Jonathan D. Regele

Effects of capillary spacing on EHD spraying from an array of cone jets

Abstract Electrohydrodynamic (EHD) sprays are fundamentally characterized by low liquid flows that are atomized into relatively small, monodisperse droplets. Since previous studies have shown that droplet size increases with increasing flow rate, the current work employs an array of capillaries intending to increase fluid throughput without increasing the size of the droplets produced. To do this, an array of four-capillary nozzles is examined by measuring the required potential needed for stable EHD spraying in the cone-jet mode as a function of capillary separation. In addition, a simple electrostatic model is used to support the experimental results, and to predict the behavior of a larger, 5×5 square array. Results show that the potential required for cone-jet spraying in a two-dimensional array of capillaries generally increases as the capillary spacing decreases (due to electrical shielding), but at very close spacing the potential can decrease if the neighboring capillaries are dry. This result suggests that EHD arrays can benefit from fine wire electrodes interspersed among the capillaries.

An adaptive wavelet-collocation method for shock computations

A simple and robust method for solving hyperbolic conservation equations based on the adaptive wavelet-collocation method, which uses a dynamically adaptive grid, are presented. The method utilises natural ability of wavelet analysis to sense localised structures and is based on analysis of wavelet coefficients on the finest level of resolution to create a discontinuity locator function Φ. Using this function, an artificial viscous term is explicitly added in the needed regions using a localised numerical viscosity that ensures the positivity and TVD non-linear stability conditions. Once the wavelet coefficients on the finest level of resolution are below the error threshold parameter ϵ, the artificial viscosity is shut off and any remaining physical waves are free to propagate undamped. Multiple examples in one and two dimensions are presented to demonstrate the methods robustness, simplicity and ease of extending to more complex problems.

Effects of high activation energies on acoustic timescale detonation initiation

Acoustic timescale Deflagration-to-Detonation Transition (DDT) has been shown to occur through the generation of compression waves emitted by a hot spot or reaction centre where the pressure and temperature increase with little diminution of density. In order to compensate for the multi-scale nature of the physico-chemical processes, previous numerical simulations in this area have been limited to relatively small activation energies. In this work, a computational study investigates the effect of increased activation energy on the time required to form a detonation wave and the change in behaviour of each hot spot as the activation energy is increased. The simulations use a localised spatially distributed thermal power deposition of limited duration into a finite volume of reactive gas to facilitate DDT. The Adaptive Wavelet-Collocation Method is used to solve efficiently the 1-D reactive Euler equations with one-step Arrhenius kinetics. The DDT process as described in previous work is characterised by the formation of hot spots during an initial transient period, explosion of the hot spots and creation of an accelerating reaction front that reaches the lead shock and forms an overdriven detonation wave. Current results indicate that as the activation energy is raised the chemical heat release becomes more temporally distributed. Hot spots that produce an accelerating reaction front with low activation energies change behaviour with increased activation energy so that no accelerating reaction front is created. An acoustic timescale ratio is defined that characterises the change in behaviour of each hot spot.

Acoustic timescale characterisation of a one-dimensional model hot spot

Hot spots have been shown to be the autoignition centre in reactive mixtures. Linear temperature gradients and thermal stratification are used to characterise their behaviour. In this work, a model hot spot is considered by combining a linear temperature gradient with a constant temperature plateau. This approach retains the simplicity of a linear temperature gradient, but captures the effects of a local temperature maximum of finite size. A one-step Arrhenius reaction for H2–air is used to model the reactive mixture. Plateaus of three different initial sizes spanning two orders of magnitude are simulated. Each length corresponds to a different ratio of excitation time to acoustic time. It is shown that ratios less than unity react at nearly isochoric conditions while ratios greater than unity react at nearly isobaric conditions. Furthermore, it is demonstrated that the gasdynamic response is characterised by the a priori prescribed hot spot acoustic timescale ratio. Based upon the prescribed timescale ratio, it is shown that the plateau can have either a substantial or negligible impact on the reaction of a surrounding temperature gradient. This is explored further as the slope of the temperature gradient is varied. Based upon the heating-to-acoustic timescale ratio, plateaus of a particular size are shown to facilitate detonation formation inside gradients that would otherwise not detonate.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order RungeKutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified HartenLaxvan Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gasliquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

Purely Gasdynamic Multidimensional Indirect Detonation Initiation Using Localized Acoustic Timescale Power Deposition

A “purely gasdynamic” indirect detonation initiation process is presented that can be independent of diffusion, viscosity and turbulence, and does not require direct initiation. In this process, energy is deposited into a finite volume of fluid in an amount of time that is similar to the acoustic timescale of the fluid volume. Highly resolved two-dimensional simulations show that the artificial diffusion implicit in the numerical method is demonstrated to accelerate detonation formation. It is shown that given sufficient resolution, the detonation formation time becomes dependent only on large-scale gasdynamics and is independent of the small scale structures.

Acoustic timescale characterisation of symmetric and asymmetric multidimensional hot spots

In this work, two-dimensional hot spots are modelled by combining a linear temperature gradient with a constant temperature plateau. This approach retains the simplicity of a linear temperature gradient, but captures the effects of a local temperature maximum of finite size. Symmetric and asymmetric plateau regions are modelled using both rectangular and elliptical geometries. A one-step Arrhenius reaction for H2–air is used to model the reactive mixture. Plateaus with different ratios of excitation to acoustic timescales, spanning two orders of magnitude, are simulated. Even with clear differences in behaviour between one and two dimensions, the a priori prescribed hot spot timescale ratio is shown to characterise the 2-D gasdynamic response. The relationship between one and two dimensions is explored using asymmetric plateau regions. It is shown that 1-D behaviour is recovered over a finite time. Furthermore, the duration of this 1-D behaviour is directly related to the asymmetry of the plateau.

An interface capturing scheme for modeling atomization in compressible flows

Abstract The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten–Lax–van Leer–Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.

Indirect detonation initiation using acoustic timescale thermal power deposition

AbstractA uid dynamics video is presented that demonstrates an indirectdetonation initiation process. In this process, a transient power depo-sition adds heat to a spatially resolved volume of uid in an amountof time that is similar to the acoustic timescale of the uid volume.A highly resolved two-dimensional simulation shows the events thatunfold after the heat is added. Traditionally, combustion modelers have concluded that detonations formeither by direct initiation or by Deagration-to-Detonation Transition (DDT).Direct initiation is accomplished by depositing a large amount of energy de-posited in a short time period such that a blast wave is created inside thereactive gas mixture. In DDT, di usion, viscosity, and turbulence play amajor role in preheating the reactive mixture to facilitate detonation for-mation [1, 4, 5, 6, 8]. These transport processes have little or no e ect indirect initiation.Direct initiation and DDT can be seen as two limiting extremes on acontinuum scale using the acoustic timescale theory of Kassoy [2]. Considera uid volume of length scale land sound speed asuch that the acoustictimescale of the uid volume can be de ned t

Numerical simulation of finite disturbances interacting with laminar premixed flames

Compression waves can be generated during combustion processes and subsequently interact with flames to augment their behaviour. The study of these interactions thus far has been limited to shock and expansion waves only. In this study, the interaction of finite compression waves with a perturbed laminar flame is investigated using numerical simulations of the compressible Navier–Stokes equations with single-step chemical kinetics. The interaction is characterised using three independent parameters: the compression wavelength, the pressure ratio of the disturbance, and the perturbation amplitude of the flame interface. The results reveal a wide range of behaviours in terms of flame length and heat release rate that could occur during such an interaction. The results are compared to the classical reactive Richtmyer–Meshkov instability and the role of baroclinic torque and vorticity generation are shown to be primary drivers of the flow instability.