The onset of double-diffusive convection in a stably stratified fluid layer heated from below

The time of the onset of double-diffusive convection in time-dependent, nonlinear temperature fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform solute gradient experiences ramp heating from below, but its stable solute concentration is to reduce thermal effects which invoke convective motion. The related stability analysis is conducted on the basis of the propagation theory. Under the linear stability theory the thermal penetration depth is used as a length scaling factor and the linearized perturbation equations of similarity transform are solved numerically. The resulting correlations of the critical time to mark the onset of regular cells are derived as a function of the thermal Rayleigh and the solute Rayleigh numbers. The predicted stability criteria are apparently consistent with existing experimental results for aqueous solution of sodium chloride.     

Thermal instability in a fluid layer subjected to transient cooling from above

The onset of natural convection in a horizontal fluid layer cooled from above is investigated theoretically. The initially quiescent fluid placed between two flat plates is cooled by decreasing the upper boundary temperature at a constant time-rate. Its stability analysis is conducted by employing the propagation theory, which considers variations of disturbances with the time upon their onset. The critical conditions predicted by this theory are found to agree favorably with the existing experimental results. Also, the effect of the Prandtl number on instability is discussed.     

The onset of instability in the flow induced by an impulsively started rotating cylinder

The onset of initial instability in a developing Couette flow following the impulsive starting of an inner rotating cylinder is analyzed using linear theory. It is well known that there is a critical Taylor number Ta_c at which Taylor vortices first appear between two concentric cylinders. For Ta>Ta_c Taylor-like vortices occur at a certain elapsed time. In the present study, the critical time t_c to represent the onset of this initiating instability, which then grows as toroidal vortices, is analyzed using propagation theory. For this purpose a self-similar transformation is forced through scaling analysis. The resulting stability criteria compare well with the available experimental data for vortices in water. The new measures represent the onset of the fastest growing instability and also suggest the detection time for the manifestation of secondary flow in the primary time-dependent Couette flow.     

Unified Theory of Thermal Shock Fracture Initiation and Crack Propagation in Brittle Ceramics

A fracture-mechanical theory is presented for crack propagation in brittle ceramics subjected to thermal shock. The criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries. Thermal stress crack instability occurs between two values of critical crack length. For short initial crack length, crack propagation occurs kinetically, with the total area of crack propagation proportional to the factor S_t² (1-2 v )/EG, where S_t is tensile strength, v is Poisson's ratio, E is Young's modulus, and G is surface fracture energy. Under these conditions the newly formed crack is subcritical and requires a finite increase in temperature difference before propagation will proceed. For long initial crack length, crack propagation occurs in a quasi-static manner and can be minimized by maximizing the thermal stress crack stability parameter R_st= [G/α² E ]^1/2, where α is the coefficient of thermal expansion. For heterogeneous brittle solids, such as porous refractories, the concept of an "effective flaw length" is introduced and illustrated on the basis of experimental data in the literature. The relative change in strength of a brittle solid as a function of increasing severity of thermal shock is estimated. Good qualitative agreement with literature data is found.     

Dynamic crack growth mechanism and lifetime assessment in plasma sprayed thermal barrier system upon temperature cycling

Failure of plasma-sprayed thermal barrier coatings (TBCs) is very complicated upon temperature cycling, therefore, to ascertain the crack propagation behavior is beneficial to understand the failure mechanism and life prediction of TBCs. In this paper, a finite element model is developed by coupling the dynamic growth of thermally grown oxide and dynamic crack propagation to explore the failure of TBCs induced by the instability of the interface between top coat (TC) and bond coat (BC). The thermal cyclic lifetime is deduced by obtaining the thermal cycles corresponding to the occurrence of complete delamination. The influence of the non-uniformity of the interface on thermal cyclic lifetime is quantitatively evaluated. Sensitivity studies including the effects of constituent properties and crack distance to the interface on the thermal cyclic lifetime are further examined. The results show that the incipient cracks usually nucleate above the valley due to the large tensile stress, and the shear stress near the peak plays a very crucial role. The crack growth involves three stages with different fracture dominated-mode. The crack propagation behavior obtained by simulation is in line with that observed by experiments. The TBCs system with a uniform interface exhibits a longer thermal cyclic lifetime compared to the non-uniform interface. Coating optimization methods proposed in this work may provide an alternative option for developing a TBCs system with longer service lifetime.     

Hydrodynamic behavior of an electrified thin film flowing down an inclined plane at high Reynolds numbers

To answer the questions on the dynamics of thin liquid flow down an inclined plane at high Reynolds numbers subjected to a uniform normal electrostatic field, we have derived evolution equations describing the free-surface behavior by using the von Kármán-Pohlhausen approximation. The integration of the evolution equations is numerically performed to address two-dimensional finite-amplitude surface-wave propagation modes. The growth of a periodic disturbance is first examined to compare with the results linear-stability theory, and then to investigate the nonlinear surface-wave behavior the evolution equations are solved numerically by a Fourier-spectral method. For small evolution time the computed nonlinear modes of instability are well consistent with the results from the linear theory. The effect of an electrostatic field makes the flow system significantly unstable.     

The onset of Taylor-Görtler vortices in impulsively decelerating swirl flow

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using propagation theory. It is well-known that the primary transient swirl flow is laminar, but with initial high velocities secondary motion sets in at a certain time. The dimensionless critical time Τ_c to mark the onset of instability is presented here as a function of the Reynolds number Re. Available experimental data indicate that for large Re deviation of the velocity profiles from their momentum diffusion occurs starting from a certain time Τ≈4Τ_c. This means that secondary motion is detected at this characteristic time. It seems evident that during Τ_c⪯Τ⪯4Τ_c, secondary motion is relatively very weak and the primary diffusive momentum transfer is dominant.     

Onset of convection in a porous mush during binary solidification

The onset of convection in a mushy layer during solidification of a binary melt is investigated by using the propagation theory we have developed. The critical conditions for the mushy-layer-mode of instability are obtained numerically for aqueous ammonium chloride solution. The mush thickness at the onset of convection is predicted as a function of the solution viscosity and compared with the experimental data. The onset time of the mushy-layer-mode convection has a minimum point with varying the superheat. When the superheat is large, the mushy layer grows slowly and a long time is required for the onset of convection.     

Recent research advances in the chemistry of poly(vinyl chloride)

Summarized briefly here are some new observations that relate to the polymerization chemistry of vinyl chloride (VC) and to the thermal degradation, thermal stabilization, fire retardance, and smoke suppression of poly(vinyl chloride) (PVC). During polymerization, head-to-head VC emplacement leads to β-chloroalkyl radicals that can transfer chlorine atoms directly to VC. Another mechanism for transfer to monomer is responsible, however, for the polymer molecular-weight reductions that occur at high VC conversions. This transfer process involves the abstraction of methylene hydrogen from the polymer by an ordinary macroradical and the subsequent bimolecular donation of a chlorine atom to VC. The propagation steps of the polymerization do not become diffusion-controlled at VC conversions near 90%, and hydrogen abstraction from the polymer by ordinary macroradicals leads to the structural defects that cause thermal instability. The thermal dehydrochlorination of PVC involves ion pairs or four-center concerted transition states that are highly polarized. Reversible thermal stabilization of the polymer by organic metal salts occurs by the Frye-Horst process, and the reductive coupling of PVC chains may suppress both smoke and flame. This coupling can result from reactions of the polymer with zero- or low-valent transition-metal species that are formed in situ from appropriate additives.     

Thermal convection in a saturated porous medium subjected to isothermal heating

A theoretical study of thermal convection in a fluid-saturated horizontal porous layer is reported for the case of isothermal heating from below. The onset time of natural convection and convective heat transport for large Darcy-Rayleigh number systems are analyzed, based on the propagation theory involving temporal dependence of perturbed quantities. Also, an overall feature of heat transport is discussed in connection with the Forchheimer modification of the Darcy flow model.     

Onset of buoyancy-driven convection in the horizontal fluid layer heated from below with time-dependent manner

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time Τ_c to mark the onset of convective instability is presented as a function of the Rayleigh number Ra_Ø and the Prandtl number Pr. The present stability analysis predicts that Τ_c decreases with increasing Pr for a given Ra_Ø. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time Τ?(2～4) Τ_c .     

Propagation of Isothermal Flame in the Low-Pressure Thermal Decomposition of Nitrogen Trichloride

The inhibition and promotion of isothermal NCl₃ flame by NOCl and H₂, respectively, are explained. The crossover from the isothermal mode of flame propagation to the thermal one is analyzed for NCl₃–He mixtures. Calculations based on a kinetic mechanism taking into account energy chain branching are performed, and qualitative agreement between the calculated and observed data is demonstrated. The one-dimensional problem of chain–thermal flame propagation by a chain reaction involving a nonlinear-branching step has two solutions corresponding, one corresponding the isothermal mode of flame propagation and the other corresponding to the chain–thermal one. Nonlinear chain branching shortens the time needed for thermal ignition and increases the flammability of the combustible mixture.     

Some Stability Aspects of Gas Combustion in Porous Media

Some aspects of the stability of hot-spot and oblique gas-combustion fronts in porous media are considered using a thermal model. A general expression for the velocity of a curved wave front of filtration gas combustion is obtained taking into account the curvature and local slope of the front. It is shown that curvature always promotes stabilization of the front. The slope of the front, in principle, can have a destabilizing effect. However, because this effect is weaker than the curvature effect, it does not cause development of instability. The roles of convective heat and mass transfer between the hot spot and the ambient gas flow and selective diffusion in the development of local instability are analyzed. Criteria are found for the development of hot-spot instability, and the ranges of system parameters in which instability is possible are determined. The effect of variation in the length of the front during wave propagation on the development of instability of an oblique front is considered. Accounting for this factor gives a criterion for instability development that coincides with the experimental one.__________Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 4, pp. 39–49, July–August, 2005.     

Interfacial stability of binary liquid—liquid systems—I. Stability analysis

Temperature gradients, resulting from thermal effects due to heats of solution and mixing, which accompany mass transfer in partially miscible liquid pairs, were found to be of the same order of magnitude as those leading to thermal instability in shallow liquid layers. Linearised perturbation analysis was therefore applied to such binary liquid systems, using linearised profiles, and the characteristic equation was analysed for the onset of spontaneous Marangoni-type interfacial convection. The stability criteria indicate that binary systems may be stable or unstable in both directions of transfer or unstable in only one direction of transfer. They also suggest that stationary instability is promoted when the heat of solution and the rate of change of interfacial tension with temperature are of opposite signs and that instabilities of oscillatory character are most likely to occur for mass transfer out of the phase of higher viscosity     

The onset of Taylor-Görtler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

The onset of Taylor-Görtler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as V _i ∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (V _i =constant). Based on the present τ _c and the Foster’s [1969] comment, the manifest stability guideline is suggested.     

Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model

Comprehensive understanding of failure mechanism of thermal barrier coatings (TBCs) is essential to develop the next generation advanced TBCs with longer lifetime. In this study, a novel numerical model coupling crack propagation and thermally grown oxide (TGO) growth is developed. The residual stresses induced in the top coat (TC) and in the TGO are calculated during thermal cycling. The stresses in the TC are used to calculate strain energy release rates (SERRs) for in-plane cracking above the valley of undulation. The overall dynamic failure process, including successive crack propagation, coalescence and spalling, is examined using extended finite element method (XFEM). The results show that the tensile stress in the TC increases continuously with an increase in an undulation amplitude. The SERRs for TC cracks accumulate with cycling, resulting in the propagation of crack toward the TC/TGO interface. The TGO cracks nucleate at the peak of the TGO/bond coat (BC) interface and propagate toward the flank region of the TC/TGO interface. Both TC cracks and TGO cracks successively propagate and finally linkup leading to coating spallation. The propagation and coalescence behavior of cracks predicted by this model are in accordance with the experiment observations. Therefore, this study proposed coating optimization methods towards advanced TBCs with prolonged thermal cyclic lifetime.     

Thermal instability of a fluid layer when cooled isothermally from above

The onset of buoyancy-driven convection in an initially motionless isothermal fluid layer is analyzed numerically. The infinite horizontal fluid layer is suddenly cooled from above to relatively low temperature. The rigid lower boundary remains at the initial temperature. In the present transient system, when the Rayleigh number Ra exceeds 1101, thermal convection sets in due to buoyancy force. To trace the temporal growth rates of the mean temperature and its fluctuations we solve the Boussinesq equation by using the finite volume method. We suggest that the system begins to be unstable when the growth rate of temperature disturbances becomes equal to that of the conduction field. Three different characteristic times are classified to interpret numerical results clearly: the onset time of intrinsic instability, the detection time of manifest convection and the undershoot time in a plot of the cooling rate versus time. The present scenario is that the thermal instability sets in at the critical time, then grows super-exponentially up to near the undershoot time, and between these two times the first visible motion is detected. Numerical results are compared with available experimental data. It is found that the above scenario looks promising and the critical time increases with decreasing the Prandtl number Pr and also the Rayleigh number Ra.     

Effect of carbon black on time dependence of the melt flow index

Time dependence in the melt indexing of polyolefins stabilized against thermally induced changes is well known, the prevalent effect being an increase in melt index toward a steady-state value. The melt index of polyethylenes compounded with carbon black has been found to decrease, in some cases radically, although oxygen uptake data show no evidence of thermal instability. The melt index–time plot can be restored to its normal shape by adding excess quantities of a standard thioether antioxidant. Data are rationalized by assuming that polyethylene adsorbs on the available pigment surface, forming a crosslink network. The thioether antioxidant, however, may adsorb preferentially, thereby restoring the normal response of the polymer to forces resulting in its capillary extrusion. The results emphasize the contribution of chain orientation effects to the time dependence of melt index.     

Observation of ceramic cracking during quenching

It is difficult to observe the thermal shock cracking in real time, so the measurement of the crack after thermal shock is considered as an alternative method. This paper proposes a new experimental method which can exhibit the thermal shock cracking in real time by water quenching of translucent ceramic and high‐speed imaging. The crack propagation is captured, and the crack growth rate is calculated. The results confirm the previous theoretical predictions of crack propagation under thermal shock. This paper expands the research on understanding the failure mechanisms of ceramic materials in thermal shock.     

Onset of solutal convection in liquid phase epitaxy system

The onset of convective instability in the liquid phase epitaxy system is analyzed with linear stability theory. New stability equations are derived under the propagation theory, and the dimensionless critical time τ _c to mark the onset of the buoyancy-driven convection is obtained numerically. It is here found that the critical Rayleigh number Ra _c is 8000, below which the flow is unconditionally stable. For Ra>Ra _c the dimensionless critical time τ _c to mark the onset of a fastest growing instability is presented as a function of the Rayleigh number and the Schmidt number. Available numerical simulation results and theoretical predictions show that the manifest convection occurs starting from a certain time τ _o (> τ _c ). It seems that during τ _c ≤τ≤τ _o secondary motion is relatively very weak. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.