layer is identified for such electromagnetically-driven flows, that can be understood as a combination of Hartmann and Shercliff layers generated by the spatio-temporal variations of the magnetic field imposed at the boundaries. An energy budget calculation shows that energy dissipation mostly occurs within these boundary layers and we observe that the ohmic dissipation Db always overcomes the viscous dissipation Dv, suggesting the existence of an upper bound for the efficiency of electromagnetic pumps. Finally, we show that the destabilization of the flow occurs when both dissipations are nearly equal.

physics.flu-dyn↗

arXiv2018

An a priori analysis of a DNS database of turbulent lean premixed methane flames for LES with finite-rate chemistry

An a priori analysis of a DNS database of turbulent lean premixed methane flames is presented considering the relative effects of turbulence and LES filtering, along with a potential modelling approach for LES with finite-rate chemistry. The leading-order effect was found to be due to the filter operation; flame response to turbulence was a secondary effect, and manifested primarily as an increase in standard deviations about conditional means. It was found that the radicals O, H and OH were less impacted by the filter than other high-temperature radicals, which were significantly reduced in magnitude by the filter. By considering reaction path diagrams, key reactions have been identified that are responsible for disparities between the desired filtered reaction rates and the reaction rates evaluated using quantities available in LES calculations (i.e. the filtered species and temperature). More specifically, the hydrogen abstraction reactions that take CH4 to CH3 (by O, H and OH) were found to have particularly enhanced reaction rates, and dominate the reaction path. Under the conditions presented, reaction paths were found to be independent of turbulence intensity. In general, the filtered reaction rates from the DNS were found to align more closely with the filtered laminar profile than the reaction rate of filtered species and temperature, (but disparities were found to decrease with increasing Karlovitz number). A simple model for scaling reaction rates is considered based on filtered laminar flame profiles, and the resulting reaction paths demonstrate proof-of-concept of a simple approach for formulating a reaction rate model for LES with finite-rate chemistry.

physics.flu-dyn↗

arXiv2018

Cascaded Lattice Boltzmann Method based on Central Moments for Axisymmetric Thermal Flows Including Swirling Effects

A cascaded lattice Boltzmann (LB) approach based on central moments and multiple relaxation times to simulate thermal convective flows, which are driven by buoyancy forces and/or swirling effects, in the cylindrical coordinate system with axial symmetry is presented. In this regard, the dynamics of the axial and radial momentum components along with the pressure are represented by means of the 2D Navier-Stokes equations with geometric mass and momentum source terms in the pseudo Cartesian form, while the evolutions of the azimuthal momentum and the temperature field are each modeled by an advection-diffusion type equation with appropriate local source terms. Based on these, cascaded LB schemes involving three distribution functions are formulated to solve for the fluid motion in the meridian plane using a D2Q9 lattice, and to solve for the azimuthal momentum and the temperature field each using a D2Q5 lattice. The geometric mass and momentum source terms for the flow fields and the energy source term for the temperature field are included using a new symmetric operator splitting technique, via pre-collision and post-collision source steps around the cascaded collision step for each distribution function. These result in a particularly simple and compact formulation to directly represent the effect of various geometric source terms consistently in terms of changes in the appropriate zeroth and first order moments. Simulations of several complex buoyancy-driven thermal flows and including rotational effects in cylindrical geometries using the new axisymmetric cascaded LB schemes show good agreement with prior benchmark results for the structures of the velocity and thermal fields as well as the heat transfer rates given in terms of the Nusselt numbers.

physics.flu-dyn↗

arXiv2018

Quantification of Model Uncertainty in RANS Simulations: A Review

In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier--Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.

physics.flu-dyn↗

arXiv2018

Predicting Uncertainty in Geometric Fluid Mechanics

We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable scales of fluid motion, due to unresolvable, small, rapid scales of fluid motion.

nlin.CD↗

arXiv2018

Vorticity dynamics of revolving wings: The role of planetary vortex tilting on the stability of the leading-edge vortex

This work investigated the vorticity dynamics and stability of leading-edge vortices (LEVs) in revolving wings. Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the LEV; however, the exact mechanism remains unclear. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vortex on limiting the growth of the LEV. Specifically, this mechanism states that a vertical gradient in spanwise flow can create a vertical gradient in Coriolis acceleration, which will in turn produce oppositely-signed vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the spanwise (radial) component of planetary vortex tilting (PVTr) that reorients the planetary vortex into the spanwise direction therefore creating oppositely-signed LEV vorticity. Using an in-house, immersed-boundary-method flow solver, this mechanism was investigated alongside the other vorticity dynamics for revolving wings of varying aspect ratio (AR=3, 5, and 7) and Reynolds number (Re=110, and 1400). Analyses of vorticity dynamics showed that the PVTr consistently produced oppositely-signed vorticity for all values of AR and Re investigated, although other three-dimensional phenomena play a similar but more dominant role when Re = 1400. In addition, the relative strength of the PVTr increased with increasing AR due to a decrease in the magnitude of advection. Finally, the effects of AR and Re on the vorticity dynamics and LEV stability were also investigated.

physics.flu-dyn↗

arXiv2018

Computing dynamics of thin films via large scale GPU-based simulations

We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based on the alternate direction implicit (ADI) method, with the main part of the compu- tational work carried out in the GPU computing environment. Efficient and accurate computations allow for simulations on large computational domains in three spatial dimensions (3D) and for long computational times. We apply the methods developed to the particular problem of instabilities of thin fluid films of nanoscale thickness. The large scale of the simulations minimizes the effects of boundaries, and also allows for simulating domains of the size encountered in published experiments. As an outcome, we can analyze the development of instabilities with an unprecedented level of detail. A particular focus is on analyzing the manner in which instability develops, in particular regarding differences between spinodal and nucleation types of dewetting for linearly unstable films, as well as instabilities of metastable films. Simulations in 3D allow for consideration of some recent results that were previously obtained in the 2D geometry (J. Fluid Mech. 841, 925 (2018)). Some of the new results include using Fourier transforms as well as topological invariants (Betti numbers) to distinguish the outcomes of spinodal and nucleation types of instabilities, describing in precise terms the complex processes that lead to the formation of satellite drops, as well as distinguishing the shape of the evolving film front in linearly unstable and metastable regimes. We also discuss direct comparison between simulations and available experimental results for nematic liquid crystal and polymer films.

physics.flu-dyn↗

arXiv2018

Microscopic Investigation of Vortex Breakdown in a Dividing T-Junction Flow

3D-printed microfluidic devices offer new ways to study fluid dynamics. We present the first clear visualization of vortex breakdown in a dividing T-junction flow. By individual control of the inflow and two outflows, we decouple the effects of swirl and rate of vorticity decay. We show that even slight outflow imbalances can greatly alter the structure of vortex breakdown, by creating a net pressure difference across the junction. Our results are summarized in a dimensionless phase diagram, which will guide the use of vortex breakdown in T-junctions to achieve specific flow manipulation.

physics.flu-dyn↗