CC BY
17iSHS 2019
Moscow, Russia
NONSTATIONARY COMBUSTION OF LAYERED HETEROGENEOUS
SYSTEMS
S. V. Kostin", P. M. Krishenik*", S. A. Rogachev", and A. E. Sytschev"
aMerzhanov Institute of Structural Macrokinetics and Materials Science, Russian Academy of
Sciences, Chernogolovka, Moscow, 142432 Russia
*e-mail: [email protected]
DOI: 10.24411/9999-0014A-2019-10069
The stability of combustion wave passing through the interface between two different SHS systems [1-4] is also of current importance in the task objective of reliable SHS joining of dissimilar materials [5]. Transition of combustion wave from one burning material to another is normally accompanied by transient phenomena such as pulsations of combustion temperature and burning velocity, which may affect the quality of SHS joining. Recent experiments [5] on SHS joining in (Ti + _ySi)/(Ti + xC) sandwiches were successful and showed the formation of
Ti3SiC2 grains within the transition layer. Capillary fluid dynamic phenomena at the interface between two reactive systems were analyzed in [6, 7]. In this work, we numerically investigated combustion in two-layer SHS systems with special emphasis on thermal conditions at their interface caused by the presence of clearance gap. We consider the propagation of combustion wave over a two-layer sandwich—such as (Ti + ^Si)/(Ti + xC) [5]— depicted in Fig. 1. The combustion wave initiated in reactive layer 1 (of thickness /1) moves downward and then ignites reactive layer 2 (with thickness L-/2) through a gaseous gap of thickness A (Fig. 1). The problem is essentially 1D and there is no heat sink through the side surfaces. When the combustion wave initiated in layer 1 approaches to gap A (Fig. 1), it can ignite layer 2 in a mode depending on the critical conditions for ignition formulated in [8]. Let us consider the transient phenomena taking place in the vicinity of gap A in more detail.
Close contact between the layers (A ^ 0).
In analysis we used our previous results [1, 2]. It is assumed that (a) both reactions are gasless and (b) during the reactions there is no change in thermophysical parameters and sample dimensions. In vicinity of the interface, the heat flux into layer 2 (Fig. 1) depends on mutual relationship b between thermophysical parameters of layers 1 and 2: b = ^(^cPp)!(^iCPi). The combustion temperature and burning velocity tend to grow upon approaching to layer 2 when b > 1, and to decrease if b < 1. And at some critical value bc < 1, the flameout takes place. The induction ignition is observed when AHX > AH2 and the mode of burning when AHX < AH2. It was received the time evolution of temperature profiles for b > 1 and different thermal conductivity and density of layers 1 and 2: X1 ^ X2, p1 ^ p2. The temperature spike at the interface is observed at within the warm up zone where v is the velocity of combustion wave propagation in layer 1. The temperature at the interface is given by the expression
+ %
Fig. 1. Two-layer system under consideration.
T ~ h +--(T - T ), where T\ = To + Q\lc\. The temperature spike can be associated with
1 + b
heat accumulation at the interface: b = .J\cxP\l^ciP ~ 16, which corresponds to the (Ti +
_ySi)l(Ti + xC) system taken as an example.
For b < \, the values of T and v were found to sharply drop on approaching to the interface (Fig. 2).
300 400 500 600 700 1500 2000 2500 3000 3500 4000
Fig. 2. (a) Time evolution of temperature profiles and (b) temperature profile at the interface, b x 0.6, where 0 and t are dimensionless temperature and time.
After long period of depression, the temperature restores to a level of
T. ~ Tn. +--(T1 — T0), just as upon ignition with an incandescent body [9].
1 + b
Heat transfer from layer 1 to layer 2 actually obeys the laws of inert heat exchange. After warm-up to a sufficiently large depth, the established steady-state temperature, Tst is markedly lower than Tad for layer 1. In case of inert heating, the reaction heat in layer 2 is negligibly small. But the latter becomes important when chemical reaction takes place in warmed up layer 2. The heat flux through the interface changes its sign, which gives rise to heat sink from the reacting volume. As a result, superadiabatic temperatures are attained within the bulk of layer 2, the maximal temperature at the interface being close to Tad. The above results quantitative agree with experiment [3].
No contact between the layers (A > 0).
According to [10], radiative heat transfer from a burning layer through a gap is commensurable with heat transfer by thermal conduction. In case of layered systems with a 'thin' gap [A < (Xi/cipi/v], one can use an effective heat transfer coefficient. Due to strong difference in thermophysical parameters of solids and gas, the combustion temperature in the vicinity of the gap gradually 'takes off from Tad. The initial temperature spike is followed by the stage of inert heating of layer 2 via the gap. A relatively long period of inert heating is followed by a shorter period of heat release from chemical reaction in the warmed up layer, and this gives rise to the backward heat flux toward the interface.
In contrast to close contact, the superadiabatic temperatures are attained in both reactive layers. It can be expected that in real conditions of SHS joining the process of heat/mass exchange between the dissimilar materials to be joined will be still more intensive.
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Fig. 3. (a) Time evolution of temperature profiles ahead of the gap (curve I), at the gap middle (curve II), and behind the gap (curve III): and (b) temperature profile at the interface: A = 0.1; b ~ 316.
If at least one reagent is able to melt at the interface below the combustion temperature and mutual dissolution happens faster than chemical reaction, the combustion reaction can be regarded as homogeneous. Interdiffusion at the interface can also affect the reaction kinetics and thus lead to formation of Ti3SiC2 within the transition layer. It should also be noted that unsteady combustion at the interface may affect the thermophysical parameters of matter and kinetic parameters and hence the character of transient processes.
Conclusions
The character of transient phenomena taking place during combustion of two-layer SHS systems depends on interrelation between thermal activities of constituent layers. In case of close contact, superadiabatic heating can be attained only in one of two adjacent systems. But in the presence of clearance gap, superadiabatic temperatures can be reached in both reactive layers. This may improve the conditions for heat/mass transfer between the layers and hence the quality of SHS joining. Our results may turn helpful for optimization of combustion in two-layer systems. Optimization of the clearance gap will be a subject of our forthcoming communication.
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