論文 - 松尾　亜紀子

Lagrangian characterization of induction and reaction timescales in a cellular gaseous detonation

Watanabe H., Matsuo A., Chinnayya A., Itouyama N., Matsuoka K., Kasahara J.

Physics of Fluids 37 （ 2 ）  2025年02月

ISSN  10706631

　概要を見る

A Lagrangian approach was proposed to analyze induction and reaction times in the cellular gaseous detonation. Two-dimensional simulations in an argon-diluted and non-diluted hydrogen-based mixtures were performed with detailed chemistry, along particle trajectories. The distribution of the induction and reaction times inside the cell was significantly different between the Eulerian and the Lagrangian perspectives, the latter showing non-monotonic behavior. Preferential thermodynamic paths laid along the Rankine-Hugoniot curve and behind transverse waves (TW). All particles were ignited within half and one cell cycle for the diluted and non-diluted mixture, respectively. The ignition mechanisms were not only one-dimensional, but also multi-dimensional, with ignition behind the TW being the most important, and collision of TW and triple points being secondary. A new topology inside the cell could be drawn, from the intersection of the ignition front with TW. TW appeared as phase waves in the ( x , t ) diagram. Comparison of H2O mass fraction between local and equilibrium values indicated that a local chemical disequilibrium remained (superequilibrium), due to TW. Equating the mean sonic plane with thermochemical equilibrium in the non-diluted case is not completely accurate. Furthermore, the characteristic time scales for chemical and hydrodynamic phenomena were compared. The diffusive phenomenon did not make any contribution in the mixtures tested. In comparison with the Zel'dovich-von Neumann-Döring model, a shorter average induction time was found in the non-diluted mixture, which is not in line with the results from previous Favre approaches. The average reaction time was also shorter in both mixtures.

• Access to Document (DOI)

Numerical Investigation of Detonation-assisted Fuel Injection Method in Scramjet Engines with Rotating Detonation Combustor

Miyashita M., Matsuo A., Shima E., Kawasaki A., Itouyama N., Matsuoka K., Kasahara J.

AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025 2025年

　概要を見る

This study conducted three-dimensional numerical analyses for the interaction of the exhaust flow of a Reflective Shuttling Detonation Combustor (RSDC) and supersonic air-flow to investigate the new concept of detonation combustion as an injection system for scramjet engines. The computational targets of RSDC are the region where the hydrogen-air premixed gas flows from three rows of injectors set at the bottom in fuel-rich conditions. The additional fuel for the supersonic turbulent combustion in the scramjet combustor was added from the side wall of RSDC. The reflective wall distance, the height, and the width of RSDC were set to 45.0 mm, 53 mm, and 5 mm. The supersonic air-flow area simulated scramjet combustor is the region where the air flows at Mach number 3, and the RSDC is related to the main flow area as an injector. The governing equations used in this study were a three-dimensional compressible Navier-Stokes equation and a chemical conservation law of 9 species. The mixed scale model for LES was also used as the turbulence model. As a result, turbulent combustion was observed in the supersonic flow area by mixing the supersonic flow and the exhaust flow of RSDC, including additional fuel. The dynamic pressure ratio of the exhaust flow was 23% greater than that of the single-hole injection (previous injection system of scramjet engine) and 13% greater than that of deflagration combustion. The penetration height was improved, and the turbulent combustion was continuously achieved without an ignition system or a cavity due to the detonation combustion inside the RSDC.

• Access to Document (DOI)

Synchronized Initiation of Two Cylindrical Rotating Detonation Engines

Sakata R., Inada M., Itouyama N., Matsuoka K., Kasahara J., Kawasaki A., Matsuo A., Funaki I.

Journal of Propulsion and Power 40 （ 6 ） 849 - 858 2024年11月

ISSN  07484658

　概要を見る

A coupled cylindrical rotating detonation engine (RDE) with two cylindrical RDEs (both combustors had a combustor inner diameter of 23 mm and an axial length of 30 mm) placed next to each other was tested for rocket clustering application. The objective of the experiment was to achieve two-engine synchronized initiation with a single igniter. Experiments were conducted on the inner wall of the combustors with different connecting-hole diameters and wall heights to evaluate the ignition delay time, combustion mode, and propulsion performance. The propellants were gaseous ethylene and oxygen, and experiments were conducted under constant conditions of mass flow rate (40 ± 2g∕s), equivalence ratio (1.0±0.1), and backpressure (approximately 10 kPa). When the two combustion chambers were completely separated by a wall, ignition occurred with a time delay of 260 ms in the chamber without an igniter. However, when a large hole (10-mm diameter) was placed in the wall separating the two combustion chambers, synchronous initiation was successful. Synchronous initiation was also successful when the wall height was lowered (7-mm height). Under both conditions, the same level of specific impulse was achieved as for RDEs operating at the same mass flux.

• Access to Document (DOI)

Wave-converging pressure increase in curved cylindrical rotating detonation combustors

Oda Y., Sawada S., Itouyama N., Matsuoka K., Kasahara J., Kawasaki A., Matsuo A., Funaki I.

Proceedings of the Combustion Institute （Proceedings of the Combustion Institute）  40 （ 1-4 ）  2024年08月

共著, 査読有り,  ISSN  15407489

　概要を見る

The internal combustion structure of a curved cylindrical rotating detonation combustor (RDC) was experimentally investigated through optical observation and pressure measurements. Experiments were conducted under low back pressure conditions using two combustion chambers having, in both cases, an internal diameter of 17.5 mm, a curvature of radius of 38.1 mm, and an outlet angle of 90 deg, with gaseous C2H4 and O2 as the propellants. One was made of SUS and the other of resin. In addition to vibrations and bottom center pressure, pressure distribution on the sidewalls was measured for the SUS combustor, and high-speed camera observations of self-luminescence from the radial direction were conducted for the resin combustor. These measurements were compared by varying the equivalence ratio. The frequency analysis results obtained from vibrations and self-luminescence indicated that the strongly-coupled detonation mode exhibited a higher peak frequency, suggesting that the detonation waves may have different propagation speeds or rotational positions. In terms of pressure distribution and self-luminescence, only the strongly-coupled detonation mode inside near the bottom surface exhibited high pressure and brightness values. This suggested the potential for converging pressure by employing rotating detonation waves and a curved tube.

• Access to Document (DOI)

Visualization and thrust measurement of rotating detonation engine with various channel expansion angles

Nakajima K., Sawada T., Matsuoka K., Itouyama N., Kasahara J., Kawasaki A., Matsuo A.

Proceedings of the Combustion Institute 40 （ 1-4 ） 105577 2024年07月

研究論文（国際会議プロシーディングス）, 共著, 査読有り,  ISSN  15407489

　概要を見る

Although a rotating detonation engine (RDE) is expected to achieve a pressure gain (PG) at which the total pressure of the product at the engine exit exceeds the total pressure of the supplied oxidizer, many non-ideal phenomena occurring in the RDE hinder PG achievement. This study focused on the channel expansion angle near the injector outlet, which is considered to affect the detonation wave structure and the PG performance. To this end, thrust and self-luminescence were conducted by varying the channel expansion angle near the axially injected oxidizer injector outlet; that is 90° 30°and 6° Results indicate that thrust was not affected by the expansion angle. However, the corresponding propagation velocities of the detonation waves were 2160, 2025, and 1755 m/s, indicating that the propagation velocity decreased as the expansion angle decreased. The PG performance, which is the ratio of the total pressure at the combustor exit to the total pressure of the oxidizer plenum, was 57, 57, and 49 %. At the expansion angle of 6°, the PG performance decreased due to a significant increase in the total pressure of the oxidizer plenum. Visualization of the self-luminescence showed that as the expansion angle decreased, the burned gas backflow became more significant, confirming unstable propagation.

• Access to Document (DOI)

Combustion Structure of a Cylindrical Rotating Detonation Engine with Liquid Ethanol and Nitrous Oxide

Sato T., Nakata K., Ishihara K., Itouyama N., Matsuoka K., Kasahara J., Kawasaki A., Nakata D., Eguchi H., Uchiumi M., Matsuo A., Funaki I.

Combustion and Flame （Combustion and Flame）  264 2024年06月

ISSN  00102180

　概要を見る

Liquid propellants are commonly used in rocket engines due to their high energy density. In this study, we focused on the use of liquid ethanol and liquid nitrous oxide as propellants in a cylindrical rotating detonation engine (RDE) for practical applications, and examined the effects of various conditions on the bipropellant RDE performance. We varied the vapor quality of nitrous oxide in a mixture of liquid and gaseous nitrous oxide due to the flash boiling. In addition, we varied the liquid ethanol temperature, the injector stiffness, and momentum angle of the propellant. We then analyzed the effects of these changes on the propagation mode of the RDE under atmospheric pressure conditions. The results showed that a rotating detonation wave was observed under the combination of high vapor quality of nitrous oxide, high injector stiffness, high liquid ethanol temperature, and high momentum angle. The propagation velocity was obtained as 73∼83 % of the Chapman-Jouguet velocity. Long-duration combustion tests were also conducted, and the internal combustion structure was confirmed from the erosion of the carbon-carbon (C/C) composite material. The detonation wave was considered to propagate near the bottom of the RDE with liquid propellants from the erosion heights of the C/C composite. The erosion height was confirmed to be consistent with the fill height calculated using the sound speed of the nitrous oxide. In addition, characteristic exhaust velocity efficiencies of more than 85 % were achieved in all combustion tests.

• Access to Document (DOI)

Combustion Structure of a Cylindrical Rotating Detonation Engine with Liquid Ethanol and Nitrous Oxide

Sato, T., Nakata, K. Ishihara, K., Itouyama, N., Matsuoka, K., Kasahara, J., Kawasaki, A., Nakata, D., Eguchi, H., Uchiumi, M., Matsuo, A., and Funaki, I.

Combustion and Flame 264 2024年06月

研究論文（学術雑誌）, 共著, 査読有り

Synchronized Initiation of the Two Cylindrical Rotating Detonation Engines

Sakata, R., Inada, M., Itouyama, N., Matsuoka, K., Kasahara, J., Kawasaki, A., Matsuo, A., and Funaki, I.

Journal of Propulsion and Power 2024年06月

研究論文（学術雑誌）, 共著, 査読有り

The circumferential force on a cylindrical rotating detonation engine

Sawada S., Ishihara K., Itouyama N., Watanabe H., Kawasaki A., Matsuoka K., Kasahara J., Matsuo A., Funaki I.

Proceedings of the Combustion Institute 40 （ 1-4 ） 105490 2024年06月

研究論文（国際会議プロシーディングス）, 共著, 査読有り,  ISSN  15407489

　概要を見る

Rotating detonation engines (RDEs) utilize single or multiple detonation waves continuously traveling at velocities ranging from 1 to 3 km/s. These waves induce a strong swirl near the inlet surface, generating circumferential shear stress on the surface of the combustion chamber. This stress works as torque in the axial direction. This characteristic is promising for turbine applications. However, for long-term operation, such applications require reduction in the thermal damage risk. While annular RDEs, which have an inner wall surface, involve the thermally independent center body, cylindrical RDEs have no center body and more suitable. On the other hand, the contact surface exposed to the swirling flow is smaller. This study evaluated the differences in combustion mode and circumferential phenomena between annular and cylindrical RDEs through the measurement of thrust and torque. The results showed that the torque generated by the cylindrical RDE was as large (around 0.1 Nm) as that generated by the annular RDE under mass flow rate of approximately 0.05 kg/s. This was due to the stronger swirl derived from the 16 % faster detonation waves. In addition, the presence of strong detonation combustion around the outer wall of the cylindrical RDE was indicated through the control surface method. When a fuel‒oxidizer was supplied to the strong detonation combustion region, the detonation waves reached velocities around the Chapman–Jouguet value, with the maximum torque in this study being 0.127 Nm. From these results, the effect of the propagation mode of detonation waves on the circumferential flow and force was evaluated. The results indicated that the increase of detonation wave velocity enhanced the circumferential flow and force. The tendency to increase became large as the number of the detonation waves increased.

• Access to Document (DOI)

Nitrous Oxide/Ethanol Cylindrical Rotating Detonation Engine for Sounding Rocket Space Flight

Ishihara K., Sato T., Kimura T., Nakajima K., Nakata K., Itouyama N., Kawasaki A., Matsuoka K., Matsuyama K., Kasahara J., Eguchi H., Nakata D., Uchiumi M., Matsuo A., Funaki I.

Journal of Spacecraft and Rockets 62 （ 1 ） 44 - 54 2024年05月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  00224650

　概要を見る

There are few experimental studies on rotating detonation engines (RDEs) with liquid propellants. This study reveals the static thrust performance of a cylindrical RDE with ethanol and liquid nitrous oxide as propellants under atmospheric pressure. This RDE had an inner diameter of 40 mm, a maximum combustor length of 230 mm, a nozzle contraction ratio of 1.7, and a nozzle expansion ratio of 9.1. Nineteen experiments were conducted at total mass flow rates of184–210 g∕s, mixtureratios of 3.6–5.9, andcombustionpressures of 0.35–0.46 MPa, resulting in a maximum detonation velocity of 1840 m∕s (approximately 80% of the theoretical detonation velocity, 2251 m∕s), maximum thrust at sea level of 294 N, and maximum specific impulse at sea level of 148 s. In addition, the maximum characteristic exhaust velocity, c*,was1716 m∕s, which was 99% of the theoretical value. The characteristic length of the combustion chamber at this time was 0.15 m. Since conventional rocket combustion requires 1.57 m to achieve the same c* efficiency, this study shows that detonation combustion can reduce the combustor size by 88%.

• Access to Document (DOI)

Effect of Channel Expansion Angle near Injector Outlet on a Rotating Detonation Engine Performance

Nakajima, K., Matsuoka, K., Itouyama, N., Kasahara, J., Kawasaki, A., and Matsuo. A.

ShockWaves（ICDERS　Special Issue） 2024年05月

研究論文（学術雑誌）, 共著, 査読有り

Effect of channel expansion angle near injector outlet on a rotating detonation engine performance

Nakajima K., Matsuoka K., Itouyama N., Kasahara J., Kawasaki A., Matsuo A.

Shock Waves （Shock Waves）  2024年

ISSN  09381287

　概要を見る

A rotating detonation engine (RDE) is expected to achieve a pressure gain (PG) in which the total pressure of the product at the engine exit exceeds the total pressure of the supplied oxidizer. However, many non-ideal phenomena exist in the RDE, which hinder the achievement of a PG. This study focused on the channel expansion angle near injector outlet which is considered to impact the structure of detonation wave and the PG performance. Combustion tests were conducted by varying the channel expansion angle near the axially injected oxidizer injector outlet to 90∘ and 30∘. As a result, the thrust was not affected by the expansion angle, but the propagation velocity of detonation wave at an expansion angle of 90∘ was approximately 5% higher than that at an expansion angle of 30∘. A comparison utilizing the pressure increase ratio obtained from the fluctuating pressure in the combustion chamber suggested that the Mach number of the detonation wave was higher for an expansion angle of 90∘. As a result of evaluating the PG performance utilizing the equivalent available pressure obtained from thrust measurements, it was not confirmed to differ with changes in the expansion angle.

• Access to Document (DOI)

The Rotating Detonation Engines with The Helical Combustion Chambers

Sawada S., Itouyama N., Matsuoka K., Kasahara J., Braun J., Paniagua G., Kawasaki A., Watanabe H., Higashino K., Matsuo A., Funaki I.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

Rotating detonation engines (RDEs) utilize a detonation wave circling at velocities on the order of kilometers inside a combustion chamber. In this study, the rotation direction was controlled by strategically positioning the ignition source at a specific location within a helical combustion chamber featuring sinusoidal circle cross section. Twenty-five combustion tests were conducted experimentally, involving two types of geometries with different helical directions. When the ignition was placed 30.3–45.7 mm far from the inlet surface, the direction of the rotating detonation wave was decided by the helical direction in all cases. By assuming that the direction of the rotating detonation wave was decided with a probability of 0.5, the probability of the 25 tests was 3×10-8, which was well beyond the 0.05 significance level. The direction of the rotating detonation wave was thus clearly depended on the helical direction. Moreover, the helical geometry is promising for the integration of combustion and torque extraction, thanks to the efficient extraction of torque primarily derived from the circumferential pressure difference on the helical crests. The torque generated was 0.040– 0.068, achieved with a mass flow rate of approximately 0.029 kg/s. The helical direction also controlled the direction of the torque.

• Access to Document (DOI)

Overview for the research and development of Rotating Detonation Engine Systems using a liquid-liquid propellant combination

Itouyama N., Matsuyama K., Matsuoka K., Sato T., Nakata K., Sawada S., Kudo Y., Nakajima K., Suzuki Y., Kasahara J., Kawasaki A., Namera M., Nakata D., Eguchi H., Uchiumi M., Matsuo A., Funaki I.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

Rotating detonation engines (RDEs) exert various characteristics and high propulsion performance depending on their operation mode. Our group has already demonstrated the RDE equipped with gas ethylene and gas oxygen in an outer-space environment using a sounding rocket. For the next step of R&D of detonation engine systems, we are planning to perform the in-space demonstration of detonation engine with liquid propellants to clarify its milestones on the achievement of space application of detonation engines as same as the conventional chemical propulsion systems, especially the propellant combination of ethanol and liquid nitrous oxide. This paper introduces the overview of our group’s measures on the in-space demonstration of the RDE system in the last few years.

• Access to Document (DOI)

Operating Characteristics of Cylindrical Rotating Detonation Engines Using Liquid Ethanol and Liquid Nitrous Oxide

Sato T., Nakata K., Sawada S., Suzuki Y., Kudo Y., Nakajima K., Itouyama N., Matsuoka K., Kasahara J., Kawasaki A., Namera M., Eguchi H., Nakata D., Uchiumi M., Matsuo A., Funaki I., Tanno H.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

Rotating detonation engine (RDE) is one of the combustors using detonation waves and is expected to simplify the system and improve thermal efficiency due to their supersonic combustion and compression performance by shock waves. Liquid propellants are commonly used in rocket engines due to their high energy density. However, most of these studies use gas propellants, so it is important to investigate the effect of the combustor length, mixture ratio, and propellant temperature on bipropellant RDE operation. In this study, cylindrical RDEs with liquid ethanol and liquid nitrous oxide were tested under atmospheric pressure conditions. The rotating detonation wave was observed in the cylindrical RDE with the liquid ethanol. About the effect on propagation mode, detonation mode was not observed when the mixture ratio was low, and the range of the mixture ratio in which the detonation mode was observed decreased as the combustor length decreased. When the ethanol liquid temperature was low, the detonation mode was not observed because the atomization performance and combustibility became lower. In addition, the rotating propagation mode was observed when the vapor quality of nitrous oxide was higher than about 9% because the propellant velocity was increased at the higher vapor quality of nitrous oxide, and this improved the atomization. Moreover, the throat pressure was close to the critical pressure for isentropic flow with a smaller ethanol injector diameter. The results of the experimental characteristic exhaust velocity in all combustion tests were in close match with the ideal value for the constant pressure mode. However, when the combustor length was 90 mm, the values in deflagration mode were much lower than the ideal value. Therefore, these results indicated that the combustion region was longer in the deflagration mode and with large ethanol injector diameter than in the detonation mode and small diameter, respectively.

• Access to Document (DOI)

Numerical Investigation on Throatless Diverging Rotating Detonation Engines

Sada T., Matsuo A., Shima E., Kawasaki A., Itouyama N., Matsuoka K., Kasahara J.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

In this study, the flow characteristics and propulsive performance of throatless diverging rotating detonation engines (RDEs) are investigated. Seven diverging angles, 0, 1, 2, 3, 4, 5, and 6 deg were examined with constant length 70 mm and bottom diameter 20 mm using stoichiometric hydrogen-air premixed gas as propellant. The temperature and pressure in the combustor decreased as the diverging angle increased, and the continuous detonation propagation could not be observed in the case of 6 deg. Supersonic exhaust was achieved for all conditions with α > 0 deg, and the exit Mach number increased with larger angle and was 1.71 in 5 deg channel. The expansion ratio increased, but the combustion efficiency decreased with larger angle, so the thrust and specific impulse did not monotonically increase with increasing diverging angle. The specific impulse reached a maximum around 3 deg in this geometry.

• Access to Document (DOI)

Experimental Research for Clustering with the Coupled Cylindrical Rotating Detonation Engine

Sakata R., Inada M., Itouyama N., Matsuoka K., Kasahara J., Kawasaki A., Matsuo A., Funaki I.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

It is possible to achieve a high flow rate and high thrust by clustering small cylindrical rotating detonation engines while reducing the axial length of the engines. In this study, a coupled cylindrical rotating detonation engine with two cylindrical RDEs (both combustors had a combustor inner diameter of 23 mm and an axial length of 30 mm) placed next to each other was fabricated and tested for clustering. The objective of the experiment was to achieve two-engine synchronized initiation with a single igniter. Experiments were conducted on the inner wall of the combustor with different connecting hole diameters d and wall heights h to evaluate the ignition mechanism, combustion mode, and propulsion performance. The propellants were gaseous ethylene and oxygen, and experiments were conducted under constant conditions of mass flow rate (the range of 40 ± 2 g/s), equivalent ratio (the range of 1 ± 0.1), and back pressure (approximately 10 kPa). The experimental results showed that when the two combustion chambers were completely separated by a wall, ignition occurred with a time delay in the chamber without an igniter. However, when a large hole (10 mm diameter) was placed in the wall separating the two combustion chambers, the flame propagated through the hole and synchronous initiation was successful. Synchronous initiation was also successful when the wall height was lowered (7 mm height), and high performance was obtained under both conditions. The flame was visualized by a high-speed camera during ignition and combustion, and the difference in combustion mode was confirmed. Frequency analysis was performed from the self-illuminated images taken by the high-speed camera to classify the

• Access to Document (DOI)

Combustion Characteristics of Reflective Shuttling Detonation Combustor with Different Equivalence Ratio

Miyashita M., Matsuo A., Shima E., Kawasaki A., Itouyama N., Matsuoka K., Kasahara J.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

A three-dimensional numerical analysis was performed on a reflective shuttling detonation combustor to investigate the propagation phenomena of detonation in a fuel-rich condition, with different equivalence ratio. The computational domain was a rectangular region where the hydrogen-air premixed gas flows in from the bottom injector with changing equivalence ratio from 1.0 to 2.0. As a result, continuous propagation of detonation was observed in each case, and the same trend of the propagation mode was observed. In addition, A decrease in the temperature value during combustion and an increase in the propagation velocity were observed as the equivalent ratio increased. Both trends were consistent with the trends of CJ temperature and CJ velocity with increasing equivalent ratio.

• Access to Document (DOI)

A Bread Board Model Testing for In-Space Flight Demonstration of a Liquid-Propellant Detonation Engine System

Kawasaki A., Nakata K., Sato T., Sawada S., Kudo Y., Suzuki Y., Itouyama N., Matsuoka K., Matsuyama K., Kasahara J., Nakata D., Namera M., Eguchi H., Uchiumi M., Matsuo A., Funaki I., Nakamura S., Higashino K., Hirashima H.

AIAA SciTech Forum and Exposition, 2024 2024年

　概要を見る

In-space flight demonstration of a rotating detonation engine system using liquid nitrous oxygen and liquid ethanol as the propellant (DES-2) is planned in FY2024 by a collaborative research group of Nagoya University, Shizuoka University, Keio University, the Muroran Institute of Technology, and Institute of Space and Astronautical Science at the Japan Aerospace Exploration Agency (ISAS/JAXA). In this manuscript, a ground combustion test of the bread board model (BBM) of the DES-2, which has been conducted in May 2023, is briefly described. In the testing, the DES-2 BBM was operated in stand-alone mode and achieved detonation combustion as planned.

• Access to Document (DOI)

Lagrangian dispersion and averaging behind a two-dimensional gaseous detonation front

Watanabe H., Matsuo A., Chinnayya A., Itouyama N., Kawasaki A., Matsuoka K., Kasahara J.

Journal of Fluid Mechanics （Journal of Fluid Mechanics）  968 2023年08月

ISSN  00221120

　概要を見る

Two-dimensional numerical simulations with the particle tracking method were conducted to analyse the dispersion behind the detonation front and its mean structure. The mixtures were 2H-O-7Ar and 2H-O of increased irregularity in ambient conditions. The detonation could be described as a two-scale phenomenon, especially for the unstable case. The first scale is related to the main heat release zone, and the second where some classical laws of turbulence remain relevant. The dispersion of the particles was promoted by the fluctuations of the leading shock and its curvature, the presence of the reaction front, and to a lesser extent transverse waves, jets and vortex motion. Indeed, the dispersion and the relative dispersion could be scaled using the reduced activation energy and the parameter, respectively, suggesting that the main mechanism driving the dispersion came from the one-dimensional leading shock fluctuations and heat release. The dispersion within the induction time scale was closely related to the cellular structure, particles accumulating along the trajectory of the triple points. Then, after a transient where the fading transverse waves and the vortical motions coming from jets and slip lines were present, the relative dispersion relaxed towards a Richardson-Obukhov regime, especially for the unstable case. Two new Lagrangian Favre average procedures for the gaseous detonation in the instantaneous shock frame were proposed and the mean profiles were compared with those from Eulerian procedure. The characteristic lengths for the detonation were similar, meaning that the Eulerian procedure gave the mean structure with a reasonable accuracy.

• Access to Document (DOI)