Detonation initiation in a supersonic reactive flow constitutes a crucial problem in fundamental combustion research and meanwhile receives great attention in the application of detonation-based propulsion systems. In this paper, we conduct theoretical analysis on detonation initiation induced by thermal nonuniformity. The underlying mechanism for detonation initiation is attributed to the self-strengthening coupling between the reaction front and the induced shock wave. A detonation initiation factor is introduced to quantify the capability of the thermal nonuniformity in causing detonation initiation. The initiation factor changes nonmonotonically, with the temperature difference describing the thermal nonuniformity. We find that there exist three regimes of detonation initiation. A threshold temperature difference of the thermal nonuniformity below which detonation initiation cannot take place is identified. Additionally, it is found that the temperature profile of the thermal nonuniformity has a substantial impact on detonation initiation. The creation of an additional induced shock wave on the reaction front due to the downward convex temperature profile significantly improves the initiation condition for weak thermal nonuniformities with relatively small temperature difference. Moreover, two-dimensional analysis is also conducted, considering the convective transport in the transverse direction. It is shown that the transverse heat transfer reduces the curvature of the reaction front, which promotes (inhibits) detonation initiation for strong (weak) thermal nonuniformity with large (small) temperature difference. In the present analysis, we provide useful insights into detonation initiation in a supersonic reactive flow.

We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a theoretical one-dimensional advection model for blood flow in microvascular networks that relies on the widely used laws for rheology and phase separation. We discuss the ramifications for microfluidic experiments and measurements using blood and implications for in vivo microcirculation. Our findings suggest that further modeling in microvascular networks should discard the usual assumption of unique, steady-state flow solutions, with crucial consequences regarding gas, nutrient, and waste transport.

The instantaneous interaction (one-way coupling) between inertial fibers and flow field in a coaxial, round water jet was investigated using planar, time-resolved particle image velocimetry at a ratio between outer and inner jet bulk velocities of $r_u=2.5$. Nylon fibers with aspect ratio of 31 were issued from the inner jet and tracked across the field of view in the downstream direction. Results indicated that translational and rotational fiber motion strongly depended on the instantaneous flow field. Close to the nozzle exit, fibers lagged the flow and were preferentially aligned with the streamwise direction. Farther downstream, mean fiber velocities exceeded those of the mean flow whereas preferential alignment was lost. Individual fiber tracks showed an abrupt change (“transition”) in velocity and orientation when interacting with the internal shear layer at different streamwise locations. Abrupt jumps in fiber velocity, orientation, rotation rates, as well as translational and rotational slip were revealed by conditionally sampling the tracks according to transition location. This was done for two groups of fibers. For fibers in the first group, transition occurred farther downstream and was less pronounced compared to those in the second group. The latter were entrained by strong toroidal vortices that rotated and propelled fibers into the fast-moving outer jet (“sling effect”). Magnitudes of rotational slip strongly increased at transition, reaching plateau values farther downstream. Local translational and rotational Stokes numbers based on fiber motion and flow field itself illustrate the complex fiber-flow interaction in this nonhomogeneous flow.

Chemical reactions in porous media play a pivotal role in various biological, environmental, and engineering applications, yet understanding flow-chemistry coupling within pores remains an outstanding challenge. This article examines a parallel between how chemical reaction fronts are impacted by (i) turbulence in unconfined flows, and (ii) hydrodynamic dispersion in porous media flows, even at laminar flow conditions. A regime diagram is constructed from which hitherto overlooked regime transitions are identified. The results are expected to improve our understanding of pore-scale coupling, with implications relevant to a broad range of applications.

We investigate the role of the correlation between a scalar quantity and the vorticity in two-dimensional mixing at infinite Péclet number. We assess, using a diffusivity-independent mixing norm, the dynamics of both Galerkin-truncated ensembles and freely evolving two-dimensional scalar mixing. Both statistical mechanics and numerical experiments show how the mixing rate is attenuated when vorticity and scalar are initially correlated. Since the vorticity is shown to be a poorly mixing scalar, the results suggest that, in general, mixing can be enhanced by minimizing the correlation between vorticity and passive scalar.

Time-resolved (TR), three-dimensional (3D) velocity fields of screeching, underexpanded jets are estimated using non-time-resolved particle image velocimetry and simultaneous TR microphone measurements. Specifically, we aim to reconstruct TR 3D velocity fluctuation fields associated with the A2, B, and C modes of a screeching jet using a linear regression model and to analyze screech dynamics of these modes. The linear regression model is constructed on the basis of a linear relationship between the velocity and acoustic fields. Three nozzle pressure ratios (NPRs) of 2.30, 2.97, and 3.40 are employed. The dominant azimuthal modes for three cases are investigated using azimuthal Fourier coefficients of the acoustic data obtained by the azimuthal array of eight microphones placed near the nozzle exit. The dominant azimuthal modes at NPRs of 2.30, 2.97, and 3.40 are $m=0$, 1, and 1, respectively. The first two proper orthogonal decomposition (POD) modes in these azimuthal modes are dominant at all NPRs and are associated with screech. 3D velocity fluctuation fields associated with screech are reconstructed from these leading POD modes of the acoustic data. The reconstructed 3D velocity fluctuation fields at NPRs of 2.97 and 3.40 exhibit two helical structures with opposite rotation directions. The present results demonstrate that, in the B mode, the flapping structure exhibits random clockwise and counterclockwise rotations over an extended time domain, while maintaining a consistent direction within short time domains. In addition, in the C mode, two helical structures with opposite rotation directions, as well as the flapping structure, are observed.

We study the influence of two mutual friction models on quantized vortices and normal fluid using two-way coupled simulations of superfluid ${}^4\mathrm{He}$. The normal fluid is affected by quantized vortices via mutual friction. A previous study [Y. Tang et al., Nat. Commun. 14, 2941 (2023)] compared the time evolutions of the vortex ring radius and determined that the self-consistent two-way coupled mutual friction (S2W) model yielded better agreement with the experimental results than the two-way coupled mutual friction (2W) model whose model parameters were determined through experiments with rotating superfluid helium. In this study, we compare the two models in more detail in terms of the quantized vortex ring propagation, reconnection, and thermal counterflow. We show that the S2W model exhibits better results than the 2W model on the microscopic scale near a quantized vortex, such as during quantized vortex ring propagation and reconnection, although the S2W model requires a higher spatial resolution. For complex flows such as a thermal counterflow, the 2W model can be applied even to a low-resolution flow while maintaining the anisotropic normal fluid velocity fluctuations. In contrast, the 2W model predicts lower normal fluid velocity fluctuations than the S2W model. The two models show probability density functions with $-3$ power-law tails for the normal fluid velocity fluctuations.

A developing turbulent boundary layer (TBL) was created using a uniform concentration of drag-reducing polymer for which the mean molecular weight was controlled and monitored throughout testing. This obtained a polymer-modified TBL with known polymer properties, including the Weissenberg number ($\text{Wi}$). The resulting mean and fluctuating velocity profiles were measured using particle image velocimetry. Polymeric tests were performed at friction Reynolds numbers (${\delta }^{+}$) ranging from 470 to 760, drag reduction (DR) levels ranging from 0% to 44%, and $\text{Wi}$ ranging from 0.2 to 13. In addition to the baseline Newtonian conditions, polymeric conditions were selected such that two had nearly the same $\text{Wi}$ with significantly different DR, and two others had the same DR with significantly different $\text{Wi}$. The mean and fluctuating velocity profiles showed $\text{Wi}$ dependence, with the suppression of wall-normal velocity fluctuations strongly dependent on $\text{Wi}$. While the streamwise velocity fluctuations (nonscaled) increased only marginally, the significant suppression in the wall-normal velocity fluctuations also indicates that this increase in anisotropic fluctuating velocity field has a $\text{Wi}$ dependence. Conditional averaging of the profiles was performed to isolate the impact of Wi on ejection and sweep events: the latter events showed suppression throughout the TBL in proportion to the $\text{Wi}$, while the former events showed similar behavior, but not as uniformly throughout the TBL. Finally, proper orthogonal decomposition was performed to quantify the reduction of complexity within the polymer-modified TBL, for which the reduction was strongly correlated with Wi, even more so than the level of DR. This indicates that the polymer chains effectively subdue specific scales (i.e., smaller scales) so that there is no longer a mere passing of energy through those scales.

The convective instability properties of a buoyant thermal boundary layer evolving along the external surface of a vertical circular cylinder are investigated with the direct stability analysis in this work. The curvature effect on flow instability is investigated in particular. To achieve this, we analyze various curvatures $A$, namely, from a flat plate ($A=0$) to a significantly curved cylinder ($A=80$). The Rayleigh number considered is from $\text{Ra}=1\times {10}^8$ to $1\times {10}^{10}$, and the Prandtl number is fixed at 7. Two types of artificial perturbations are considered, namely, a random and a single-mode perturbation. Calculation of the governing equations demonstrates that disturbances are induced by the introduced perturbations. The random perturbation calculation suggests that the boundary layer could filter disturbances for one outstanding frequency band and the single-mode perturbation calculation precisely determines the characteristic frequency $f_{\mathrm{c}}$ of the flow. The results suggest that as curvature $A$ increases, the characteristic frequency of the thermal boundary layer increases, while the amplitude of the disturbance decreases. Meanwhile, the width of the amplifying band first increases mildly and then reduces drastically with $A$. Analysis of the fluctuating velocity components indicates that the Reynolds stress of the flow is strongly amplified toward the downstream at $f_{\mathrm{c}}$ and it dramatically decreases at a decaying frequency $f_{\mathrm{c}}-3.5\mathrm{\Delta }$. It is also found that when the boundary layer is perturbed with $f_{\mathrm{c}}$, the time-averaged Reynolds stress grows exponentially with the streamwise location $y$ according to $\sim e^{8.95y-0.98}$. The results also reveal that the propagation speed of the instability wave is always larger than the flow velocity. A scale law $c_y\sim \text{Ra}{}^{1/2}{y}^{1/2}\left(1+0.024A\right)/\left(1+0.025A\right)$ is proposed for the wave propagation speed $c_y$.

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges.

Predicting extreme events in turbulent flows represents a challenge due to chaos or modeling uncertainty. This paper addresses a fundamental but unexplored limitation in extreme-event forecasting: the minimum computational cost of producing accurate forecasts. The information bottleneck method is applied to massive ensembles of Kolmogorov flow simulations to construct optimal predictive models of dissipation bursts. It is shown that, to maintain relative predictive skill, the minimum model complexity (size) and the cost of predictions increase exponentially with the forecast horizon. This limitation is connected to causal uncertainty, whereby the number of states from which an extreme event may emerge increases with the forecast horizon. It is argued that, to maintain accuracy, data-driven models need to encode theses states, increasing their size and the amount of data necessary for training.

We conduct a numerical investigation on the spreading characteristics of a liquid metal droplet impacting onto a solid substrate, specifically under the influence of a horizontal magnetic field. In such circumstances, we propose a theoretical model to predict the maximum spreading area of the droplet. In the absence of a magnetic field, available models attempting to predict the maximum spreading of an impacting droplet based on the principle of energy conservation have been proven to be unsuitable for our current context. We find that this inadequacy arises from the notably high surface tension exhibited by the liquid metal. In response, we have developed a new model that evaluates the residual kinetic energy and gives a more precise estimation of the spreading time. Our model demonstrates a remarkable congruence with our experimental and numerical results. Subsequently, we extend our inquiry to encompass the influence of the horizontal magnetic field on the droplet's spreading characteristics. We identify an anisotropic spreading behavior attributed to the nonaxisymmetric distribution of the Lorentz force. Notably, we propose a theoretical model for predicting the maximum spreading in this magnetic field scenario by incorporating the work of Lorentz force into the energy balance equation. The predictions exhibit excellent agreement with our numerical results, even if the impacting conditions are varied in a large extent of parameter space. Furthermore, we generalize this model to situations involving a vertical magnetic field, recognizing that the residual kinetic energy is no longer independent of magnetic field strength.

This paper explores the micro-macro modeling of polymeric fluids using the proposed microscopic elastic-plastic (EP) potential energy, in order to illustrate the effects of irreversible bond-breaking of microscopic polymer chains. Precisely, we first revisit the derivation of a thermodynamically consistent micro-macro model using the energy variational method. To demonstrate the model's predictions, we perform numerical simulations using a deterministic particle finite element method. Our numerical investigations reveal the behaviors of polymer chains with irreversible bond breaking at the microscale and their influence on induced shear stresses and macroscale velocities under shear flow. We also conduct numerical investigations with other classical microscopic potential energies as a comparison, including the Hookean, the FENE (finite extensible nonlinear elastic), and the modified Morse potentials, involving pure elastic, finite extension. and reversible bond breaking, respectively. We find that polymer elongation, rotation, and bond breaking contribute to differences in polymer-induced stresses and velocities in the micro-macro models. Additionally, we observe that at high shear rates, polymer rotation induces shear-thinning behavior in the micro-macro models.

We present an experimental study on the freezing of alkane drops impacted on a liquid bath. More specifically, for drops of hexadecane and tetradecane on brine, we found a morphological transition of the solid between a flat disk and a cupped shape. We show that this transition depends mainly on melting temperatures and thermal shock, and varies weakly with impact velocity. We observed that the impact dynamics do not depend on the thermal shock before the drop starts to solidify, which allows a rationalization of the solid size by models established for impact without phase change. Finally, we show that the relevant timescale setting the onset of solidification is associated with the formation of a thin solid layer between the drop and the bath, a timescale much shorter than the total solidification time. These findings offer the possibility of collapsing the data for both liquids in a single-phase diagram.

We consider the influence of a transverse magnetic field on the transient growth of perturbations in a liquid-metal circular pipe flow with an electrically insulating or conducting wall. In this configuration, the mean flow profile and the amplification of perturbations are strongly affected by the applied magnetic field, leading to a rich dynamical landscape depending on its intensity. The analysis is performed in the quasistatic limit ($Rm\to 0$) for Reynolds numbers 5000 and 10 000, close to the transitional regime for moderate values of the Hartmann number, a nondimensional parameter proportional to the applied magnetic field's intensity. Aside from a slight modification of hydrodynamic optimal perturbations at very small Hartmann numbers, we observe three other characteristic topologies of optimal perturbations depending on the intensity of the magnetic field. Their growth mechanisms differ, with the lift-up effect dominating at low Hartmann numbers and the Orr mechanism becoming increasingly important as the magnetic field intensity is increased. In particular, we show in the intermediate regime of Hartmann numbers how transient growth occurs in two stages, with initial growth through the lift-up effect followed by a further increase of energy through the Orr mechanism. We also conduct three-dimensional nonlinear simulations to track the time evolution of optimal perturbations, illustrating their nonlinear growth and eventual breakdown to a sustained turbulent state or the return of the system to a laminar state.

The drag-out problem for small Reynolds numbers ($\mathrm{Re}$) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers ($\mathrm{Ca}$), and Derjaguin's solution for large $\mathrm{Ca}$. We investigate whether these solutions are absolutely or convectively unstable, solving the Orr-Sommerfeld eigenvalue problem. We show that the Derjaguin's solution is convectively unstable for $\mathrm{Ka}<17$ and absolutely unstable for $\mathrm{Ka}\gtrsim 0.15{\mathrm{Re}}^{1.7}$ when $\mathrm{Re}>10$. For water ($\mathrm{Ka}=3400$), the LLD solution is always convectively unstable. The absolute instability is observed only when the dip-coated film is additionally fed from above.

Multiscale structures and fluid compressibility constitute intrinsic features of natural cavitation. However, incorporating these two factors into cavitation simulations remains a formidable challenge. In this work, we propose a compressible Euler-Lagrange method based on the compressible Navier-Stokes equations and a compressible Rayleigh-Plesset (R-P) equation in OpenFOAM. The transient flow field and the Eulerian vapor volumes are calculated with a large eddy simulation approach coupled with a phase transport equation. A bubble motion model along with a compressible R-P equation is solved to predict the trajectory and dynamics of dispersed bubbles. To bridge the macroscopic cavities and microscopic bubbles and consider the bubble-bubble interaction, a four-way coupling algorithm is implemented. The predicted results are validated by comparing with published experiments, and a good agreement is obtained. Further analysis of our results shows that dispersed bubbles will affect the pressure fluctuation characteristics, contributing to more pronounced content in the mid- and high-frequency bands. Additionally, the transient properties of microscopic bubbles will be influenced by the macroscopic cavity with its associated vortex structure. Furthermore, two distinct power laws for bubble size, −4/3 for small bubbles and −10/3 for large bubbles, are obtained. This aligns well with an earlier study [Liu et al., Phys. Fluids 35, 063305 (2023)] and further confirms the reliability of our bubble predictions. This work provides guidance for the setup of bubble size distributions for other numerical algorithms considering the bubble evolution in cavitating flows.

The transport properties of the plane Poiseuille flow in which a two-dimensional, nonlinearly saturated Tollmien-Schlichting wave is propagating are studied in terms of residence time distributions (RTDs). First, a method for computing RTDs in any type of open flows is developed, making use of a single trajectory over a long period of time, with a controlled level of diffusion. With this method, RTDs of this perturbed flow are computed, along with a quantitative measure of their dispersion through the mean absolute deviation. Depending on the travel distance, RTDs display two kinds of pattern. For short travel distances, a pattern of peaks and valleys is observed for long residence times, originating in regions of negative streamwise velocity produced by the wave. For longer travel distances, a large probability peak is observed at $t={\tau }_{\text{wave}}$, the time needed for the wave to travel one section downstream. This peak is attributed to the cat's eye pattern characteristic of this type of traveling wave. It is shown that the increased dispersion of the RTD is mainly due to the nonlinear correction of the mean velocity profile.

Computational models for high-pressure transcritical turbulence in wall-modeled large-eddy simulations typically rely on wall-function models to overcome the need for resolving the boundary layer structures. However, the mechanisms and models of a turbulent boundary layer at transcritical conditions remain poorly understood since the near-wall flow and heat transfer are significantly affected by the enhanced fluctuations and steep gradients in thermodynamic properties. To address this issue, we study the mechanisms of transcritical turbulent boundary layers and wall-attached models at transcritical conditions. It is shown that the real-fluid variable-property effects are associated with the coupling between the near-wall cycle and the wall-normal coherent motions in the outer layer, resulting in the amplification of turbulent energy in the outer layer and noticeable energy transfer between the logarithmic layer and the outer layer; hence, turbulence in the logarithmic layer is modulated by the outer layer. Based on this underlying physical principle, we propose the characteristic velocity and length scales for the attached eddy at transcritical conditions, and extend the attached eddy model to transcritical turbulent boundary layers by introducing a mixed scaling that incorporates both inner and outer scalings. We show that the characteristic scales and extended attached eddy model perform well in characterizing the structures in transcritical turbulent boundary layers.

In this paper, we experimentally investigate the impact of a submillimetric water jet on a horizontal surface heated well above the “static” Leidenfrost temperature of water. We observe the transition from a regime where a single drop grows at the impingement point to a regime of spray formation. The main control parameter appears to be the jet Weber number ($\mathrm{We}$). The first regime persists until $\mathrm{We}\lesssim 30$ whereas the spray formation occurs for $\mathrm{We}\gtrsim 40$. Surprisingly, we found no influence of the hot plate's temperature on the reported phenomena. We particularly focus on the second regime, where the liquid jet spreads on the plate, forming a liquid sheet that eventually lifts off and breaks into droplets. We characterized this regime by the radius $r_c$ of the liquid sheet when it is still in contact with the plate and the angle of ejection $\theta$ of the droplets. We further examine the ejected droplets by characterizing their speed and sizes. Simple models are proposed to predict the dependencies and order of magnitudes of $r_c$ and $\theta$ through the establishment of scaling laws. We also aim to predict the critical Weber number at which the transition between the two regimes occurs. Our models show reasonable agreement with our experimental data. Finally, we compare the energy transferred from the jet to the droplets with results reported in the literature for impacts on unheated surfaces, finding a difference of nearly a factor of 2.