Chemical Energy Release Rate Research Articles

High-output diesel engine heat transfer: Part 2 – instantaneous spatially averaged heat transfer correlation

A new temporally resolved spatially averaged heat transfer correlation was developed using the local piston heat flux data presented in the first part of this paper. The new correlation extends previous correlations that relate the Nusselt and Reynolds numbers through a power law by adding a dimensionless chemical energy release rate term. The new term, which arises from dimensional analysis, should enable similitude for diesel engines. Additionally, the characteristic velocity used in the Reynolds number was modified to include the integrated fuel mass injection rate. The new correlation was calibrated to the experimental data by minimizing the least squares error, and compared to existing correlations from the literature. On average, the new formulation was found to match the experimental data better than the existing models even when the existing models’ constants were adjusted to best fit the measured data.

Effect of volumetric expansion on shock-induced ignition of H2–NO2/N2O4 mixtures

The competition between chemical energy release rate and volumetric expansion related to shock wave’s dynamics is of primary importance for a number of situations relevant to explosion safety. While studies have been performed on this topic over the years, they have been limited to mixtures with monotonous energy release profile. In the present study, the ignition of H2–NO2/N2O4 mixtures, which exhibit a single-step or a two-step energy release rate profile depending on the equivalence ratio, has been investigated under volumetric expansion conditions. The rate of expansion has been calculated using the Taylor–Sedov solution and accounted for using 0-D numerical simulations with time-dependent specific volume. The results were analyzed in terms of a Damkohler number defined as the ratio of the expansion to ignition times. For mixtures with non-monotonous energy release rate profiles, two critical Damkohler numbers can be identified for individual steps of energy release. It was also shown that the fluid element behind a shock propagating at the Chapman–Jouguet velocity is most likely to ignite. The thermo-chemical dynamics have been analyzed about the critical conditions using energy release rate per reaction, rate of production and sensitivity analyses.

Development and Characterization of 3D Printable Thermite Component Materials

AbstractAdditive manufacturing (AM) has recently shown great promise as a means to tailor a wide range of material properties, both quasi‐static and dynamic. An example of controlling the dynamic behavior is to tailor the chemical energy release rate in composite energetic materials such as thermites – which are a subset of pyrotechnics that use a metal fuel and a metal oxide as an oxidizer. Since these materials are most hazardous once finely mixed, the approach taken here is to formulate the fuel and oxidizer separately such that they can be mixed on‐the‐fly. Herein, the development, formulation, and characterization of two respective aqueous 3D printable inks consisting of Al and CuO are discussed. The rheological properties and ability of the material to span gaps are characterized. To demonstrate that the materials could be mixed and sustain a reaction, the inks are fed into a static mixing nozzle and extruded into a high‐aspect ratio test strip. Upon drying, the material can be ignited and sustain a propagation through the part. These results present a facile, and safe, way to AM thermite which can be used for more detailed follow on studies looking at the role of architecture on the reactivity.

Intensity and efficiency of spray fuel-fed well-mixed adiabatic combustors

Motivated by the insights it can provide, we revisit the classical problem of liquid fuel-fed idealized steady-flow combustors. New quadrature-based results are presented for the theoretical combustion intensity and corresponding efficiency for well-stirred adiabatic vessels fed with a prescribed polydispersed spray. Each droplet of the spray is assumed to evaporate according to a non-quasi-steady (non-QS) gas-phase energy/mass diffusion-controlled rate for the pseudo-single-component fuel. As a byproduct, we calculate the complete droplet size distribution (DSD) function exiting the chamber, of interest for the design of downstream components. We explicitly assume that the volumetric rate of chemical energy release in such “primary” combustion chambers is controlled by the liquid fuel physical vaporization process (with negligible lags due to propellant droplet heat-up or vapor-phase ignition). In this instructive asymptotic limit, two decisive non-dimensional parameters are shown to be: (1) a vaporization Damköhler number (defined by the ratio of the mean residence time of the chemically reacting vapor mixture in the combustion space, to the reference value of the vaporization lifetime of a droplet with the injector-Sauter-mean diameter, and (2) a single dimensionless non-QS parameter. Illustrative numerical results for a kerosene-like fuel burning in air at pressures up to 24 atm are displayed for the case of a log-normal feedstream DSD with a range of spreads. Our results reveal the existence of an optimum vaporization Damköhler number which maximizes the combustion intensity—with maximum intensities, occurring well before nearly complete fuel evaporation, being quite sensitive to the non-QS parameter at high pressures. These deliberately idealized mathematical model results, spanning more than a 1000 combinations of operational parameters, set instructive bounds to the achievable performance of “real” spray combustors. Even without tractable enhancements (see Section 5.2), this approach can be used to economically map the sensitivity of spray combustor performance to a large number of important design and control parameters.

A quick, simplified approach to the evaluation of combustion rate from an internal combustion engine indicator diagram

In this paper a simplified procedure of an internal combustion engine in-cylinder pressure record analysis has been presented. The method is very easy for programming and provides quick evaluation of the gas temperature and the rate of combustion. It is based on the consideration proposed by Hohenberg and Killman, but enhances the approach by involving the rate of heat transferred to the walls that was omitted in the original approach. It enables the evaluation of the complete rate of heat released by combustion (often designated as ?gross heat release rate? or ?fuel chemical energy release rate?), not only the rate of heat transferred to the gas (which is often designated as ?net heat release rate?). The accuracy of the method has been also analyzed and it is shown that the errors caused by the simplifications in the model are very small, particularly if the crank angle step is also small. A several practical applications on recorded pressure diagrams taken from both spark ignition and compression ignition engine are presented as well.

Aspects of solid propellant combustion

Internal ballistics describes the combustion of solid propellant within a closed combustion chamber. This is achieved by modelling a mixture of incompressible solid particles and compressible reactive gases with averaged equations of two–phase flow. The combustion of the solid is described with interaction terms that define the rate of mass, momentum and energy exchange from solid into gas. This work concentrates on modelling ignition and the initial stages of combustion, proposing the concept of ‘gaseous ignition’ by including time–scales of chemical reaction in the gas–phase. These non–equilibrium effects are placed firmly within the context of internal ballistics by making direct comparisons between experimental pressure–time histories. In particular, excellent agreement can be achieved between numerical simulations and experimental work by assuming a two–stage reaction process during which the rate of chemical energy release will significantly differ from a single exothermic reaction.

Modeling flows with curved detonation waves

The nonzero width of a curved detonation front has a significant effect on its propagation. Physically, the curvature effect is a small but important correction. In numerical simulations, the curvature effect tends to be greatly exaggerated due to an artificially large width of an underresolved wave. In the context of reactive fluid flow, a detonation wave consists of a lead shock followed by a thin reaction zone. The curvature effect is determined by the dynamics within the reaction zone; in particular, the competition between a source term for the rate of chemical energy release and a geometric source term due to front curvature. When the width of the reaction zone is small compared with the radius of curvature of the front, the reaction zone can be approximated as quasi-steady and be modeled locally by a system of ordinary differential equations (ODEs) in which the front curvature enters as a parameter. Front curvature breaks the Galilean invariance and the quasi-steady approximation is only valid in a distinguished frame determined by both the front curvature and the tangential velocity divergence ahead of the front. The quasi-steady ODEs determine the reaction zone profile to leading order and can be viewed as an extension of the ZND model. However, the source terms in the ODEs lead to modified Hugoniot jump conditions that take into account front curvature and reaction zone width. When the reaction zone is underresolved, a calculation in effect reduces to a “capturing algorithm” in which the burn model plays an analogous role for detonation waves as artificial viscosity does for shock waves. In particular, the reaction zone has an unphysically large width that is proportional to the cell size. As a consequence of the modified jump conditions, the numerical reaction zone width gives rise to an artificial curvature effect. This causes numerical solutions to depend on the cell size and orientation of a detonation front relative to the grid. Two algorithms that eliminate numerical curvature effects are discussed, detonation shock dynamics and front tracking.

Computational investigation of oblique detonation ramjet-in-tube concepts

Ramjet-in-tube techniques have been proposed to accelerate masses up to thousands of kilograms to velocities of 0.7-12.0 km/s by chemical means. CFD calculations for three oblique detonation ramjet-in-tube drive modes are presented; the operational velocities for the present results range from 3.5 to 10.0 km/s. The first drive mode achieves ignition on the reflection of the nose cone bow shock. The second drive mode relies on a sudden, steep, but small increase in projectile radius to initiate a detonation wave, following a deliberately gentle, gradual compression process. The third drive mode is similar to the second mode except that the projectile is thermally protected by flying it through a core of pure hydrogen gas surrounded by a detonable mixture. At optimum operating conditions, the thrust pressure ratios (defined as the effective thrust pressure divided by the maximum cycle pressure) for the three modes range from 0.12 to 0.30, and the efficiencies (defined as the thrust times the velocity divided by the rate of chemical energy release) range from 0.09 to 0.26. Tables of thrust pressure ratios and efficiency data and representative plots of the pressure fields around the projectiles are presented.

Relation of chemical and physical processes in two-phase detonations

Both physical and chemical factors influence combusion instabilities and explosions in two-phase systems consisting of fuel liquid drops in a gaseous oxidizer. It is generally agreed that in two-phase detonations, fuel drops are broken up via a mass stripping mechanism and form combustible mixtures of fuel micromist and hot gaseous oxidizer in the wake of each parent drop. The large surface area between the micromist (micron size drops) and the hot oxidizer enable chemical reactions to proceed at a rapid enough rate to support the incident shock front. Therefore, the detonability of two-phase mixtures is affected by both the fuel drop breakup and the chemical energy release rate. An experimental study was undertaken to elucidate the relative importance of the roles of chemical and physical processes. Additives were employed to alter the physical properties (such as viscosity) and the chemical properties (such as ignition delay) of the fuel. In addition, fuel drop size was systemically varied, since this also affects breakup time. The sensitivity of a hydrocarbon fuel drop-air mixture to detonate was significantly increased by using additives which alter the chemical energy release rate and by decreasing the initial fuel drop size.