A parametric study of autoigniting hydrogen jets under compression-ignition engine conditions

This study examines the flame evolution of autoigniting H₂ jets with high-speed schlieren and OH1 chemiluminescence optical methods in a constant-volume combustion chamber over a wide range of simulated compression-ignition engine conditions. Parametric variations include the injector nozzle orifice diameter (0.31–0.83 mm), injection reservoir pressure (100–200 bar), ambient temperature (1000–1140 K), density (12.5–24 kg/m³) and O₂ concentration (10–21 vol.%). The jet ignition delay was found to be highly sensitive to changes in ambient temperature while all other parameter variations resulted in minor ignition delay changes. Optical imaging reveals that in most cases, the reaction front of the H₂ jet initiates from a localised kernel, before engulfing the entire jet volume downstream and recessing towards the nozzle. The flames attach to the nozzle, except at the lowest ambient oxygen condition of 10 vol.% O₂ for which a lifted flame is observed. The H₂ diffusion flame length shows a dependence on both the mass flow rate and the level of O₂ entrainment that follows the same correlations as previously established for atmospheric H₂ jet flames.     

The ignition characteristics of the pre-chamber turbulent jet ignition of the hydrogen and methane based on different orifices

In this paper, the combustion characteristics of premixed CH₄-air and H₂-air mixtures with different excess air coefficients ignited by hot jet or jet flame are investigated experimentally in a constant volume combustion chamber (CVCC). The small volume pre-chambers with different orifices (2 or 3 mm in diameter) in the passive or active pre-chamber were selected. Both the high-speed Schlieren and OH1 chemiluminescence imaging are applied to visualize the turbulent jet ignition (TJI) process in the main chamber. Results show that the variation of orifice has diverse influences on the turbulent jet ignitions of methane and hydrogen. Smaller orifices will reduce the temperature of the jet due to the stronger stretch and throttling effect, including change of lean flammability limit, ignition delay, and re-ignition location. Furthermore, shock waves and pressure oscillations were captured in the experiments with hydrogen jets. The former is related to the jet velocity, while the latter is mainly affected by the mixture thermodynamic states in the main chamber. Furthermore, the re-ignition location is discussed. If the mixture reactivity and the jet energy are sufficiently high, the reaction will be initiated at the tip of the jet in a short time. On the contrary, a relatively long time is required to prepare the mixture during the entrainment when the reactivity is not high enough, and the corresponding re-ignition location will move towards the orifice exit owing to the temperature decline at the tip. Finally, the ignition mode transition of hydrogen jet in lean cases with a 2 mm orifice is explained.     

Ignition and heat radiation of cryogenic hydrogen jets

In the present work release and ignition experiments with horizontal cryogenic hydrogen jets at temperatures of 35–65 K and pressures from 0.7 to 3.5 MPa were performed in the ICESAFE facility at KIT. This facility is specially designed for experiments under steady-state sonic release conditions with constant temperature and pressure in the hydrogen reservoir. In distribution experiments the temperature, velocity, turbulence and concentration distribution of hydrogen with different circular nozzle diameters and reservoir conditions was investigated for releases into stagnant ambient air. Subsequent combustion experiments of hydrogen jets included investigations on the stability of the flame and its propagation behaviour as function of the ignition position. Furthermore combustion pressures and heat radiation from the sonic jet flame during the combustion process were measured. Safety distances were evaluated and an extrapolation model to other jet conditions was proposed. The results of this work provide novel data on cryogenic sonic hydrogen jets and give information on the hazard potential arising from leaks in liquid hydrogen reservoirs.     

The structure and flame propagation regimes in turbulent hydrogen jets

Experiments on flame propagation regimes in a turbulent hydrogen jet with velocity and hydrogen concentration gradients have been performed. Horizontal stationary hydrogen jets released at normal and cryogenic temperatures of 290, 80 and 35 K with different nozzle diameters and mass flow rates have been investigated. Sampling probe method and laser PIV techniques have been used to evaluate the distribution of hydrogen concentration and flow velocity. High-speed photography combined with a Background Oriented Schlieren (BOS) system was used for the visual observation of the turbulent flame propagation. In order to investigate different flame propagation regimes the ignition position was changed along the jet axis. It was found that the flame propagates in both directions, up- and downstream of the jet flow if hydrogen concentration is >11%, whereas in case [H₂] < 11%, the flame propagates only downstream. This means that at normal temperature the flame is able to accelerate effectively only if the expansion ratio σ of the H₂-air mixture is higher than a critical value σ* = 3.75 defined for a closed geometry.     

Optimization of the flame characteristics of H2–O2 coaxial injection applied to hydrogen-fueled argon cycle engines

The argon power cycle is one of the most promising technologies for high efficiency and low emission hydrogen-fueled internal combustion engines. The application of coaxial injection technology in the hydrogen-fueled argon engine can improve the mixing process and the combustion performance of the H₂/O₂ mixture. In this study, an innovative H₂–O₂ coaxial injection combustion system was designed to investigate the jet flame characteristics of oxygen coaxially wrapped by hydrogen in a controllable argon thermal atmosphere. The findings of this study could provide a new perspective for designing hydrogen-fueled argon engines in the future. The influences of co-flow temperature, jet injection pressure, and excess oxygen coefficient were all determined. Observations of the flame showed a bright blue flame with a reddish glow in the far-burner region. Experimental results show that the flame length, cross-sectional area, and area/perimeter ratio first decrease with increasing jet injection pressure and subsequently increase, reaching maximum values at 0.4–0.6 MPa. When increasing the co-flow temperature from 1023 K to 1223 K, the cross-sectional area of the flame increases significantly by 61.1% at an excess oxygen coefficient of 0.4. Furthermore, the liftoff flame height shrinks when the co-flow temperature and the excess oxygen coefficient increase, while it rises along with an increasing jet injection pressure.     

Hysteresis in flame stabilization in a hydrogen fueled supersonic combustor

Hysteresis in flame stabilization mode transitions in a hydrogen-fueled strut-stabilized supersonic combustion test rig was experimentally observed and studied. Air was vitiated using H₂–O₂ combustion products to stagnation conditions of 8.65 bar and 1350 K and was expanded through a rectangular nozzle to Mach number 2.5. H₂ fuel was injected transversely using a strut positioned at the center of the combustor. The equivalence ratio (ER) was changed in time to study its effects on flame stabilization modes. Shadowgraph and wall pressure measurements were used to study the shock system generated by the strut in the supersonic combustor. High-speed OH1 chemiluminescence and high-speed flame imaging were used to study the heat release zones and flame structure of different combustion modes and transitions between them. Three different combustion modes were observed, namely: divergent section flame (CM1), strut wake stabilized flame (CM2), and jet stabilized flame (CM3). CM1 was observed at a very low ER, where the H₂ was ignited by the normal shock positioned in the divergent section. At this point, the weak shock system at the strut is unable to ignite the fuel. At higher ER, CM2 was observed, as a stronger shock system ignites the richer mixture at the wake of the strut. It was observed that the mixture auto-ignites in the strut wake and doesn't flashback from the divergent section. When the ER is further increased, the stronger injection shock reduces the local velocity and increases the static temperature, enhancing the flame speed of the richer mixture. Thus, the flame flashes back to the fuel jet. Two hysteresis were observed in the supersonic combustor based on ER as a time-varying input. The flame stabilization mode has two solutions based on the history of the change in ER, hence indicating hysteresis. The hysteresis between CM1 and CM2 is because of the retention of the temperature and radicals in the recirculation zone at the wake of the strut. The hysteresis between CM3 and CM2 is because of the retention of the temperature and radicals in the horseshoe vortices around the fuel jets. Understanding hysteresis will help design scramjets with wider operability.     

Stochastic reactor modelling of multi modes combustion with diesel direct injection or hydrogen jet ignition start of combustion

Recent papers 1, 2, 3, 4 and 5 have proposed two different systems to more efficiently and more rapidly burn the fuel in highly boosted, high compression ratio, directly injected internal combustion engines permitting multi-mode combustion operation. In a first system, a second direct injector is coupled with the standard Diesel direct injector and glow plug. The second direct injector introduces the most of the fuel while the Diesel direct injector only introduces a minimum amount of fuel to control the start of the combustion about top dead centre. The fuel injected before the Diesel ignition injection burns premixed, the fuel injected after the Diesel ignition injection burns diffusion. This design permits combustion premixed gasoline-like if all the fuel is injected before the Diesel ignition injection, diffusion Diesel-like if all the fuel is injected after the Diesel ignition injection (as done in the Westport High Pressure Direct Injection concept [12]), and mixed gasoline/Diesel like injecting the fuel before and after the Diesel ignition injection. The premixed gasoline-like mode is actually a homogeneous charge compression ignition (HCCI)-like mode, where an amount of fuel smaller than the threshold value producing top dead centre auto ignition is then ignited at top dead centre by the Diesel ignition injection in a more robust, stable and repeatable operation unaffected by small changes in properties and composition of the fuel and air mixture. In an alternative design, the glow plug is replaced by a jet ignition devices feed preferably with H₂. In this case, a spark ignition ignites the stoichiometric H₂-air mixture within the jet ignition pre-chamber. The jets of hot reacting H₂-air combusting gases then ignite the main chamber premixed mixture in the gasoline-like operation or create suitable conditions for the fuel subsequently injected to burn diffusion in the Diesel-like operation or perform both duties in the mixed gasoline/Diesel-like operation. A single main chamber direct injector is generally needed (for example with H₂, CH₄ or C₃H₈ fuels). With NH₃, a second main chamber direct injector with H₂ is also used to limit the volume of the jet ignition pre-chamber. In this short communications, the results of detailed chemistry simulations with the SRM (Stochastic Reactor Model) suite, a sophisticated engineering tool combining conventional 1D or 3D fluid dynamics approaches are presented to further support these two engine concepts working with fuels H₂, CH₄, C₃H₈, NH₃, I-C₈H₁₈ and N-C₇H₁₆ and adopting two different mechanisms for chemical kinetics. Within the limits of the present simulations (a very accurate chemical kinetic for combustion of I-C₈H₁₈ and N-C₇H₁₆ but a much less accurate chemical kinetic for the other fuels and especially for NH₃, unavailability of variable composition and variable properties multiple injections), the Diesel injection ignition and the hydrogen jet ignition are proved to permit combustion modes leading to indicated thermal efficiencies up to 10% better than the latest Diesels at high loads within the same peak pressure and peak temperature constraints.     

Comparison of the combustion and emission characteristics of NH3/NH4NO2 and NH3/H2 in a two-stroke low speed marine engine

As a marine engine fuel of great concern, ammonia needs to be mixed with another high reactive fuel to improve its combustion performance. In this work, the combustion performance of NH₃/NH₄NO₂ and NH₃/H₂ was compared under different boundary conditions (excess air coefficient, initial temperature, pressure and mixing ratio). The numerical simulation of compression combustion is carried out under different power loads. The addition of ammonium nitrite decreases the ignition requirement of ammonia and shortens the ignition delay time of the mixture fuel. The boundary conditions of compression ignition can be reduced by mixing hydrogen and mixing ammonium nitrite, but it is not enough to achieve compression ignition under NH₃/H₂ mode. The addition of 30% ammonium nitrite can reduce the intake temperature to 300–360 K, which makes the compression ignition of the mixed fuel feasible. Meanwhile, in order to reduce the high in-cylinder combustion pressure and improve the combustion performance of the mixed fuel, the fuel injection strategy was proposed to achieve constant combustion pressure of 30 MPa under the premise of less power loss, which is a potential solution for the combustion of ammonia fuel.     

Numerical simulation of high-pressure hydrogen jet flames during bonfire test

Characteristics of high-pressure hydrogen jet flames resulting from ignition of hydrogen discharge during the bonfire test of composite hydrogen storage vessels are studied. Firstly, a 3-D numerical model is established based on the species transfer model and SST k − ω turbulence model to study the high-pressure hydrogen jet flow. It is revealed that under-expanded jets are formed after the high-pressure hydrogen discharging from the vessel. Secondly, the mathematical methods are adopted to study the high-pressure hydrogen jet flames. The effects of pressure, initial temperature and the nozzle diameter on the jet flames are investigated. The results show that the jet flame length increases with the increase of discharge pressure, but decreases with the increase of nozzle diameter and temperature difference between the filling hydrogen temperature and the environment temperature. Finally, the simulation models are established to study the characteristics of hydrogen jet flames in an open space. The effects of barrier walls on the distribution of jet flames are also studied. The results show that the barrier walls can greatly reduce the damage from hydrogen jet flames to testers and properties around.     

Combustion and emission characteristics of an Acetone-Butanol-Ethanol (ABE) spark ignition engine with hydrogen direct injection

Butanol could reduce emissions and alleviate the energy crisis as a bio-fuel used on engines, but the production cost problem limits the application of butanol. During the butanol production, ABE (Acetone-Butanol-Ethanol) is a critical intermediate product. Many studies researched the direct application of ABE on engines instead of butanol to solve the production cost problem of butanol. ABE has the defects of large ignition energy and vaporization heat. Hydrogen is a gaseous fuel with small ignition energy and high flame temperature. In this research, ABE port injection combines with hydrogen direct injection, forming a stratified state of the hydrogen-rich mixture around the spark plug. The engine speed is 1500 rpm, and λ is 1. Five αH₂ (hydrogen blending fractions: 0, 5%, 10%, 15%, 20%) and five spark timings (5°, 10°, 15°, 20°, 25° CA BTDC) are studied to observe the effects of them on combustion and emissions of the test engine. The results show that hydrogen addition increases the maximum cylinder pressure and maximum heat release rate, increases the maximum cylinder temperature and IMEP, but the exhaust temperature decreases. The flame development period and flame propagation period shorten after adding hydrogen. Hydrogen addition improves HC and CO emissions but increases NO_x emissions. Particle emissions decrease distinctly after hydrogen addition. Hydrogen changes the combustion properties of ABE and improves the test engine's power and emissions. The combustion in the cylinder becomes better with the increase of αH₂, but a further increase in αH₂ beyond 5% brings minor improvements on combustion.     

Study of the characteristic of diesel spray combustion and soot formation using laser-induced incandescence (LII)

In this paper, the planar images of diesel spray combustion flame and soot formation were measured and analyzed by using LII, in a constant volume combustion vessel. The effects of combustion flame and fuel–air mixing characteristics on soot formation and distribution of soot concentration were studied at different conditions. The result indicates that, with increase in ambient temperature and pressure, the ignition delay of diesel fuel is shorter. The increase of ambient temperature and pressure and the reduction of injection pressure shorten the diesel flame lift-off length. The lower the ambient temperature and pressure, the weaker LII signal intensity. At the same ambient temperature and pressure condition, the higher the diesel injection pressure, the smaller the soot production in diesel jet spray, and soot particles are primarily produced in the relative fuel-rich region, which is encompassed by the flame surface front at the downstream of the diesel jet.     

Stability characteristics of non-premixed turbulent jet flames of hydrogen and syngas blends with coaxial air

The stability characteristics of attached hydrogen (H₂) and syngas (H₂/CO) turbulent jet flames with coaxial air were studied experimentally. The flame stability was investigated by varying the fuel and air stream velocities. Effects of the coaxial nozzle diameter, fuel nozzle lip thickness and syngas fuel composition are addressed in detail. The detachment stability limit of the syngas single jet flame was found to decrease with increasing amount of carbon monoxide in the fuel. For jet flames with coaxial air, the critical coaxial air velocity leading to flame detachment first increases with increasing fuel jet velocity and subsequently decreases. This non-monotonic trend appears for all syngas composition herein investigated (50/50 → 100/0% H₂/CO). OH^∗ chemiluminescence imaging was performed to qualitatively identify the mechanisms responsible for the flame detachment. For all fuel compositions, local extinction close to the burner rim is observed at lower fuel velocities (ascending stability limit), while local flame extinction downstream of the burner rim is observed at higher fuel velocities (descending stability limit). Extrema of the non-monotonic trends appear to be identical when the nozzle fuel velocity is normalized by the critical fuel velocity obtained for the single jet cases.     

Effects of hydrogen addition on the combustion characteristics of diesel fuel jets under ultra-high injection pressures

Many applications use hydrogen addition and high-pressure fuel injection technology to improve combustion performance. In this study, spray atomization and combustion characteristics of a diesel fuel jet, under the injection pressure of 350 MPa, injecting into a constant volume combustion vessel filled with air-hydrogen mixture at the diesel engine relevant condition are investigated by simulation method. A simplified mechanism of the n-heptane (C₇H₁₆) oxidation chemistry mechanism consisting of 26 reactions and 25 species integrated with the Kéromnès-2013 hydrogen combustion mechanism and EDC combustion model are utilized to predict the diesel fuel spray auto-ignition and combustion. The ambient gas is the mixture of air and hydrogen range in volume fraction from 0% to 10%. The ambient temperature and pressure is set to 1000 K and 3.5 MPa, respectively. The results indicate that as the hydrogen volume fraction is 2%, the minimum overall droplet SMD (Sauter Mean Diameter) is approximately 0.95 μm, which is obviously smaller than that of the case with the conventional high injection pressure. In cases that H₂ v/v% larger than 4%, the maximum gaseous temperature increased significantly up to 2700 K. There are two peaks in the temperature growth rate curves as the hydrogen fraction of 8% and 10%. The high temperature at the outer edge of the spray is clearly seen due to its high value when the hydrogen fraction is larger than 4%. The hot reaction layer is the main location of CO formation. The H, OH radicals are formed at the edge of the spray where the temperature is high. The hydrogen species obviously promotes the oxidation and combustion of diesel fuel.     

Study on hydrogen dynamic leakage and flame propagation at normal-temperature and high-pressure

Experiments of two nozzle diameters at three ignition positions under three initial pressure conditions were carried out. The dynamic leakage characteristics and the stagnation parameters of flame propagation under normal temperature and high pressure conditions were studied. Based on van der Waal's equation, a model for predicting stagnation parameters, jet velocity and flow rate of hydrogen leakage was proposed. Compared with the experimental results, it was found that the maximum error occurred when the initial pressure was 200 bar. Theoretical leakage time was 1.66 s, experiment leakage time was 1.84 s, the error was 9.8%. Background-Oriented Schlieren image technology was used to record the flame development and propagation process after ignition. For the same nozzle diameter and ignition location, the higher pressure caused the flame to propagate faster upstream and downstream. For the same initial pressure and ignition position, a flame with a large nozzle diameter propagated faster upstream and downstream. For the same initial pressure and nozzle diameter, the farther the ignition point was, the greater the slope of flame attenuation when propagating upstream. Due to the attenuation of hydrogen concentration and jet velocity, the flame propagation velocity to the downstream decreased linearly with the increase of distance from the ignition location.     

Mixing enhancement mechanism of combined H2–Water jets in supersonic crossflows in a combustor with an expanded section

To obtain the mixing enhancement mechanism of H₂–Water combined jets in supersonic crossflows in a combustor with expanded section for rotating detonation ramjet, the flow field shape and spray structure were studied by experimental and numerical methods. The Eulerian–Lagrangian method was used to investigate the diffusion mechanism and H₂–Water interaction law of combined jets with different sequences. At the same time, high-speed photography and the schlieren technique were used to capture the flow field. The effects of jet pressure drop, orifice diameter, orifice spacing, incoming Mach number, and other parameters on the penetration depth of water jets were studied. The results of experiment and simulation show that using H₂–Water combined jets, the penetration depth of the jet spray can be greatly increased and the jet mixing effect can be significantly improved, which will contribute to the engine's ignition and stable combustion. In the case of pre-water/post-H₂, the penetration depth of the hydrogen jet is greater. In the case of pre-H₂/post-water, the hydrogen jet raises the water spray mainly by protecting the integrity of the water column.     

Under-expansion jet flame propagation characteristics of premixed H2/air in explosion venting

In premixed H₂/air explosion venting, an under-expansion jet may be caused by the pressure difference between the inside and outside of the explosion vent. Based upon the under-expansion jet, studying the structure of the under-expansion jet flame and the factors influencing its formation is essential to hydrogen safety in explosion venting. This study explored the basic characteristics of the under-expansion jet flame in premixed H₂/air explosion venting, and discussed the formation of two under-expansion structures (Mach disk and diamond shock wave) of such jet flames by conducting a premixed H₂/air explosion venting experiment. The influences of hydrogen fraction, explosion venting diameter, and duct length on the structure of under-expansion jet flames were evaluated. The results showed that after successful explosion venting, the under-expansion jet flame would be generated when the hydrogen fractions were 30–60 vol.%, and as the hydrogen fractions were 30–50 vol.%, the lengths of the venting duct were 30 and 50 cm. The duration of under-expansion jet flame was the longest when the hydrogen fraction was 40 vol.%. With the explosion venting diameter and hydrogen fraction increased, the spacing between under-expansion jet flame structures (S) increased. However, an increase in duct length led to the attenuation of the S. During the explosion venting, the under-expansion jet caused a pressure imbalance near the explosion vent and high-intensity convection forms on both sides of a jet, which can generate two or more explosions. Therefore, understanding the basic characteristics of under-expansion jet flame can aid the effective development of measures to prevent, mitigate, and protect against premixed H₂/air explosions.     

Improvement of H2/O2 chemical kinetic mechanism for high pressure combustion

An updated H₂/O₂ kinetic mechanism was proposed by incorporating carefully selected reaction rate coefficient and great progress in radical chain mechanisms, in which the uncertainties of rate coefficient were discussed. The performance of the current mechanism was compared to other H₂ mechanism and validated against a wide range kinetic targets, including oxidation, decomposition in shock waves, ignition, flame speed and flame structure. Results show that the current mechanism obtains an overall improvement of performance, especially for the flame speed. By using the updated binary diffusion coefficient from ab initio calculations and the chemically termolecular reactions, the current mechanism presents better agreement with the new experimental flame speed at atmospheric pressure and obtains the improved performance with respect to the negative pressure dependence of high-pressure H₂ flame. Furthermore, the flame speed predictions are strongly sensitive to the H₂O third body efficiency in the H₂ mechanism, affecting the water-contained H₂ flame. The modeling results of rapid compression machine ignition show that present mechanism can more accurately predicts the ignition delay under engine-like conditions. However, all three mechanisms cannot accurately reproduce the negative pressure dependence behavior of mass burning rate in high-pressure H₂ flame, which may be attributed to the fact that the important reaction O + OH(+M) = HO₂(+M) that significantly affects lean high-pressure H₂ flame is not included in current mechanism. Consequently, continuous works should be emphasized on the reactions that are important but neglected in H₂ mechanism. All these not only develop an improved H₂ reaction mechanism for high-pressure combustion, but also point out the direction for refining the H₂ mechanism.     

Characterisation of hydrogen jet flames under different pressures with varying coflow oxygen concentrations

The elevated temperature of hydrogen combustion increases the formation of thermal NO_x. Moderate or intense low oxygen dilution (MILD) combustion is known to reduce NO_x emissions and increase thermal efficiency. Pressure is often also used for increasing thermal efficiency. The impact that pressure has on fluid dynamics and chemical kinetics is especially relevant in MILD combustion conditions. Hydrogen jet flames issuing into a hot and vitiated coflow were imaged using OH¹ chemiluminescence at different pressures (1–7 bar) and oxygen levels (3–9% by vol.). Laminar flame simulations complemented the experiments. The observed mean radial OH¹ width increased with increased pressure, but only at O₂ content less than 9%, suggesting that pressure has greater influence on kinetics when oxygen is reduced. The integrated OH¹ signal strength remained constant at 3% coflow O₂, despite an apparent increase in flame width, suggesting a spatial broadening of the flame with pressure. Numerical results indicate that at 3–6% O₂, conditions for MILD combustion of H₂ are met across a wide range of strains and pressures, supporting the experimental observations for 3% O₂.     

Ignition of hydrogen jet fires from high pressure storage

Self-ignition behaviour of highly transient jets from hydrogen high pressure tanks were investigated up to 26 MPa. The jet development and related ignition/combustion phenomena were characterized by high speed video techniques and time resolved spectroscopy. Video cross correlation method BOS, brightness subtraction and 1-dimensional image contraction were used for data evaluation. Results gained provided information on ignition region, flame head jet velocity, flame contours, pressure wave propagation, reacting species and temperatures. On burst of the rupture disc, the combustion of the jet starts close to the nozzle at the boundary layer to the surrounding air. Combustion velocity decelerated in correlation to an approximated drag force of constant value which was obtained by analysing the head velocity. The burning at the outer jet layer develops to an explosion converting to a nearly spherical volume at the jet head; the movement of the centroid is nearly unchanged and follows the jet front in parallel. The progress of the nearly spherical explosion could be evaluated by assuming an averaged flame ball radius. An apparent flame velocity could be derived to be about 20 m/s. It seems to increase slightly on the pressure in the tank or the related initial jet momentum. Self-initiation is nearly always achieved especially induced the interaction of shock waves and their reflections from the orifice. The combustion process is composed of shell combustion of the jet cone at the bases with a superimposed explosion of the decelerating jet head volume.