From Laminar Flame to Tornado. What Is the Difference between Laminar Flame and Detonation Combustion?
As the journal publishes the paper “On the way to the detonation engine” (by F. A. Bykovskii et al.), we decided to tell the reader more about the evolution of the combustion process: from simple laminar flame to turbulent flame. The mode of a high-velocity vortex flow organized by tangential injection into a cylindrical channel with simultaneous superposition of a detonation wave propagating across the combustible mixture flow is also considered. The resultant flow is a microscale analog of the tornado...
Maybe the most mysterious and fascinating natural phenomenon is the flame. It is amazing that only human beings out of all living creatures became friends with this defender and breadwinner, which cannot be replaced by anything else and which ensures the survival, if not the existence of human beings. The fascinating visual appearance and the hot inner content of the flame resembles a bodiless spirit of a living creature who merrily dances in the clouds of sparks of various colors and, simultaneously, illuminates hungry but frightened predators in the dark.
Yet, we have to study more pragmatic things: the physical and chemical parameters of the combustion process rather than the mysterious origin of fire.
What is the flame front and how it is “glued” to its boundaries, or a calm blue sea
The simplest form of the flame is laminar combustion of a homogeneous combustible mixture. A homogeneous combustible mixture is a mixture of the fuel and oxidizer (chemical reagents) premixed at the molecular level; they are capable of a local exothermic reaction induced by a single act of addition of thermal energy sufficient for initiation. Then the mechanism of spatial and temporal self-organization of laminar combustion is spontaneously (automatically) actuated; the original mixture and combustion products become separated from each other in a short time by a thin transparent fluorescent continuous boundary which acquires the shape of a surface “film” or a zone where a chemical reaction between the fuel and oxidizer occurs. This surface is usually called the “flame front”. In the laminar (undisturbed) flow, the flame front usually takes the form of the flow velocity profile, which shows that the burning velocity directed normal to the front surface is identical at all points of the front. This is why it is usually called the “normal burning velocity”. Obviously, the cold combustible mixture is transformed in the thin film of the combustion front (normally, a millimeter or smaller) into hot combustion products. For convenience, the velocity profile is often artificially smoothed to a certain shape, which can range from the classical Poisseuille profile (bell-shaped) to a planar profile, by a set of tubes of different lengths over the entire area of the burner (honeycombs). The “gluing” of the open boundaries of the front, the so-called flame stabilization, is provided by flame holders — arbitrary obstacles generating a vortex zone of flow deceleration of a required configuration over the flame perimeter. In this “stagnant” zone, the flame burns stably and serves as a permanent source of ignition.
Rough sea and light breeze are storm precursors
The next form is the flame of the first kind with a continuous “glued” front, whose surface is curved by large-scale irregular, sometimes almost stochastic or completely chaotic perturbations (“smooth” depressions and bulges of versatile fantastic shapes and sizes). This is a clear feature of the early stage of turbulence production with virtual vortices generated in a continuous, molecularly homogeneous medium; these vortices may be large or small, swirled as Swiss rolls, doughnut-shaped “bread rolls” with holes, or just holes without “bread rolls”. These vortices are generated not only on the walls of the device but also inside the flow, owing to shear stresses of pressure gradients. This stage is called the “inertial mode of vortex generation”, and the translational and rotational energy of vortices originates from the kinetic energy of the entire flow. Moving downstream, the vortices deform the front surface, the amount of combustion products increasing proportionally; the combustible mixture is consumed, and the integral content of heat in the flame increases.
Turbulent storm blows into the sail-front and tears it to pieces
With a further increase in flow stress, which is characterized by an increase in the Reynolds number (proportional to the product of flow velocity and the diameter of the device), the amplitude of vortex velocity also increases. Large vortices start to disintegrate; doughnut-shaped “bread rolls” start to break up and crack; they collide with each other at high velocity, drum on the flame front, and tear the latter into small pieces.
This is the final, turbulent flow mode, and the flame front is not only strongly corrugated but has holes made by high-energy vortices. A region “stuffed” with various possible inhomogeneities is formed. These inhomogeneities are mixed scraps of the flame-front film, of zones of the homogeneous combustible mixture, as well as of a mixture of hot combustion products and cold fuel. In a poorly balanced engine, the thickness of this layer can be so large that the fuel may be injected into the zone of cooled combustion products, no ignition will occur, and the unburned mixture will be ejected outside, through the exhaust pipe, into the atmosphere.
An outwardly simple phenomenon, laminar homogeneous combustion is a dissipative process with an extremely complicated and strongly nonequilibrium character from the viewpoint of thermodynamics and with nonlinear dependences on almost all physical and chemical parameters.
As the normal burning velocity is finite and the temperature of the igniting medium surrounding the fuel has to be equal to or higher than the ignition temperature, two important constraints are imposed on the range of existence of the combustion process. First, the time of residence of the combustible mixture in the combustion chamber has to be longer than the reaction time; otherwise, the fuel will be ejected through the nozzle before it burns down. Second, during intense turbulent mixing with combustion products, the concentrations of the components and the temperature should retain values at which combustion is possible altogether. Therefore, the process is bounded by a corridor of optimal flow parameters, which is clearly seen when superhigh-speed vehicles are being made. Thus, there is a natural limit of effectiveness of this method of fuel combustion.
Scenario of “tornado” emergence, or how the turbulent flame is affected by the detonation wave
The process of interaction of the turbulent flame structure with detonation and shock waves is extremely complicated, but we would regret it if we did not give some interesting ideas: the pattern of this imaginary experiment is rather nontrivial, illustrative, and promising. We mean a “tornado” on a microscopic scale. Indeed, when the mixture is injected tangentially, at a high velocity, into a cylindrical combustor containing a shock wave (normal to the direction of the combustible mixture flow), which pulls, like a locomotive, the long high-velocity “tail” into the combustor, a powerful upward-swirling ring-shaped centrally-symmetric single vortex is generated, which is the analog of a tornado. The “tail” is a sophisticated superposition of compression and rarefaction waves, capable of forming the flame front even from small scraps. A unique phenomenon occurs: a “pseudolaminar” thick front composed from fragments of the primary laminar continuous front! When interacting with the “funnel”, the global combustion zone consisting of completely disparate microzones in terms of density (with an almost fractal character) is subjected to a complex mechanism of “dynamic separation” in terms of its composition and heat content. Let us recall that a funnel is also formed if we stir tea with a spoon in circular motions; as the liquid becomes calmer, the heavy tealeaves gather into a “bundle” near the glass centerline (the so-called Einstein’s effect) and on the bottom around the central point. In a similar manner, the rarefaction arising inside the “tornado” will pull into the funnel mostly hot (“lighter” fraction) flame spots and non-cooled combustion products which are ready to “float up” like a balloon. The thick “pseudolaminar” front formed by the shock wave (or by several shock waves) can be sucked into the funnel as a whole, because its heat content is high. The comparatively cold fraction of combustion products and cold unburned fuel (“heavier” fraction) will be thrown by the centripetal force and by the Coriolis force to the periphery, to the combustor walls. The combination of hydrodynamic and buoyancy forces will generate convective vortices of tremendous power, because the velocity of funnel rotation may be sonic or even higher, and the difference between the temperatures of the cold and hot fractions can be enormously large. The phrases “tornado in a barrel with flame” and “tornado with a lightning” are almost complete by analogous because the parameters of these two phenomena are equivalent in order of magnitude, and fractally similar. A considerable difference in pressure at the boundaries of inhomogeneities and molecular friction on the way to periphery and into the cone makes the fluid more homogeneous, thus, compacting the cold fraction closer to the walls. This effect of additional cooling of the wall can turn out to be very useful, because one of the primary problems of supersonic engines is intense heating of the walls of the vehicle and combustor. The fate of hotter fractions sucked into the cone can also be favorable, because the integral heat content of this fraction increases; hence, the conditions for more effective combustion of the fuel are improved, and this is another extremely important problem, in addition to cooling. The process of combustion in the combustion chamber is continuous because the fuel is continuously injected. Synchronization of the rate of fire of a detonation gun with injection with the characteristic time of fuel burnout and with the period of tornado relaxation between the shots may substantially affect combustion intensification, especially if combining these complex phenomena is accompanied by resonance effects. The dynamics of tornado amplification during the shot and of its attenuation in the periods between the shots can lead to the above-mentioned Einstein’s effect, partly reversing the process of “drift” of the fractions. Studying the pulsed dynamics of this process may reveal unexpected effects and interesting results, for instance, in investigating the periodic character of the opposing flows of the fractions.
The Ranque vortex effect is also worth mentioning. This effect contributes to the separation of hot and cold gases and is widely used in various engineering applications. It occurs in intensely swirled flows in an axisymmetric channel, where the original thermally homogeneous flow can be separated into hot and cold parts.
Thus, the qualitative pattern of the process shows that the dynamic effect of the “tornado” can significantly modernize the process of turbulent combustion, thus expanding the optimal boundaries of the range of its existence, especially when using this effect in combustors of supersonic and hypersonic flying vehicles. The above-considered scenario of microtornado evolution and the present discussion are neither useless nor groundless. Vice versa, they make it possible to trace promising research directions without going into too much detail, which is often done in practice, based on intuitive estimates. To look at the problem from aside, to understand the interrelationships of many phenomena and the qualitative changes in the evolution of the process through all stages of its development, to assess everything in retrospect, and construct a logically consistent fractal and self-organizing chain for a gradually complicated structure — this is the path that is still to be covered.
The material was prepared by V. A. Souyushev, candidate of physics and mathematics