Detonability of THDCPD-exo–air mixtures

In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure (1 bar < P ₀ < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T ₀ ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L _i corresponds to cell size value with a coefficient k = λ/L _i = 24 at P ₀ = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on the critical initiation energy E _c, critical tube diameter d _c and deflagration to detonation transition length L _DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.

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This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006.     

Stabilization using fractional-order PI and PID controllers

This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PIλ and PI^λD^μ controllers. It is based on plotting the global stability region in the (k _p, k _i)-plane for the PI^λ controller and in the (k _p , k _i , k _d)-space for the PIλDμ controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.     

Measurements of heat transfer coefficients between turbulent liquid jets and a radially finned heated disk placed at the bottom of an open vertical circular cavity

 Experiments have been performed to assess the impact of an extended surface on the heat transfer enhancement for axisymmetric, turbulent liquid jet impingement on a heated round disk. The disk, with an array of integral radial fins mounted on its surface, is placed at the bottom of an open vertical circular cavity. Hydrodynamic and heat transfer data were obtained for a dielectric fluorocarbon liquid FC-77. For a fixed circular heater of diameter D=22.23 mm, several geometric parameters were tested: the nozzle diameter (4.42≤d≤9.27 mm), the confining wall diameter of the vertical cavity (22.23≤D _c≤30.16 mm), and the nozzle-to-heater spacing (0.5≤S/d≤5.0). The FC-77 flow rates varied from =0.2 to 11.0 l/min producing Reynolds numbers in the wide interval 700≤Re _d ≤44,000. For d=4.42 mm, the heat transfer response to the separation distance S/d was small but increased gradually with increasing nozzle diameter up to d=9.27 mm. The thermal resistance R _th increased with the confining wall diameter D _c and also with the nozzle diameter d. A minimum value of the thermal resistance of R _th,min=0.4 cm² K/W was attained for a combination of d=4.42 mm, D _c=22.23 mm, S/d=1, and =7.5 l/min. Based on a simplified heat transfer model, reasonable agreement was obtained between measured values of the thermal resistance and the R _th-predictions. The total fin effectiveness ɛ_f was shown to increase with increasing nozzle diameter, but was invariant with the flow rate (or the jet exit velocity). More than a three-fold heat transfer enhancement was realized through the addition of the array of integral radial fins on the heated round disk. Received on 30 August 2000 / Published online: 29 November 2001     

Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.     

Investigation of detonation initiation in aluminium suspensions

Detonation initiation is investigated in aluminium/oxygen and aluminium/air mixtures. Critical conditions for initiation of spherical detonations are examined in analogy with the criteria defined for gaseous mixtures, which correlate critical parameters of detonation initiation to the characteristic size of the cellular structure. However, experimental data on the detonation cell size in these two-phase mixtures are very scarce, on account of the difficulty to perform large-scale experiments. Therefore, 2D numerical simulations of the detonation cellular structure have been undertaken, with the same combustion model for Al/air and Al/O₂ mixtures. The cell size is found to be λ = 37.5 cm for a rich (r = 1.61) aluminium–air mixture, and λ = 7.5 cm for a stoichiometric aluminium-oxygen mixture, which is in reasonable agreement with available experimental data. Calculations performed in large-scale configurations (up to 25 m in length and 1.5 m in lateral direction) suggest that the critical initiation energy and predetonation radius for direct initiation of the unconfined detonation in the aluminium–air mixture are, respectively, 10 kg of TNT and 8 m. Moreover, numerical simulations reveal that the structure of the detonation wave behind the leading front is even more complicated than in pure gaseous mixtures, due to two-phase flow effects. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Influence of mixture sensitivity and pore size on detonation velocities in porous media

Experiments have been carried out to determine the dependence of the detonation velocity in porous media, on mixture sensitivity and pore size. A detonation is established at the top end of a vertical tube and allowed to propagate to the bottom section housing the porous bed, comprised of alumina spheres of equal diameter (1–32 mm). Several of the common detonable fuels were tested at atmospheric initial pressure. Results indicate the existence of a continuous range of velocities with change in Φ, spanning the lean and the rich propagation limits. For all fuels in a given porous bed, the velocity decreases from a maximum value at the most sensitive mixture near Φ≈1 (minimum induction length), toV/V _CJ≈0.3 at the limits. A decrease in pore size brings about a reduction inV/V _CJ and a narrowing of the detonability range for each fuel. For porous media comprised of spherical particles, it was possible to correlate the velocity data corresponding to a variety of different mixtures and for a broad range of particle sizes, using the following empirical expression:V/V _CJ=[1–0.35 log(d _c /d _p)]±0.1. The critical tube diameterd _c is used as a measure of mixture sensitivity andd _p denotes the pore diameter. An examination of the phenomenon at the composition limits, suggests that wave failure is controlled by a turbulent quenching mechanism.     

Mechanisms of detonation transmission in layered H2-O2 mixtures

When a plane detonation propagating through an explosive comes into contact with a bounding explosive, different types of diffraction patterns, which may result in the transmission of a detonation into the bounding mixture, are observed. The nature of these diffraction patterns and the mode of detonation transmission depend on the properties of the primary and bounding explosives. An experimental and analytical study of such diffractions, which are fundamental to many explosive applications, has been conducted in a two channel shock tube, using H₂-O₂ mixtures of different equivalence ratios as the primary and bounding or secondary explosive. The combination of mixtures was varied from rich primary / lean secondary to lean primary / rich secondary since the nature of the diffraction was found to depend on whether the Chapman-Jouguet velocity of the primary mixture,D _p, was greater than or less than that of the secondary mixture,D _s. Schlieren framing photographs of the different diffraction patterns were obtained and used to measure shock and oblique detonation wave angles and velocities for the different diffraction patterns, and these were compared with the results of a steady-state shock-polar solution of the diffraction problem. Two basic types of diffraction and modes of detonation reinitiation were observed. WhenD _p>D _s, an oblique shock connecting the primary detonation to an oblique detonation in the secondary mixture was observed. WithD _p<D _s, two modes of reinitiation were observed. In some cases, ignition occurs behind the Mach reflection of the shock wave, which is transmitted into the secondary mixture when the primary detonation first comes into contact with it, from the walls of the shock tube. In other cases, a detonation is initiated in the secondary mixture when the reflected shock crosses the contact surface behind the incident detonation. These observed modes of Mach stem and contact surface ignition have also been observed in numerical simulations of layered detonation interactions, as has the combined oblique-shock oblique-detonation configuration whenD _p>D _s. WhenD _p>D _s, the primary wave acts like a wedge moving into the secondary mixture with velocityD _p after steady state has been reached, a configuration which also arises in oblique-detonation ramjets and hypervelocity drivers.     

Detonation diffraction from an annular channel

In this study, gaseous detonation diffraction from an annular channel was investigated with a streak camera and the critical pressure for transmission of the detonation wave was obtained. The annular channel was used to approximate an infinite slot resulting in cylindrically expanding detonation waves. Two mixtures, stoichiometric acetylene–oxygen and stoichiometric acetylene–oxygen with 70% Ar dilution, were tested in a 4.3 and 14.3 mm channel width (W). The undiluted and diluted mixtures were found to have values of the critical channel width over the cell size around 3 and 12 respectively. Comparing these results to values of the critical diameter (d _c ), in which a spherical detonation occurs, a value of critical d _c /W _c near 2 is observed for the highly diluted mixture. This value corresponds to the geometrical factor of the curvature term between a spherical and cylindrical diverging wave. Hence, the result is in support of Lee’s proposed mechanism [Lee in Dynamics of Exothermicity, pp. 321, Gordon and Breach, Amsterdam, 1996] for failure due to diffraction based on curvature in stable mixtures such as those highly argon diluted with very regular detonation cellular patterns.     

Asymptotics of the Fast Diffusion Equation via Entropy Estimates

We consider non-negative solutions of the fast diffusion equation u _t  = Δ u ^m with m ∈ (0, 1) in the Euclidean space , d ≧ 3, and study the asymptotic behavior of a natural class of solutions in the limit corresponding to t → ∞ for m ≧ m _c  = (d − 2)/d, or as t approaches the extinction time when m < m _c . For a class of initial data, we prove that the solution converges with a polynomial rate to a self-similar solution, for t large enough if m ≧ m _c , or close enough to the extinction time if m < m _c . Such results are new in the range m ≦ m _c where previous approaches fail. In the range m _c  < m < 1, we improve on known results.     

DDT in a smooth tube filled with a hydrogen–oxygen mixture

Results of experimental study on DDT in a smooth tube filled with sensitive mixtures having detonation cell size from 1 to 3 orders of magnitude smaller than the tube diameter are presented. Stoichiometric hydrogen–oxygen mixtures were used in the tests with initial pressure ranging from 0.2 to 8 bar. A dependence of the run-up distance to DDT on the initial pressure is studied. This dependence is found to be close to the inverse proportionality. It is suggested that the flow ahead of the flame results in formation of the turbulent boundary layer. This boundary layer controls the scale of turbulent motions in the flow. A simple model to estimate the maximum scale of the turbulent pulsations (boundary layer thickness) at flame positions along the tube is presented. The largest scale of the turbulent motions at the location of the onset of detonation is shown to be 1 order of magnitude greater than the detonation cell widths, λ, in all the tests. It is suggested that the onset of detonation is triggered during flame acceleration as soon as the maximum scale of the turbulent pulsations increases up to about 10 λ. The model to estimate the maximum size of turbulent motions, δ, and the correlation δ≈ 10λ, give a basis for estimations of the run-up distances to DDT in tubes with internal diameter D > 20λ. PACS 47.40.-x; 47.27.Nz This paper was based on work that was presented at the 19th Inter-national Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27 - August 1, 2003     

Prediction of CHF in concentric-tube open thermosiphon using artificial neural network and genetic algorithm

In this paper, an artificial neural network (ANN) for predicting critical heat flux (CHF) of concentric-tube open thermosiphon has been trained successfully based on the experimental data from the literature. The dimensionless input parameters of the ANN are density ratio, ρ _l/ρ _v; the ratio of the heated tube length to the inner diameter of the outer tube, L/D _i; the ratio of frictional area, d _i/(D _i + d _o); and the ratio of equivalent heated diameter to characteristic bubble size, D _he/[σ/g(ρ _l−ρ _v)]^0.5, the output is Kutateladze number, Ku. The predicted values of ANN are found to be in reasonable agreement with the actual values from the experiments with a mean relative error (MRE) of 8.46%. New correlations for predicting CHF were also proposed by using genetic algorithm (GA) and succeeded to correlate the existing CHF data with better accuracy than the existing empirical correlations.     

Improvement of cold-wire response for measurement of temperature dissipation

This work aimed at improving fine-scale measurements using cold-wire anemometry. The dissipation ɛ _θ of the temperature variance was measured on the axis of a heated turbulent round jet. The measurements were performed with a constant current anemometer (CCA) operating fine Pt–10%Rh wires at very low overheat. The CCA developed for this purpose allowed the use of the current injection method in order to estimate the time constant of the wire. In the first part of the paper, it is shown that the time constants obtained for two wire diameters −d=1.2 and d=0.58 μm – compare well with those measured at the same time using two other methods (laser excitation and pulsed wire). Moreover, for these two wires, the estimated time constants were in good agreement with those obtained from a semi-empirical relation. In the second part of the paper, a compensation procedure – post-processing filtering – was developed in order to improved the frequency response of the cold-wire probes. The measurements carried out on the axis of the jet (Re _D =16 500, Re _λ  ≃ 167) showed that the frequency response of the 1.2 μm wire was significantly improved. In fact, the spectral characteristics of the compensated signal obtained with the 1.2 μm wire compared fairly well with those from the 0.58 μm wire. Moreover, the results indicated that the compensation procedure must be applied when the cut-off frequency of the cold-wire f _c is lower than two times the Kolmogorov frequency f _K. In the case where f _c ≃ 0.6f _K, the compensation procedure can reduce the error in the estimate of ɛ _θ by more than 20%. When f _c ≃ 2f _K, the effect of the compensation is reduced to about 5%. Received: 3 November 2000/Accepted: 23 March 2001     

Mixed Convection Boundary-Layer Flow in a Porous Medium Filled with Water Close to its Maximum Density

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ₀ is found for which there are dual solutions for a range λ_c < λ < 0 of λ (the value of λ_c dependent on δ) and single solutions for all λ ≥ 0. Another value of δ₁ of δ, with δ₁ > δ₀, is found for which there are dual solutions for a range 0 < λ < λ_c of positive values of λ, with solutions for all λ≤ 0. There is also a range δ₀ <  δ < δ₁ where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.     

Scale-adaptive simulation of flow past wavy cylinders at a subcritical Reynolds number

The Xu & Yan scale-adaptive simulation (XYSAS) model is employed to simulate the flows past wavy cylinders at Reynolds number 8 × 10 3.This approach yields results in good agreement with experimental measurements.The mean flow field and near wake vortex structure are replicated and compared with that of a corresponding circular cylinder.The effects of wavelength ratios λ/D m from 3 to 7,together with the amplitude ratios a /D m of 0.091 and 0.25,are fully investigated.Owing to the wavy configuration,a maximum reduction of Strouhal number and root-meansquare (r.m.s) fluctuating lift coefficients are up to 50% and 92%,respectively,which means the vortex induced vibration (VIV) could be effectively alleviated at certain larger values of λ/D m and a /D m.Also,the drag coefficients can be reduced by 30%.It is found that the flow field presents contrary patterns with the increase of λ/D m.The free shear layer becomes much more stable and rolls up into mature vortex only further downstream when λ/D m falls in the range of 5-7.The amplitude ratio a /D m greatly changes the separation line,and subsequently influences the wake structures.     

A rotating elliptic airfoil in fluid at rest and in a parallel freestream

This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re _c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro _c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re _c,u  = 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α ₀ = 0°) or normal (α ₀ = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re _c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re _c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect, the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding, and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro _c,Ω) transformed the flow topology from periodic vortex shedding at Ro _c,Ω = 2.4 to the generation of a “hovering vortex” at Ro _c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein, which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the corresponding force characteristics, particularly for those conditions with the presence of hovering vortex.     

2-D Simulation of Non-Isothermal Fate and Transport of a Drip-Applied Fumigant in Plastic-Mulched Soil Beds. II. Sensitivity Analysis and Model Application

Temperature dependence of selected parameters was defined and illustrated. The order of sensitivity among tested model parameters (sorption coefficient, K _D; diffusion coefficient, D _g; vapor pressure, P; degradation rate, k; Henry’s constant, H) was k > P > K _D > H > D _g for 1-day simulations and k > P and K _D > D _g > H for 2-day simulations. The most sensitive parameter for both days was k. Mass balance errors were calculated using NRMSE (normalized root mean square error) to evaluate the level of agreement. The numerical model was applied to predict fumigant movement in the soil bed.     

Global Semigroup of Conservative Solutions of the Nonlinear Variational Wave Equation

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation u _tt − c(u)(c(u)u _x ) _x  = 0. We allow for initial data u| _{t = 0} and u _t | _t=0 that contain measures. We assume that 0 < k^-1 \leqq c(u) \leqq k{0 < \kappa^{-1} \leqq c(u) \leqq \kappa}. Solutions of this equation may experience concentration of the energy density (u_t²+c(u)²u_x²)dx{(u_t^2+c(u)^2u_x^2){\rm d}x} into sets of measure zero. The solution is constructed by introducing new variables related to the characteristics, whereby singularities in the energy density become manageable. Furthermore, we prove that the energy may focus only on a set of times of zero measure or at points where c′(u) vanishes. A new numerical method for constructing conservative solutions is provided and illustrated with examples.     

Streamwise evolution of a high-Schmidt-number passive scalar in a turbulent plane wake

The concentration fluctuation c of diluted fluorescein dye, a high-Schmidt-number passive scalar (Sc=ν/D ≈ 2000, ν and D are the fluid momentum and dye diffusivities, respectively), is measured in the wake of a circular cylinder using a single-point laser-induced fluorescence (SPLIF) technique. The streamwise decay rate of the mean and rms values of c is slow in comparison to that of θ, the temperature fluctuation for which the molecular Prandtl number Pr=ν/κ is about 0.7 (κ is the thermal diffusivity). The comparison between mean and rms distributions of c and θ highlights the combined role the Reynolds and Schmidt numbers play in terms of dispersing the scalar. The streamwise evolution of the probability density functions (pdfs) of c and θ suggest that while p(θ) is approximately Gaussian in the intermediate wake (x/d ≈ 80), p(c) is strongly non-Gaussian, and depends on both x/d and Re. The skewness of c is larger than that of θ along the wake centreline. Arguably, the asymmetry of p(c) reflects the relatively strong organisation of the large-scale motion in the far-wake. Received: 27 July 2000/Accepted: 22 December 2000     

Experimental and numerical investigations on PDE performance augmentation by means of an ejector

To improve the performance of pulse detonation engines, a 48 cm long cylindrical combustion chamber of 5cm internal diameter (i.d.) is fitted with an ejector of constant section. The role of the ejector is (i) to provide partial confinement of the detonation products escaping from the chamber and (ii) to suck in fresh air and then to increase the mass ejected compared to the ejection of burned gases alone.The combustion chamber is fully filled with a stoichiometric ethylene/oxygen mixture at ambient conditions. Three parameters of the ejector are varied: the i.d. D, the length L, and the position d relative to the thrust wall of the combustion chamber. For various configurations, the specific impulse (I _sp) is determined in single shot experiments. The maximum operating frequency (f _max) and the maximum thrust are then deduced. I _sp is measured by means of the ballistic pendulum method, and f _max is derived from the pressure signal recorded on the combustion chamber thrust wall.The addition of an ejector increases the specific impulse up to 60% in the best configuration tested, from 164s without ejector to 260s with ejector. The specific impulse can be represented by a single curve using suitable dimensionless parameters. The thrust results for the main ejector studied (D = 80mm) indicate an optimal (L, d) configuration that provides a 28% thrust gain. For the same ejector, f _max remains constant and equal to the frequency obtained without ejector in a large range of (L, d) values, before decreasing.Two-dimensional unsteady numerical computations agree reasonably with the experiments, slightly overestimating the experimental values. The results indicate that 80% of the I _sp gain comes from the action of the expanding detonation products on the annular end surface of the combustion chamber, governed by the tube wall thickness.This paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003 PACS 47.40.Rs