Transition Front Research Articles

Phase separation in swelling and deswelling hydrogels with a free boundary.

We present a full kinetic model of a hydrogel that undergoes phase separation during swelling and deswelling. The model accounts for the interfacial energy of coexisting phases, finite strain of the polymer network, and solvent transport across free boundaries. For the geometry of an initially dry layer bonded to a rigid substrate, the model predicts that forcing solvent into the gel at a fixed rate can induce a volume phase transition, which gives rise to coexisting phases with different degrees of swelling, in systems where this cannot occur in the free-swelling case. While a nonzero shear modulus assists in the propagation of the transition front separating these phases in the driven-swelling case, increasing it beyond a critical threshold suppresses its formation. Quenching a swollen hydrogel induces spinodal decomposition, which produces several highly localized, highly swollen phases which coarsen and are then ejected from free boundary. The wealth of dynamic scenarios of this system is discussed using phase-plane analysis and numerical solutions in a one-dimensional setting.

Experimental investigation of boundary layer transition over a delta wing at Mach number 6

An experimental study on the boundary layer transition over a delta wing was carried out at Mach number 6 in a quiet wind tunnel. The Nano-tracer-based Planar Laser Scattering (NPLS) and Temperature-Sensitive Paints (TSP) techniques were used to measure the fine flow field structure and the wall Stanton number of the delta wing. The influence of factors such as the angle of attack and the Reynolds number was studied. The following results were obtained. The boundary layer transition between the leading edge and the centerline was dominated by the crossflow instability. At the location of the initial appearance of the traveling crossflow waves, the Stanton number began to rise. The Stanton number reached a maximum when the crossflow waves were broken up to turbulence. Increasing the angle of attack increased the spanwise pressure gradient at the windward side of the delta wing, thereby increasing the crossflow instability and advancing the boundary layer transition front. However, increasing the angle of attack caused the transition front to move backward at the leeward side. In addition, the sensitivity of the boundary layer transition to the Reynolds number varied with the angle of attack and the region.

Critical Evolution of Finite Perturbations of a Water Evaporation Surface in Porous Media

It is shown that the approximate steady-state solutions, which satisfy the model dissipative equation that describes the process of water evaporation in the neighborhood of the instability threshold of a phase transition interface, determine localized damped finite-amplitude perturbations when a certain condition is fulfilled. These steady-state solutions can be used for forecasting the scenario of the development of a perturbation with sufficient accuracy if this perturbation has no common points with any steady-state solution. If the initial position of the phase transition front is located between the spectrally stable solution and any of the steady-state solutions, this front damps. If the initial position of the front is located above at least one of the spectrally unstable steady-state solutions, then the solution is catastrophically restructured.

Natural Convection in Water-Saturated Rock Mass under Artificial Freezing

The authors study theoretically the non-isometric natural convection of pore water in rock mass subjected to artificial ground freezing. The mathematical model is developed for a permeable water-saturated layer of rocks under artificial freezing. The model assumptions allowed transition to a two-dimension axially symmetric model. The numerical computation gives critical Rayleigh number values such that natural convection of pore water has a significant influence on temperature and position of phase transition front. Three possible convection regimes of pore water are determined as function of alternating-sign ability of thermal expansion factor.

On the mean speed of bistable transition fronts in unbounded domains

This paper is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior domains we show that all transition fronts propagate with the same global mean speed, which turns out to be equal to the uniquely defined planar speed. In domains with multiple cylindrical branches, we show that the solutions emanating from some branches and propagating completely are transition fronts propagating with the unique planar speed. We also give some geometrical and scaling conditions on the domain, either exterior or with multiple cylindrical branches, which guarantee that any transition front has a global mean speed.

V-shaped fronts around an obstacle

In this paper, we investigate V-shaped fronts around an obstacle K. We first prove that there exist solutions emanating from any homogeneous transition front including V-shaped front for exterior domains $$\varOmega ={\mathbb {R}}^N{\setminus } K$$. By providing the complete propagation of the V-shaped front, we prove that the V-shaped front can recover after passing the obstacle.

Advanced infrared thermography data analysis for unsteady boundary layer transition detection

Advanced data processing methods for detecting unsteady boundary layer transition in periodic aerodynamic processes by means of infrared thermography measurements are presented. The thermal radiation emitted from the heated suction surface of a pitching airfoil model in subsonic flow is measured with an infrared camera. The unsteady boundary layer transition location is detected by analyzing the difference in the infrared radiation signal over short periods of time with differential infrared thermography (DIT). The DIT method is optimized and automated in the present study, which facilitates the extension of the part of the motion period where valid DIT transition measurements are produced. Additionally, a new infrared thermography data processing method is introduced in this study. The extraction of the extrema of the measured radiation signal at fixed locations on the model surface yields instants of the motion period that relate to the occurrence of boundary layer transition. The local infrared thermography (LIT) approach can be extended to measuring the two-dimensional unsteady boundary layer transition front.

X-FEM: An efficient algorithm for simulation of phase transition during prostate cryosurgery

Cryosurgery is a surgical technique to ablate abnormal tumor tissues with the help of extreme cold using cryogens such as liquid nitrogen, solid carbon dioxide, argon etc. This therapy may be used as a primary treatment for early prostate cancers effectively. During the process of freezing in cryosurgery, a phase transition occurs between the frozen tumor tissues and unfrozen surrounding tissues. The present study aims to showcase the efficiency of fixed grid X-FEM to numerically simulate the evolving phase transition front with time which further illustrates location & dimensions of ice ball generated after freezing. It has been observed that X-FEM with a fixed mesh is capable to capture phase transitions front and temperature fields accurately while traditional form of FEM requires adaptive re-meshing at each time step. From physician point of view, obtained temperature fields are really important to decide the extent of freezing, location of different cryoprobes, and numbers of cryoprobes to be used for a successful treatment.

Existence, uniqueness and stability of transition fronts of non-local equations in time heterogeneous bistable media

The present paper is devoted to the study of the existence, the uniqueness and the stability of transition fronts of non-local dispersal equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space non-increasing transition fronts and prove various important qualitative properties, including uniform steepness, stability, uniform stability and exponential decaying estimates. Then, we show that any transition front, after certain space shift, coincides with a space non-increasing transition front (if it exists), which implies the uniqueness, up-to-space shifts and monotonicity of transition fronts provided that a space non-increasing transition front exists. Moreover, we show that a transition front must be a periodic travelling front in periodic media and asymptotic speeds of transition fronts exist in uniquely ergodic media. Finally, we prove the existence of space non-increasing transition fronts, whose proof does not need the unbalanced condition.

Analytical solution of the problem of hydrate formation in a porous medium with a temperature jump at the phase transition front

The results of theoretical study of the methane hydrate formation during the hydrocarbon gas injection into a porous reservoir initially saturated with methane and water are presented. In the axisymmetric approximation, mathematical model with a stepwise temperature distribution in the reservoir is considered. For this case, an approximate analytical solution is constructed with a temperature jump at the gas hydrate formation front in the form of an explicit functional dependence of the self-similar coordinate of this boundary on the parameters of a porous medium and an injected gas.

Stochastic traveling waves of a stochastic Fisher–KPP equation and bifurcations for asymptotic behaviors

In this paper, traveling wave for a Fisher–KPP equation with stochastic advection and stochastic environmental capacity is investigated. Some conditions are imposed on the reaction rate and noise intensities such that the stochastic transition front exists. Following the results on stochastic transition front, the existence of stochastic traveling waves for the equation is established. Explicit relation between the wave speed and noise attributes including noise intensities and correlation is shown, which can realize the noise effects. It is found that noises reduce the wave speed. In addition, the positive correlation of noises may complement this reduction in a way. But the negative correlation of noises will further aggravate this reduction. There exists a threshold value on the noise correlation making the traveling wave wandering. If the correlation is larger than this threshold value, the wave travels with a forward tendency. Otherwise, the wave travels with a backward tendency. Bifurcations for asymptotic behaviors of the equation induced by the noise intensities and correlation are presented.

Transport dynamics of charged colloidal particles during directional drying of suspensions in a confined microchannel.

Directional drying of colloidal suspensions, experimentally observed to exhibit mechanical instabilities, is a nonequilibrium procedure that is susceptible to geometric confinement and the properties of colloidal particles. Here, we develop an advection-diffusion model to characterize the transport dynamics for unidirectional drying of a suspension consisting of charged particles in a confined Hele-Shaw cell. We consider the electrostatic interactions by means of the Poisson-Boltzmann cell approach with the viscous flow confined to the cell. By solving the nonequilibrium transport equations, we clarify how the multiple parameters, such as drying rate, confinement ratio, and the monovalent slat concentration, affect the transport dynamics of charged colloidal particles. We find that the drying front recedes into the cell with linear behavior, while the liquid-solid transition front recedes with power law behaviors. The faster evaporation rate creates a rapid formation of the drying front and produces a thinner transition layer. We show that confinement is equivalent to raising the effective concentration in the cell, and, accordingly, the drying front appears earlier and grows more rapidly. Under geometric confinement, a longer fully dried film is created while the total drying time is shortened. Moreover, we have theoretically illustrated that low salt loadings cause a large collective diffusivity of charged colloidal particles, which results in a colloidal network by aggregation. Thus, the drying behavior alters dramatically as salt loadings decrease, since the resulting compacted clusters of charged particles eventually convert the suspension into a gel-like material instead of a simple fluid. Our model is consistent with the current experiments and provides a simple insight for applications in directional solidification and microfluidics.

Experimental and numerical study of wing boundary layer behavior in propeller flowfield

In this research, the effects of propeller slipstream on wing boundary layer and transition front were studied through wind tunnel tests and numerical analysis. In this respect, the flow around a NACA 6-series airfoil section was simulated in a computational fluid dynamics solver without and with propeller flowfield. The numerical study, presented in this paper, was concerned with the effect of propeller slipstream on both wing aerodynamics and boundary layer treatment. For experimental tests, oil flow visualization technique was used to determine laminar to turbulent transition location, laminar separation bubble with turbulent reattachment and turbulent separation line over the wing surfaces. Existence of propeller slipstream changed pressure and skin friction distribution over the wing surfaces, in both chordwise and spanwise directions and it hence affected on the wing loading distribution. Also upstream propeller affected on boundary layer characteristics including laminar/turbulent transition onset and separation over the wing. The results showed that the transition location moved toward the leading edge, and the separation bubble was washed out due to propeller slipstream.

Heat-flux measurements on a hypersonic inlet ramp using fast-response temperature-sensitive paint

Global heat-flux measurements are performed using a newly developed temperature-sensitive paint (TSP) on an inclined ramp with sidewalls in a hypersonic shock tunnel. The paint response and image acquisition rate are sufficiently fast to allow flow phenomena on timescales of around $$100\,\upmu \mathrm{{s}}$$ to be resolved. Although a priori calibration of the new TSP proves inaccurate, in situ calibration allows the recovery of heat fluxes that agree well with embedded thermocouple measurements on both short and long timescales. At low unit Reynolds numbers, the flow on the main ramp surface is entirely laminar, but transition occurs in the corner-flow regions, causing a turbulent region to spread inwards from each sidewall and producing weak, unsteady features in the heat-flux distribution of the main laminar region. Within this laminar region, roughly steady streamwise streaks with a period of approximately ten times the boundary-layer thickness are also observed. At higher unit Reynolds numbers, the boundary layer on the main ramp surface transitions to turbulence. The fast-response TSP allows tracking of the time-resolved transition front: significant unsteadiness is observed, which appears to be only weakly correlated to unsteadiness in the freestream flow conditions. Based on the heat-flux signature in the transition region, the breakdown mechanism seems to be quite different from that observed in earlier measurements on a slender cone at similar conditions.

Effects of Attitude on HIFiRE-5b Boundary-Layer Transition

HIFiRE-5 is a hypersonic flight-test experiment designed to investigate the aerothermodynamics of a three-dimensional geometry. The vehicle is an elliptic cone with a 2:1 aspect ratio and 2.5 mm nose radius. The HIFiRE-5b achieved a Mach number of 7.7 to 7.9 and freestream unit Reynolds number of to during descent. Heat flux was calculated from thermocouple pairs, and boundary-layer transition locations were identified from these heating rates. A multilobed transition front was observed; it is suspected that a different mechanism is responsible for each of these lobes. The first round of flight-test data analysis did not control for attitude variation, resulting in oscillating heat-flux rates. The current work subsamples the data based on angle of attack and yaw, enabling a more precise investigation of other relevant variables. Regions of the flowfield especially sensitive to attitude variation can be better analyzed. The heating rate at the leading edge exhibits the expected dependence on yaw angle and insensitivity to angle of attack. Data from the crossflow-dominated portion of the flowfield show the region’s sensitivity to angle of attack and dependence on yaw. Transition near the centerline exhibited a small dependence on angle of attack, but a large effect from yaw.

HIFiRE-5 Boundary-Layer Transition Measured in a Mach-6 Quiet Tunnel with Infrared Thermography

The principal goal of the Hypersonic International Flight Research Experimentation (HIFiRE) flight 5 is to measure hypersonic boundary-layer transition on a three-dimensional body. This paper presents measurements of heat flux and boundary-layer transition in the Boeing/U.S. Air Force Office of Scientific Research Mach-6 Quiet Tunnel. This facility has been developed to provide quiet flow at high Reynolds number, with low noise levels comparable to flight. Previously, the global heat flux and location of the transition front were measured with temperature-sensitive paint (TSP). A new HIFiRE-5 model was built with a polyether ether ketone shell, which is suitable for infrared–thermographic heat-flux measurements. Quiet-flow tests at Reynolds numbers of and zero angle of attack indicate a centerline transition location within 4% of the earlier TSP results, on the order of the uncertainty of the two techniques. This good agreement reinforces confidence in the earlier measurements and the new infrared-based technique. Examination of the off-centerline transition front indicates that the wavelength of stationary crossflow vortices is the same for both models and instrumentation techniques, although the streaks do not coincide precisely.

The effect of cryogenic suction on the monitoring data of ice barrier formation in a porous water-saturated soil

Artificial ice wall formation is one of the most frequently used techniques for waterproofing of mineshafts constructed in water-saturated rock massifs. In this work, we have developed a complex monitoring system for control of formation of ice. The system includes hydro-observation and temperature monitoring wells combined with simulation module. At the beginning of the monitoring process, we observed contradictory indications of ice wall closing moment by hydro-observation and temperature monitoring subsystems. To explain this effect we introduced in the simulation module two models of ground freezing, which consider the key effects observed under the phase transition in a saturated soil. There are existing of nonequilibrium moisture content in the soil at negative temperatures, kinetic peculiarities of water-ice transition in a porous medium and redistribution of moisture in partially saturated soil. Based on the detail simulation model we have shown that moisture content inside the closed ice wall can decrease due to water migration towards the phase transition front, which, consequently, slows down the water level in hydro-observation wells.

Application of the Fokker-Planck Kolmogorov equation to determining the mean value of nucleons generated by the direct ejection process

The statistical description of the process of direct nucleon ejection is the subject of this paper. This description is based on the generalized Fokker-Planck-Kolmogorov equation. The basic proposal is this: deterministic equations and their solutions have the mean values of the stochastic model of the ablation problem. The problem of deformation of the phase transition front is considered. The study is carried out by using the introduced stability position for the dispersion of solutions for mean values. The result of the study is the conclusion that the influence of the Markov diffusion coefficient leads to distortion of the original shape of the boundary phase transition front. The effect of the initial aspiration to resist changing the shape of the phase transition front was found.

CFD ANALYSIS OF THE HEAT TRANSFER OF SUPERCRITICAL WATER UNDER CONDITIONS OF MIXED CONVECTION

The results of computer modeling of heat exchange supercritical water, associated with the influence of gravity, are presented. CFD prediction data on heat transfer coefficients and temperatures of the inside surface of the tube wall, obtained with and without buoyancy, are presented. An interpretation of these predictions, which is associated with the turbulent transfer extinction near the tube wall in the case of buoyancy forces, is given. The analysis of the influence of buoyancy forces on the configuration of the radial temperature profiles of supercritical water was performed. The data on the regularities of motion of the pseudo-phase transition front in the presence and absence of accounting for buoyancy forces have been obtained.

A Multifront Problem of Freezing-Thawing Moist Soil

Construction activities in the North of Western Siberia is carried out in specific conditions of the cryolithozone. The study of heat transfer processes in freezing soils near buildings is necessary to ensure their successful operation. Heat exchange with phase transition is traditionally described by Stefan problem, which is a system of differential equations of parabolic type with standard boundary conditions and a subsidiary condition on the phase transition boundary. It is possible to formally pass on to one equation of the conductivity type, but in that case the delta function appears in one of the coefficients. The delta function reflects the Joule heat release at the phase transition temperature. A widespread “pass-through counting” method reduces the Stefan problem to a boundary problem for a nonlinear heat conductivity equation. With this approach, the calculation results in a temperature field. But it is difficult to identify the position of the phase transition boundary on the temperature field. A large number of methods for solving the Stefan problem are developed, in which the required value is the phase transition front coordinate. The common disadvantage of these methods is their unsuitability for situations with several fronts, when these fronts appear and disappear, change the movement direction, merge with each other. The article presents a method for solving the Stefan problem, which allows to obtain the front coordinate as a zero isotherm. As an example this method is used to solve the problem of freezing-thawing of moist soil under the influence of seasonal surface temperature fluctuations. The method eliminates the need to control the evolution of each front. The Stefan problem is considered as a limiting case of the general phase transition problem in a certain temperature range. Standard transformations and application of Green’s function allow to write down a problem in the form of an integral equation. The approximate solution is obtained in the form of a recurrent formula.