No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
High-fidelity Simulation of Oblique Detonation Waves
... Adaptive mesh refinement allows a 655 million cell case, if the finest resolution was applied uniformly throughout the domain, to be simulated with 50 million cells. Further details on this study can be found in Ref. [70]. ...
This work presents a comprehensive framework for the efficient implementation of finite-volume-based reacting flow solvers, specifically tailored for high speed propulsion applications. Using the exascale computing project (ECP) based AMReX framework, a compressible flow solver for handling high-speed reacting flows is developed. This work is complementary to the existing PeleC solver, emphasizing specific applications that include confined shock-containing flows, stationary and moving shocks and detonations. The framework begins with a detailed exposition of the numerical methods employed, emphasizing their application to complex geometries and their effectiveness in ensuring accurate and stable numerical simulations. Subsequently, an in-depth analysis evaluates the solver's performance across canonical and practical geometries, with particular focus on computational cost and efficiency. The solver's scalability and robustness are demonstrated through practical test cases, including flow path simulations of scramjet engines and detailed analysis of various detonation phenomena.
Conical oblique detonation waves (ODWs) are studied with high-fidelity numerical simulations, including complex chemical kinetics for an ethylene-air mixture at standard temperature and pressure at a stoichiometric equivalence ratio and 14.6 μm spatial resolution resulting in 42 cells per induction length at a minimum. Control volume analysis is proposed through an equilibrium-based detonation polar algorithm to identify ODW regimes and perform thermodynamic analysis. This analysis enables the correct conditions for the three-dimensional simulation of conical ODWs that further informs their practical use in engine design. Detonation instabilities are shown to behave differently in three dimensions as multiple detonation instabilities collide, forming Mach stems with increased strength compared to two-dimensional detonations. The weak overdriven conical ODW allows cellular detonation structure that is highly irregular with instabilities moving axially along the detonation front. Large subsonic regions also provide opportunities for pressure waves to impact the detonation surface, potentially influencing the formation of detonation instability. The detonation structure observed in conical systems resembles that of two-dimensional oblique detonations formed by wedges and of planar cellular detonations.
This study investigates the structure of conical detonations in premixed ethylene–air mixtures through two complementary approaches. First, a control volume-based model identifies the weakly overdriven region for stable wave formation, showing dependence on the inflow Mach number and highlighting the impact of incomplete heat release. Second, high-fidelity simulations with multistep chemical kinetics capture the formation of surface instabilities and the nature of the detonation waves. The thermodynamic analysis tool, validated against experimental data, computes detonation polars using a multi-species gas description and provides crucial insights into post-detonation properties and deflection angles for various cone half-angles. The results indicate that the regime of weakly overdriven detonations is confined by flow conditions and turning angles, with net heat release diminishing as these parameters increase. For the highest Mach number and turning angle considered, the heat release is observed to be less than 25% of the reaction enthalpy for the mixture. High-fidelity simulations corroborate the thermodynamic analysis and further demonstrate the formation of cellular instabilities on the detonation surface. For a conical system characterized by significant isentropic expansion and weaker initial shock compared to two-dimensional wedges, transverse waves reflecting off the cone surface lead to the formation of triple points, which catalyze instabilities. The overall detonation structure in conical systems is similar to that of two-dimensional wedge-based oblique detonations and planar cellular detonations.
The stationary characteristics of the oblique detonation wave (ODW) induced by the double wedge with an expansion corner are investigated using two-dimensional Navier–Stokes equations long with a two-step induction-exothermic kinetic model. The results show that the detached ODW can be reattached by expansion waves induced by the double wedge so that the standing window of ODW can be expanded. The re-standing position of ODW depends on the location and strength of the expansion waves, which are governed by the first wedge length L and the corner angle between the first and second wedge surface θC. There is a critical angle reattachment that determines whether the ODW can be reattached by expansion waves, and this critical angle increases as wedge length increases. However, the detached
ODW cannot be reattached when the wedge length is increased to a critical value regardless of the wedge corner. The re-standing position moves downstream with the increment of θC until the last Mach wave tangent to the subsonic zone behind the strong overdriven ODW because no more Mach waves interact with the initiation zone. Moreover, the comparison of viscous and inviscid fields demonstrates that a shorter wedge length is necessary for the viscous field to reattach the ODW because the recirculation zone forms a gas wedge that extends the first wedge surface.
Significance
There is now an intensifying international effort to develop robust propulsion systems for hypersonic and supersonic flight. Such a system would allow flight through our atmosphere at very high speeds and allow efficient entry and exit from planetary atmospheres. The possibility of basing such a system on detonations, the most powerful form of combustion, has the potential to provide higher thermodynamic efficiency, enhanced reliability, and reduced emissions. This work reports a significant step in attaining this goal: the discovery of an experimental configuration and flow conditions that generate a stabilized oblique detonation, a phenomenon that has the potential to revolutionize high-speed propulsion of the future.
The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.
The formation and structure of oblique detonation waves initiated by semi-infinite wedges and cones are presented. For wedge or cone angles less than the deflection angle required for an oblique Chapman-Jouguet (CJ) detonation, different wave structures have been previously reported. Using the method of characteristics and numerical simulations, it is shown that, for such low wedge or cone angles, a CJ oblique detonation is eventually initiated following an induction process. It its thus demonstrated that shock-induced combustion with the reaction front remaining uncoupled to the oblique shock in the far field is not a valid solution. Simulations with semi-infinite cones reveal that the effect of the front curvature around the cone axis allows oblique detonations to be formed at angles lower than that of a planar CJ oblique detonation.
The approximation of transient detonation waves requires numerical methods that are able to
resolve a wide range of different scales. Especially the accurate consideration of detailed
chemical kinetics is extremely demanding. This thesis describes an efficient solution strategy
for the Euler equations of gas dynamics for mixtures of thermally perfect species with detailed,
non-equilibrium reaction that tackles the problem of source term stiffness by temporal and
spatial dynamic mesh adaptation. All gas dynamically relevant scales are sufficiently resolved.
The blockstructured adaptive mesh refinement technique of Berger and Colella is utilized to
supply the required resolution locally on the basis of hydrodynamic refinement criteria. This
adaptive method is tailored especially for time-explicit finite volume schemes and uses a
hierarchy of spatially refined subgrids which are integrated recursively with reduced time steps.
A parallelization strategy for distributed memory machines is developed and implemented. It
follows a rigorous domain decomposition approach and partitions the entire grid hierarchy.
A time-operator splitting technique is employed to decouple hydrodynamic transport and chemical
reaction. It allows the separate numerical integration of the homogeneous Euler equations with
time-explicit finite volume methods and the usage of an time-implicit discretization only for
the stiff reaction terms. High-resolution shock capturing schemes are constructed for the
homogeneous Euler equations with complex equation of state. In particular, a reliable hybrid
Roe-solver-based method is derived. The scheme avoids unphysical values due to the Roe
linearization and utilizes additional numerical viscosity to stabilize the approximation of
strong shocks that inherently appear at the head of detonation waves. In different test
configurations it is shown that this hybrid Roe-type method is superior for detonation
simulation to any other method considered.
Large-scale simulations of unstable detonation structures of hydrogen-oxygen detonations run on
recent Beowulf clusters demonstrate the efficiency of the entire approach. In particular,
computations of regular cellular structures in two and three space dimensions and their
development under transient conditions, e.g. Mach reflection and diffraction, are presented. The
achieved resolutions go far beyond previously published results and provide new reference
solutions.
In this paper we describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at the contact discontinuity is computed, we derive a numerical approximation for the largest and smallest signal velocity in the Riemann problem. Having obtained the numerical signal velocities, we use theoretical results by Harten, Lax and van Leer to obtain the full approximation.
A stability condition for the numerical signal velocities is derived. We also demonstrate a relation between the signal velocities and the dissipation contained in the corresponding Godunov-type method.
The computation of signal velocities for a general (convex) equation of state is discussed. Numerical results for the one- and two-dimensional compressible gas dynamics equations are also given.
A robust method is developed and used to provide rational estimates of reaction zone thicknesses in one-dimensional steady gas-phase detonations in mixtures of inviscid ideal reacting gases whose chemistry is described by detailed kinetics of the interactions of N molecular species constituted from L atomic elements. The conser-vation principles are cast as a set of algebraic relations giving pressure, temperature, density, velocity, and L species mass fractions as functions of the remaining N–L species mass fractions. These are used to recast the N–L species evolution equations as a self-contained system of nonlinear ordinary differential equations of the form dY i /dx = f i (Y 1 , . . . , Y N–L). These equations are numerically integrated from a shock to an equilibrium end state. The eigenvalues of the Jacobian of f i are calculated at every point in space, and their reciprocals give local esti-mates of all length scales. Application of the method to the standard problem of a stoichiometric Chapman–Jouguet hydrogen–air detonation in a mixture with ambient pressure of 1 atm and temperature of 298 K reveals that the finest length scale is on the order of 10 −5 cm; this is orders of magnitude smaller than both the induction zone length, 10 −2 cm, and the overall reaction zone length, 10 0 cm. To achieve numerical stability and convergence of the solution at a rate consistent with the order of accuracy of the numerical method as the spatial grid is refined, it is shown that one must employ a grid with a finer spatial discretization than the smallest physical length scale. It is shown that published results of detonation structures predicted by models with detailed kinetics are typically underresolved by one to five orders of magnitude.
The oblique detonation induced by a two-dimensional semi-infinite wedge is simulated numerically with the Navier-Stokes equations and a detailed H 2 /air reaction model based on the open source program AMROC Adaptive Mesh Refinement in Object-oriented C++. A spatially seventh-order-accurate WENO scheme is adopted for the convective flux discretization. The formation and evolution of the oblique detonation induced by wedges at different angles and inflow conditions are investigated and a prediction model for oblique detonation flow field is proposed. The results show that the formation of oblique detonation flow field can be divided into two processes. The first process is similar to the oblique shock flow field with unreactive inflow. When the inflow passes through the wedge, the oblique shock wave starts to form at the tip, followed by the unstable curved shock surface and triple point. In this process, a thin reaction layer is formed on the wedge front, but the thickness of the reaction layer is almost constant. The second process is similar to DDT. As the reaction rate increases, the deflagration front is fixed on the wedge, the reaction layer thickens, and the deflagration front gradually approaches the oblique shock wave. When the deflagration front is coupled with the oblique shock wave, the oblique detonation is formed. Moreover, a theoretical prediction model for the triple point location is proposed. Compared with the numerical simulation results, the theoretical model prediction for the position of the transition point of OSW-ODW is relatively acceptable.
In this paper, we investigate the formation and development characteristics of oblique detonation wave in stoichiometric hydrogen-oxygen mixtures diluted with argon using Euler equations coupled with the 19-step or 34-step chemical reaction model. The novelty of this work lies in the study of differences in the characteristics of the initiation region and the formation processes of oblique detonation by different chemical kinetic processes. The formation processes of radicals in the induction region and heat release region for the oblique detonation flow field are emphatically analyzed, and the differences in the sensitivity on the key chemical reaction channels to radicals are also discussed. The results show that under the action of 19-step mechanism, the oblique detonation forms relatively early, the wave morphology of the flow field is complex, and the type of the initiation region is abrupt transition. While for the 34-step mechanism, the structure of flow field is simple with smooth transition type. The existence of transverse wave in the mainstream region contributes a lot to the formation of a sonic region and the abrupt transition structure. The chemical kinetic process directly affects the flow field structure of oblique detonation, and H2O2 plays an important role on triggering and accelerating the exothermic process. The radicals of H, O and H2O2 have different properties in different chemical reaction models.
The influence of the viscous boundary layer on the oblique detonation wave structure has been simulated and analyzed by solving the two-dimensional Navier–Stokes equations containing the hydrogen/air elementary reaction model. It is found that the effect of the viscous boundary layer can be neglected in the smooth transition initiation structure, but not in the abrupt transition initiation structure. The interaction of the lateral shock wave and the viscous boundary layer results in the formation of a high-temperature recirculation zone near the wall of the initiation zone, a novel structure that does not appear in inviscid formulations. Within this structure, the chemical reaction is triggered to occur in advance, eventually leading to the equilibrium initiation position relocating upstream compared with the inviscid case. Nevertheless, the viscous boundary layer has a limited impact on the main flow region downstream of the oblique detonation. The shock wave structures and pressure distributions at various Mach numbers are obtained computationally and analyzed in detail.
The flow structure and stability of oblique detonation waves (ODWs) affected by shock wave-boundary layer interactions (SBLIs) are investigated based on Reynolds averaging method. ODWs with smooth and abrupt transitions are studied separately. The results show that there are no shock waves behind detonation wave surface for ODWs with smooth transitions, so the flow structures are only affected by the ramp-induced SBLI. Under the circumstances, the compression effects of the focused shock instead of the separation shock is the main cause of the initiation of ODW, which leads to an obvious increase in the initiation length. In ODWs with abrupt transitions, the primary transverse wave is formed and reflects on the wedge surface. Besides the ramp-induced SBLI, post-wave SBLI also occurs. The two kinds of SBLIs are influenced by the thickness of the inflow boundary layer and the activity of the inflow mixture. When the inflow boundary layer is thin and the activity is low, the separation zone is small and the distance between the ramp-induced separation zone and the post-wave separation zone is large, which makes the ramp-induced separation separated from the post-wave subsonic area. The post-wave SBLI makes the shock configuration at the end of the induction zone change from the λ-shaped to the Y-shaped, which weakens the stability of the ODW. When the inflow boundary layer is thick or the activity is high, the separation zone is large and the distance between the two separation areas is large, which makes the ramp-induced separation merge with the post-wave subsonic area and an extended separation is formed which covers the wedge surface. As the flowfield develops, the extended separation becomes larger and larger, leading to further increase of the initiation length. Finally the ODW propagates out of the calculation domain and fails to be stabilized on the wedge surface.
The propagation of two-dimensional cellular gaseous detonation bounded by an inert layer is examined via computational simulations. The analysis is based on the high-order integration of the reactive Euler equations with a one-step irreversible reaction. To assess whether the cellular instabilities have a significant influence on a detonation yielding confinement, we achieved numerical simulations for several mixtures from very stable to mildly unstable. The cell regularity was controlled through the value of the activation energy, while keeping constant the ideal Zel’dovich - von Neumann - Döring (ZND) half-reaction length. For stable detonations, the detonation velocity deficit and structure are in accordance with the generalized ZND model, which incorporates the losses due to the front curvature. The deviation with this laminar solution is clear as the activation energy is more significant, increasing the flow field complexity, the variations of the detonation velocity, and the transverse wave strength. The chemical length scale gets thicker, as well as the hydrodynamic thickness. The sonic location is delayed due to the presence of hydrodynamic fluctuations, for which the intensity is increased with the activation energy as well as with the losses to a lesser extent. The flow field has been studied through numerical soot foils, detonation velocities, and 2D detonation front profiles, which are consistent with experimental findings. The velocity deficit increases with the cell irregularity. Moreover, the relation between the detonation limits obtained numerically and in detonation experiments with losses is discussed.
Operator splitting is a numerical method of computing the solution to a differential equation. The splitting method separates the original equation into two parts over a time step, separately computes the solution to each part, and then combines the two separate solutions to form a solution to the original equation. A canonical example is splitting of diffusion terms and convection terms in a convection-diffusion partial differential equation. Related applications of splitting for reaction-diffusion partial differential equations in chemistry and in biology are emphasized here. The splitting idea generalizes in a natural way to equations with more than two operators. In all cases, the computational advantage is that it is faster to compute the solution of the split terms separately, than to compute the solution directly when they are treated together. However, this comes at the cost of an error introduced by the splitting, so strategies have been devised to control this error. This chapter introduces splitting methods and surveys recent developments in the area. An interesting perspective on absorbing boundary conditions in wave equations comes via Toeplitz-plus-Hankel splitting. One recent development, balanced splitting, deserves and receives special mention: it is a new splitting method that correctly captures steady state behavior.
The structure of oblique detonation waves stabilized on a hypersonic wedge in mixtures characterized by a large activation energy is investigated via steady method of characteristics (MoC) calculations and unsteady computational flowfield simulations. The steady MoC solutions show that, after the transition from shock-induced combustion to an overdriven oblique detonation, the shock and reaction complex exhibit a spatial oscillation. The degree of overdrive required to suppress this oscillation was found to be nearly equal to the overdrive required to force a one-dimensional piston-driven detonation to be stable, demonstrating the equivalence of two-dimensional steady oblique detonations and one-dimensional unsteady detonations. Full unsteady computational simulations of the flowfield using an adaptive refinement scheme showed that these spatial oscillations are transient in nature, evolving in time into transverse waves on the leading shock front. The formation of left-running transverse waves (facing upstream) precedes the formation of right-running transverse waves (facing downstream). Both sets of waves are convected downstream away from the wedge in the supersonic flow behind the leading oblique front, such that the mechanism of instability must continuously generate new transverse waves from an initially uniform flow. Together, these waves define a cellular structure that is qualitatively similar to a normal propagating detonation.
In this study, the onset of cellular structure on oblique detonation surfaces is investigated numerically using a one-step irreversible Arrhenius reaction kinetic model. Two types of oblique detonations are observed from the simulations. One is weakly unstable characterized by the existence of a planar surface, and the other is strongly unstable characterized by the immediate formation of the cellular structure. It is found that a high degree of overdrive suppresses the formation of cellular structures as confirmed by the results of many previous studies. However, the present investigation demonstrates that cellular structures also appear with degree of overdrive of 2.06 and 2.37, values much higher than similar to 1.8 suggested previously in the literature for the critical value defining the instability boundary of oblique detonations. This contradiction could be explained by the use of differently shaped walls, a straight wall used in this study and a custom-designed curved wedge system so as to induce straight oblique detonations in previous studies. Another possible reason could be due to the low and possibly insufficient resolution used in previously published studies. Hence, simulations with different grid sizes are also performed to examine the effect of resolution on the numerical solutions. Using the present results, analysis also shows that although the characteristic lengths of unstable surfaces are different when the incident Mach number changes, these length scales are proportional to tangential velocities. Hence, the interior time determined by the overdrive degree is identified, and its limitation as the instability parameter is discussed.
Oblique detonation waves are simulated to study the evolution of their morphology as gasdynamic and chemical parameters are varied. Although two kinds of transition pattern have previously been observed, specifically an abrupt transition and a smooth one, the determining factors for the transition pattern are still unclear. Numerical results show that the transition pattern is influenced by the inflow Mach number, chemical activation energy and heat release. Despite the fact that these parameters were known to influence the detonation instability, the transition pattern variation cannot be predicted according to the instability criterion. In this study, the difference in the oblique shock and detonation angles is proposed as the criterion to determine the transition pattern with the aid of shock-polar analysis. It is found that the smooth transition will appear when the angle difference is small, while the abrupt transition will occur when the difference is large. The shift from the smooth transition to the abrupt transition occurs when the angle difference is about –. The previously proposed criterion using the characteristic time ratio is also examined and compared with the present angle difference criterion, and the latter is proved to provide better results.
A survey of propulsion based on detonation of chemical systems is provided in this paper. After a short historical review, basic schematics of engines utilizing detonation as the combustion mechanism are described. Possible improvement of propulsive efficiency due to detonative combustion which results in a significant pressure increase is presented, and a comparison of deflagrative and detonative combustion is discussed. Basic research on Pulsed Detonation Engines (PDE) and rotating detonations in cylindrical and disk-like chambers for different mixtures is presented. Basic principles of engines utilizing Standing Detonation Waves as well as Ram Accelerators are also provided. Detailed descriptions of PDE as well as Rotating Detonation Engines (RDE) are given. Different implementations of the PDE concept are presented and experimental and theoretical results to date are reviewed. Special attention is given to RDE, since rotating detonation can be applied to all kinds of propulsive engines including rocket, ramjet, turbine, and combined-cycle engines. A survey of detonative propulsion research carried out at different laboratories is presented, and possible future applications of such propulsion systems are discussed. A short note on detonative propulsion using non-chemical energy sources is also given.
An oblique detonation wave (ODW) for a Mach 7 inlet flow over a long enough wedge of 30 turning angle was simulated numerically using Euler equation with one-step rection model. The fifth-order WENO scheme was adopted to capture the shock wave. The numerical results show that three regions in the flow field behind ODW are defined: ZND model-like strcuture, single-sided triple point structure and dual-headed triple point strucuture according to the wavelet structures. The first structure is the smooth straight. The latter two structures are very complicated. In single-sided triple point structure all triple points facing upstream propagate dowanstream with almost same velocities and have the character of temporal periodicity. Simultaneously, the triple point traces are recorded to obtain cell structure of parallel straight lines. In the last structure the triple points move down with two different velocities. The velocity of triple points facing downstream is obviously faster than that facing upstream, which leads to the periodic collisions of the triple point. This period has the character of temporal and spatial periodicity. Cell structure is the inclining “fish scale” patterns due to the velocity component of the incoming flow tangential to the oblique detonation wave.
The detailed detonation structure generated by multiple shocks on ram-accelerator projectiles is studied using highly resolved numerical stimulations. The simulations show that the detonation structure on the projectile consists of the following basic elements: nonreactive shocks, induction regions, deflagration waves, and detonation waves. The shape and location of these basic elements strongly depends on the projectile Mach number. In some cases, the induction region and the related detonation wave are primarily associated with one single shock. In other cases, the induction region extends across several shocks and the detonation structure is much more complex. These simulations also confirm that the detonations on the projectile are stable in a wide range of flow conditions and, therefore, can be used to generate the high pressure needed for projectile propulsion.
Detailed oblique detonation wave structure produced by a wedge at hypersonic speed (Mach number M48.3) is studied experimentally using the oblique shock tube facility of the Laboratoire de Combustion et de Détonique (LCD) Laboratory. The flowfield induced by the wedge is visualized using multiframe schlieren and planar laser-induced fluorescence (PLIF) imaging. In addition, the story of the establishment and propagating phase of the structure is followed by smoked foil technique. Experiments performed in H2 + 2.38O2 mixture show that onset of oblique detonation is triggered by oblique shock wave, after a delay corresponding to the chemical induction time. The basic configuration appears as a three waves structure issued from a triple point, that is, the oblique shock wave, the oblique detonation wave, and a transverse detonation wave. The transverse detonation wave is found especially overdriven. For relatively short induction time corresponding to an initial pressure of p0 = 0.5 bar, the triple point is fairly stable. Reducing the initial pressure (p0 ≤ 0.4 bar) causes the apparition of periodic instabilities: the triple point oscillates around an average position. These periodic instabilities seem to be linked to the chemical induction time. These instabilities correspond to an explosion behind the oblique shock wave and ahead of the triple point structure, giving birth to a new triple point, replacing the old one. At that time, computational fluid dynamics (CFD) models failed to simulate this structure and linked mechanism of instabilities. New improvements in modeling may provide better results.
Applications of detonations to propulsion are reviewed. First, the advantages of the detonation cycle over the constant pressure combustion cycle, typical of conventional propulsion engines, are discussed. Then the early studies of standing normal detonations, intermittent (or pulsed) detonations, rotating detonations, and oblique shock-induced detonations are reviewed. This is followed by a brief discussion of detonation thrusters, laser- supported detonations and oblique detonation wave engines. Finally, a more detailed review of research during the past decade on ram accelerators and pulsed detonation engines is presented. The impact of the early work on these recent developments and some of the outstanding issues are also discussed. In this paper, the status of propulsion applications of detonations is reviewed. First, a cycle analysis is performed to show that the ef- é ciencyof a detonation cycleisclosetothat of the constant-volume Humphrey cycle, which is much more efécient than the constant- pressure Brayton cycle,characteristicof most conventional propul- sion systems. Other advantages of detonations are also discussed. Then a review of the early attempts to use detonations for propul- sionispresented.Aftera briefdiscussionof the possible reasonsfor the successes and failures of the early attempts, more recent work during the 1980s on oblique detonation wave engines is reviewed. This is followed by a detailedanalysis of the ram acceleratorin the detonative mode and the pulsed detonation engine, a topic of great current interest. Finally, some observations from the lessons learnt in the past and their potential implications for further development of detonations for propulsion applications are presented.
We have experimentally studied self-sustained oblique detonation waves around projectiles as part of a fundamental investigation of the application of an oblique detonation wave engine and a high-efficiency detonation wave combustor as a power generator. In previous papers we used optical observation to clarify the fluid-dynamic structure of self-sustained oblique detonations stabilized around cone-nosed projectiles. In this study we investigated the criticality for detonation waves. The first expression of the criticality was a mean-curvature coefficient, a rate between a detonation cell width and a mean-curvature radius in which the normal velocity component was the Chapman-Jouguet (C-J) velocit)4 of 5.03. The mean-curvature coefficient was constant and did not depend on the type of fuel mixture (H-2/O-2/Ar or C2H2/O-2/Ar), initial mixture pressure, projectile diameter, projectile velocity, or diluent mole fraction. We obtained a more accurate mean-curvature coefficient for stabilized oblique detonation around symmetric spherical bodies in highly krypton-diluted acetylene/oxygen mixtures that have extremely low C-J velocities. The mean-curvature coefficient of 7.8 was determined to be the most important value for stabilizing the self-sustained oblique detonation waves around multidimensional bodies. Based on experimental results obtained at high- and low-projectile-velocity ranges, it may be concluded that a lower-velocity projectile can stabilize a self-sustained oblique detonation wave more effectively than can a higher-velocity one. In the high-projectile-velocity region, the experimental critical condition is inconsistent with Lee's detonation initiation theory. We propose a semiempirical criticality equation for the stabilization, which was the secondary expression of the criticality and identical with present and past experimental results.
Oblique detonation structures induced by the wedge in the supersonic combustible gas mixtures are simulated numerically. The results show that the stationary oblique detonation structures are influenced by the gas flow Mach number, and a novel critical oblique detonation structure, which is characterized by a more complicated wave system, appears in the low Mach number cases. By introducing the inflow disturbance, its nonstationary evolution process is illustrated and its stability is verified.
The missing contact surface in the approximate Riemann solver of Harten, Lax, and van Leer is restored. This is achieved following the same principles as in the original solver. We also present new ways of obtaining wave-speed estimates. The resulting solver is as accurate and robust as the exact Riemann solver, but it is simpler and computationally more efficient than the latter, particulaly for non-ideal gases. The improved Riemann solver is implemented in the second-order WAF method and tested for one-dimensional problems with exact solutions and for a two-dimensional problem with experimental results.
Stable delayed oblique detonation waves have been observed both numerically and experimentally in hydrogen-air stoichiometric mixtures for Mach numbers 6 and 7.5. The experimental results obtained using an oblique shock tube facility are compared to calculations made by solving the full conservation equations for a reactive gas. The overall flow structure obtained experimentally is compared to detailed computations of an oblique shock wave to oblique detonation-wave transition over a wedge, and resulting flow fields are analyzed on the basis of shock and detonation polars.