Unstretched Flame Propagation Speed Research Articles

Flame Characteristics and Ignition Delay Times of 2,5-Dimethylfuran: A Systematic Review With Comparative Analysis

Abstract Global concerns about CO2 levels in the atmosphere, energy security, and the depletion of fossil fuel supply have been the key motivation to develop bio-based fuel resources, which leads to promising and potential strategies of renewable and carbon-neutral biofuels. Among biofuels being strongly developed, 2,5-dimethylfuran (DMF) is a new alternative biofuel candidate since DMF could be synthesized from available and durable lignocellulosic biomass, as well as DMF's physicochemical properties were found to be similar to those of fossil fuels. Therefore, the comprehensive investigation on DMF is very essential before putting DMF into the commercial scale and the engine application. In this current work, the temporal evolutions of laminar flame characteristics including laminar burning velocities, unstretched flame propagation speed, and Schlieren images were critically reviewed based on the comparison of DMF with other fuels. Besides, flame instabilities were also evaluated in detail. Finally, ignition delay times were thoroughly analyzed with the variation of the initial parameters such as temperature, pressure, and equivalent ratio, suggesting that DMF could become the potential fuel for the spark ignition engine. In the future, the experimental studies on the real engines fueled with DMF should be carefully and completely performed to have a comprehensive evaluation of this promising biofuel class.

Influence of pressure and temperature on explosion characteristics of n-hexane/air mixtures

N-hexane is an important alternative fuel for aviation kerosene in recent years. In this study, experiments of n-hexane in air at various initial temperatures of 353–393 K, initial pressures of 60–100 kPa and equivalence ratio of 0.7–1.7 were carried out in a cylindrical vessel with central ignition. The pressure histories and outward propagations of the spherical flame in the explosion process were recorded by the pressure sensor and Schlieren system, respectively. Explosion characteristics including the explosion pressure Pmax, the maximum rate of pressure rise (dP/dt)max and laminar burning velocity U1 were obtained and analyzed. Results show that all explosion parameters strongly depend on the n-hexane/air ratio, initial pressures and temperatures. The explosion pressure Pmax and maximum rate of pressure rise (dP/dt)max raise with the increase in initial pressure and decrease in temperature. However, the dimensionless explosion pressure Pmax/P0 remains constant with an increased initial pressure. Furthermore, the n-hexane/air flame propagation characteristics were investigated and the Markstein length were studied. The unstretched flame propagation speed S1 and laminar burning velocity U1 share the similar variation tendency with equivalence ratios, and they are increased with the increase of initial temperatures and decrease of pressures.

Flame propagation speed and Markstein length of spherically expanding flames: Assessment of extrapolation and measurement techniques

Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar.

Laminar burning characteristics of upgraded biomass pyrolysis fuel derived from rice husk at elevated pressures and temperatures

Biomass energy is an emerging alternative energy source with an attractive carbon balance in its life cycle. Recently, a biomass fast pyrolysis fuel was produced from rice husk, and it was further upgraded using supercritical ethanol with a 5%Pt/SO42−/ZrO2/SBA-15 catalyst in a hydrogen atmosphere. This upgraded biomass pyrolysis fuel is mainly composed of ethers, esters, alcohols and ketones. After analysing the composition of this upgraded biomass pyrolysis fuel, the authors reproduced a mixed fuel to mimic the upgraded biomass pyrolysis fuel. This mixed fuel contained ethanol, ethyl acetate, diethyl ether, acetone, and 2-butanone, with mass ratios of 9:6:2:1:1. This fuel has been used in a gasoline engine with some minor modifications; however, there is no data available for its laminar burning characteristics. In this study, the laminar burning characteristics of this mixed fuel were investigated in a constant volume combustion chamber (CVCC) at an initial pressure of 0.1MPa and initial temperatures of 358, 388 and 418K), and at an initial temperature of 358K and initial pressures of 0.1, 0.2 and 0.4MPa. By using a Schlieren high-speed imaging technique and a linear extrapolation method, laminar burning characteristics including the unstretched flame propagation speed, laminar burning velocity and other key parameters were calculated and discussed. Experiments were also conducted for two main components, ethanol and ethyl acetate, and results were used as benchmarks. The results indicated that the peak laminar burning velocity of the mixed fuel can be observed near the equivalence ratio of 1.1 under the tested conditions. At the same equivalence ratio, the laminar burning velocity was increased as initial temperature was increased, and it was decreased as initial pressure was increased. Markstein length decreased as equivalence ratio was increased, and it dropped below zero when the equivalence ratio was 1.4, indicating increased flame instability with equivalence ratio increased. Among the three examined fuels, the laminar burning velocity ranking was: ethanol>mixed fuel>ethyl acetate.

Laminar flame characteristics of cyclopentanone at elevated temperatures

Cyclopentanone, a product of biomass pyrolysis of agricultural waste, has certain advantages as a biofuel candidate but so far little is known about its combustion characteristics. In this paper, the laminar flame characteristics of cyclopentanone, including stretched flame propagation speed, unstretched flame propagation speed, and laminar burning velocity, were measured and compared with gasoline and ethanol, using the outwardly propagating spherical flame method and the high-speed Schlieren photography technique. The experiments were conducted in a constant-volume vessel using various fuel-air equivalence ratios (ϕ=0.8–1.6) at elevated initial temperatures (T0=423, 448 and 473K) and a fixed initial pressure (P0=0.1MPa). Linear and non-linear extrapolations were used to characterise the relationship between the stretch rate and the stretched flame propagation speed when Markstein length was near to or away from zero respectively. Empirical functions were obtained to calculate the laminar burning velocities of cyclopentanone for various fuel-air equivalence ratios and initial temperatures. The results show that Markstein length of cyclopentanone decreases when equivalence ratio is increased, and the turning point of equivalence ratio at which it changes from positive to negative is slightly below 1.4. The maximum laminar burning velocity of cyclopentanone appears at the equivalence ratio of approximately 1.2, regardless of the initial temperature. The laminar burning velocity of cyclopentanone has a smaller difference to that of ethanol and gasoline when equivalence ratio is leaner than stoichiometric, but when equivalence ratio increases from 1.0 to 1.4, it becomes increasingly lower than that of ethanol and higher than that of gasoline. The maximum laminar burning velocity of cyclopentanone is 0.82m/s; for gasoline it is 0.72m/s and for ethanol it is 0.86m/s, at an initial temperature of 423K and pressure of 0.1MPa.

Laminar burning characteristics of 2-MTHF compared with ethanol and isooctane

2-Methyl tetrahydrofuran (2-MTHF) is one of the promising second-generation biofuel candidates, raising increasing interest because of the recent breakthrough in producing 2-MTHF from biomass. As a potential gasoline extender and renewable oxygenate, its high energy density and avoidance of competing with food make it attractive compared with ethanol. In the current work, the laminar burning characteristics of 2-MTHF-air mixtures are studied with varying equivalent ratios (0.88–1.43) and initial temperatures (333K, 363K and 393K) at ambient pressure in a constant-volume vessel. The results are compared with ethanol and isooctane, a representative component in gasoline. The stretched flame speed, un-stretched flame speed, Markstein length, flame thickness, Markstein number, laminar burning velocity and burning flux are calculated and analyzed. The result shows that for most tests, the ranking of un-stretched flame propagation speed is ethanol, 2-MTHF and isooctane. The peaks of un-stretched flame speeds against varying equivalent ratios appear at Φ=1.1–1.2 for three tested fuels. The Markstein length indicates that generally isooctane has the most diffusion-thermal stable flame than 2-MTHF and ethanol when Φ<1.2 at 393K. Ethanol shows the smallest flame thickness in most of the test points. The laminar burning velocity of 2-MTHF is much faster than isooctane and is comparative with ethanol, indicating its fast-burning property and potential of improving engine thermal efficiency.

Laminar burning characteristics of ethyl propionate, ethyl butyrate, ethyl acetate, gasoline and ethanol fuels

Ethyl esters have been considered as promising second-generation biofuel candidates, due to the available production from low grade biomass waste. Furthermore, with desirable energy densities, emissions performance, low solubility and higher Research Octane Number (RON), ethyl esters have proven attractive as fuel additives or alternatives for gasoline. In this study, high-speed schlieren photography was used to investigate the laminar burning characteristics of three ethyl ester fuels: ethyl acetate, ethyl propionate, and ethyl butyrate, in comparison with gasoline and ethanol at different initial temperatures and a variety of equivalence ratios, with an initial pressure of 0.1MPa in a constant-volume vessel. For the five fuels, the stretched flame speeds, the un-stretched flame speeds, Markstein lengths, Markstein number, laminar burning velocities and laminar burning flux were calculated and analysed using the outwardly spherical flame method. The results show that for all examined initial temperatures (60°C, 90°C and 120°C) and equivalence ratios; ethanol had the highest un-stretched flame propagation speeds, whilst ethyl acetate (EA) had the lowest. At high initial temperatures (120°C), it was observed that the un-stretched flame speed trends of ethyl propionate (EP) and ethyl butyrate (EB) proved faster compared to gasoline, especially for rich conditions. The EB and EA flames demonstrated greater stability when compared to ethanol, EP, and gasoline. Analysis showed that ethanol yielded the fastest flame velocities, whilst EA consistently had the lowest among all the five fuels. The laminar burning velocities of the EP fuel were faster compared to EB and EA, whilst slower than ethanol and gasoline at 60°C. Further increase of the initial temperature, up to 120°C, showed the laminar flame speed of EP and EB to be faster than gasoline, indicating a fast-burning property, and potential of improving engine thermal efficiency.

An Experimental Measurement on Laminar Burning Velocities and Markstein Length of Iso-Butane-Air Mixtures at Ambient Conditions

In the present work, experimental investigation on laminar combustion of iso-butane-air mixtures was conducted in constant volume explosion vessel. The experiments were conducted at wide range of equivalence ratios ranging between Ф = 0.6 and 1.4 and atmospheric pressure of 0.1 MPa and ambient temperature of 303K. Using spherically expanding flame method, flame parameters including stretched, unstretched flame propagation speeds, laminar burning velocities and Markstein length were calculated. For laminar burning velocities the method of error bars of 95% confidence level was applied. In addition, values of Markstein lengths were measured in wide range of equivalence ratios to study the influence of stretch rate on flame instability and burning velocity. It was found that the stretched flame speed and laminar burning velocities increased with equivalence ratios and the peak value was obtained at equivalence ratio of Ф = 1.1. The Markstein length decreased with the increases in equivalence ratios, which indicates that the diffusion thermal flame instability increased at high equivalence ratios in richer mixture side. However, the total deviations in the laminar burning velocities have discrepancies of 1.2-2.9% for all investigated mixtures.

Effects of pressure and temperature on laminar burning velocity and flame instability of iso-octane/methane fuel blend

In this work, spherically expanding flames are used to measure the unstretched flame propagation speed and Markstein length of an alternative fuel (iso-octane/methane fuel blend) at initial temperatures between 368 and 448K, and pressures between 1 and 5.5bar by using the Schlieren photography method.Methane is added in two volumetric fractions of 70% and 95% to iso-octane in a constant volume chamber. Markstein lengths are obtained via nonlinear methodology over an extensive range of equivalence ratios between 0.85 and 1.2. From these new experimental data, a laminar burning velocity correlation based on unburned gas temperature, pressure, equivalence ratio and methane mass fraction was proposed.It is seen that the unstretched flame propagation speed of blended fuel are located between the pure fuels but did not follow simple mole-fraction based weighted average of parent fuels and flame stability is enhanced by adding more methane to the fuel blend. Initial pressure rise has a suppression effect on flame propagation and pure methane receives the most influence from this effect. Initial temperature rise increase the propagating speed in all mixtures.

Effect of iso-octane/methane blend on laminar burning velocity and flame instability

CNG–gasoline blended fuel has been considered as a potential choice of alternative fuel for spark ignition (SI) engines specially turbocharged one to utilize advantages of both fuels.In this study methane (main component of CNG) is added in two volumetric fractions of 30% and 70% to iso-octane (representative fuel of gasoline). Spherical flames are experimentally investigated at initial temperature of 363K and pressure of 1bar in constant volume chamber. Classical schlieren technique used to characterize the combustion of blended and base fuels. Unstretched flame propagation speed and Markstein lengths are obtained via nonlinear methodology in different equivalence ratio. The laminar burning velocities, Markstein number and burning flux of blended fuel are then extracted and compared with base fuels. The results show that addition of methane to iso-octane increases the unstretched propagation speed in lean region but decrease the unstretched propagation speed in rich region. Blended fuels response to stretch is a linear combination of base fuels in lean region (Ø>1); but methane has more Markstein length and Markstein number than the other fuels in rich region (Ø>1). Laminar burning velocity and flame stability of 30% methane blended fuel is close to iso-octane. Laminar burning velocity of 70% methane blended fuel is higher than base fuel at Ø=0.9. The tests also repeated for CNG/iso-octane blended fuel and similar trend obtained for laminar burning velocities.

Effects of hydrogen addition on the premixed laminar-flames of ethanol–air gaseous mixtures: An experimental study

The effects of hydrogen addition on the laminar premixed-flame characteristics of ethanol–air gaseous mixtures were investigated experimentally by using outwardly propagating spherical flames. The experiments were conducted in a constant-volume combustion vessel with a central ignition at an initial temperature of 383 K, a pressure of 0.1 MPa, a hydrogen fraction from 0% to 100%, and an equivalence ratio from 0.6 to 1.6, and the flame images were obtained by a high-speed schlieren camera system. The results show that the unstretched flame propagation speeds and burning velocities increase exponentially with the increase in hydrogen fraction for a constant equivalence ratio. When the hydrogen fraction is equal to or less than 60%, the burned gas Markstein length reduces with the increase of equivalence ratio, indicating a positive correlation between the flame instability and hydrogen fraction, while the opposite effect is observed when the hydrogen fraction is greater than 60%. At an equivalence ratio below 1.4, the Markstein length decreases with increased hydrogen fraction, indicating that the flame instability is exacerbated with hydrogen addition, while the reverse holds in the case of equivalence ratio above 1.4. Finally, an empirical formula is developed to estimate the laminar burning velocity of ethanol–hydrogen–air flames on the basis of present experimental data.

Experimental determination of laminar burning velocities and Markstein lengths for 75% hydrous-ethanol, hydrogen and air gaseous mixtures

Hydrogen-rich mixtures generated by the on-board reforming of biomass-derived hydrous-ethanol can be used as a potential alternative fuel (i.e., reformed ethanol fuel, RE fuel). In this paper, outwardly propagating spherical flames were employed to observe the laminar flame characteristics of the gaseous mixtures composed of simulated RE fuel (mixture of 75% hydrous-ethanol and hydrogen) and air in a constant-volume combustion vessel at an initial temperature of 383 K, a pressure of 0.1 MPa, a hydrogen fraction from 0% to 80%, and an equivalence ratio from 0.6 to 1.6. The results show that the unstretched flame propagation speeds and burning velocities increase with increasing hydrogen fraction, especially when the fraction is above 40%. When the hydrogen fraction is less than 40%, the Markstein length and flame instability decrease and increase with the equivalence ratio, respectively, while the reverse holds when the hydrogen fraction is greater than 40%. At an equivalence ratio below 1.4, the Markstein length decreases with increasing hydrogen fraction, indicating a positive correlation between the flame instability and hydrogen fraction. At an equivalence ratio above 1.4, a negative relationship is observed. Finally, it is concluded that a hydrogen fraction of approximately 40% in simulated RE fuel is feasible for spark ignition engines by comparing the laminar burning characteristics of ethanol–air mixtures.

Measurement of laminar flame speeds and flame stability analysis of tert-butanol–air mixtures at elevated pressures

Laminar flame speeds and Markstein lengths of tert-butanol–air premixed mixtures were measured over a wide range of equivalence ratios at different initial temperatures and pressures by using the spherically propagating flame in a constant volume combustion chamber. Effects of Markstein number, flame thickness and density ratio at two sides of flame front on flame instability were analyzed combined with the schlieren photos. Results show that the unstretched flame propagation speeds and laminar flame speeds of the tert-butanol–air mixtures increase with the increase of initial temperature and decrease with the increase of initial pressure. Peak values of laminar flame speeds present at equivalence ratio of 1.1 regardless of initial pressure and temperature. Markstein length decreases with the increase of initial pressure. Flame front instability increases as equivalence ratio and initial pressure increase. Cellular structure appears at elevated pressure. The combined effect of diffusional–thermal instability and hydrodynamic instability leads to the increase of flame instability as initial pressure increases.

Laminar Burning Velocities and Markstein Lengths of 2,5-Dimethylfuran-Air Premixed Flames at Elevated Temperatures

Laminar burning velocities and Markstein lengths of 2,5-dimethylfuran (DMF)-air premixed mixtures at different initial temperatures and equivalence ratios were obtained using a constant volume combustion chamber and high-speed schlieren imaging system. The results indicate that both unstretched flame propagation speed and laminar burning velocity peak near the equivalence ratio of 1.2, and increase with increasing initial temperature. The peak unstretched flame propagation speed moves to the rich mixture side as the initial temperature increases, whereas the peak laminar burning velocity is unaffected by the variation of initial temperature. The Markstein length decreases with increasing equivalence ratio and increases with the increasing initial temperature. Based on the experimental data, a formula to calculate the laminar burning velocities of 2,5-DMF-air mixtures is provided.

Study on Laminar Burning Characteristics of Premixed High-Octane Fuel−Air Mixtures at Elevated Pressures and Temperatures

Laminar burning characteristics of high-octane fuel−air premixed mixtures (ETBE, TBA, and ethanol) were studied in a constant-volume bomb at various equivalence ratios, initial temperatures, and initial pressures by using outwardly propagating spherical flames with a high-speed schlieren imaging system. The flame propagation speed, the laminar burning velocity, the Markstein length, the adiabatic flame temperature, the flame thickness, and the density ratio were obtained and the influence of equivalence ratio, initial temperature, and initial pressure on these parameters was analyzed. The experimental results show that both the unstretched flame propagation speed and unstretched laminar burning velocity increase with the increase of initial temperature and decrease with the increase of initial pressure. Thermal-diffusive instabilities (Markstein length) decrease at higher initial temperature and/or at lower initial pressure. Meanwhile, the unstretched flame propagation speed and the unstretched laminar bu...

Measurements of Laminar Burning Velocities and Markstein Lengths of 2,5-Dimethylfuran−Air−Diluent Premixed Flames

Laminar burning velocities and Markstein lengths of 2,5-dimethylfuran (DMF)−air−N2/CO2 premixed mixtures at the atmospheric pressure and initial temperature of 393 K over three different dilution ratios were obtained by using the outwardly propagating spherical flame and high-speed schlieren photograph system. Addition of diluent was used to simulate the effects of exhaust gas recirculation on the flame propagation. The results show that both unstretched flame propagation speed and laminar burning velocity decrease with the increase of dilution ratio. Markstein length is increased with the increase of dilution ratio, indicating that addition of diluent will improve the stability of the flame. The dilution effects of CO2 as diluent on the flame propagation and the flame stability are stronger than those of N2 as diluent. For a specific equivalence ratio, the laminar burning velocity shows a linear decreasing trend with the increase of dilution ratio. The ratio of the laminar burning velocities with and wit...

Measurements of laminar burning velocities and onset of cellular instabilities of methane–hydrogen–air flames at elevated pressures and temperatures

An experimental study on laminar burning velocities and onset of cellular instabilities of the premixed methane–hydrogen–air flames was conducted in a constant volume combustion vessel at elevated pressures and temperatures. The unstretched laminar burning velocity and Markstein length were obtained over a wide range of hydrogen fractions. Besides, the effects of hydrogen addition, initial pressure and initial temperature on flame instabilities were analyzed. The results show that the unstretched flame propagation speed and the unstretched laminar burning velocity are increased with the increase of initial temperature and hydrogen fraction, and they are decreased with the increase of initial pressure. Early onset of cellular instability is presented and the critical radius and Markstein length are decreased with the increase of initial pressure, indicating the increase of hydrodynamic instability with the increase of initial pressure. Flame instability is insensitive to initial temperature compared to initial pressure. With the increase of hydrogen fraction, significant decrease in critical radius and Markstein length is presented, indicating the increase in both diffusional-thermal and hydrodynamic instabilities as hydrogen fraction is increased.

Measurement of Laminar Burning Velocities and Markstein Lengths for Diethyl Ether−Air Mixtures at Different Initial Pressure and Temperature

Measurement of laminar burning velocities and Markstein lengths were made for the diethyl ether−air mixtures at different equivalence ratios, initial temperatures, and pressures by using spherically propagating flame and schlieren photography method. The results show that the stretched flame propagation speeds, the unstretched flame propagation speeds, the stretched laminar burning velocities, the stretched mass burning velocities, and the unstretched laminar burning velocities increase with the increase of the initial temperature. Although the Markstein lengths decreases with the increase of the initial temperature. The stretched flame propagation speeds, the unstretched flame propagation speeds, the stretched laminar burning velocities, the stretched mass burning velocities, the unstretched laminar burning velocities and the Markstein lengths are decreased with the increase of the initial pressure, and the Markstein lengths are also decreased with the increase of the equivalence ratio. On the basis of t...

Measurement of Laminar Burning Velocities of Dimethyl Ether−Air Premixed Mixtures with N2 and CO2 Dilution

Measurements of laminar burning velocities of dimethyl ether−air premixed mixtures with N2 and CO2 dilution were made at room temperature and atmospheric pressure using the spherically expanding flame and schlieren photography over a wide range of dilution and equivalence ratios. The stretched flame propagation speed, the unstretched flame propagation speed, the unstretched laminar burning velocity, and the Markstein length (Lb) were obtained and analyzed. The results show that the flame speeds and the burning velocities decrease monotonously with the increase of the dilution ratio. The maximum value of the unstretched laminar burning velocity is presented at the equivalence ratio of 1.1, regardless of N2 dilution ratios, while it slightly shifts to the rich mixture side with the increase of the CO2 dilution ratio. This phenomenon reveals the different dilution effect on the unstretched laminar burning velocity between the triatomic molecule gas CO2 and the diatomic molecule gas N2. The Markstein length increases with the increase of the dilution ratio. The addition of diluents to the stoichiometric and/or the lean mixture has a larger influence on the Markstein length compared to those of the rich mixture. The addition of diluents obviously enhances the stability of the flame front for the lean mixture, but the impact is slight for the rich mixture. The influence of CO2 as the diluent on the flame speed and the flame stability is larger than that of N2 as the diluent for dimethyl ether−air mixture combustion.

Measurements of laminar burning velocities and Markstein lengths of propane–hydrogen–air mixtures at elevated pressures and temperatures

Experimental study on the laminar burning velocities and the onset of cellular instabilities of propane–hydrogen–air mixtures with spherically expanding flames was conducted at elevated pressures and temperatures and different hydrogen fractions at the equivalence ratio of 0.8 and 1.2. The results show that the unstretched flame propagation speed and the unstretched laminar burning velocity increase with the increase of hydrogen fraction and initial temperature, and they decrease with the increase of initial pressure. An earlier onset of cellular instability and the decrease in the critical radius and the Markstein length are presented with the increase of initial pressure, indicating that the hydrodynamic instability is enhanced with the increase of initial pressure. At the equivalence ratio of 0.8, where the propane–air mixture is thermal-diffusionally stable and the hydrogen–air mixture is thermal-diffusionally unstable, the critical radius and the Markstein length decrease significantly with the increase of hydrogen fraction, indicating that hydrogen addition will increase the diffusional-thermal and the hydrodynamic instability. At equivalence ratio of 1.2, where the propane–air mixture and hydrogen–air mixture are both thermal-diffusionally neutral, a moderate decrease in the critical radius and the Markstein length is presented. This indicates the increase of hydrodynamic instability as hydrogen is added.