Shock-induced Combustion Research Articles

Prediction Method of Unsteady Combustion Around Hypersonic Projectile in Stoichiometric Hydrogen-Air

An effective nondimensional parameter, referred to as the first Damkohler parameter, is proposed to quantitatively classify the unsteady flow regime of shock-induced combustion around a hypervelocity spherical projectile in the stoichiometric hydrogen-air mixture. The parameter consists of the ratio of the fluid characteristic timescale to the chemical characteristic timescale. The fluid characteristic time is defined as a projectile diameter divided by a speed of sound behind the normal segment of the steady bow shock. The chemical characteristic time is defined as a temperature behind the normal segment of the steady bow shock over the maximum temperature increase per unit time for the exothermicity. The temperature increase for the exothermicity is estimated by the time integration of the species equations in the zero dimension in space. The proposed first Damkohler number can be analytically computed by the chemical and fluid characteristics only, without ballistic range experiments or expensive simulations on high-performance computers. The parameter is quantitatively characterized from the two distinct flow regimes observed in the experimental and numerical results. Also, features of the transition between two regimes are clarified by changing the projectile diameter, the projectile speed, and the test gas pressure.

NUMERICAL METHODS FOR TREATING DISPARATE SCALES IN HIGH-SPEED REACTING FLOWS

Multiple length and time scales exist in high-speed reacting flows and need to be treated with due care when such flows are modeled. In this study, two numerical aspects relevant to reacting flow computations are addressed: (I) alternatively a fully implicit and a prediction-correction splitting procedure for treating the stiff source terms arising in the chemically reacting flow field, and (2) a source term reseating procedure to accommodate the disparate scales in the flow field. A shock-induced combustion scenario resulting from a hypersonic projectile flow is used as the test problem to facilitate investigation of these issues. It is found that the splitting procedure can capture the coupling of the fluid dynamics and chemical reactions accurately, while reducing the computational requirements, and the reseating treatment can compensate for the error caused by inadequate numerical resolutions.

An Induction Parameter Model for Shock-Induced Hydrogen Combustion Simulations

An induction parameter model has been constructed for the simulation of shock-induced combustion that incorporates the repro-modeling approach for the description of the energy release phase. The model applies only explicit, algebraic functions for the description of the chemical kinetics. These functions parameterize a set of data calculated from homogeneous combustion simulations using a complete and detailed reaction mechanism. Based on this method a model has been created for the simulation of shock-induced combustion of hydrogen in an argon atmosphere. The parameterized model approximates the results of the full chemistry very closely, but the algebraic functions can be computed in a fraction of the time of the full chemistry solution. We use the parameterized model in one- and two-dimensional reactive flow simulations. The results simulate experimental results well, including transitions to detonations and the propagation of detonation waves.

Shock-induced combustion in high-speed wedge flows

OH planar laser-induced fluorescence (PLIF) and schlieren imaging were applied to investigate shock-induced combustion phenomena on a 40° wedge in an expansion tube. OH PLIF was utilized to determine the regions of combustion in the flow field, while schlieren imaging provided complementary shock-wave visualization. Stoichiometric H 2 /O 2 gas mixtures, at three different levels of nitrogen dilution (75, 80, and 85%), were tested at two different test-flow conditions in these experiments. A pressure transducer was mounted in the wedge to obtain a record of the surface-pressure history on the model. Three test cases yielded shock-induced combustion behind an attached shock at the tip of the wedge. Depending on the sensitivity of the mixture employed, the flame front either rapidly converged with the shock or slowly diverged away from it. The measured wave angles and surface pressures in these tests were, in general, well modeled by shock-polar theory using frozen thermochemistry. Two other test cases, using the most sensitive gas mixtures, produced a closely coupled flame front behind a detached shock wave near the wedge tip. The measured surface pressure in this latter case was better modeled by a shock polar using equilibrium chemistry. Simple finite-rate chemistry modeling of the ignition zone agrees well with the experimental results in all cases.

Numerical and theoretical studies on detonation initiation by a supersonic projectile

Conditions of detonation initiation induced by a supersonic sphere in a stoichiometric hydrogen/oxygen mixture with 70% argon dilution are investigated numerically and theoretically. Transitions of the two extremes, shock-induced combustion and detonation initiation, are examined over pressures ranging between 0.2 and 10 bar. Numerical results show a very distinct detonation initiation boundary that separates the detonatable and undetonatable regions. A good agreement is shown through the comparison of the numerical results with the recent experimenetal data. Additionally, a theoretical investigation on the determination of detonation initiation boundary is carried out by introducing a concept of the kinetic limit. The kinetic limit is defined by the ignition Damkohler number. A joint theory for the determination of the detonation initiation boundary is presented by relating the present kinetic limit defined by the unity ignition Damkohler number with the energy limit given by Lee. Comparison between the theory and the experiment over a wide pressure range shows that the detonation initiation boundary can be well defined by the present joint theory.

Experimental Studies on Supersonic Combustion Phenomena of C0-O2-H2 Premixed Gases around Hypersonic Projectiles.

Hypersonic projectiles were fired into CO-O2 and CO-O2-H2 gas mixtures. For observation of combustion phenomena around the projectiles, we employed a high-speed framing schlieren technique. When we used CO-O2 mixtures as combustible gases, no shock-induced combustion was observed. However, addition of a small amount of H2 into the CO-O2 mixtures enabled combustion. We experimentally investigated the dependence of combustion phenomena on the molar fraction of H2 in the CO-O2-H2 gas mixtures. The high-speed framing schlieren technique made it possible to observe and discuss unsteady shock-induced combustion phenomena.

Reacting Flow Establishment in Ram Accelerators: A Numerical Study

The temporal evolution of the combustion process that is established during projectile transition from the launch tube into the ram accelerator section containing an explosive hydrogen ‐ oxygen‐ argon gas mixture is examined. The Navier ‐ Stokes equations for chemically reacting e ow are solved in a fully coupled manner, using an implicit, time-accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen ‐ oxygen‐ argon chemistry is modeled with a nine-species, 19-step reaction mechanism. Results of the numerical simulations are presented for two representative cases. We study the temporal developments of shock-induced combustion and thrust force. Positive thrust occurs in both ram accelerator cone gurations presented; however, combustion in the boundary layer enhances its separation, ultimately resulting in unstart.

Prediction method of unsteady combustion around hypersonic projectile in stoichiometric hydrogen-air

An effective nondimensional parameter, referred to as the first Damkohler parameter, is proposed to quantitatively classify the unsteady flow regime of shock-induced combustion around a hypervelocity spherical projectile in the stoichiometric hydrogen-air mixture. The parameter consists of the ratio of the fluid characteristic timescale to the chemical characteristic timescale. The fluid characteristic time is defined as a projectile diameter divided by a speed of sound behind the normal segment of the steady bow shock. The chemical characteristic time is defined as a temperature behind the normal segment of the steady bow shock over the maximum temperature increase per unit time for the exothermicity. The temperature increase for the exothermicity is estimated by the time integration of the species equations in the zero dimension in space. The proposed first Damkohler number can be analytically computed by the chemical and fluid characteristics only, without ballistic range experiments or expensive simulations on high-performance computers. The parameter is quantitatively characterized from the two distinct flow regimes observed in the experimental and numerical results. Also, features of the transition between two regimes are clarified by changing the projectile diameter, the projectile speed, and the test gas pressure.

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart.

Numerical investigation of the one-dimensional piston supported detonation waves

One-dimensional detonation waves supported by a piston are numerically investigated. The analysis is carried out based on the numerical simulation using a finite difference method. A simplified two-step chemical reaction model consisting of the induction and exothermic reactions is used. Two types of unsteady oscillations are observed at the shock front in the simulation results: one shows a high frequency and low amplitude oscillation and the other shows a low frequency and low amplitude one. In the simulation results, the oscillation type does not depends on the intensity of the concentration of the heat release due to the combustion, even though the oscillation type depends on the piston speed. The flow features of the oscillatory shock front are clarified with the x- t diagram. The mechanism obtained in the present study is discussed in comparison with the unsteady phenomena observed as the shock-induced combustion around a hypersonic spherical projectile.

Nonequilibrium hydrogen combustion in one- and two-phase supersonic flow

A time-splitting method for the numerical simulation of stiff nonequilibrium combustion problem was developed. The algorithm has been applied to simulate the shock-induced combustion and to investigate a supersonic one- and two-phase flowfield. The results are physically reasonable and demonstrate that the presence of particles has a dramatic effect on the nozzle flowfield and the the thrust.

Experimental Studies on Supersonic Combustion Phenomena of CO-O2-H2 Premixed Gases around Hypersonic Projectiles.

Hypersonic projectiles were fired into CO-O2 and CO-O2-H2 gas mixtures. For observation of combustion phenomena around the projectiles, we used a high-speed framing schlieren technique. When we used CO-O2 mixtures as combustible gases, no shock-induced combustion was observed. However, addition of a small amount of H2 into the CO-O2 mixtures enabled combustion. We experimentally investigated the dependence of combustion phenomena on the molar fraction of H2 in the combustible gases. The high-speed framing schlieren technique made it possible to observe and discuss unsteady shock-induced combustion phenomena.

Detailed mechanism of the unsteady combustion around hypersonic projectiles

Flow features of an unsteady shock-induced combustion around projectiles are numerically studied using a finite difference method. The large-disturbance regime of the unsteady combustion, characterized by a low-frequency and high-amplitude oscillation, is investigated by a series of simulations considering an oxygen-hydrogen combustion mechanism under the same condition as the experiment. The time-evolving flowfield is obtained in the simulation, and the mechanism of the unsteady phenomenon is investigated. The mechanism on the stagnation streamline agrees with our previously proposed model using a simplified chemical reaction model. Several detailed features characterizing the large-disturbance regime of unsteady combustion are revealed in the computations, and an improved mechanism is proposed. The grid refinement study is carried out to confirm that the flow features obtained are grid independent and are not fictitious. Nomenclature M = projectile Mach number P = pressure T - temperature t = time V = projectile velocity x = distance T = oscillation period TV = induction time

Upwind unstructured scheme for three-dimensional combusting flows

As an interim step towards the development of a hybrid upwind structured/unstructured solver for combusting/multiphase flowfields, the TRI3D unstructured code of Barth has been extended to analyze multicomponent combusting flows. The extensions mimic the Roe/total variation diminishing (TVD) based thermochemical extensions in the structured solver, CRAFT, and entail a strong coupling of chemical species equations and complete linearization of the chemical source term, treated hi a fully implicit manner. Issues regarding the quality of solutions obtained using locally one-dimensional Riemann flux procedures and TVD limiters are more pronounced in unstructured formulations and are dealt with in depth in this article. Comparative studies of structured and unstructured analyses of laminar premixed flames, ducted shock-induced combustion, and blunt-body shock-induced combustion serve to delineate these issues and the need for solution adaptive gridding and unproved flux limiters to capture flame zones properly.

Simulation of shock-induced combustion past blunt projectiles using shock-fitting technique

Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shockinduced combustion at Mach 5.11 and 6.46 in hydrogen-air mixture. A finite difference, shock-fitting method is used to solve the complete set of Navier- Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since the shock-fitting approach reduces the amount of artificial dissipation, all intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with a one-dimensional wave-interacti on model.

Numerical modeling of chemistry and gas dynamics during shock-induced ethylene combustion

Numerical modeling of chemistry and gas dynamics during shock-induced ethylene combustion

Numerical modeling of chemistry and gas dynamics during shock-induced ethylene combustion

We present the results of a numerical study of shock-induced ethylene combustion. As in other reactive flow problems the computational time increases significantly when finite rate chemistry is included. We compare the accuracy and efficiency of a variety of methods when applied to this combustion problem. For a full kinetics scheme we consider the speed of a range of alternative ordinary differential equation solvers. We find that for the coupled ODE-hydrodynamic problem an extrapolated linearly implicit Euler method is the fastest of the methods used, but that otherwise a fourth-order Rosenbrock scheme is the fastest solution method. The identity of the fastest method changes because of the start up conditions having to be recalculated at the start of every step in a coupled ODE-hydrodynamics module. The faster methods in a static simulation, where the values of the variables can be carried over between time-steps without recalculation, generally have higher start-up penalties, and as a consequence are generally slower in a reactive flow model. We then apply a detailed reduction strategy to a chemical kinetics reaction data set and find that it cannot be reduced by many reactions as it is already a fairly compact set. We then introduce an induction parameter model based on the two parameter model of Taki and Fujiwara [1] and the work of Oran et al. [2]. We derive functions that model the induction times and the energy release rates predicted using the chemical kinetics data set. We show some results of coupled gas dynamics and reactive flow calculations using these models and compare with experiment. We find that the induction parameter model reproduces the experimental results well whilst using less than 5% of the computational time of the chemical kinetics model.

A fully implicit time accurate method for hypersonic combustion: application to shock-induced combustion instability

A fully implicit time accurate method for hypersonic combustion: application to shock-induced combustion instability

Dimensional analysis of the effect of flow conditions on shock-induced combustion

A dimensional analysis is attempted to elucidate the effects of the flow conditions on the regines of shock-induced combustion around a blunt body in stoichiometric hydrogen-oxygen mixtures. At a given Mach number, the effects of body size, inflow pressure, and inflow temperature are investigated. The analysis is based on a series of numerical simulations employing a fully implicit method and an upwind scheme. From the results of the numerical simulations with various flow conditions, different regimes of shock-induced combustion are observed ranging from decoupled shock-deflagration to overdriven detonation. From a viewpoint of nondimensionalization, the two flow-field-configuration variables (the shock standoff distance and the induction distance) and the two dimensionless parameters (the first Damköhler number and the heat release parameter) are redefined along the stagnation streamline. The configuration variables and the dimensionless parameters are evaluated from the flow-field data to analyze quantitatively the global features of a shock-induced combustion flow field. The effects of flow conditions are identified in terms of the configuration variables and the dimensionless parameters. The correlations between the configuration variables and the dimensionless parameters are also investigated to understand the effects of flow conditions within a frame of reference.

Plif imaging of hypersonic reactive flow around blunt bodies

Qualitative OH planar laser-induced fluorescence (PLIF) imaging experiments of supersonic reactive flows over a 40° wedge and a 19-mm-diameter blunted cylinder are reported. Hydrogen-, ethylene-, and methane-based mixtures have been used in this work. Three different free stream conditions. M∞=6.7, 5.2 and 4.2, were used to study the combustion modes around the wedge and blunted cylinder. Separate schlieren imaging results were also obtained for several of the test cases, providing complementary shock wave visualization. In several cases for the wedge, shock-induced combustion was observed a finite distance behind the nonreacting oblique shock wave. For the most sensitive hydrogen mixture, an oblique detonation occurred in which the shock wave and combustion front were fully coupled. In the experiments with the blunted cylinder, two different regimes of combustion were observed. When the velocity of the flow was larger than the CJ velocity of the mixture, the mode was that of an adiabatic shock followed by a smooth combustion front. For cases of flow velocity similar to the CJ velocity or less, regular oscillations were observed on the image and in the stagnation pressure history. These observations are qualitatively consistent with previous work.