Research Article

A unified mechanism for unconfined deflagration-to-detonation transition in terrestrial chemical systems and type Ia supernovae

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Science  01 Nov 2019:
Vol. 366, Issue 6465, eaau7365
DOI: 10.1126/science.aau7365

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Achieving unconfined supersonic explosions

In some forms of supernovae and chemical explosions, a flame moving at subsonic speeds (deflagration) spontaneously evolves into one driven by a supersonic shock (detonation), vastly increasing the power output. The mechanism of this deflagration-to-detonation transition (DDT) is poorly understood. Poludnenko et al. developed an analytical model to describe DDTs, then tested it with lab experiments and numerical simulations. Their model successfully reproduced the DDT seen in the experiments and predicted a DDT in type Ia supernovae, which is consistent with observational constraints. The same mechanism may apply to DDTs in any unconfined explosion.

Science, this issue p. eaau7365

Structured Abstract


The nature of type Ia supernovae (SNIa)—thermonuclear explosions of white dwarf (WD) stars—is an open question in astrophysics. There is a general consensus that SNIa explosions are driven by fast thermonuclear burning in 12C/16O WD stars with a mass close to, or below, the Chandrasekhar-mass limit of 1.4 solar masses. Beyond this general statement, however, the exact mechanisms of SNIa remain unclear, with a number of possible scenarios.

Virtually all existing theoretical models of normal, bright SNIa—including the classical, single-degenerate Chandrasekhar-mass and sub-Chandrasekhar-mass scenarios, along with the double-degenerate merger model—require formation of a supersonic detonation wave. This wave consumes all of the stellar material as a WD begins to expand during the explosion. Detonation initiation in unconfined systems, such as the interior of a WD, remains poorly understood and is particularly difficult to achieve in the absence of the confining effect of walls and obstacles or preexisting or externally introduced strong shocks. Numerical models of SNIa are unable to capture detonation formation from first principles because of the extreme range of scales involved. Instead, they are forced to make two crucial assumptions: (i) that detonation ignition always occurs during an explosion and (ii) the time and location of the detonation formation. As a result, detonation initiation conditions are free parameters present in most existing SNIa models, which limits their predictive power.


Thermonuclear combustion waves in SNIa are qualitatively similar to chemical combustion waves on Earth because they are controlled by the same physical mechanisms. This similarity allows us to seek insights into the fundamental aspects of the physical processes that control SNIa explosions by using theoretical, numerical, and experimental results obtained for terrestrial chemical systems. This includes detonation initiation phenomena that are also relevant to terrestrial applications that range from detonation-based propulsion and power-generation systems to the explosion safety of industrial facilities related to coal mining, fuel storage, chemical processing, and nuclear power generation.

Prior direct numerical simulations (DNS) have shown that chemical flames interacting with high-intensity turbulence can spontaneously accelerate and produce strong shocks or detonations. Such turbulence-driven deflagration-to-detonation transition (tDDT) can occur in essentially unconfined settings.


We present a general analytical theory of tDDT in unconfined systems. The theory explains the behavior of fast turbulent flames that become unstable, produce shocks, and can transition to detonations. This occurs when the turbulent burning speed exceeds the Chapman-Jouguet deflagration velocity, which is the maximum possible speed of a steady-state reaction wave without a shock. We describe an experimental confirmation of this process in terrestrial H2-air flames. Next, we used numerical simulations of a fully resolved turbulent thermonuclear flame in a degenerate 12C stellar plasma to show that under conditions representative of those in a SNIa explosion, this mechanism can also result in the spontaneous formation of strong shocks. We show that these shocks can rapidly amplify by interacting with surrounding turbulent flames and ultimately trigger a detonation. Last, we used the developed theory to determine the criteria for detonation initiation in the classical single-degenerate Chandrasekhar-mass model of SNIa. We found that DDT is almost inevitable at densities in the range of 107 to 108 g cm−3, with the maximum probability at 3 × 107 g cm−3.


We developed a theory of turbulence-induced DDT and validated it by using experiments on chemical flames and numerical simulations of thermonuclear deflagrations. Our results describe a unified mechanism of unconfined DDT both in chemical and thermonuclear reacting flows. This theory is parameter free and can be used to predict self-consistently the conditions for detonation initiation in SNIa explosions.

Understanding the mechanism of the unconfined DDT in SNIa.

The DDT in SNIa is predicted to occur on scales of ~103 to 106 cm, which is well below the characteristic scale of a WD star (109 cm) and mostly below the smallest scales resolvable in three-dimensional simulations, ~105 cm. To demonstrate the turbulence-driven, unconfined DDT in experiments and DNS, we considered turbulence-flame interaction on small scales of ~10−5 to 10 cm. The synergy between the experiments and DNS of chemical and thermonuclear flames led to our unified theory of DDT.


The nature of type Ia supernovae (SNIa)—thermonuclear explosions of white dwarf stars—is an open question in astrophysics. Virtually all existing theoretical models of normal, bright SNIa require the explosion to produce a detonation in order to consume all of stellar material, but the mechanism for the deflagration-to-detonation transition (DDT) remains unclear. We present a unified theory of turbulence-induced DDT that describes the mechanism and conditions for initiating detonation both in unconfined chemical and thermonuclear explosions. The model is validated by using experiments with chemical flames and numerical simulations of thermonuclear flames. We use the developed theory to determine criteria for detonation initiation in the single-degenerate Chandrasekhar-mass SNIa model and show that DDT is almost inevitable at densities of 107 to 108 grams per cubic centimeter.

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