Laminar Flame Characteristics of Premixed Methanol–Water–Air Mixture

: Methanol is hygroscopic in a gaseous state and is a promising alternative fuel for internal combustion engines. It is understood that adding water can improve the antiknock performance for spark ignition engines, but this will also a ﬀ ect the ﬂame speed and stability. In this work, laminar ﬂame characteristics of methanol / water / air mixtures were experimentally investigated at a temperature range of 380–450 K, a pressure range of 1–4 bar, and water fractions (vaporous water molar fraction in the water–methanol fuel gas) of 0–40%. The results show that laminar burning velocity increases with temperature but decreases with pressure. The burning velocity decreases linearly with water fraction at a stoichiometric ratio. For rich mixtures and high pressures, the laminar ﬂames tend to be more sensitive to stretch and, thus, more prone to being unstable. Increasing the water fraction can slightly increase the Markstein length. Increasing the initial pressure enhances the general ﬂame instability, while increasing the initial temperature suppresses the general ﬂame instability. Increasing the water fraction can lead to a decreasing thermal expansion ratio and an elevated ﬂame thickness, both of which can lead to a suppression of hydrodynamic instability. An increase in the water fraction decreases the Lewis number, resulting in preferential di ﬀ usion instability. There is no direct relationship between the onset of cellularity and general ﬂame instability.


Introduction
Increasingly serious environmental pollution and energy shortage have drawn widespread concerns and are strongly require promising replacements for conventional fossil fuels [1]. Different kinds of alternative fuels are becoming growing interests including natural gas, hydrogen, and alcohols [2][3][4]. Both methanol and ethanol are being used more and more widely. The addition of ethanol to spark ignition engines can decrease some pollutants but can also increase others [5,6]. Methanol is regarded as an ideal alternative fuel for internal combustion engines (IC engines) owing to its high octane rating, high latent heat, low combustion temperatures, and relatively clean emissions [7][8][9], which can help to achieve higher power output, higher efficiency, and lower pollution. Methanol can be produced through fossil fuel-based feedstocks, as well as gasification of wood, agricultural byproducts, and urban waste [10]. Methanol is hygroscopic, as purified gaseous methanol can absorb water from the atmosphere, which can improve the antiknock performance but also lead to a decrease in the calorific value and phase separation of methanol-gasoline blends [7]. Water may cause negative effects on the combustion performance of methanol fuels.
Laminar flame characteristics are essential parameters of fuels and are closely related to the performance when used in internal combustion engines. Laminar flame velocity is highly related to the burning duration, power output, and efficiency. It also can be used for validation of the chemical kinetic mechanism and prediction of the turbulent combustion stage. The flame instability strongly influences the cyclical variation [11,12]. Laminar flame characteristics can be investigated via many methods including constant volume chambers (CVCs).
To date, a number of studies on methanol burning and mechanisms have been conducted. Vancoillie et al. [13] investigated the effect of nitrogen and water vapor dilution on the laminar burning velocity of methanol flame through heat flux method experiments and simulation. It was found that the chemical effect was negligible when diluted by nitrogen and when the water fraction (vaporous water molar fraction in the water-methanol fuel gas) was lower than 20%. The effect of dilution on laminar burning velocity was regarded as adequately approximated by a linear decrease in terms of the diluent molar fraction. Li et al. [14] developed a mechanism for the prediction of CO, CH 2 O, and methanol combustion. Katoch et al. [15] used a mesoscale diverging channel method to measure the laminar burning velocity and compared the results with those from a kinetic simulation. It was found that the values from experiments and simulations agreed well at low temperatures, but the San Diego [16] and Li mechanisms [14] would overpredict the burning velocity.
Despite the number of studies on methanol mentioned above, most of them focused on the burning velocity measurements without taking water vapor into account. There is no study in the literature on the flame stability characteristics of methanol/water mixture. Note that flame instability is also essential for understanding properties of fuels, and burning at high temperature and pressure with absorbing water is closer to a real combustion atmosphere for methanol. It is significant to comprehensively investigate both the burning velocity and the flame instability of methanol/water vapor mixtures. In this work, a constant volume chamber with a Schlieren imaging system was applied to investigate the laminar flame propagation speed and flame instabilities of methanol/water vapor mixtures at high temperatures ranging up to 450 K and high pressures ranging up to 4 bar.

Experimental Set-Up
The experiments were conducted using a constant volume chamber (CVC) and a Schlieren imaging system shown as Figure 1. The CVC had a pair of windows with diameter of 40 mm for imaging. A light-emitting diode (LED; green Prolight Power Star/O, power 1 W) was used for illumination. A high-speed camera (Photron 1024 PCI) with a 512 × 512 pixel resolution and a frame rate of 3000 frames per second (fps) was used for photographing. The Schlieren system for this work was a folded z-type arrangement, and two oppositely tilted off-axis spherical mirrors were applied to produce the collimated beam. The constant volume chamber was a stainless-steel spherical one with a diameter of 160 mm, allowing a maximum working pressure of 34 bar inside. The initial temperature control was achieved by a fan oven enclosing the CVC, which could heat the chamber up to 450 K. Two electrodes formed an ignition gap at the center of the chamber. The mass flow rate of the intake air was monitored and controlled by a mass flow controller. A subsequent injection block was adopted to heat the air and evaporate the liquid fuel. A syringe controller was used to control the volume and injection speed of the liquid fuel. Table 1 shows the test conditions of burning velocity for methanol/water mixtures. For all test conditions, there was a duration of 5 min before ignition to make the mixtures homogeneous in the chamber, as suggested in [7,17]. (a) (b) Figure 1. Schematic of the (a) constant volume combustion bomb with optical window for Schlieren imaging system, and (b) arrangement of folded z-type Schlieren imaging system [10].

Extraction of Flame Radius
The extraction process of the flame radius is shown in Figure 2. As shown, five main steps were implemented via a MATLAB code. The midpoint of the red horizontal line (point Q in Figure 2) was chosen as the center of the flame. Based on the center point, six radii, with an angle interval of 60°, were defined after identifying the flame front, and their average was computed to increase accuracy. Furthermore, values of flame radius at the ignition electrode were invalid due to the impact of the boundary layer, and these values were excluded. To ensure that the influence of ignition energy and pressure variations was negligible, images with 6 mm < R < 25 mm were deemed suitable for computing the flame propagation speed [18]. Since the diameter of the window was 40 mm, images with 6 mm < R < 20 mm were selected. For each test condition, 30-50 flame images of the propagation process with fixed time interval were selected to calculate the flame propagation speed (through the differences in radius and the time interval).

Extraction of Flame Radius
The extraction process of the flame radius is shown in Figure 2. As shown, five main steps were implemented via a MATLAB code. The midpoint of the red horizontal line (point Q in Figure 2) was chosen as the center of the flame. Based on the center point, six radii, with an angle interval of 60 • , were defined after identifying the flame front, and their average was computed to increase accuracy. Furthermore, values of flame radius at the ignition electrode were invalid due to the impact of the boundary layer, and these values were excluded. To ensure that the influence of ignition energy and pressure variations was negligible, images with 6 mm < R < 25 mm were deemed suitable for computing the flame propagation speed [18]. Since the diameter of the window was 40 mm, images with 6 mm < R < 20 mm were selected. For each test condition, 30-50 flame images of the propagation process with fixed time interval were selected to calculate the flame propagation speed (through the differences in radius and the time interval).

Data Reduction
The stretched propagation flame speed Sn can be defined as the derivative of the flame radius Ru with respect to time t, as shown in Equation (1).

Data Reduction
The stretched propagation flame speed S n can be defined as the derivative of the flame radius R u with respect to time t, as shown in Equation (1).
The flame stretch rate K is obtained through Equation (2).
where κ = 2/R u is the curvature of the flame front. According to Chen [19], in order to get the unstretched flame propagation speed S l and Markstein length L b (indicating the sensitivity of the flame to stretch), there are three models that can be used, which are the linear model (Equation (3)), nonlinear model I (Equation (4)) [20], and nonlinear model II (Equation (5)) [21].
The inaccuracy of the linear model has been proven when the equivalence ratio is not stoichiometric. The nonlinear model I has been proven to be the most accurate for mixtures with Lewis number Le > 1, while nonlinear model II has been proven to be the most accurate for mixtures with Lewis number Le < 1. The Lewis number can be obtained as follows: where λ is the thermal conductivity of the mixture, c p is the specific heat at constant pressure of the mixture, ρ u is the density of unburned gas, D T is the thermal diffusion coefficient of the mixture, and D m is the mass diffusion coefficient of the deficient reactant to the inert gas, which can be calculated through Equation (7). The Lewis numbers of most test conditions in this study were greater than one; thus, nonlinear model I was predominantly used.
where T is the initial temperature, p is the initial pressure, µ A and µ B are the molar masses of A and B, and V A and V B are the liquid molar volumes at normal boiling point of A and B. The calculation was conducted using the Binary Components Diffusion Coefficient software V1.3 (Xi'an Weiwei Computer Technology Co. LTD [22]). For the mixtures, the heat capacity and the thermal conductivity could be calculated as shown in Equations (8) and (9) [23], respectively.
In Equation (8), y i is the i-th component's mass fraction, and c p,i is the i-th component's heat capacity. In Equation (9), x i is the i-th component's volume (mole) fraction, and λ i is the i-th component's thermal conductivity. In this paper, nonlinear model I was applied because Le > 1 was satisfied for all the test conditions. The Lewis number is also an essential parameter to evaluate the preferential diffusion instability of the flame as it is essentially a ratio of heat diffusion to mass diffusion. The preferential diffusion instability is stronger when there is a decrease in Le. Generally, the flame tends to be stable from the view of diffusion when Le > 1, but the opposite is true when Le < 1.
The laminar burning velocity u L could be calculated as follows: where ρ b and ρ u are the density of burned and unburned gas, respectively. Their ratio is the thermal expansion ratio σ, shown in Equation (11). A decrease in σ can lead to a weaker hydrodynamic instability.
where ρ u can be calculated through initial parameters, while ρ b can be computed through a thermal equilibrium model in Chemkin-Pro.
Another parameter related to the hydrodynamic instability is the flame thickness l f , shown in Equation (12). A smaller flame thickness results in weaker self-bending and stronger gas torque at the flame front (equivalent torque when gas pressure acting on the flame front), thus leading to a stronger hydrodynamic instability [24].

Uncertainty Propagation
In this work, inaccuracy was mainly caused by the error in Schlieren image recognition, ignition energy, and flame radiation [25]. The maximum error in Schlieren image recognition was 1 pixel, causing a maximum error of 0.083 mm in the flame radius. In this work, the minimum time interval was 0.33 ms; thus, the maximum error in S n was 25 cm·s −1 , causing a potential maximum error of 5.7 cm·s −1 in u L . The inaccuracy brought about by ignition energy could be eliminated by selecting images with suitable radii, as stated in Section 3.1.
The effect of flame radiation could be calculated using Equation (13) [26].
where S 0 = 0.01 m·s −1 , T 0 = 298 K, p 0 = 0.1 MPa, and u L,RCFS and u L,EXP are laminar burning velocities obtained experimentally taking radiation into account and measured practically, respectively. In this work, the inaccuracy caused by radiation did not exceed 0.7 cm·s −1 , which was considered acceptable. All error bars of the burning velocity are highlighted in the figures below, indicating the possible maximum uncertainty.  [27]. All of these studies showed peak values at the equivalence ratio of 1.1-1.2. However, results from Liao et al. (constant volume chamber Schilieren method) [28] showed peak values at an equivalence ratio of 1.0. Note that the San Diego mechanism may overpredict the burning velocity of methanol. Metghalchi and Kech [29] also predicted higher burning velocity. The results in Energies 2020, 13, 6504 6 of 13 this study (the red thicker dashed line with error bars) were deemed acceptable for the analysis as the differences were not too significant considering the uncertainty.

Laminar Burning Velocity and Markstein Length
interesting to see that the present results (the red thicker dashed line with error bars) show a similar trend to the results obtained by Liang (San Diego mechanism) [ [27]. All of these studies showed peak values at the equivalence ratio of 1.1-1.2. However, results from Liao et al. (constant volume chamber Schilieren method) [28] showed peak values at an equivalence ratio of 1.0. Note that the San Diego mechanism may overpredict the burning velocity of methanol. Metghalchi and Kech [29] also predicted higher burning velocity. The results in this study (the red thicker dashed line with error bars) were deemed acceptable for the analysis as the differences were not too significant considering the uncertainty.  Figure 4 plots the laminar burning velocities at different pressures and temperatures, and curves of second-order polynomial fitting are also shown. It is clear to see that the laminar burning velocity increased with temperature but decreased with pressure. At the equivalence ratio of 1.0, when the pressure increased from 1 to 2 bar and then 2 to 4 bar, the burning velocity decreased by 15.8% and 15.4% at a stoichiometric ratio, respectively. When the temperature increased from 380 K to 450 K, the burning velocity increased by 51.5% at a stoichiometric ratio. It is also interesting to see that, for the curves at the pressure of 1 bar and 2 bar, the peak burning velocity appeared at the equivalence ratio of 1.1-1.2, while the peak burning velocity appeared at the equivalence ratio of 1.2-1.3 for the curve of 4 bar. It is suspected that increasing the initial pressure may switch the peak burning velocity to the rich side, whereas the initial temperature has no effect.  Figure 4 plots the laminar burning velocities at different pressures and temperatures, and curves of second-order polynomial fitting are also shown. It is clear to see that the laminar burning velocity increased with temperature but decreased with pressure. At the equivalence ratio of 1.0, when the pressure increased from 1 to 2 bar and then 2 to 4 bar, the burning velocity decreased by 15.8% and 15.4% at a stoichiometric ratio, respectively. When the temperature increased from 380 K to 450 K, the burning velocity increased by 51.5% at a stoichiometric ratio. It is also interesting to see that, for the curves at the pressure of 1 bar and 2 bar, the peak burning velocity appeared at the equivalence ratio of 1.1-1.2, while the peak burning velocity appeared at the equivalence ratio of 1.2-1.3 for the curve of 4 bar. It is suspected that increasing the initial pressure may switch the peak burning velocity to the rich side, whereas the initial temperature has no effect.   Figure 5 shows the laminar burning velocities at different water fractions at a stoichiometric ratio. The laminar burning velocity decreased dramatically when the water fraction increased from 0% to 40%, and it showed an approximately linear decrease as the water fraction increased linearly with an average R 2 value of 0.93601. Among the results, the curve of 450 K, 1 bar showed the highest degree of linearity with an R 2 value of 0.99939. This agrees well with [13]. At initial conditions of 450 K, 1 bar, the laminar burning velocity decreased by 31.1% and 47.9% when the water fraction increased from 0% to 20% and then 40%.   Figure 5 shows the laminar burning velocities at different water fractions at a stoichiometric ratio. The laminar burning velocity decreased dramatically when the water fraction increased from 0% to 40%, and it showed an approximately linear decrease as the water fraction increased linearly with an average R 2 value of 0.93601. Among the results, the curve of 450 K, 1 bar showed the highest degree of linearity with an R 2 value of 0.99939. This agrees well with [13]. At initial conditions of 450 K, 1 bar, Energies 2020, 13, 6504 7 of 13 the laminar burning velocity decreased by 31.1% and 47.9% when the water fraction increased from 0% to 20% and then 40%.  Figure 5 shows the laminar burning velocities at different water fractions at a stoichiometric ratio. The laminar burning velocity decreased dramatically when the water fraction increased from 0% to 40%, and it showed an approximately linear decrease as the water fraction increased linearly with an average R 2 value of 0.93601. Among the results, the curve of 450 K, 1 bar showed the highest degree of linearity with an R 2 value of 0.99939. This agrees well with [13]. At initial conditions of 450 K, 1 bar, the laminar burning velocity decreased by 31.1% and 47.9% when the water fraction increased from 0% to 20% and then 40%.  Figure 6 plots the Markstein lengths at different pressures, and linear fitting was applied to show the trend. It can be seen that Markstein length decreased with the equivalence ratio. According to [30,31], Markstein length is mainly affected by the reactant which has a stronger diffusion capacity in the mixture. When the stronger diffusive component decreases, the flame becomes more sensitive to the stretching, thus decreasing the Markstein length and enhancing the tendency to be unstable. In this work, the diffusivity of oxygen into nitrogen was stronger than that of methanol into nitrogen. Therefore, with the equivalence ratio increasing, oxygen became relatively less while methanol became relatively more, leading to a declined Markstein length. It can also be seen that Markstein length decreased with pressure. Note that the flame tended to be unstable when Lb < 0 (and tended to be stable when Lb > 0), while the flame instability at the rich side (Φ > 1.2) at a pressure of 4 bar was relatively strong.  Figure 6 plots the Markstein lengths at different pressures, and linear fitting was applied to show the trend. It can be seen that Markstein length decreased with the equivalence ratio. According to [30,31], Markstein length is mainly affected by the reactant which has a stronger diffusion capacity in the mixture. When the stronger diffusive component decreases, the flame becomes more sensitive to the stretching, thus decreasing the Markstein length and enhancing the tendency to be unstable. In this work, the diffusivity of oxygen into nitrogen was stronger than that of methanol into nitrogen. Therefore, with the equivalence ratio increasing, oxygen became relatively less while methanol became relatively more, leading to a declined Markstein length. It can also be seen that Markstein length decreased with pressure. Note that the flame tended to be unstable when L b < 0 (and tended to be stable when L b > 0), while the flame instability at the rich side (Φ > 1.2) at a pressure of 4 bar was relatively strong.       Figure 7 plots the Markstein lengths at different temperatures and water fractions at a stoichiometric ratio. Compared to the initial pressure, the initial temperature had a much weaker influence on Markstein length. Generally, with an increase in water fraction, the Markstein length increased slightly, thus giving the flame a trend of being stable.

Flame Instability and Cellularity
The flame instability can be classified as preferential diffusion instability, hydrodynamic instability, and buoyancy instability. Buoyancy instability happens at very low burning velocity, showing a floating spherical flame. Buoyancy instability was not considered in the present study as most test conditions for combustion analysis did not experience such a phenomenon. The preferential diffusion instability can be evaluated through the Lewis number. A decrease in Lewis number can enhance the preferential diffusion instability. The hydrodynamic instability can be evaluated through thermal expansion ratio and flame thickness. A smaller thermal expansion ratio and a larger flame thickness denote weaker hydrodynamic instability. Figure 8 shows the Lewis numbers at different pressures and temperatures. It is clear that the Lewis number decreased with the equivalence ratio as the methanol increased while oxygen decreased (the same reason as for Markstein length according to [30,31]), resulting in an enhancement in preferential diffusion instability. It can also be seen that pressure had no influence on the Lewis number because diffusion was only affected by temperature. With temperature increasing, the Lewis number increased, as the enhancement in thermal diffusion was stronger than that in mass diffusion,

Flame Instability and Cellularity
The flame instability can be classified as preferential diffusion instability, hydrodynamic instability, and buoyancy instability. Buoyancy instability happens at very low burning velocity, showing a floating spherical flame. Buoyancy instability was not considered in the present study as most test conditions for combustion analysis did not experience such a phenomenon. The preferential diffusion instability can be evaluated through the Lewis number. A decrease in Lewis number can enhance the preferential diffusion instability. The hydrodynamic instability can be evaluated through thermal expansion ratio and flame thickness. A smaller thermal expansion ratio and a larger flame thickness denote weaker hydrodynamic instability. Figure 8 shows the Lewis numbers at different pressures and temperatures. It is clear that the Lewis number decreased with the equivalence ratio as the methanol increased while oxygen decreased (the same reason as for Markstein length according to [30,31]), resulting in an enhancement in preferential diffusion instability. It can also be seen that pressure had no influence on the Lewis number because diffusion was only affected by temperature. With temperature increasing, the Lewis number increased, as the enhancement in thermal diffusion was stronger than that in mass diffusion, leading to a suppression of preferential diffusion instability. At a stoichiometric ratio, the Lewis number increased by 4.6% when the temperature increased from 380 K to 450 K.   Figure 9 plots Lewis numbers at different water fractions. It is clear that an increase in water fraction decreased the Lewis number, enhancing the trend of preferential diffusion instability. At a stoichiometric ratio, the Lewis number decreased by 10% and then a further 10% when the water fraction was increased from 0% to 20% and 40%. It is also interesting to note that, with water fraction increasing, the trend of Lewis number decreasing with equivalence ratio became flatter. The Lewis number decreased by 0.36, 0.3, and 0.24 from Φ = 0.7-1.4 at water fractions of 0%, 20%, and 40%, respectively. Generally, as the Lewis numbers of all test conditions were greater than 1, the  stoichiometric ratio, the Lewis number decreased by 10% and then a further 10% when the water fraction was increased from 0% to 20% and 40%. It is also interesting to note that, with water fraction increasing, the trend of Lewis number decreasing with equivalence ratio became flatter. The Lewis number decreased by 0.36, 0.3, and 0.24 from Φ = 0.7-1.4 at water fractions of 0%, 20%, and 40%, respectively. Generally, as the Lewis numbers of all test conditions were greater than 1, the preferential diffusion instability was weak.  Figure 9 plots Lewis numbers at different water fractions. It is clear that an increase in water fraction decreased the Lewis number, enhancing the trend of preferential diffusion instability. At a stoichiometric ratio, the Lewis number decreased by 10% and then a further 10% when the water fraction was increased from 0% to 20% and 40%. It is also interesting to note that, with water fraction increasing, the trend of Lewis number decreasing with equivalence ratio became flatter. The Lewis number decreased by 0.36, 0.3, and 0.24 from Φ = 0.7-1.4 at water fractions of 0%, 20%, and 40%, respectively. Generally, as the Lewis numbers of all test conditions were greater than 1, the preferential diffusion instability was weak.

Lewis number Le
Equivalence ratio Φ W0 450K 4bar W20 450K 4bar W40 450K 4bar Figure 9. Lewis numbers at different water fractions. Figure 10 shows the thermal expansion ratios and flame thicknesses at different pressures. It can be seen that, with pressure increasing, the thermal expansion ratio slightly increased and the flame thickness decreased significantly, both of which led to a stronger hydrodynamic instability. Therefore, increasing pressure can enhance the hydrodynamic instability. Furthermore, considering the more significant changes in flame thickness, it is clear that the flame thickness mainly affected the hydrodynamic instability when changing initial pressure.  Figure 10 shows the thermal expansion ratios and flame thicknesses at different pressures. It can be seen that, with pressure increasing, the thermal expansion ratio slightly increased and the flame thickness decreased significantly, both of which led to a stronger hydrodynamic instability. Therefore, increasing pressure can enhance the hydrodynamic instability. Furthermore, considering the more significant changes in flame thickness, it is clear that the flame thickness mainly affected the hydrodynamic instability when changing initial pressure.  Figure 11 shows the thermal expansion ratios and flame thicknesses at different temperatures. With the increase in temperature, the thermal expansion ratio decreased, indicating a suppression of hydrodynamic instability; however, the flame thickness also decreased, indicating an enhancement in hydrodynamic instability. It can be seen that the change in initial temperature caused a more significant change in thermal expansion ratio than flame thickness (apart from the very lean mixtures of Φ = 0.7). It can be inferred that the hydrodynamic instability is suppressed when elevating initial temperature, and the thermal expansion ratio mainly affects the hydrodynamic instability when changing initial temperature.   Figure 11 shows the thermal expansion ratios and flame thicknesses at different temperatures. With the increase in temperature, the thermal expansion ratio decreased, indicating a suppression of hydrodynamic instability; however, the flame thickness also decreased, indicating an enhancement in hydrodynamic instability. It can be seen that the change in initial temperature caused a more significant change in thermal expansion ratio than flame thickness (apart from the very lean mixtures of Φ = 0.7). It can be inferred that the hydrodynamic instability is suppressed when elevating initial temperature, and the thermal expansion ratio mainly affects the hydrodynamic instability when changing initial temperature. hydrodynamic instability; however, the flame thickness also decreased, indicating an enhancement in hydrodynamic instability. It can be seen that the change in initial temperature caused a more significant change in thermal expansion ratio than flame thickness (apart from the very lean mixtures of Φ = 0.7). It can be inferred that the hydrodynamic instability is suppressed when elevating initial temperature, and the thermal expansion ratio mainly affects the hydrodynamic instability when changing initial temperature. Flame thickness l f (mm) Figure 11. Thermal expansion ratios and flame thicknesses at different temperatures. Figure 12 shows the thermal expansion ratios and flame thicknesses at different water fractions. It is clear that an increased water fraction led to a reduced thermal expansion ratio and an increased flame thickness, both of which led to a suppression of hydrodynamic instability. Therefore, the diluent effect of water can suppress the hydrodynamic instability of the methanol flame. It can also be seen that, with the equivalence ratio increasing from 0.7 to 1.4, the expansion ratio increased first and then decreased, while the flame thickness decreased first and then increased, which indicates that the hydrodynamic instability was enhanced first and then suppressed. It is interesting to note that both the peak value of the expansion ratio and the trough value of the flame thickness appeared at Φ = 1.0-1.2, where the peak burning velocity happened. However, as increasing pressure and decreasing temperature (suppressing the burning velocity) enhance the hydrodynamic instability, a direct connection between the hydrodynamic instability and laminar burning velocity cannot be speculated. Figure 11. Thermal expansion ratios and flame thicknesses at different temperatures. Figure 12 shows the thermal expansion ratios and flame thicknesses at different water fractions. It is clear that an increased water fraction led to a reduced thermal expansion ratio and an increased flame thickness, both of which led to a suppression of hydrodynamic instability. Therefore, the diluent effect of water can suppress the hydrodynamic instability of the methanol flame. It can also be seen that, with the equivalence ratio increasing from 0.7 to 1.4, the expansion ratio increased first and then decreased, while the flame thickness decreased first and then increased, which indicates that the hydrodynamic instability was enhanced first and then suppressed. It is interesting to note that both the peak value of the expansion ratio and the trough value of the flame thickness appeared at Φ = 1.0-1.2, where the peak burning velocity happened. However, as increasing pressure and decreasing temperature (suppressing the burning velocity) enhance the hydrodynamic instability, a direct connection between the hydrodynamic instability and laminar burning velocity cannot be speculated.   Figure 13 plots the onset time (after ignition) of cellularity at different pressures and temperatures. It is clear to see that, for most test conditions, an elevated pressure resulted in an earlier onset of cellularity. However, for the very lean mixture (Φ = 0.7), a higher initial temperature led to an earlier onset of cellularity. Moreover, elevating the initial temperature could cause an earlier onset of cellularity in the whole equivalence ratio range.   It is clear to see that, for most test conditions, an elevated pressure resulted in an earlier onset of cellularity. However, for the very lean mixture (Φ = 0.7), a higher initial temperature led to an earlier onset of cellularity. Moreover, elevating the initial temperature could cause an earlier onset of cellularity in the whole equivalence ratio range. Figure 13 plots the onset time (after ignition) of cellularity at different pressures and temperatures. It is clear to see that, for most test conditions, an elevated pressure resulted in an earlier onset of cellularity. However, for the very lean mixture (Φ = 0.7), a higher initial temperature led to an earlier onset of cellularity. Moreover, elevating the initial temperature could cause an earlier onset of cellularity in the whole equivalence ratio range.    Comprehensively, increasing initial pressure had no effect on the preferential diffusion instability but enhanced the hydrodynamic instability, thus enhancing the general instability. Increasing initial temperature suppressed both preferential diffusion and hydrodynamic instability, thus suppressing the general instability. Increasing the water fraction enhanced the preferential diffusion instability but suppressed the hydrodynamic instability; thus, it is not clear how it affects the general instability. Note that increasing pressure or temperature could lead to an earlier onset of cellularity, while increasing water fraction could lead to a later onset, but there was no direct relationship between the onset of cellularity and general flame instability.

Conclusions
The laminar flame characteristics of hydrous methanol were experimentally studied using a constant volume chamber with a Schlieren system over a wide range of equivalence ratios, initial temperatures, and pressures at water fractions of 0-40%. The laminar burning velocity, flame instability, and regularity of onset of cellularity were comprehensively investigated. Key conclusions are described below.
(1) The laminar burning velocity of methanol increased with temperature and decreased with pressure. Increasing the initial pressure could switch the peak burning velocity to the rich side, while initial temperature had no effect. Burning velocity linearly decreased with water fraction at a stoichiometric ratio. Comprehensively, increasing initial pressure had no effect on the preferential diffusion instability but enhanced the hydrodynamic instability, thus enhancing the general instability. Increasing initial temperature suppressed both preferential diffusion and hydrodynamic instability, thus suppressing the general instability. Increasing the water fraction enhanced the preferential diffusion instability but suppressed the hydrodynamic instability; thus, it is not clear how it affects the general instability. Note that increasing pressure or temperature could lead to an earlier onset of cellularity, while increasing water fraction could lead to a later onset, but there was no direct relationship between the onset of cellularity and general flame instability.

Conclusions
The laminar flame characteristics of hydrous methanol were experimentally studied using a constant volume chamber with a Schlieren system over a wide range of equivalence ratios, initial temperatures, and pressures at water fractions of 0-40%. The laminar burning velocity, flame instability, and regularity of onset of cellularity were comprehensively investigated. Key conclusions are described below.
(1) The laminar burning velocity of methanol increased with temperature and decreased with pressure. Increasing the initial pressure could switch the peak burning velocity to the rich side, while initial temperature had no effect. Burning velocity linearly decreased with water fraction at a stoichiometric ratio. (2) Markstein length decreased with equivalence ratio and pressure. At rich mixtures under high pressures, the methanol flame tended to be more sensitive to stretch and, thus, unstable. An increase in water fraction could slightly increase the Markstein length. (3) The Lewis number decreased with equivalence ratio, resulting in an enhancement in preferential diffusion instability. Pressure had no influence on Lewis number because diffusion was only affected by temperature. With the temperature increasing, Lewis number increased as the enhancement in thermal diffusion was stronger than that in mass diffusion. Increasing water fraction enhanced the preferential diffusion instability. (4) Increasing the water fraction could lead to a decreasing thermal expansion ratio and an elevated flame thickness, both of which could lead to a suppression of hydrodynamic instability. (5) A higher initial pressure led to an earlier onset of cellularity except in very lean mixtures, and a higher initial temperature could cause an earlier onset of cellularity over the whole equivalence ratio range. A higher water fraction led to a later onset of cellularity. There was no direct relationship between the onset of cellularity and general flame instability.