Reactive Compressible Flow

Combustion initiation by localized energy sources

While low-Mach-number flow prevails in most combustion devices, there exist a number of applications for which compressibility is of central importance, that being for instance the case in spark ignition processes. Our early work contributed to clarifying how the energy deposited from a concentrated source (a laser or an electric spark) is transferred to the surrounding gas, with heat conduction and pressure waves playing a dominant role in two different, neatly defined spatial regions of comparable size. Around the source, we find a conductive region of very high temperature where the spatial pressure variations are negligible. The edge of the resulting strongly heated low-density region appears as a contact surface that acts as a piston for the outer flow, where the pressure disturbances generate a shock wave that heats up the outer gas as it propagates outwards.

This basic fluid mechanical structure needs to be taken into account, for instance, in computations of minimum ignition energies for deflagration initiation, a quantity of direct interest in internal combustion engines that is also relevant when assessing explosion hazards in fuel-storage facilities. It is also relevant for direct-initiation of detonations, which requires considerably larger amounts of energy.

Related publications

  1. Initiation of reactive blast waves by external energy sources
    A. Liñán, V. Kurdyumov, A. L. Sánchez, C. R. Mecanique, 340 829–844 (2012). [DOI]
  2. On the Calculation of the Minimum Ignition Energy
    V. Kurdyumov, J. Blasco, A. L. Sánchez and A. Liñán, Combust. Flame, 136, 394–397 (2004). [DOI]
  3. The Coupling of Motion and Conductive Heating of a Gas by Localized Energy Sources
    A. L. Sánchez, J. L. Jiménez-Alvarez, A. Liñán, SIAM J. Appl. Math., 63, 937–961 (2003). [DOI]
  4. Heat Propagation from a Concentrated External Energy Source in a Gas
    V. Kurdyumov, A. L. Sánchez and A. Liñán, J. Fluid Mec., 491, 379–410 (2003). [DOI]

Interactions of detonations with turbulence

Compressibility is also essential to the structure, dynamics, and stability of detonation fronts and shock waves, of interest in supersonic-combustion applications. Our initial work investigated the stability of overdriven detonations on the basis of realistic chemistry descriptions. More recently attention has been focused on examining the interactions of strong detonations with turbulence. Understanding these interactions is needed in assessing the viability of hypersonic vehicles and is also of interest in astrophysics, where ionization fronts resemble combustion waves in many respects, with the so-called R-type fronts being qualitatively similar to strong chemical detonations.


Linear theory for the interaction of overdriven detonations with isotropic turbulent flows in two opposite limits: thin detonation/large-scale perturbations (left picture), and thick detonation/small-scale perturbations (right picture).

Analytical descriptions of the linear interaction of a planar detonation front with nonuniform fields have been obtained by application of Laplace-transform and normal-mode techniques in the limiting cases in which the turbulence scales are either small or large compared with the thickness of the reaction zone. Disturbances in the fresh mixture that involve only velocity fluctuations without any fluctuation of thermodynamic properties (rotational disturbances), and disturbances that involve fluctuations of the density of the fresh mixture without any velocity fluctuation (entropic disturbances) are considered separately. The results obtained, including explicit analytic formulas for all quantities of interest, can be useful in analyzing the linear response of detonations to turbulence.

Related publications

  1. Linear theory for the interaction of small-scale turbulence with overdriven detonations
    C. Huete, A. L. Sánchez, F. A. Williams, Phys. Fluids, 26 116101 (2014). [DOI]
  2. Theory of interactions of thin strong detonations with turbulent gases
    C. Huete, A. L. Sánchez, F. A. Williams, Phys. Fluids, 25 076105 (2013). [DOI]
  3. One-Dimensional Overdriven Detonations with Branched-Chain Kinetics
    A. L. Sánchez, M. Carretero, P. Clavin and F. A. Williams, Phys. Fluids, 13, 776–792 (2001). [DOI]

Shock-induced combustion processes

Mixing layers and shock waves are two different phenomena that coexist in hypersonic and supersonic propulsion devices. For instance, in supersonic-combustor ramjets, shock waves are typically generated ahead of the combustion zone, where the supersonic incoming flow enters a converging nozzle and interacts with wedged walls and fuel injectors. Along its path through the combustor, the flow is subject to complex shock trains and expansion waves. In one configuration, the shock waves may interact with the mixing layer generated downstream from the fuel injector, which separates the supersonic incoming hot-air stream and the subsonic fuel flow. Since the residence time of the reactants in the combustor is short in supersonic regimes, ignition typically cannot be achieved by relying on diffusion and heat conduction alone. Shock waves may help, however, to heat the mixture and speed the mixing process, the former arising from the inherent temperature rise across the shock wave, and the latter associated with the interaction of the shock with the non-uniform flow.


Theoretical model and numerical results for shock-induced ignition in supersonic mixing layers. The plots at the bottom show the pressure perturbation due to chemical reaction behind the shock front. The precipitous pressure rise observed as the Damköhler number increases towards a critical value is indicative of a thermal runaway.

Analytical solutions to related simplified problems can be helpful in studying such supersonic-combustion processes, not only for increasing understanding but also for suggesting scaling concepts that may prove useful. Besides purely fluid-mechanical studies, addressing the chemically frozen interaction of the shock wave and the mixing layer, there is interest in determining the critical conditions for ignition. The associated study requires consideration of the flow structure of the post-shock ignition kernel around the point of maximum temperature, which may be located either near the edge of the mixing layer or in its interior. The critical ignition conditions are obtained from the balance between the rates of chemical reaction and post-shock flow expansion, including the acoustic interactions of the chemical heat release with the shock wave leading to increased front curvature. Besides analytical results based on activation-energy asymptotics for one-step Arrhenius kinetics extensions to realistic chemistry descriptions are being sought, in particular in connection with hydrogen-oxygen systems.

Related publications

  1. Theory of weak-shock interactions with transonic mixing layers
    C. Huete, J. Urzay, A. L. Sánchez, F. A. Williams, in preparation.
  2. Diffusion-flame ignition by shock-wave impingement on a supersonic mixing layer
    C. Huete, J. Urzay, A. L. Sánchez, F. A. Williams, in preparation.