Direct observations of reaction zone structure in propagating detonations

We report experimental observations of the reaction zone structure of self-sustaining, cellular detonations propagating near the Chapman-Jouguet state in hydrogen-oxygen-argon/nitrogen mixtures. Two-dimensional cross sections perpendicular to the propagation direction were imaged using the technique of planar laser induced fluorescence (PLIF) and, in some cases, compared to simultaneously acquired schlieren images. Images are obtained which clearly show the nature of the disturbances in an intermediate chemical species (OH) created by the variations in the strength of the leading shock front associated with the transverse wave instability of a propagating detonation. The images are compared to 2-D, unsteady simulations with a reduced model of the chemical reaction processes in the hydrogen-oxygen-argon system. We interpret the experimental and numerical images using simple models of the detonation front structure based on the “weak” version of the flow near the triple point or intersection of three shock waves, two of which make up the shock front and the third corresponding to the wave propagating transversely to the front. Both the unsteady simulations and the triple point calculations are consistent with the creation of keystone-shaped regions of low reactivity behind the incident shock near the end of the oscillation cycle within the “cell.”     

Transverse waves resulting from pulsating instability of two-dimensional flames

We present results of fully compressible Navier–Stokes simulations of pulsating flame instabilities in two dimensions using single-step, first-order Arrhenius kinetics. Model parameters correspond to Zel’dovich and Lewis numbers of Ze = 9.5 and Le = 10, respectively, and flame Mach numbers M_L between 4.62 × 10⁻³ and 2.31 × 10⁻². The results show that the pulsating instability creates two types of transverse waves: deflagrations and detonations. Both types of waves can coexist for the same reactive system, but transverse detonations become more likely as M_L increases. The transverse detonations observed for our model system are of the intermediate type with most of the chemical energy release accompanying the pressure rise. They propagate inside the large preheat zone of the pulsating flame and do not spread into cold material. The results expand our knowledge of possible new phenomena associated with pulsating instability.     

Flame acceleration and DDT of hydrogen-oxygen gaseous mixtures in channels with no-slip walls

Hydrogen-oxygen flame acceleration and transition from deflagration to detonation (DDT) in channels with no-slip walls were studied theoretically and using high resolution simulations of 2D reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, real equation of state and a detailed chemical reaction mechanism. It is shown that in “wide” channels (D > 1 mm) there are three distinctive stages of the combustion wave propagation: the initial short stage of exponential acceleration; the second stage of slower flame acceleration; the third stage of the actual transition to detonation. In a thin channel (D < 1 mm) the flame exponential acceleration is not bounded till the transition to detonation. While velocity of the steady detonation waves formed in wider channels (10, 5, 3, 2 mm) is close to the Chapman-Jouguet velocity, the oscillating detonation waves with velocities slightly below the CJ velocity are formed in thinner channels (D < 1.0 mm). We analyse applicability of the gradient mechanism of detonation ignition for a detailed chemical reaction model to be a mechanism of the deflagration-to-detonation transition. The results of high resolution simulations are fully consistent with experimental observations of flame acceleration and DDT in hydrogen-oxygen gaseous mixtures.     

Self-organized generation of transverse waves in diverging cylindrical detonations

Self-organized generation of transverse waves associated with the transverse wave instabilities at a diverging cylindrical detonation front was numerically studied by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. After solution validation, four mechanisms of the transverse wave generation were identified from numerical simulations, and referred to as the concave front focusing, the kinked front evolution, the wrinkled front evolution and the transverse wave merging, respectively. The propagation of the cylindrical detonation is maintained by the growth of the transverse waves that match the rate of increase in surface area of the detonation front to asymptotically approach a constant average number of transverse waves per unit length along the circumference of the detonation front. This cell bifurcation phenomenon of cellular detonations is discussed in detail to gain better understanding on detonation physics.     

Velocity fluctuation near the detonation limits

In this study, the velocity fluctuation near the detonation limits is investigated experimentally. Five explosive mixtures in five different diameter tubes were used and the choice of the mixtures included those considered as “stable” with regular cellular pattern and “unstable” with highly irregular cellular pattern. Photodiodes spaced at regular intervals along the tube were used to measure the detonation velocity. Piezoelectric transducers were also used to record the pressure profiles. Smoked foils were used to register the cellular detonation structure. Away from the limits, the detonation is found to propagate at a steady velocity throughout the length of the tube and the fluctuations of the local velocity are generally small. For stable mixtures with high argon dilution, the onset of the detonation limits is indicated by an abrupt drop in the detonation velocity to about 0.4V_CJ after a short distance of travel. The detonation may continue to propagate at this low velocity before decaying eventually to a deflagration wave. For deflagrations the optical detector sometimes failed to register a signal due to low luminosity of the front. In unstable mixtures, galloping detonations are observed only in small diameter tubes (e.g., D = 12.7, 3.2 and 1.5 mm). A large number of fairly reproducible cycles of galloping detonations can be observed in very small diameter tubes. In large diameter tubes (e.g., D = 31.7 and 50.8 mm), no galloping detonations are observed in all stable and unstable mixtures. For stable mixtures, no galloping detonations are observed even in small diameter tubes of D = 3.2 and 1.5 mm. Smoked foils records show that the cellular detonation structure changes from multi-headed to single-headed spin as the limit is approached. In a galloping detonation cycle, a decay from multi-headed to single-headed detonation is observed. However, the cellular structure vanishes for further decay of the galloping detonation to the low velocity phase of the galloping cycle. Although galloping detonations could be considered to define the boundary for detonation limits, this definition lacks generality since galloping detonations are not always observed in all mixtures and in all tube diameters. Thus the onset of single-headed spin is perhaps the most appropriate criterion of the detonation limits in tubes.     

Measurement of endwall heat transfer and pressure drop in a pin-fin wedge duct

This paper discusses the measurements of endwall heat transfer and pressure drop in a wedge-shaped duct inserted with an array of circular pin fins. The endwall surface is coated with a thin layer of thermochromic liquid crystals and a transient test is run to obtain detailed heat transfer distributions. Parametric studies include Reynolds number (10,000?Re?50,000), outlet flow orientation (straight and lateral) and pin configuration (staggered and in-line). The wedge duct has a convergent angle of 12.7°. The pin spacing-to-diameter ratios along the longitude and transverse directions are fixed at s_x/d=s_y/d=2.5. Pin-less wedge duct results are also obtained for comparison. Results indicated that the straight wedge duct with a staggered pin array is most recommended because of its significant endwall heat transfer and moderate pressure-drop penalty; while the turned wedge duct with a staggered pin array is least recommended since it yields the highest pressure drops and raises severe hot spots. A similarity of the pin Reynolds-number dependence of row-averaged Nusselt number is developed in the present wedge duct of accelerating flow.     

Transmission of near-limit detonation wave through a planar sudden expansion in a narrow channel

Transmission of single-cell and spinning detonation waves in C₂H₄ + 3(O₂ + βN₂) mixtures through a 2-D sudden expansion experimentally studied using high-speed cinematography and soot film visualization. Nitrogen dilution ratio, β, is utilized to control cell size and detonation mode. Detonation wave of ethylene/oxygen/nitrogen mixture was initiated via DDT in the 1 mm × 1 mm cross-section and 250 mm long initiator channel before propagating into the 3 mm × 1 mm receptor channel. Visualizations show that detonation waves were extinct and accompanied with abrupt decrease in visible reaction front propagating velocities right after passing through the sudden expansion. However, re-acceleration of the reaction front and re-initiation of the detonation wave were observed downstream in the expanded receptor section. Two re-initiation modes with large disparity in the re-initiation distance were experimentally characterized. For mixtures with nitrogen dilution ratio equals 0.3 or less, the cellular detonation front propagated with single cell in the initiator section before entering the sudden expansion. The re-initiation distance was less than 50 mm and was likely achieved via shock reflection. Velocity characterization shows that steady propagating speed of the detonation wave is ～100 m/s higher in receptor section than in the initiator section. Since the cell size became larger than 1 mm for mixtures with β ? 0.3, the detonation wave propagated in spinning detonation mode before transmitting into the expanded section. The reaction front would have to go through another DDT process to reach detonation state in the receptor section, and the re-initiation distance was increased to more than 150 mm. Moreover, step height of the sudden expansion was proposed as the characteristic length scale to obtain a unified non-dimensional correlation between re-initiation distance and detonation cell size.     

Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct

In this study, we present a numerical solution for combined laminar fluid flow and heat transfer of Herschel–Bulkley non-Newtonian fluids in the entrance region of a rectangular duct. The governing equations are solved iteratively by using finite difference method to obtain temperature, bulk temperature, and Nusselt number. Two cases of the thermal boundary conditions are considered; (i) T thermal boundary condition “constant temperature at the wall” and (ii) H2 thermal boundary condition “constant heat flux at the wall”. The results are presented in tables and figures for different parameters for the fluid and the duct geometry.     

Effect of oscillatory motion on heat transfer at vertical flat surfaces

The effect of oscillations on heat transfer at vertical surfaces is investigated and a model is developed that predicted both the transient and time average heat transfer rates. The transient behavior of the heat transfer indicates the presence of an oscillatory component superimposed on a larger steady one that does not reach zero during flow reversal. This was explained in terms of the interaction between a “quasi-steady oscillatory” mechanism near the leading edge, and a “pseudo-steady diffusive” far from it. The analysis further revealed that the time average heat transfer rate can be adequately estimated using a mixed “forced-natural” convections correlation, with the forced convection component estimated based on the time average oscillatory Reynolds number Re_v = awL/ν. The agreement between the model predictions and the experimental measurements makes it applicable for predicting heat transfer characteristics and velocity fluctuations near heated vertical surfaces in presence of oscillatory motion. The model is also applicable for predicting heat transfer rates under conditions where oscillatory motion is used to achieve specificity in temperature control without affecting process residence time, such as in biomedical and biochemical applications. The modest heat transfer enhancement (<2) due to oscillatory motion is attributed to the small convective term in the energy equation, which is consistent with previous investigations where increasing the axial temperature gradient in presence of oscillatory motion was shown to achieve much higher heat transfer enhancement.     

Effect of perforated plate with high blockage rate on detonation re-initiation in H2–O2-Ar mixture

An experimental investigation was performed to study the pressure limits and mechanism of the detonation re-initiation behind the perforated plate with various thicknesses and hole diameters in H₂–O₂-Ar mixture by schlieren and soot track measurement. The Chapman-Jouguet (CJ) detonation and overdriven detonation were used to collide with the perforated plate. For the CJ detonation transmission, the detonation re-initiation distance is larger than 3.9 times the tube hydraulic diameter. Both the thickness and the hole size have significant effects on the critical pressure and the re-initiation distance. The ratios of the hole hydraulic diameter and the critical cell size ($d_H/{\lambda }_c$) are less than 1. The cellular structure can be observed near the perforated plate on the smoked foils due to the collision of the arc-sharp shock waves via multi-jet structure. For the overdriven detonation transmission, the detonation can be re-initiated quickly, and the re-initiation distances are all less than twice the tube hydraulic diameter. The re-initiation distance increases with the hole size while the thickness has little effect on the re-initiation distance. The “abrupt” mode of the detonation re-initiation is transformed into the “gradual” mode with the increase of the initial pressure. The pressure limit of the re-initiation mode transformation also increases with the decrease of the hole size. Two mechanisms of the multi-jet initiation: rapid turbulent mixing initiation and the induction by the collisions of transverse waves were verified experimentally, corresponding to the “abrupt” and “gradual” modes, respectively. The critical condition of detonation propagation can be quantified as d_H/λ¹ > 3.37 and 3.77 for the 3 mm-hole and 2 mm-hole perforated plates, respectively, where d_H is the hydraulic diameter and λ is the detonation cell size.     

Characterization of the effect of Froude number on surface waves and heat transfer in inclined turbulent open channel water flows

Interfacial heat transport in open channel turbulent flows is strongly dependent on surface waves that can appear as a result of the interaction of bulk turbulence with the free surface. The paper describes wave/heat transfer phenomena in inclined turbulent open surface water flows. The experiments were conducted in a regime of transition from “weak” to “strong” turbulence, in which the stabilizing influences of gravity and surface tension are relatively small against the disturbing effects of turbulence. A key role of the Froude number, Fr_⊥, built through the surface-normal component of g has been revealed. As Fr_⊥ grows, the wave amplitude grows, and the frequency spectrum shifts towards shorter waves. These changes lead to a heat transfer improvement, enough to double the heat transfer coefficient. The experimental data have been compared with calculations based on a “K-ε” model. As a result, the range of applicability of the standard model has been established as Fr_⊥<2000. The turbulent Prandtl number has been evaluated for Fr_⊥<700.     

Deregulating with no regulator: Is the German electricity transmission regime institutionally correct?

From 1998 to 2005, the German transmission grid has been put under a self-regulated arrangement. It seems hard to believe that transmission lines can be opened to “third-party access” only with a “negotiated access regime” and no regulator supervision. It seems contradictory with the notion of “ex post contractual hazards” promoted by V. Goldberg and O. Williamson. If a weak institutional arrangement is implemented, one might assume that it has to be harmful to network and market access. If it is not to be inefficient, why and how could it work? When looking at rules and prices for accessing the transmission network and the corresponding wholesale markets in Germany, the “club” arrangement for transmission opening does not appear so harmful. Accordingly, we have to reconsider the ex ante and ex post institutional mechanism of such a “club” arrangement. Ex ante, we first reconsider skills and strengths of industrial consumers and German Business associations in defining and assessing rules of transmission access. We underline that incomplete vertical and horizontal integration of German electricity companies impeded extensive cartel collusion. Ex post, we first look at a strong Competition Authority backing. Then we discover that ex ante and ex post dimensions are much more mixed and reinforced in an open “cumulative pro-competition process” framed by the Competition Authority.     

Stable detonation wave propagation in rectangular-cross-section curved channels

The detonation propagation phenomena in curved channels were experimentally studied in order to determine the stable propagation condition. A stoichiometric ethylene–oxygen mixture gas and five types of rectangular-cross-section curved channels with different inner radii of curvature were employed. The detonation waves propagating through the curved channels were visualized using a high-speed video camera. Multi-frame short-time open-shutter photography (MSOP) was developed in the present study to simultaneously observe the front shock shape of the detonation wave and the trajectories of triple points on the detonation wave. The detonation wave became more stable under the conditions of a higher filling pressure of the mixture gas and/or a larger inner radius of curvature of the curved channel. The critical condition under which the propagation mode of the detonation wave transitioned from unstable to stable was having an inner radius of curvature of the curved channel (r_i) equivalent to 21–32 times the normal detonation cell width (λ). In the stable propagation mode, the normal detonation velocity (D_n) increased with the distance from the inner wall of the curved channel and approached the velocity of the planar detonation propagating through the straight section of the curved channel (D_str). The smallest D_n was observed on the inner wall and decreased with decreasing r_i/λ. The distribution of D_n on the detonation wave in the stable mode was approximately formulated. The approximated D_n given by the formula agreed well with the experimental results. The front shock shape of the detonation wave could be reconstructed accurately using the formula. The local curvature of the detonation wave (κ) nondimensionalized by λ decreased with increasing distance from the inner wall. The largest λκ was observed on the inner wall and increased with increasing r_i/λ. D_n/D_str decreased with increasing λκ. This nondimensionalized D_n–κ relation was nearly independent of r_i/λ.     

Numerical simulation of radial-stratified rotating detonation flow field structures with different injection patterns

Rotating detonation engine has been widely studied in recent years because of its high theoretical efficiency and heat release rate. In many numerical simulations, the combustible mixture is injected and fully filled at the head of the combustor. In this paper, annular injection slits are proposed and three representative injection patterns are simulated by changing the injection directions. Stable single-wave modes are formed in all three patterns and two kinds of combustible mixture layer structures are found, namely “L-shape” and “T-shape” structures. Following the combustible mixture layer, the detonation wave is not fully filled in the radial direction, thus radial and circumferential shock waves are induced from the detonation wave, forming more complex wave structures. After the radial shock wave, velocity vortex and significant deflagration are found and propagate with the shock wave, thus maintaining a higher pressure and temperature there.     

Hydrogen–oxygen flame acceleration and deflagration-to-detonation transition in three-dimensional rectangular channels with no-slip walls

Hydrogen–oxygen flame acceleration and the transition from deflagration to detonation (DDT) in channels with no-slip walls are studied using high resolution simulations of 3D reactive Navier–Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, real equation of state and detailed (reduced) chemical reaction mechanism. The acceleration of the flame propagating from the closed end of a channel, which is a key factor for understanding of the mechanism of DDT, is thoroughly studied. The three dimensional modeling of the flame acceleration and DDT in a semi-closed rectangular channel with cross section 10 × 10 mm and length 250 mm confirms validity of the mechanism of deflagration-to-detonation transition, which was proposed earlier theoretically and verified using 2D simulations. We show that 3D model contrary to 2D models allows to understand clearly the meaning of schlieren photos obtained in experimental studies. The “numerical schlieren” and “numerical shadowgraph” obtained using 3D calculations clarify the meaning of the experimental schlieren and shadow photos and some earlier misinterpretations of experimental data.     

Detonation-induced coal gasification

A preliminary experimental and theorotical investigation of the feasibility of detonation-induced pulverized coal gasification is described. The concept envisions a closed annular detonation duct through which a hydrogen/oxygen gasphase detonation propagates continuously. Coal particles injected into the violent and rapidly changing atmosphere produced by the detonation would undergo gasification reactions and be subsequently expelled from the duct. These events would occur in a time period compatible with one revolution of the detonation. A one-dimensional analysis of the response of a single coal particle within the expansion-wave region behind the detonation front is presented. Independent variables include particle diameter, initial H₂/O₂ stoichiometry and expansion wavelength (at the time the particle is overtaken by the detonation front). The most significant result of this analysis is the prediction of relative gas/particle velocities ranging between 125 and 1500m/s, which are sustained throughout particle residence times of 1–15 ms corresponding to 10–1000 μm diameter particles. An experimental facility comprising a 47 m ‘single-shot’ detonation duct that was built for this study is discussed. The duct was 2.54 cm square and was terminated at each end by a 0.36 m diameter × 2.44 m long cylindrical tank which contained helium gas during a test. Sized coal particles were placed at a point within the first 3.7 m length of the duct, and thin brass diaphragms initially separated the duct from the two helium-filled tanks. Detonation was initiated at the duct, end closest to these particles. The diaphragm at that end burst, allowing combustion and gasification products to exhaust into the adjoining tank where they were quenched and decelerated. When the detonation reached the far end of the duct the second diaphragm burst, minimizing wave reflections which would otherwise return to the ‘test section’ end and interfere with the flow field there. After a test the contents of both tanks and the duct were circulated and mixed. A gas sample was then drawn and analysed for yield. Results from preliminary experiments using this facility are presented. Although too few tests were conducted for conclusive observations to be reported, in two experiments yields of CO + CH₄ representing 40 per cent of the total initial carbon content in the coal samples were obtained.     

Large eddy simulation of heat and mass transport in turbulent flows. Part 2: Scalar field

Several subgrid-scale (SGS) scalar flux (τ_iA) and unmixedness (λ_AB) models are presented for large eddy simulation (LES) of heat and mass transport in turbulent flows. The models are similar to those considered in [Int. J. Heat Mass Transfer, in press] for SGS stresses and are based on the information residing at filtered or resolved field. All closures are implemented “locally” and are assessed a priori and a posteriori via data generated by direct numerical simulations of several nonreacting and reacting turbulent flows. A priori assessment indicates that the local values of τ_iA and λ_AB obtained by new “serial decomposition” closures are closer to “true” values than those obtained by dynamic-diffusivity and two-parameter mixed models. A posteriori assessment also indicates that the statistics of the scalar field in nonreacting and reacting flows are better predicted by LES when new SGS models are used.     

Derivation of burning velocities of premixed hydrogen/air flames at engine-relevant conditions using a single-cylinder compression machine with optical access

With respect to hydrogen internal combustion engines beside turbulence also flame front instabilities of high-pressure combustion provoke an acceleration of the flame. To account for this effect within engine simulations, it is suggested to include the impact of flame front instabilities directly into a “quasi-laminar” burning velocity that is an input for turbulent combustion models. Premixed hydrogen/air flames are investigated in a single-cylinder compression machine using OH-chemiluminescence and in-cylinder pressure analysis. Values of burning velocities are calculated from flame front velocities considering thermal expansion effects. A flame speed correlation is derived which covers temperatures and pressures of the unburned mixture, relevant for internal combustion engines, ranging from 350 K to 700 K and 5 bar to 45 bar. Values of air/fuel equivalence ratio cover lean and rich regimes between 0.4 ≤ λ ≤ 2.8. For an evaluation of stretch and instability effects a comparison to fundamental laminar burning velocities of a one-dimensional flame computed with a detailed chemical kinetic-mechanism is given. At high-pressure conditions flame speed measurements demonstrate that flame front instabilities have an accelerating effect on the value of laminar burning velocities, which cannot be reproduced by computations with a chemical model. A linear stability analysis is applied in order to estimate the magnitude of instabilities. The proposed “quasi-laminar” burning velocity does not account for interaction between turbulence and instability effects. Consequently, at increasing turbulence levels partially counter-balancing of instabilities by turbulence is not followed which may allegorize a possible limitation of the suggested approach.     

Influence of longitudinal obstacle spacing on the deflagration-to-detonation transition through a bank of obstacles in a hydrogen-air mixture

Flame acceleration and deflagration-to-detonation transition (DDT) in a channel containing an array of staggered cylindrical obstacles and a stoichiometric hydrogen-air mixture were studied by solving the fully-compressible reactive Navier-Stokes equations using a high-order numerical algorithm and adaptive mesh refinement. Four different longitudinal spacings (ls) of the neighboring obstacle rows (i.e., ls = 15.28, 19.1, 25.4, and 38.2 mm, corresponding to 1.2, 1.5, 2 and 3 times of obstacle diameter, respectively) were used to examine the effect of obstacle spacing on flame acceleration and DDT. The results show that the main mechanisms of flame acceleration and transition to detonation in all the cases studied are consistent. While the flame acceleration is caused by the growth of flame surface area in the initial stage, it is governed by shock-flame interactions in the later stage when shock waves are generated. The focusing of strong shocks at flame front is responsible for the initiation of detonation. It was found that the flame propagation speed and the DDT run-up distance and time are highly dependent on ls. Specifically, the flame acceleration declines as ls increases, since a larger ls leads to less disturbance of flow by obstacles per unit channel length. For detonation initiation, both the run-up distance and time increase with the increase of ls. It is interesting to note that the DDT distance and time increase significantly as ls increases from 19.1 mm to 25.4 mm. This is related to the slowdown of the increase rate of energy release over a period before DDT occurs under large ls condition, because every time the flame passes over an obstacle row the shock-flame interaction is delayed and numerous isolated pockets of unburned gas material are formed.     

Synthesis,studies and fuel cell performance of “core–shell” electrocatalysts for oxygen reduction reaction based on a PtNix carbon nitride “shell” and a pyrolyzed polyketone nanoball “core”

This report describes a new class of “core–shell” electrocatalysts for oxygen reduction reaction (ORR) processes for application in Proton Exchange Membrane Fuel Cells (PEMFCs). The electrocatalysts are obtained by supporting a “shell” consisting of PtNi_x alloy nanoparticles embedded into a carbon nitride matrix (indicated as PtNi_x-CN) on a “core” of pyrolyzed polyketone nanoballs, labeled ‘ST_p’. ST_ps are obtained by the sulfonation and pyrolysis of a precursor consisting of XC-72R carbon nanoparticles wrapped by polyketone (PK) fibers. The ST_ps are extensively characterized in terms of the chemical composition, thermal stability, degree of graphitization and morphology. The “core–shell” ORR electrocatalysts are prepared by the pyrolysis of precursors obtained impregnating the ST_p “cores” with a zeolitic inorganic–organic polymer electrolyte (Z-IOPE) plastic material. The electrochemical performance of the electrocatalysts in the ORR is tested “in situ” by single fuel cell tests. The interplay between the chemical composition, the degree of graphitization of both PtNi_x-CN “shell” and ST_ps “cores”, the morphology of the electrocatalysts and the fuel cell performance is elucidated. The most crucial preparation parameters for the optimization of the various features affecting the fuel cell performance of this promising class of ORR electrocatalysts are identified.