Stretch rate

The stretching properties of polymers are investigated by examining the effect of polymer orientation, polymer chain length, stretching rate, and temperature. Homogeneity of polymer films and consistency between lots of polymer films also are investigated. Statistical analysis of data includes Q-tests and f-tests. 

The crystallite orientation in PET fibers depends first and basically on the applicated draw ratio and sec ond on the stretching rate. The values off. characteristics for PET fibers as established by the authors are in Table 5. 

The factor having the strongest effect is the elongation imparted in the process of production stretching. Second, the overall orientation is affected by the stretching rate. For the same draw ratio, the overall orientation grows with an increase in the stretching rate. The effect of the draw ratio on the value of Hermans function of orientation is illustrated by the values of/o, established by the authors and depicted in Table 7. 

Fig. 6. Variation of elasticity modulus (E) under tension and yield strain (es) of the polymer matrix (I, I ) and polyethylene-based composites polymerization filled with kaolin (2,20 in function of polymer MM [320], Kaolin content 30% by mass. The specimens were pressed 0.3-0.4mm thick blates stretching rate e = 0.67 min-1...

The flame stretch rate distribution was calculated based on experimental PIV data, using the semitheoretical... 

The shape of the stretch rate distribution curve for the lean limit propane flame, shown in Figure 3.1.9b, is very similar. However, for this flame, the estimated contribution of the curvature is more important than with the methane flame, reaching about 40% of the maximum stretch rate. 

Stretch rate as a function of distance, from the top leading point along the flame front, (a) for a lean limit methane flame and (b) lean limit propane flame propagating upward in a standard cylindrical tube. 

Direct images of the three counterflow twin flames with decreasing stretch rate through the reduction of the mixture flow rate (from top photo to bottom photo), while keeping the flow mixture composition constant. 

It can also be noted that the slope of the S , .,f-Ka plot reflects the combined effect of stretch rate and non-equidiffusion on the flame speed. Figure 4.1.6 clearly shows that the flame response with stretch rate variation differs for lean and rich mixtures. In particular, as Ka increases, the S for stoichiometric and rich mixtures increases, but decreases for the mixture of equivalence ratio = 0.7. This is because the effective Lewis numbers of lean w-heptane/ air and lean /so-octane/air flames are... 

The counterflow configuration has been extensively utilized to provide benchmark experimental data for the study of stretched flame phenomena and the modeling of turbulent flames through the concept of laminar flamelets. Global flame properties of a fuel/oxidizer mixture obtained using this configuration, such as laminar flame speed and extinction stretch rate, have also been widely used as target responses for the development, validation, and optimization of a detailed reaction mechanism. In particular, extinction stretch rate represents a kinetics-affected phenomenon and characterizes the interaction between a characteristic flame time and a characteristic flow time. Furthermore, the study of extinction phenomena is of fundamental and practical importance in the field of combustion, and is closely related to the areas of safety, fire suppression, and control of combustion processes. 

One significant result from the studies of stretched premixed flames is that the flame temperature and the consequent burning intensity are critically affected by the combined effects of nonequidiffusion and aerodynamic stretch of the mixture (e.g.. Refs. [1-7]). These influences can be collectively quantified by a lumped parameter S (Le i-l)x, where Le is the mixture Lewis number and K the stretch rate experienced by the flame. Specifically, the flame temperature is increased if S > 0, and decreased otherwise. Since Le can be greater or smaller than unity, while K can be positive or negative, the flame response can reverse its trend when either Le or v crosses its respective critical value. For instance, in the case of the positively stretched, counterflow flame, with k>0, the burning intensity is increased over the corresponding unstretched, planar, one-dimensional flame for Le < 1 mixtures, but is decreased for Le > 1 mixtures. 

It is also well known that there exist different extinction modes in the presence of radiative heat loss (RHL) from the stretched premixed flame (e.g.. Refs. [8-13]). When RHL is included, the radiative flames can behave differently from the adiabatic ones, both qualitatively and quantitatively. Figure 6.3.1 shows the computed maximum flame temperature as a function of the stretch rate xfor lean counterflow methane/air flames of equivalence ratio (j) = 0.455, with and without RHL. The stretch rate in this case is defined as the negative maximum of the local axial-velocity gradient ahead of the thermal mixing layer. For the lean methane/air flames,... 

Maximum flame temperature a function of the stretch rate... 

For the adiabatic condition in which RHL is suppressed, the flame response exhibits the conventional upper and middle branches of the characteristic ignition-extinction curve, with the upper branch representing the physically realistic solutions. It can be noted that the effective Le of this lean methane/air mixture is sub-unity. It can be seen from Figure 6.3.1 that, with increasing stretch rate, first increases owing to the nonequidiffusion effects (S > 0), and then decreases as the extinction state is approached, owing to incomplete reaction. Furthermore, is also expected to degenerate to the adiabatic flame temperature, when v = 0. 

Experimentally, two modes of extinction, based on the separation between the twin flames are observed. Specifically, the extinction of lean counterflow flames of n-decane/02/N2 mixtures occurs with a finite separation distance, while that of rich flames exhibits a merging of two luminous flamelets. The two distinct extinction modes can be clearly seen in Figure 6.3.2. As discussed earlier, the reactivity of a positively stretched flame with Le smaller (greater) than unity increases (decreases) with the increasing stretch rate. Therefore, the experimental observation is in agreement with the... 

The measured extinction stretch rates for n-decane/ O2/N2 mixtures at 400 K preheat temperature as a function of equivalence ratio are shown in Figure 6.3.3. The flame response curves at varying equivalence ratios are also computed using the kinetic mechanisms of Bikas and Peters (67 species and 354 reactions) [17] and Zhao... 

Experimental (symbols) and computed (lines) extinction stretch rates of w-decane/02/N2 mixtures with T, = 400 K. The molar ratio of N2/ (Nj + O2) is 0.84. 

We re-examined the results of Kee et al. [19] with respect to three considerations. First, as the axial-velocity gradient of fhe outer flow confinuously changes for the plug-flow formulation, if is reasonable to expect that there would be considerable uncertainty in determining the effective stretch rate and consequently, in assessing the difference found in fhe comparison. Second, it is somewhat perplexing that the computed extinction stretch rates of Kee ef al. [19] was observed to differ from each ofher for fhe fwo formulations, while the flame sfrucfure remained nearly fhe same. Third, there is no explicit display of fhe flame sfrucfure used in... 

To scrutinize the sensitivity of the flame structure to the description of the outer-flow field, we compared the flame structure obtained from the two limiting boundary conditions at the extinction state, which can be considered to be the most aerodynamically and kinetically sensitive state of the flame for a given mixture concentration, and demonstrated that they were basically indistinguishable from each other. This result thus suggests that the reported discrepancies in the extinction stretch rates as mentioned in the work by Kee et al. [19] are simply the consequences of the "errors" associated with the evaluation of the velocity gradients. 

Variations of extinction stretch rate and extinction temperature of methane/air mixtures with equivalence ratio for the five different cases as in Figure 6.3.4. 

Since stretch affects the onset of flame pulsation, it should correspondingly affect the state of extinction in the pulsating mode. We shall therefore assess the influence of stretch in modifying the state of extinction. If the extinction turning point of a steady-flame response curve is neutrally stable, the entire upper branch should be dynamically stable then, the corresponding static-extinction stretch rate is the physical limit. 

Comparison of static- and dynamic-extinction stretch rates for various hydrogen/air flames. When the equivalence ratio is sufficiently rich, the dynamic-extinction strain rate can be substantially lower than the corresponding static extinction limit. 

---