Stretch Rate Research Articles

On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames

Large discrepancies among the laminar flame speeds and Markstein lengths of methane/air mixtures measured by different researchers using the same constant-pressure spherical flame method are observed. As an effort to reduce these discrepancies, one linear model (LM, the stretched flame speed changes linearly with the stretch rate) and two non-linear models (NM I and NM II, the stretched flame speed changes non-linearly with the stretch rate) for extracting the laminar flame speed and Markstein length from propagating spherical flames are investigated. The accuracy and performance of the LM, NM I, and NM II are found to strongly depend on the Lewis number. It is demonstrated that NM I is the most accurate for mixtures with large Lewis number (positive Markstein length) while NM II is the most accurate for mixtures with small Lewis number (negative Markstein length). Therefore, in order to get accurate laminar flame speed and Markstein length from spherical flame experiments, different non-linear models should be used for different mixtures. The validity of the theoretical results is further demonstrated by numerical and experimental studies. The results of this study can be used directly in spherical flame experiments measuring the laminar flame speed and Markstein length.

Nonhyperelastic Nature of an Elastomeric High Strain Material

Rubber materials have mostly been modeled by utilizing hyperelasticity, which have led to greater understanding and acceptable predictability of their stress-strain response. However, inherent inelastic behavior excluded by approximation has never been characterized by time-dependent parameters such as time, strain-rate, and strain history. We hypothesized that time, stretch rate, and stretch history were prominent factors that induce the inelasticity, and we characterized the inelasticity in terms of those factors using a randomized stretch-controlled testing protocol. We applied the custom randomized testing protocol with the fundamental statistical theory to characterize inelastic behavior imbedded in the high strain material. We hypothesized that time spent testing (T), rate-related stretch history (Ht2), and long-term stretch history (Ht1) give rise to the inelastic deviation from hyperelasticity. We examined the significance, effectiveness, and differences of T, Ht2, and Ht1 by looking at the derived multivariable linear regression models. Distribution of prediction deviation was also examined to see if we missed any other significant variable. Predictability of the multivariable linear regression models was validated by utilizing the unused data from the randomized testing protocol and data from the conventional cyclic testing protocol. We found that the inelasticity of the rubber-like material is highly related to T, Ht2, and Ht1, but not equally influential to all stretches. At smaller deformations, greater inelastic deviation occurs. Inelasticity exponentially decreased over stretch and was nonlinearly related to time. This study successfully determined the elastic/inelastic responses and factors that induce the inelastic response of the rubber-like material. This investigation suggests a way to better describe the elastic/inelastic properties and phenomenological models of rubber-like materials.

Ignition propensity of hydrogen/air mixtures impinging on a platinum stagnation surface

An experimental investigation into the ignition characteristics of lean pre-mixed hydrogen/air mixtures is conducted using a stagnation-point flow configuration against a platinum surface, with a special emphasis on the determination of potential fire safety hazards associated with hydrogen release in the presence of a catalyst. Two distinct regimes are observed for this system – catalytic surface reactions and gas-phase ignition. It is demonstrated that depending on mixture equivalence ratio, catalytic surface reactions can be initiated with or without surface heating. When significant surface heat is released via catalytic reactions, gas-phase ignition can be induced, greatly increasing the apparent danger of hydrogen leaks in the presence of a platinum surface. The critical surface temperatures leading to catalytic ignition for hydrogen/air mixtures over a platinum surface are further investigated over a range of equivalence ratios and stretch rates. It is shown that ultra-lean hydrogen/air mixtures can be catalytically ignited even in the absence of external heat addition, suggesting that hydrogen leakage in the presence of a platinum surface may pose a fire safety risk even at room temperature. Furthermore, even without a transition to gas-phase ignition, the surface temperature that can be sustained with surface reactions alone may contribute to component degradation or itself pose a safety hazard.

Derivation of a finite-element model of lingual deformation during swallowing from the mechanics of mesoscale myofiber tracts obtained by MRI.

To demonstrate the relationship between lingual myoarchitecture and mechanics during swallowing, we performed a finite-element (FE) simulation of lingual deformation employing mesh aligned with the vector coordinates of myofiber tracts obtained by diffusion tensor imaging with tractography in humans. Material properties of individual elements were depicted in terms of Hill's three-component phenomenological model, assuming that the FE mesh was composed of anisotropic muscle and isotropic connective tissue. Moreover, the mechanical model accounted for elastic constraints by passive and active elements from the superior and inferior directions and the effect of out-of-plane muscles and connective tissue. Passive bolus effects were negligible. Myofiber tract activation was simulated over 500 ms in 1-ms steps following lingual tip association with the hard palate and incorporated specifically the accommodative and propulsive phases of the swallow. Examining the displacement field, active and passive muscle stress, elemental stretch, and strain rate relative to changes of global shape, we demonstrate that lingual reconfiguration during these swallow phases is characterized by (in sequence) the following: 1) lingual tip elevation and shortening in the anterior-posterior direction; 2) inferior displacement related to hyoglossus contraction at its inferior-most position; and 3) dominant clockwise rotation related to regional contraction of the genioglossus and contraction of the hyoglossus following anterior displacement. These simulations demonstrate that lingual deformation during the indicated phases of swallowing requires temporally patterned activation of intrinsic and extrinsic muscles and delineate a method to ascertain the mechanics of normal and pathological swallowing.

Effect of a small amount of NOx on extinction limit of lean premixed counterflow flame

The effect of a small amount of NOx (NO and NO2) on the extinction of CH4 and C2H4 flames was experimentally and numerically investigated. The extinction stretch rates of counterflow premixed flames when NO2 was added to the mixture were measured at pressures ranging from 0.1 to 0.3MPa. Calculations by using one-dimensional flame code with full chemistry were also conducted to clarify the effect of NOx on the extinction limit and burning velocity. Extinction stretch rates of mixtures near the flammability limit increased by adding NOx at high pressure in the experiments and the calculations. The catalytic effect of NOx for CH4 was via the low temperature chemistry involving CH3, CH3O, CH3O2, and HO2, and that for C2H4 was via reactions that included HO2 species. The change in extinction stretch rates with NOx addition reflected the behavior of the burning velocity with NOx addition. The burning velocities of mixtures near the flammability limit increased with the addition of NOx at high pressure, the same as the extinction stretch rate.

Heat transfer on a power law stretching sheet subjected to free stream pressure gradient

The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations, irrespective of the condition whether U w > U ∞ or U w < U ∞, containing three parameters: β measuring the stretch rate of the moving boundary, ε is the ratio of free stream velocity to composite reference velocity and Pr is the Prandtl number of the ambient fluid. The numerical solutions of the thermal boundary layer equations are obtained for three Prandtl numbers 0.7, 1.0 and 10 for 0 ⩽ ε ⩽ 1 and for 0 ⩽ β ⩽ 2. The heat transfer coefficient show appreciable dependence on the ratio of free stream velocity to union of velocities of the stretching surface boundary and free stream.

Cardiac Electromechanics: The Effect of Contraction Model on the Mathematical Problem and Accuracy of the Numerical Scheme

Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electrophysiology but can also be dependent on the stretch and stretch rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing partial differential equations, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding 'unnatural' material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models, we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the time step prior to the bulk deformation being computed) is (i) appropriate for stretch-independent contraction models; (ii) only conditionally stable, with the stability criterion independent of time step, for contractions models which just depend on stretch (but not stretch rate) and (iii) inappropriate for stretch-rate-dependent models.

Numerical Study of High-Frequency Oscillatory Air Flow and Convective Mixing in a CT-Based Human Airway Model

High-frequency oscillatory ventilation (HFOV) is considered an efficient and safe respiratory technique to ventilate neonates and patients with acute respiratory distress syndrome. HFOV has very different characteristics from normal breathing physiology, with a much smaller tidal volume and a higher breathing frequency. In this study, the high-frequency oscillatory flow is studied using a computational fluid dynamics analysis in three different geometrical models with increasing complexity: a straight tube, a single-bifurcation tube model, and a computed tomography (CT)-based human airway model of up to seven generations. We aim to understand the counter-flow phenomenon at flow reversal and its role in convective mixing in these models using sinusoidal waveforms of different frequencies and Reynolds (Re) numbers. Mixing is quantified by the stretch rate analysis. In the straight-tube model, coaxial counter flow with opposing fluid streams is formed around flow reversal, agreeing with an analytical Womersley solution. However, counter flow yields no net convective mixing at end cycle. In the single-bifurcation model, counter flow at high Re is intervened with secondary vortices in the parent (child) branch at end expiration (inspiration), resulting in an irreversible mixing process. For the CT-based airway model three cases are considered, consisting of the normal breathing case, the high-frequency-normal-Re (HFNR) case, and the HFOV case. The counter-flow structure is more evident in the HFNR case than the HFOV case. The instantaneous and time-averaged stretch rates at the end of two breathing cycles and in the vicinity of flow reversal are computed. It is found that counter flow contributes about 20% to mixing in HFOV.

Measurement of laminar burning velocities of iso-butanol-air mixtures

The laminar burning velocity of iso-butanol-air mixtures was measured under different initial pressures, initial temperatures and equivalence ratios using high-speed schlieren photography and outwardly propagation flame in a constant volume combustion bomb. Based on the analysis of stretched flame propagation speed and stretch rate, the laminar burning velocities and Markstein lengths of iso-butanol-air flames are obtained. In accordance, with photos of flame, an analysis of flame stability and the influencing factors is carried out. The results show that the laminar burning velocity is decreased with the increase of initial pressure and is increased with the increase of initial temperature. The maximum value of laminar burning velocity is presented at the equivalence ratio of 1.2. The Markstein length is decreased with the increase of equivalence ratio. For specified equivalence ratio, the Markstein length is decreased with the increase of initial temperature and initial pressure. Thus, the flame instability is increased with the increase of equivalence ratio, initial temperature and initial pressure.

Mechanics of the Mitral Valve Strut Chordae Insertion Region

Interest in developing durable mitral valve repair methods is growing, underscoring the need to better understand the native mitral valve mechanics. In this study, the authors investigate the dynamic deformation of the mitral valve strut chordae-to-anterior leaflet transition zone using a novel stretch mapping method and report the complex mechanics of this region for the first time. Eight structurally normal porcine mitral valves were studied in a pulsatile left heart simulator under physiological hemodynamic conditions -120 mm peak transvalvular pressure, 5 l/min cardiac output at 70 bpm. The chordal insertion region was marked with a structured array of 31 miniature markers, and their motions throughout the cardiac cycle were tracked using two high speed cameras. 3D marker coordinates were calculated using direct linear transformation, and a second order continuous surface was fit to the marker cloud at each time frame. Average areal stretch, principal stretch magnitudes and directions, and stretch rates were computed, and temporal changes in each parameter were mapped over the insertion region. Stretch distribution was heterogeneous over the entire strut chordae insertion region, with the highest magnitudes along the edges of the chordal insertion region and the least along the axis of the strut chordae. At early systole, radial stretch was predominant, but by mid systole, significant stretch was observed in both radial and circumferential directions. The compressive stretches measured during systole indicate a strong coupling between the two principal directions, explaining the small magnitude of the systolic areal stretch. This study for the first time provides the dynamic kinematics of the strut chordae insertion region in the functioning mitral valve. A heterogeneous stretch pattern was measured, with the mechanics of this region governed by the complex underlying collagen architecture. The insertion region seemed to be under stretch during both systole and diastole, indicating a transfer of forces from the leaflets to the chordae and vice versa throughout the cardiac cycle, and demonstrating its role in optimal valve function.

Topological analysis of methane lean premixed flame in turbulent jet flow by direct numerical simulation

Direct numerical simulation is employed to investigate the premixed jet flame of methane in lean, combined with a detailed chemical kinetics including 17 species and 58 elemental steps and distinct Lewis numbers. Cold methane-air mixture at 0.55 equivalence ratio is injected into the coflow area with 9500 Reynolds number. The coflow ambient gas is set to be the burnt gas of the methane-air mixture in main jet and temperature is assigned to be the corresponding adiabatic flame temperature 1515 K. The whole simulation process is run based on paralleled calculation method, and chemical sources are acquired by dynamically calling CHEMKIN library function. The flame structure at 6.98 ms is shown to demonstrate the obvious dependence of flame structure and reaction rate on vortices motion. Then by tracing the interaction between different flame elements and vortices, the mechanism behind this dependence is found. The concepts including surface density function, mean curvature and stretch rate are used to describe the geometrical structure of vortex-affected flame. Those are all calculated according to simulation result and statistically associated with heat release rate that indicates reaction intensity. The statistical results show that surface density function and reaction rate own direct positive correlation; largely wrinkled flames with greater curvatures magnitude tend to become thick and weaken surface density function and reaction rate, appearing local extinction phenomena; large tangential stretch rates exerted on flame usually produce a local thinning effect in normal making reaction rate intensified. The DNS presented will supply beneficial references to better understanding of flame-vortex interaction and development of more accurate general model for turbulent premixed combustion.

Analysis of entropy generation in non-premixed hydrogen versus heated air counter-flow combustion

In this paper, entropy generation in non-premixed hydrogen versus heated air counter-flow combustion confined by planar opposing jets is investigated for the first time. The effects of the volume percentage of hydrogen in fuel mixture and the inlet Reynolds number (corresponding to the global stretch rate) on entropy generation are studied by numerical evaluating the entropy generation equation. The lattice Boltzmann model proposed in our previous work, instead of traditional numerical methods, is used to solve the governing equations for combustion process. Through the present study, three interesting features of this kind of combustion, which are quite different from that reported in previous literature on entropy generation analysis for diffusion hydrogen-air flames, are revealed. Moreover, it is observed that the whole investigated domain can be divided into two parts according to the predominant irreversibilities. The total entropy generation number can be approximated as a linear increasing function of the volume percentage of hydrogen in fuel mixture and the inlet Reynolds number for all the cases under the present study. It is very interesting that most characteristics in this kind of diffusion combustion also can be found in its premixed counterpart investigated in our previous work. Especially, the critical Reynolds numbers determining the order of the predominant irreversibilities in this type of diffusion flame are same as its premixed counterpart, although the flow and scalar fields between them are quite different.

Laminar burning velocities of three C 3H 6O isomers at atmospheric pressure

Laminar flames of three C 3H 6O isomers (propylene oxide, propionaldehyde and acetone), representative of cyclic ether, aldehyde and ketone species important as intermediates in oxygenated fuel combustion, have been studied experimentally and computationally. Most of these flames exhibited a non-linear dependency of flame speed upon stretch rate and two complementary independent techniques were adopted to provide the most reliable burning velocity data. Significant differences in burning velocity were noted for the three isomers: propylene oxide + air mixtures burned fastest, then propionaldehyde + air, with acetone + air flames being the slowest; the latter also required stronger ignition sources. Numerical modelling of these flames was based on the Konnov mechanism, enhanced with reactions specific to these oxygenated fuels. The chemical kinetics mechanism predicted flame velocities in qualitative rather than quantitative agreement with the measurements. Sensitivity analysis suggested that the calculated flame speeds had only a weak dependency upon parent fuel-specific reactions rates; however, consideration of possible break-up routes of the primary fuels has allowed identification of intermediate compounds, the chemistry of which requires a better definition.

Blowoff dynamics of bluff body stabilized turbulent premixed flames

This article concerns the flame dynamics of a bluff body stabilized turbulent premixed flame as it approaches lean blowoff. Time resolved chemiluminescence imaging along with simultaneous particle image velocimetry and OH planar laser-induced fluorescence were utilized in an axisymmetric bluff body stabilized, propane-air flame to determine the sequence of events leading to blowoff and provide a quantitative analysis of the experimental results. It was found that as lean blowoff is approached by reduction of equivalence ratio, flame speed decreases and the flame shape progressively changes from a conical to a columnar shape. For a stably burning conical flame away from blowoff, the flame front envelopes the shear layer vortices. Near blowoff, the columnar flame front and shear layer vortices overlap to induce high local stretch rates that exceed the extinction stretch rates instantaneously and in the mean, resulting in local flame extinction along the shear layers. Following shear layer extinction, fresh reactants can pass through the shear layers to react within the recirculation zone with all other parts of the flame extinguished. This flame kernel within the recirculation zone may survive for a few milliseconds and can reignite the shear layers such that the entire flame is reestablished for a short period. This extinction and reignition event can happen several times before final blowoff which occurs when the flame kernel fails to reignite the shear layers and ultimately leads to total flame extinguishment.

円筒状拡散火炎の消炎(熱工学,内燃機関,動力など)

An experimental study was performed on the behavior and extinction characteristics of the cylindrical diffusion flame affected by both factors of stretch and curvature. The cylindrical diffusion flame treated here has the convex curvature toward the air stream. The fuels used were propane and methane, and they were diluted with two kinds of inert gas, nitrogen and helium. The obtained results are described as follows. (1) The burner used in this study can form the cylindrical flame with good circularity. The minimum flame diameter is approximately 2.5mm. (2) The flame radius increases (decreases) with the increase in the fuel (air) flow velocity. (3) Flame luminosity has a maximum value when the air flow velocity is varied. On the other hand, the luminosity decreases monotonously with the increase in the fuel flow velocity. (4) Extinction stretch rate of counterflow propane 20%/nitrogen 80% vs. air flame is lower than that of counterflow methane 50%/nitrogen 50% vs. air flame. However, this extinction stretch rate relation is reversed in the case of cylindrical diffusion flame owing to the Lewis number effect caused by the flame curvature. (5) When the Lewis number of fuel flow is considerably larger than unity, the cylindrical diffusion flame can be formed even at the dilution rate with which the counterflow diffusion flame cannot be formed.

Local Stretch Rates at Non-stationary Non-premixed Edge Flames

Local Stretch Rates at Non-stationary Non-premixed Edge Flames

Rod-shaped Tissue Engineered Skeletal Muscle with Artificial Anchors to Utilize as a Bio-Actuator

Living muscle tissue seems to have an efficient potential as an actuator. We propose to utilize a tissue engineered skeletal muscle (TESM) as a bio-actuator by connecting to the object through artificial anchors. We designed a rod-shaped TESM with artificial anchors and fabricated it by culturing myoblasts in collagen gel for several days. The contractile ability and controllability of the TESM were confirmed by stimulating electrically. The contractions were evoked forcibly and synchronously by electrical pulses under 4.5 Hz. The electrical pulses at 8 Hz kept the contractile state. As potential anchor materials, silicone sponge and nonwoven nylon mesh were examined. The anchors made of nonwoven nylon mesh held a rod-shaped TESM for more than 3 weeks successfully, while the anchors made of silicone sponge held it for only 2-4 days and the TESM broke down at the connecting area. The mechanical endurance between the TESM and the nylon anchors was examined using our original stretching device. No damage was observed from the repeated mechanical loading at 0.5 Hz with 5 % stretch rate for 10 days. We concluded that the TESM has good potential for utilization as a bio-actuator and its abilities can be exploited by connecting it to an object through artificial anchors.

Propagation and Extinction of a Cylindrical Premixed Flame Undergoing Equivalence Ratio Fluctuation Near the Lean Limit

Experimental study was made to investigate the propagation and extinction characteristics of a stretched cylindrical flame undergoing periodic fluctuation of equivalence ratio near the lean limit. With a lean methane-air and a lean propane-air mixture, burning velocity, flame luminosity and flame stretch rate were measured or evaluated for the fluctuation frequencies of 5Hz and 20Hz. The results were summarized as follows: (1) In some part of a period, burning velocity and flame luminosity of the dynamic flame near the lean limit were possible to become lower than those at the lean flammability limit of the static flame. (2) At the high frequency of 20Hz, the burning velocity took a negative value in a certain time range. In spite of this loss of propagation ability, the flame was not extinguished but sustained, indicating the recovery of the flame intensity due to the dynamic effect of fluctuating flame. (3) Flame recovery phenomenon could occur more easily for the methane flame which was strengthened by the Lewis number effect than the propane flame which was weakened by that effect.

Analysis of entropy generation in counter-flow premixed hydrogen–air combustion

In this paper, entropy generation in counter-flow premixed hydrogen–air combustion confined by planar opposing jets is investigated for the first time. The effects of the equivalence ratio and the inlet Reynolds number (corresponding to the global stretch rate) on entropy generation are studied by numerical evaluating the entropy generation equation. The lattice Boltzmann model proposed in our previous work, instead of traditional numerical methods, is used to solve the governing equations for combustion process. Through the present study, three interesting features of this kind of combustion, which are quite different from that reported in previous literature on entropy generation analysis for reactive flows, are revealed. Moreover, it is observed that the whole investigated domain can be divided into two parts according to the predominant irreversibilities. The total entropy generation number can be approximated as a linear increasing function of the equivalence ratio and the inlet Reynolds number for all the cases under the present study.

Studies on properties of laminar premixed hydrogen-added ammonia/air flames for hydrogen production

In order to evaluate the potential of burning and reforming ammonia as a carbon-free fuel in production of hydrogen, fundamental unstretched laminar burning velocities, and flame response to stretch (represented by the Markstein number) for laminar premixed hydrogen-added ammonia/air flames were studied both experimentally and computationally. Freely (outwardly)-propagating spherical laminar premixed flames at normal temperature and pressure were considered for a wide range of global fuel-equivalence ratios, flame stretch rates (represented by the Karlovitz number) and the extent of hydrogen substitution. Results show the substantial increase of laminar burning velocities with hydrogen substitution, particularly under fuel-rich conditions. Also, predicted flame structures show that the hydrogen substitution enhances nitrogen oxide (NO x ) and nitrous oxide (N 2O) formation. At fuel-rich conditions, however, the amount of NO x and N 2O emissions and the extent of the increase with the hydrogen substitution are much lower than those under fuel-lean conditions. These observations support the potential of hydrogen as an additive for improving the burning performance with low NO x and N 2O emissions in fuel-rich ammonia/air flames and hence the potential of using ammonia as a clean fuel. Increasing the amount of added hydrogen tends to enhance flame sensitivity to stretch.