Convergent Geometry Research Articles

Double cylinder implosion experiments at the National Ignition Facility

Cylindrical implosion experiments are used to directly measure instability growth in a convergent geometry, providing a wealth of data for model validation. Double cylinders are a natural extension of the platform and enable measurements at a classically unstable interface, the outer surface of the inner cylinder, which experiences no ablative stabilization from the laser drive. However, the utility of this platform relies upon maintaining adequate axial uniformity of the inner cylinder during the implosion. Although previous smaller-scale double cylinder experiments exhibited acceptable levels of axial uniformity, radiation-hydrodynamics simulations of larger-scale double cylinders predict more axial non-uniformity induced by the impedance mismatch as the shock wraps around the axial ends of the inner cylinder. A mechanism to reduce axial non-uniformity in these larger double cylinder implosions is presented, and preliminary experimental data confirms the efficacy of the selected mitigation approach.

Optical study on spray mixing, flame propagation and jets evolution within visible methanol active pre-chamber for turbulent jet ignition

Methanol spray impingement, mixing, flame propagation and jet evolution within the narrow-confined active pre-chamber (APC) with complex walls were experimentally observed by optical method for the first time. The effects of injection pressure and duration was investigated on an actual-geometry optical APC assembled in constant volume combustion chamber (CVC). Exploration on APC internal processes within static environments forms the basis for optimization of APC and analysis of jet formation. Mie scattering coupled with flame natural luminosity imaging were used to record spray mixing and combustion. The results show that in the APC with narrow-confined space, methanol spray undergoes three wall impingements, inducing a tumble that promotes mixing. High injection pressure enhances rapid spray tip penetration, while long injection duration slows methanol diffusion. In longer injection duration cases, the spray tip after the third impingement interferes with subsequent sprays. For higher injection pressure, this interference occurs in the APC cone section due to a larger spray cone angle, whereas for lower pressure, it happens in the APC duct section. Higher injection pressure also causes more spray to impact the APC bottom after the first wall impingement, hindering flame acceleration in the duct section. Irregular flame propagation is observed in the APC cone section due to wider space and uneven mixture conditions, while the convergent geometry from the APC throat to the duct section significantly accelerates flame propagation. The APC jet appears due to the pressure difference between the APC and the main chamber, with the brightness and length of the visible flame jet increasing with APC flame luminosity and pressure difference. A Mach ring structure is observed initially, but the jet velocity decreases as the Mach ring disappears during the APC inner flame extinguishing process. Through this study, the actual spraying and combustion process in APC is experimentally captured and revealed, which are an important contribution for APC optimization and development.

A Comparative Study on Hydrodynamic Analysis with and without Cavitation Modelling: A Study on Textured Slip Journal Bearing

In journal bearing modeling, the phenomenon of cavitation is very important to improve the accuracy of the simulation results. This is because cavitation will almost certainly occur because there are convergent and divergent geometries. The results of the simulation will be close to real conditions so that it can have a positive effect on researchers in order to design optimal journal bearings. The effect of modeling without cavitation and with cavitation on journal bearing modeling has a great influence on the lubrication performance of journal bearings. In modeling with cavitation, the maximum hydrodynamic pressure and load carrying capacity that the journal bearing is capable of relying on has a fairly rapid increase. The modeling results also relate to the friction force that occurs in the journal bearing. The aim of the present study is to explore the effect of inclusion of modeling of the Hydrodynamic pressure. The finite volume method based on software is used to compare the result with and without cavitation. Here, The mixture multiphase cavitation is adopted. The numerical result show t he effect of modelling without cavitation and with cavitation on journal bearing modelling has a great influence on the lubrication performance of journal bearings. In modelling with cavitation, the maximum hydrodynamic pressure and load cmarrying capacity that the journal bearing is capable of relying on has a fairly rapid increase. The modelling results also relate to the friction force that occurs in the journal bearing.

Toward constraint of ionization-potential depression models in a convergent geometry

We demonstrate the value of inner-shell X-ray absorption spectroscopy for dense-plasma atomic physics and explore the coupling between constraint of the thermodynamic state and constraint of ionization-potential depression models. Synthetic K-shell absorption spectra are generated along a radius from a point-like core and analyzed using different ionization-potential depression models. Within this synthetic analysis framework, we identify plasma conditions (Te=400 eV, ρ=40 g/cm3) accessible by spherical implosions where K-shell absorption spectra discriminate between models if the material temperature is measured to a precision of 20%. The analysis is extensible to a finite-sized core and can be used to guide future studies of ionization-potential depression, informing material and radiative properties of matter in fusion plasmas and stellar interiors.

Richtmyer–Meshkov instability of a single-mode heavy–light interface in cylindrical geometry

Richtmyer–Meshkov (RM) instability of a single-mode SF6–air interface subjected to a convergent shock is investigated experimentally. The convergent shock tube is specially designed with an opening tail to weaken the Rayleigh–Taylor effect and eliminate the reflected waves' effect. The gas layer scheme is used to create a heavy gas environment at the upstream side of the interface. Before phase inversion is finished, the amplitude reduction is accelerated, but the Bell–Plesset (BP) effect in this process is found to be negligible. After phase inversion is completed, the linear growth rate is generally predicted due to small amplitude and the weak BP effect. In nonlinear regime, an existing nonlinear model is revised based on the Padé approximation to give a better prediction of amplitude growth. The spike amplitude grows almost linearly, whereas the bubble amplitude gradually saturates and even reduces. For a heavy-light interface in convergent geometry, although both the spike and bubble amplitude growths are promoted by the BP effect, the spike growth is more promoted than the bubble. The BP effect enhances generation of the second-order harmonic, which results in saturation and reduction of the bubble amplitude. The discrepancy in the BP effect between light-heavy and heavy-light interfaces is qualitatively demonstrated for the first time.

Numerical investigation of capacitive deionization (CDI) with divergent and convergent channels

This research aims to explore the impact of tilted channel configurations of CDI cells on desalination performance. The results reveal that the titled convergent channels have a faster average salt adsorption rate (ASAR) than the regular straight geometry. For desalination operations that end at a quarter of the equilibrium salt adsorption capacity (SAC), the convergent spacer with a slight slope of 1.5 degrees has a 20 % higher ASAR than the typical straight geometry (0.15 mg/g/min for convergent and 0.12 mg/g/min for straight). This gain increases to about 24, 29.5, and 33%, respectively, for slopes of 3.5, 5.5, and 7 degrees, compared to the straight geometry with the same spacer thickness. By looking at the underlying mechanisms, the spacer geometry is found to shift the location of the initial adsorption. This affects how quickly the device outputs the cleaned water. Interestingly, the geometry angle can also affect the location of the depletion zone, so tilted spacers can also affect the behavior during electrode starvation. Specifically, the convergent geometry has the depletion zone in the middle of the electrode instead of the corner near the outlet, as seen for straight and divergent channels. Together, these findings indicate how to construct tilted spacers to enhance CDI performance.

Convergent Richtmyer–Meshkov instability on two-dimensional dual-mode interfaces

We report the first shock-tube experiments on two-dimensional dual-mode air–SF $_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

On the importance of three-dimensional modeling for high-energy-density physics experiments

Laser-driven cylindrical implosion experiments enable direct measurements of hydrodynamic instability growth in convergent geometries, providing a wealth of validation data in the high-energy-density regime. These experiments are designed to be nearly axially invariant, allowing for modeling with complementary two-dimensional slices of the cylinder. Two distinct hydrodynamics codes are employed to model a subset of these experiments, and the results are shown to be in very good agreement with each other and the available experimental data. While this 2D modeling approach adequately captures most of the physics of the implosion and ensuing instability growth, there are crucial aspects from the three-dimensional nature of the experiments that are missed in 2D. The first fully 3D simulations of these experiments are presented, and small but significant differences are found to arise from both the axial and azimuthal non-uniformity in the laser drive. Recent experimental results confirming the drive asymmetry are discussed.

Dynamic of shock–bubble interactions and nonlinear evolution of ablative hydrodynamic instabilities initialed by capsule interior isolated defects

It is believed that isolated defects within the capsule (e.g., void, high-density inclusion) can be one of the essential factors for implosion performance degradation by seeding hydrodynamic instabilities in implosions. Nonetheless, a systematic study on how the isolated defects evolve and why they are not stabilized by ablation given the length scale comparable with the typical cutoff wavelength is still lacking. This paper addresses the above concerns by looking into a simplified model where a planar shell (without convergent geometry) is driven by laser direct-drive, with a single defect (low/high density) of micrometer or sub-micrometer scale residing at different locations inside. The underlying dynamics of two key physical processes are analyzed, i.e., the shock–bubble interactions as well as the subsequent nonlinear evolution of ablative hydrodynamic instabilities initiated by the direct interaction of the deformed defect and ablation front, revealing that compressibility and baroclinic effects drive vorticity production during the interactions between the shock wave and the isolated defect. In the “light-bubble” case, the vortex pair generated in the first process is further strengthened by the laser ablation. Hence, a directed flow is formed in companion with the persistent flow entering the bubble of the surrounding ablator. The bubble exhibits a remarkable growth both laterally and deeply, seriously threatening the shell's integrity. The positive feedback mechanism of the vortex pair is absent in the “heavy-bubble” counterpart, and the ablation stabilization manifested itself in the reduction of spike amplitude. A systematic study of localized perturbation growth as a function of defect placement, size, and preheating intensity is presented.

NUMERICAL INVESTIGATIONS OF A SWIRLING TWO-PHASE AIR-WATER UPWARD FLOW IN STRAIGHT AND CONVERGENT VERTICAL PIPE

In this study, a numerical study is presented to analyze the flow parameters such as longitudinal and transverse velocities, hydrodynamic pressure, and volume fraction inside a vertical pipe. A vertical ascending swirl flow is established with the specified boundary conditions and compared between straight and convergent geometry pipes. Normalized film thickness is found to vary between 0.4 and 0.6, where the numerical output data from the present study resemble wire-mesh sensor data from literature. Convergent pipe flow includes the variation of hydrodynamic pressure thereby affecting the slug and bubble flow region. Longitudinal and transverse velocities are plotted against time and compared at the three inspection planes near the inlet, mid-portion, and outlet, respectively. In order to understand the effectiveness of rotational effect of gas and liquid phases, the vorticity components are studied. Parameters such as Q-criterion and vortex stretching term indicate the straining and shearing flow near the peripheral and core regions. The temporal volume fraction variation at the output section indicates the increase in the output liquid yield of convergent pipe outlet by 17%.

NUMERICAL INVESTIGATION OF HVAF-SPRAYED Fe-BASED AMORPHOUS COATINGS

A numerical analysis was performed to predict the effect of the convergent section geometry of a gun nozzle on the high-velocity air-fuel (HVAF) thermal spray Fe-based amorphous coating (AC) process. A computational fluid dynamics model was applied to investigate the gas-flow field and the behavior of in-flight particles at nozzle entrance convergent section length ranging from 28 mm to 56.8 mm and different shapes of the Laval nozzle convergent section (a straight line and Vitosinski convergence curve). On the one hand, the change in the gas-flame flow characteristics for the Vitosinski curve shows a uniform and stable flame compared with the straight-line curve in the convergent section. The straight-line curve shape of the Laval nozzle convergent section has a higher particle temperature compared with the Vitosinski-curve shape of the Laval nozzle convergent section. The particle dwell time for the straight-line curve shape of the Laval nozzle convergent section is longer than that for the Vitosinski curve shape of the Laval nozzle convergent section. On the other hand, the nozzle entrance convergent section length obviously affects the particle temperature, and the particle dwell time increases with the increasing nozzle entrance convergent section length. By analyzing both the melt status of the particles and particle velocity, the optimal gun configuration (0.7 V) producing low-porosity coatings was predicted. These calculations were experimentally verified by producing a low-porosity (1.37 %) Fe-based AC, fabricated with HVAF using the predicted optimal gun configuration.

WITHDRAWN: Shock wave implosion in water

Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence, which is not described by the models of self-similar shock propagation far from and in the vicinity of the piston. The model is based on an analysis of the change in pressure and kinetic energy density, as well as on the corresponding fluxes of internal and kinetic energy densities behind the shock front. The model shows that the spatial evolution of the shock velocity strongly depends on the initial compression, the adiabatic index of water, and the geometry of convergence. The model also explains the transition to a rapid increase in the shock velocity at only a certain radius of the shock that is observed in experiments. The dependence of the threshold radius, where the shock implosion follows the power law (quasi self-similarity), on the initial compression is determined. It is stated that in the entire range of the shock radii the internal and kinetic energy density fluxes are equal, which is in agreement with known experimental data.

Impact of the convergent geometric profile on boundary layer separation in the supersonic over-expanded nozzle

Abstract This article aims to conduct a numerical investigation of phenomena induced by gas expansion in chemical propulsion nozzles. A numerical simulation of full-scale flat convergent-divergent nozzle geometry using the finite volume method on structured meshes is performed to predict the change in the convergent geometry on the boundary layer separation resulting from a shock/shock and shock/boundary layer. Two turbulence models are tested, namely, the k−ε and k−ω shear-stress transport (SST) models. Three steps are considered to achieve this work. First, 10 numerical schemes are tested to select the accurate one. The findings of the first step are used to predict the boundary layer separation in a supersonic overexpanded nozzle. The available experimental data from the NASA Langley Research Center are used to validate the results. The third step concerns investigating the impact of the convergent geometric profile on the downstream flow of the nozzle. The obtained results are analyzed and compared with the experimental data. These results show that convergent geometry may cause the formation of different shock structures and different points of flow separation and modifies several parameters of the flow and nozzle performance downstream the throat. The findings indicated that the convergent profile must be considered during the design phase when focusing on the problem of boundary layer separation in the supersonic overexpanded regime nozzles.

Control of extrudate swell and instabilities using a rotating roller die

• The moving walls (rotating rollers) provide a flexible mean to control die swell and instabilities • The smooth convergent geometry of the rotating die prevents volume instabilities normally related to entrance effect. However very large stresses on the melt are generated in the stationary mode so much so that surface roughness instabilities, not usually reported with polystyrene, appear on the extrudate surface. • This surface roughness resembles sharkskin but the mechanism leading to it is different to that leading to sharkskin. • This observation is a first as PS is reported to never exhibit surface roughness. • The rotating die is a versatile tool to produce sheet of various thicknesses as the gap can be changed by moving the rollers up and down. • The experimental data presented are underpinned by simple theoretical considerations, showing the importance of the wall shear stress and the changes in extension at the die exit. Thermoplastics extruded from dies will always swell and above a critical flow rate display instabilities (sharkskin, stick-spurt or gross melt fracture). Prior research has shown that the best way to suppress these instabilities is to reduce the entry converging angle using a smooth convergence and induce permanent wall slip. In this research we go a step further by allowing the walls to move using a rotating roller die. Thus both extrudate swell and flow instabilities become controllable. This paper presents data to support this claim. The practical benefits are important as stable operation at higher flow rates become permissible. Also, by providing extra control variables, this device becomes a useful tool to help unravel the causes of the various instabilities that arise in polymer melt die extrusion. A first from this research, using this roller die geometry we were able to tease out surface roughness instability with polystyrene hitherto not reported.

Development and theoretical analysis of slippery walls flow of third-grade fluid through the convergent symmetric channel

The present investigation is a study of third-grade fluid muddled with tiny-sized round-shaped hafnium particles drifting through a convergent geometry under the influence of slip boundary conditions. The impact of electro-osmotic is also examined in this investigation. The Debye Hückel linearization is used to investigate the current problem. Fluid and particulate phases are illustrated in convergent geometry having momentous utilizations in industry and different strolls of science. The problem is modeled in terms of nonlinear complex differential equations by using the fluid and particle phase models. The normalized quantities are used to convert the dimensional equations into dimensionless form and the perturbation method is selected to obtain the solution in analytical form. The effects of pertinent parameters on each type of flow are also presented graphically. Promotion in the velocity profile is observed for the volumetric flow parameter. The slip parameter boost motion of the fluid particle inside the channel. The current study can be utilized in the chemical industry, reservoir engineering, and microfabrication technique in which mass exchanges and electro-osmotic energy play a vital role.

Particles Focusing and Separation by a Novel Inertial Microfluidic Device: Divergent Serpentine Microchannel

Microfluidic experiments have found wide applications in medical sciences and engineering, such as cell separation and focusing. In the present study, focusing and separation of particles with different sizes and densities were investigated by designing inertial microfluidic devices. The microfluidic channel is designed by analyzing the induced forces on the particles. In the designing process, the objective was to focus and separate the particles in the shortest length of the channel with the lowest possible cycles and high efficiency. The simulation is then used for analyzing the two proposed geometries to evaluate their particle separation and focusing ability, named convergent and divergent serpentine microchannels. Another critical issue is the low number of cycles required to complete the particle separation and focusing process in the proposed geometries, which shortens the channel length and improves the detection speed. Eventually, divergent geometry showed an excellent performance compared to the convergent geometry in focusing and separating particles. Also, it was shown that in the divergent geometry, the separation of the particles with bigger sizes (e.g., circulating tumor cells) or higher densities from the particles of smaller sizes (e.g., red blood cells) or lower densities has high efficiency.

Investigation of electro-osmotic flow of Hafnium particles mixed-up with Casson fluid in convergent geometry: Theoretical study of multiphase flow

Two-phase flow of a non-Newtonian fluid is presented. Bi-phase suspension is obtained by using Casson fluid as the base liquid and tiny size metallic particles. The transport of Hafnium (Hf) particles through a convergent channel are governed by the electro-osmotic phenomenon. An analytical solution is achieved by solving differential equations for the flow dynamics of electro-osmotic flow (EOF). This prominent feature is owing to the density of the metal that suggests that Hafnium alloy is the most appropriate application in nuclear reactors, as a coolant.

Compound flooding in convergent estuaries: insights from an analytical model

Abstract. We investigate here the effects of geometric properties (channel depth and cross-sectional convergence length), storm surge characteristics, friction, and river flow on the spatial and temporal variability of compound flooding along an idealized, meso-tidal coastal-plain estuary. An analytical model is developed that includes exponentially convergent geometry, tidal forcing, constant river flow, and a representation of storm surge as a combination of two sinusoidal waves. Nonlinear bed friction is treated using Chebyshev polynomials and trigonometric functions, and a multi-segment approach is used to increase accuracy. Model results show that river discharge increases the damping of surge amplitudes in an estuary, while increasing channel depth has the opposite effect. Sensitivity studies indicate that the impact of river flow on peak water level decreases as channel depth increases, while the influence of tide and surge increases in the landward portion of an estuary. Moreover, model results show less surge damping in deeper configurations and even amplification in some cases, while increased convergence length scale increases damping of surge waves with periods of 12–72 h. For every modeled scenario, there is a point where river discharge effects on water level outweigh tide/surge effects. As a channel is deepened, this cross-over point moves progressively upstream. Thus, channel deepening may alter flood risk spatially along an estuary and reduce the length of a river estuary, within which fluvial flooding is dominant.

Evaluating the stretching/compression effect of Richtmyer–Meshkov instability in convergent geometries

Richtmyer–Meshkov (RM) instability in convergent geometries (such as cylinders and spheres) plays a fundamental role in natural phenomena and engineering applications, e.g. supernova explosion and inertial confinement fusion. Convergent geometry refers to a system in which the interface converges and the fluids are compressed correspondingly. By applying a decomposition formula, the stretching or compression (S(C)) effect is separated from the perturbation growth as one of the main contributions, which is defined as the averaged velocity difference between two ends of the mixing zone. Starting from linear theories, the S(C) effect in planar, cylindrical and spherical geometries is derived as a function of geometrical convergence ratio, compression ratio and mixing width. Specifically, geometrical convergence stretches the mixing zone, while fluid compression compresses the mixing zone. Moreover, the contribution of geometrical convergence in the spherical geometry is more important than that in the cylindrical geometry. A series of cylindrical cases with high convergence ratio is simulated, and the growth of perturbations is compared with that of the corresponding planar cases. As a result, the theoretical results of the S(C) effect agree well with the numerical results. Furthermore, results show that the S(C) effect is a significant feature in convergent geometries. Therefore, the S(C) effect is an important part of the Bell–Plesset effect. The present work on the S(C) effect is important for further modelling of the mixing width of convergent RM instabilities.

Extrusion foaming of linear and branched polypropylenes – input of the thermomechanical analysis of pressure drop in the die

Abstract This paper aims at a better understanding of the polypropylene (PP) physical extrusion foaming process with the objective of obtaining the lowest possible foam density. Two branched PPs were compared to the corresponding linear ones. Their shear and elongation viscosities were measured as well as their crystalline properties. Trials were conducted in a single screw extruder equipped with a gear pump and a static mixer cooler to adjust the melt temperature at the final die. The effect of decreasing this temperature on the PP foamability and on the pressure drop in the die was analyzed. The foam density of branched PPs varies from high to low values while decreasing the foaming temperature. In the same processing conditions, the foam density of linear PPs does not decrease so much, as already evidenced in the literature. The foamability transition coincides with an increase of the pressure drop in the die. The originality of the work lies in the thermomechanical analysis of the polymer flow in the die which allows the identification of the relevant physical phenomena for a good foamability. The comparison of the experimental pressure drops in the die and the computed ones with the identified purely viscous behavior points out the influence of the foaming temperature and of the PP structure. At high foaming temperature the discrepancy between experimental measurements and the computed pressure drops remains limited. It increases when decreasing the foaming temperature, but the mismatch is much more important for branched PPs than for linear ones. This difference is analyzed as a combination of the activation energy of the viscosity, the elongational viscosity in the convergent geometry of the die which is much more important for branched PPs than for linear ones, and the onset of crystallization which occurs at higher temperature for branched PPs than for linear PPs.