Stretch Rate Research Articles

Some experimental results for converging flow of dilute polymer solution

This paper presents the results of experimental studies of the flow of a dilute polymer solution in a converging pipe. Three geometries with restriction rates are considered: 2.41, 3.92, and 5.65. A water–glycerin solution of 0.1% polyacrylamide was used as a working fluid. Point velocity measurements are made by using the smoke image velocimetry technique, which previously was proved by the construction of velocity profiles corresponding to the laminar viscoelastic flow in a straight pipe. The influence of the Weissenberg number and the restriction rate of the channel on the velocity profiles are established for both transverse and longitudinal directions. For small Weissenberg numbers, the experimental results are compared with the numerical results obtained using the Giesekus and exponential form of Phan-Thien–Tanner rheological models. Three flow regimes are identified: flow without vortex, vortex enhancement, and divergent flow, which is consistent with published results on the abrupt contraction and converging flows. Vortex length for a wide range of Weissenberg numbers is well predicted by a logarithm function. Modified expression of stretch rate with location of detachment plane can predict the flow regimes and the onset of unsteady flow in converging channels.

Role of the microtubule network in the passive anisotropic viscoelasticity of right ventricle with pulmonary hypertension progression

Cardiomyocytes are viscoelastic and contribute significantly to right ventricle (RV) mechanics. Microtubule, a cytoskeletal protein, has been shown to regulate cardiomyocyte viscoelasticity. Additionally, hypertrophied cardiomyocytes from failing myocardium have increased microtubules and cell stiffness. How the microtubules contribute to the tissue-level viscoelastic behavior in RV failure remains unknown. Our aim was to investigate the role of the microtubules in the passive anisotropic viscoelasticity of the RV free wall (RVFW) during pulmonary hypertension (PH) progression. Equibiaxial stress relaxation tests were conducted in the RVFW from healthy and PH rats under early (6%) and end (15%) diastolic strains, and at sub- (1Hz) and physiological (5Hz) stretch-rates. The RVFW viscoelasticity was also measured before and after the depolymerization of microtubules at 5Hz. In intact tissues, PH increased RV viscosity and elasticity at both stretch rates and strain levels, and the increase was stronger in the circumferential than longitudinal direction. At 6% of strain, the removal of microtubules reduced elasticity, viscosity, and the ratio of viscosity to elasticity in both directions and for both healthy and diseased RVs. However, at 15% of strain, the effect of microtubules was different between groups – both viscosity and elasticity were reduced in healthy RVs, but in the diseased RVs only the circumferential viscosity and the ratio of viscosity to elasticity were reduced. These data suggest that, at a large strain with collagen recruitment, microtubules play more significant roles in healthy RV tissue elasticity and diseased RV tissue viscosity. Our findings suggest cardiomyocyte cytoskeletons are critical to RV passive viscoelasticity under pressure overload. Statement of SignificanceThis study investigated the impact of microtubules on the passive anisotropic viscoelasticity of the right ventricular (RV) free wall at healthy and pressure-overloaded states. We originally found that the microtubules contribute significantly to healthy and diseased RV viscoelasticity in both (longitudinal and circumferential) directions at early diastolic strains. At end diastolic strains (with the engagement of collagen fibers), microtubules contribute more to the tissue elasticity of healthy RVs and tissue viscosity of diseased RVs. Our findings reveal the critical role of microtubules in the anisotropic viscoelasticity of the RV tissue, and the altered contribution from healthy to diseased state suggests that therapies targeting microtubules may have potentials for RV failure patients.

Experimental investigations of uniaxial and biaxial cold stretching within PC‐films and bars using optical measurements

AbstractPolycarbonate (PC) is an amorphous polymer that is an extremely robust material with a high tenacity, and thus suitable for a lightweight construction with glass‐like transparency. Due to these advantageous properties, PC is often used in industry for example in medical devices, automotive headlamps, sporting equipment, electronics, and a variety of other products. PC is often subjected to uniaxial and biaxial loading conditions. Therefore, reliable material models have to take into account the various resulting experimental effects. For those reasons, we investigate PC specimens under uniaxial and biaxial loading by using different stretch rates and loading scenarios. In addition to that, we propose methods for optical measurement of local stretches to obtain the approximated local true stress. In future work, the displacement fields and the resulting reaction forces will be used for parameter identification of constitutive equations.

Local statistics of turbulent spherical expanding flames for NH3/CH4/H2/air measured by 10 kHz PIV

In this paper, we present high-speed particle image velocimetry measurements to quantify combustion-induced turbulence and turbulent stretch rate effects on flame propagation in a fan-stirred constant-volume combustion vessel. Three stoichiometric fuel/air mixtures including methane/air, methane/hydrogen/air and ammonia/methane/air were tested. The expansion rate of flame radius is found to scale with a half-power law of the mean-radius based Reynolds number. Measurements of velocity in the reactant zone show that the gas mean and rms velocity increase within the flame brush then gradually decrease when approaching the detection edge. Combustion enhances the measured non-reacting flow turbulence by ∼64 % within the reactant side of the flame brush of this expanding spherical flame. The evolution of rms velocity is found to be insensitive to pressure but sensitive to initial turbulent intensity and laminar flame speed, scaling with Reynolds number in a similar manner as the rate of expansion of the flame radius. Hydrogen blending shows the largest absolute value of rms velocity increase, but ammonia blending leads to the largest increase in rms velocity relative to laminar flame speed. The pdfs of 2D curvature are broadened as u′ and p increase but gradually saturate at high u′ for all mixtures, those of stretch rate are widened by flame speed. The temporal evolution of statistical flame stretch rates suggests the tangential stretch rate is larger than and anti-correlated with the normal stretch, and that there is a strong positive correlation between instantaneous flame propagation rate and the rms strain rate. Finally, the mean flame curvature and mean stretch rate are found to be near zero as flame propagates outwardly.

How do stretch rate, temperature, and solvent exchange affect elastic network rupture?

In this study, we investigate three different polymeric networks in terms of their tensile strength as a function of stretching rate, or temperature, or medium viscosity. Both an acrylate-based elastomer and a crosslinked poly(methyl acrylate) are stronger, more stretchable, and tougher at high rates. They are also much stronger at lower temperatures. Such phenomena systematically suggest that the kinetics of bond dissociation in backbones of those load-bearing strands dictate the rate and temperature dependencies. We apply Eyring's activation idea for chain scission to rationalize the influence of rate and temperature on rupture for both elastomers and hydrogels where hydrogels become much more stretchable and stronger when water is replaced by glycerol.

Effects of radiative heat loss on extinction limits of counterflow premixed ammonia-air flames

The effect of radiative heat loss on counterflow premixed ammonia-air flames has been investigated as a function of equivalence ratio and system pressure. Non-adiabatic counterflow premixed flame simulations incorporating detailed chemistry, transport, and radiative heat transfer in the optically thin limit have been employed to elucidate important underlying physics and extinction characteristics. Similar to methane-air flame systems, non-adiabatic counterflow premixed computations show that the combined effects of positive flame stretch, sub-unity Lewis number, and radiative heat loss lead to the extension of the lean flammability limit for ammonia-air flames, revealing a C-shaped curve near the lean flammability limit that exhibits both radiation-induced and stretch-induced extinction states. The computations compare favorably with the experimentally determined extinction stretch rate values for the stretch-induced extinction states over a wide range of equivalence ratios at different pressures up to 5 atm. A novel feature sensitivity analysis has also been developed to highlight important sensitive reactions for the stretch- and radiation-induced extinction states. Furthermore, the controlling chemistry at the dual-extinction states and at varying pressures are compared and discussed.

Measurement of Laminar Burning Speed of Methane/Hydrogen/Air Mixtures at High Pressures and Temperatures

Abstract Green hydrogen which could be produced from renewable sources by solar water splitting or photovoltaic electrolysis will play an important role in achieving net-zero in the near future. One possible approach will be to mix hydrogen with natural gas for power generation in gas turbine systems. It is necessary to know the physical properties of burning speed of the mixture of natural gas and hydrogen. Since natural gas is mainly made up of methane, the burning speed of mixtures of methane and hydrogen has been measured and reported in this paper. Adding hydrogen gas during the combustion of methane enhances flame stability, expands the lean flammability range, decreases pollutant emissions, and boosts the burning speed. Burning speed measurement is performed in a cylindrical and spherical chamber. The pressure rise due to combustion was measured by a pressure transducer on the top of cylindrical and spherical chambers. The Z-shaped Schlieren system, equipped with a high-speed complementary metal oxide semiconductor (CMOS) camera, obtains pictures of flame propagation. Laminar burning speed is measured exclusively for flames that have a smooth and spherical shape. In addition, burning speed is only measured for large flame radii with low stretch rates. Burning speed is calculated by a thermodynamic model with the pressure rise data as an input. Measurements cover a wide range of operating conditions. The hydrogen mole fraction is 0%, 20%, and 40%, with temperatures of 298–400 K, pressures between 0.5 and 5.5 atmospheres and equivalence ratios of 0.8, 1, and 1.2.

Effect of Ignition Energy on the Initial Propagation of Hydrogen-Oxygen Premixed Flame

The purpose of this study is to determine the effect of changes in the ignition energy and hydrogen volume percentage of a hydrogen oxygen combustible mixture on the Markstein length of the hydrogen flame at the beginning of ignition. A – static combustor with a diameter of approximately 60 mm and an internal volume of 350 ml was manufactured, and flame propagation images were obtained under various ignition energies and hydrogen volume percentages of the hydrogen oxygen – mixed combustible to measure the initial propagation of the flame. Using the captured images, the stretched burning velocity (<i>S<sub>b</sub></i>) and stretch rate (<i>K</i>) under stretch were measured. The unstretched burning velocity (<i>S<sub>b</sub><sup>0</sup></i>) was calculated using the Chemkin code, and the effects of the ignition energy and hydrogen volume percentage of the combustible mixture were analyzed. As the hydrogen volume percentage of the combustible mixture increased, the Markstein length decreased. When the hydrogen percentage of the combustible mixture was held constant, the Markstein length decreased as the ignition energy decreased. The influence of the ignition energy increased as the hydrogen volume percentage of the combustible mixture decreased.

Turbulent burning velocity of hydrogen/n-heptane/air propagating spherical flames: Effects of hydrogen content

This study investigated the flame propagation and turbulent burning velocity of hydrogen/n-heptane/air mixtures subjected to differential diffusion and flame stretch induced by turbulence at different hydrogen molar fractions (XH2 = 0–100%), equivalence ratios (ϕ = 0.5–1.0) and turbulence intensities (u’ = 0–3.62 m/s). The experiments were carried out on a medium-scale, fan-stirred cylindrical combustion chamber generating near-isotropic turbulence. Results show that as hydrogen content increases, the turbulent flame propagation speed tends to be affected by stronger differential diffusion and weakened turbulence, characterized by decreasing Lewis number (Le) and Karlovitz number (Ka) within a similar range of turbulence intensity. Among them, the effect of differential diffusion on the normalized turbulent propagation speed (d<r>/dtσSL) appears to be well correlated with ReT,flameLe-2, where ReT,flame represents the turbulent flame Reynolds number. However, inconsistencies in the fitting parameters for this scale are observed at different XH2, highlighting the impact of substantial variations in flame stretch induced by turbulence. Therefore, the normalized turbulent flame propagation velocity under varying hydrogen contents is proposed to be accurately predicted by d<r>/dtσSL-1 = 0.07Ka0.32(ReT,flameLe−2)0.5. The synergistic effects of Le and Ka can also account for the peak phenomenon in the normalized turbulent burning velocity (ST/SL) observed at 85% hydrogen content. Furthermore, the quantitative characterization of turbulence and differential diffusion under extensive experimental data (Ka = 0.03–90) is studied. As evidenced by the Damköhler theoretical hypothesis, the two-stage trend between ST/SL and (u’/SL)Le-1 is identified with a transition near unity Ka. The modified correlations for turbulent burning velocity in terms of (u’/SL)Le-1 and Ka0.2 are obtained with consideration of the differential diffusion and flame stretch rate induced by turbulence, which show good predictive performance for data at different turbulence regime diagrams regardless of fuel type and equipment size.

Objective determination of peridynamic material parameters for fiber-reinforced composites with shear nonlinearity – Part 2: Strength properties and strain rate dependence

Formulation and implementation of peridynamic strength parameters and strain rate-dependent behavior of fiber-reinforced composite laminates are presented. This work builds on the earlier framework [1] objectively determining elastic parameters for laminates exhibiting shear nonlinearity. The formulation of the strength parameters uses energy-based failure criteria, specifically addressing intralaminar and interlaminar behaviors. A novel implementation of strain rate effects includes conversion from local strain to nonlocal stretch rates. The current peridynamic approach with shear nonlinearity and strain rate dependence accurately captures multiple experimentally measured metrics, including force vs. time, force vs. displacement, energy vs. time, and damage and delamination extents.

Numerical studies on the ignition and propagation for spherically expanding premixed cool flames under gravitational conditions

Cool flame speed is a fundamental parameter, which requires special consideration in terrestrial measurement due to the slow propagation of the cool flame, the intrusion of gravity, and multiple flame regimes (cool, hot, and double flames). The current study employs multiscale numerical simulations with and without gravity to investigate premixed spherical cool flame ignition and propagation. One-dimensional simulations without gravity are adopted to study the effects of initial ambient temperature T0, pressure P0, equivalence ratio ϕ, and ignition kernel temperature TH on feasible conditions for an isolated cool flame measurement, emphasizing the intrinsic couplings among the cool flame, hot flame, and autoignition. Besides considering the minimum and maximum ignition energies for low-temperature ignition (LTI), the results highlight the impacts of the auto-ignition upstream and hot flame downstream of the cool flame on speed measurement. Comprehensive effects of T0, P0, and ϕ are evaluated in order to obtain accurate flame speed versus stretch rate data for extrapolation. Two-dimensional simulations focus on the cool flame deformation with buoyancy. Buoyancy induces a toroidal vortex, causing the spherical cool flame to be mushroom-like at high Richardson numbers, a non-dimensional metric used to evaluate the relative importance of buoyancy. The flame deformation at different ambient temperatures and equivalence ratios are observed. Detailed analyses of the flow field, the deformed flame structure, and the effects of stretch and diffusion are performed. In addition, three equivalent flame radius definitions are proposed and compared to extrapolate cool flame speed. Different from the previous studies on the gravitational hot flames, the current results identify the flame volume-based radius (i.e., Req,V) to be the best one for extrapolating non-spherical cool flame speed, with which cool flames faster than 8 cm/s can be measured within 5% uncertainty. Finally, a systematic strategy is proposed to guide the experimental design. The current work reveals unique cool flame dynamics under gravity conditions and helps to measure the cool flame speed in a terrestrial environment.

Simulation of the dynamic cracking of brittle materials using a nonlocal damage model with an effective strain rate effect

In this study, a nonlocal multiscale damage model that considers the effect of a strain rate is presented. Moreover, this model is combined with the scaled boundary finite element method (SBFEM) and quadtree mesh for dynamic crack propagation in quasi-brittle materials. The scaling centre of each SBFEM subdomain was selected as the material point, and the bond connecting two material points was referred to as the material bond. Microscopic damage was quantified based on the stretch rate of the material bond, and macroscale topological damage was calculated by taking the weighted average of the microscopic damage over the bonds within the influence domain. The bell distribution function is utilised as the weight function in the calculation of the nonlocal weight function. To account for the impact of the strain rate during dynamic loading, an effective rate R is introduced to enhance multiscale damage by modifying the damage threshold and bond softening coefficient throughout the analysis process. By analysing the energetic degradation function of the phase field, which establishes a connection between the macroscale topological damage and energy-based damage, a nonlocal multiscale damage model was incorporated into the framework of the SBFEM. Quadtree mesh discretization was employed to achieve rapid and high-quality multilevel mesh generation by effectively utilising the hanging nodes. Three typical dynamic cracking examples were simulated using the proposed model, and the results were compared with the relevant experimental results and references. The results show that the method is suitable for accurate dynamic cracking simulation in quasi-brittle materials. Moreover, the results indicate that the proposed method can spontaneously simulate dynamic crack bifurcation without introducing additional crack bifurcation criteria. For a compact tensile test of concrete under different loading rates, the method proposed in this study can accurately simulate the corresponding failure modes. The results also show that without considering the effect of the strain rate, the damage develops rapidly in an unconstrained state, which is inconsistent with the actual case.

Assessment of Bödewadt flow over a stretchable porous surface with variable physical properties: A comparative study

Rotating flows occurring over stationary or revolving boundaries have widespread applications in engineering related processes including electrochemistry, turbomachinery (because it involves turbines), compressors and centrifugal pumps, rheometers etc. and in food and chemical processing industries. Bödewadt flow situation concerns a laminar three-dimensional motion taking place over a planar surface in a viscous fluid which is in a state of rigid body rotation at the far field. Present research applies two distinct viscosity-temperature relations to analyze the Bödewadt flow over a stretching porous surface. . A user friendly and robust computational tool bvp4c of MATLAB is utilized to inspect the behaviors of controlling parameters on the resulting boundary layer formations. Interestingly, results corresponding to the two variable viscosity models in case of water are close to each other. The results indicate that either sufficient wall permeability or sufficient surface stretch rate is necessary to have a meaningful solution for the temperature profile. In the case of variable properties, computational data for the drag exhibited at the disk substantially differs from that found for the case of constant fluid properties.

Near-extinction transient behaviors of counterflow nonpremixed flames in a porous spherical burner at very low stretch rate

Near extinction transient behaviors of CH4/N2 versus O2/N2 counterflow nonpremixed flames were investigated by adopting a porous spherical burner with a large radius of curvature to achieve a very low buoyant stretch rate. By varying the oxygen concentrations in the oxidizer stream, four regimes were identified by three limits of sooting, instability, and extinction. The sooting limit was sensitive to flame temperature, and was characterized by two indexes of fuel injection velocity uF and oxygen concentration XO2. When decreasing uF, the sooting limit was different from high stretch flames because of appreciable heat loss toward the burner surface. In the instability regime, periodic holes were observed whose frequency decreased with XO2. Periodic holes were also found to occur with N2 dilution in the fuel stream, which were more regular with larger frequencies compared with the periodic holes in the diluted oxidizer streams. The edge propagation behaviors for periodic holes in diluted fuel streams were analyzed. The statistical average of the propagation speed of advancing edge (hole closing) Se decreased with increasing fuel concentration gradient, and the ratio of Se with the stoichiometric laminar burning velocity SLst of Se/SLst was larger than unity. Also, the stretch rate significantly affected the propagation speed of advancing edge flames. Determination of the propagation speed of the retreating edge (hole opening) had intrinsic difficulty in estimating the transient radial flow velocity, however, the approximated |Se/SLst| was larger than unity and decreased with the fuel mole fraction. Nitrogen dilution in the oxidizer stream was proven to be more effective than in the fuel stream for flame suppression of methane. This study could enrich the understanding of very low-stretch nonpremixed flames in a counterflow burner and provide information regarding low-stretch flame suppression, which may be relevant to microgravity flame behaviors.

Measurements and simulations on effects of elevated pressure and strain rate on NOx emissions in laminar premixed NH3/CH4/air and NH3/H2/air flames

Efforts to reduce NOx emissions by utilizing ammonia-fired combustors are made through various methods; this work investigates the possibility of combining the effects of pressure and stretch rate to reduce NOxemissions in laminar premixed flames. NOx emissions, including NO, NO2, N2O, NH3,and HCN, from NH3/CH4/air and NH3/H2/air unstrained and strained laminar premixed flames were separately measured and simulated with a high-pressure heat flux burner and CHEMKIN software. The key points are that increasing the pressure can decrease most NOx emissions, including NO, N2O, and HCN. However, it slightly increases the unburnt ammonia emissions and largely increases the NO2 formation. Medium XNH3 conditions are the most favorable for reducing NO emissions by increasing pressure. High strain rates can reduce NO emissions, but only in stoichiometric and rich conditions; they reversely increase NO emissions for lean equivalence ratios before the NO peak equivalence ratio (ϕ). The reason is explained by kinetic and reaction pathway analyses, which showed that in high-strain flames, more fuel-N species participated in the reaction to form N2 instead of NO for higher ϕ, while O and OH increased for lower ϕ, promotingNO formation. The combination of increasing pressure and strain rate can efficiently reduce NO emissions but ensure full ammonia oxidation for the medium ammonia content at ϕ = 0.9 ∼ 1.1. This sheds light on the utilization of highly strained ammonia-blend flames in more practical high-pressure burners to reduce NOx emissions.

Enhancement and suppression of counterflow diffusion flame by HFC-125

Efficient fire extinguishing is a safety prerequisite for protecting the environment from fire damage. Understanding the effect of fire extinguishing agent on flame in complex environment is basic work for efficient fire extinguishing. We investigate the impact of HFC-125 on the extinguishment of propane-air highly stretched diffusion flames. Flame thickness is measured using the proportional method. Parameters such as dimensionless flame stand-off distance and flame stretch rate are calculated. Low concentrations of HFC-125 initially increase the flame thickness, but as the concentration increases further, the flame thickness decreases and the flame suppression effect of HFC-125 intensifies. HFC-125 reduces the amount of carbon soot generated and accelerates the transition from yellow to blue flame. Within a specific concentration range, N2 has a minimal effect on flame structural parameters compared to HFC-125. High concentration of N2 forms a high bright blue flame, while HFC-125 reacts with the flame to form a blue-violet flame. Compared to HFC-125, HFC-227ea can significantly reduce flame thickness and increase dimensionless flame stand-off distance, exhibiting a notable suppression effect. Furthermore, high concentrations of HFC-125 substantially reduce the critical flame stretch rate and provide a lower extinguishing concentration in counterflow diffusion flames than in the cup burner.

Construction of the visco-elastic constitutive model for polyethylene terephthalate in a rubbery state

Polyethylene terephthalate (PET) is an important commercial engineering polyester thermoplastic used in beverage bottles. PET is usually biaxial stretched above its glass transition temperature (T g ) and molded into containers by injection stretch blow molding (ISBM) under a rubbery state. This paper constructs a visco-elastic constitutive model for PET above T g . The stress-strain behaviors of PET can be explained by the Eyring activation mechanism and the Arruda-Boyce eight-chain rubber model(A-B model). In the constitutive model, the overall stress of PET is equivalent to the sum of Eyring dashpot and A-B model stresses. The uniaxial tensile test data confirms the constitutive model under three stretch rates and temperatures. The constitutive model can furtherly be applied in the numerical simulation of the PET ISBM process.

Spherically expanding flame simulations using Cantera coupled to an unsteady Lagrangian formulation

A Lagrangian-based one-dimensional approach has been applied, using Cantera libraries, to study the dynamics of spherically expanding flames. Detailed reaction models have been employed to examine spherical flame propagation in hydrogen-air mixtures. In the first part, our approach was validated against laminar flame speed and Markstein number data from the literature. It was shown that the laminar flame speed was predicted within 5% on average but that significant discrepancies were observed for the Markstein number, especially for rich mixtures. This suggests that even application of detailed reaction models can lead to inaccurate prediction of the stability of rich flames, which can be detrimental to the prediction of flame acceleration and the deflagration to detonation transition process. In the second part, a detailed analysis of the thermo-chemical dynamics along the path of Lagrangian particles propagating in stretched flames was performed. For mixtures with negative Markstein lengths, it was found that at high stretch rates, the mixture entering the reaction-dominated period is less lean with respect to the initial mixture than at low stretch rates. This induces faster rates of chemical heat release and active radical production which results in higher flame propagation speed. Opposite effects were observed for mixtures with positive Markstein lengths, for which slower flame propagation was observed at high stretch rates compared to low stretch rates.

Structure and extinction of methane and propane nonpremixed counterflow flames at extremely low stretch rates in buoyant flowfields

This study experimentally investigated the structures and extinction behaviors of methane-air and propane-air counterflow nonpremixed flames influenced by individually controlled fuel injection velocity uF at extremely low stretch rates, which were induced by natural convection alone. A sooting limit fuel injection velocity (SLFIV) index was introduced, which increased with stretch rate in the low stretch rate region. Methane had higher SLFIV than propane. Quasi-one-dimensional blue flames appeared for both methane and propane within a certain uF range. The range for methane was higher than that for propane. The steady flame standoff distances yf had a relationship with uF and low stretch rate ab of yf∝uFabλ∞1/2, which differed from high-stretch flames. Different flame instabilities occurred for methane and propane by changing uF only without fuel or oxidizer dilutions. At low uF near extinction limit of methane, periodic flame holes appeared, which was due to large heat loss. This instability finally caused flame extinction by keeping retreating edges. At high uF, simultaneous cellular and wave flame instability appeared for propane, which differed from cellular flames occurred alone in highly diluted oxy-fuel flames. By modulating uF alone in this experiment, the cellular/wave flame was due to Rayleigh-Taylor and hydrodynamic instabilities. Flame extinction at the lowest uF for propane was through outer edge shrinking, where the displacement speed increased with stretch rate. Flammability maps of limit uF versus low ab were established for both methane and propane. Both maps were divided into four regions by sooting, instability and extinction limits. The three limits uF all increased with ab. This changing tendency was opposite with high-stretch flames reported previously. For propane, the instability limit uF approached infinity at higher ab. This work provided knowledge of extremely low stretch flame combustion, which can be applied to microgravity flames, because the combustion characteristics of microgravity forced low stretch flames were identical to those of low stretch flame induced by natural convection alone.

An Entropy Dynamics Approach for Deriving and Applying Fractal and Fractional Order Viscoelasticity to Elastomers

Abstract Entropy dynamics is a Bayesian inference methodology that can be used to quantify time-dependent posterior probability densities that guide the development of complex material models using information theory. Here, we expand its application to non-Gaussian processes to evaluate how fractal structure can influence fractional hyperelasticity and viscoelasticity in elastomers. We investigate how kinematic constraints on fractal polymer network deformation influences the form of hyperelastic constitutive behavior and viscoelasticity in soft materials such as dielectric elastomers, which have applications in the development of adaptive structures. The modeling framework is validated on two dielectric elastomers, VHB 4910 and 4949, over a broad range of stretch rates. It is shown that local fractal time derivatives are equally effective at predicting viscoelasticity in these materials in comparison to nonlocal fractional time derivatives under constant stretch rates. We describe the origin of this accuracy that has implications for simulating large-scale problems such as finite element analysis given the differences in computational efficiency of nonlocal fractional derivatives versus local fractal derivatives.