Investigation of the Flame Stability and Laminar Burning Speed of Propylene/Air/Carbon Dioxide Mixtures Under Conditions of Elevated Temperatures and Pressures

Refrigerants are substances used in refrigeration systems and air conditioning units to transfer thermal energy from one area to another. Common refrigerants include chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrofluorocarbons (HFCs), and hydrocarbons (HCs). However, due to their environmental impact, many countries are phasing out the use of CFCs and HCFCs in favor of more environmentally friendly alternatives, such as HFCs like 2,3,3,3-tetrafluoropropene (C₃H₂F₄, R-1234yf) with lower global warming potential (GWP) or natural refrigerants like ammonia, carbon dioxide, and hydrocarbons.

Hydrocarbon refrigerants are a class of refrigerants composed solely of hydrogen and carbon atoms. They are considered natural refrigerants. Common hydrocarbon refrigerants include propane (R-290), isobutane (R-600a), and propylene (R-1270). These refrigerants have low GWP and zero ozone depletion potential (ODP), making them environmentally friendly alternatives to synthetic refrigerants like CFCs and HCFCs. However, their flammability requires careful handling and safety precautions in their use. Hydrocarbon refrigerants are gaining popularity due to their environmental benefits and energy efficiency.

Carbon dioxide (CO₂) can also be used as a refrigerant, especially in transcritical and subcritical cycles. Carbon dioxide has gained attention as a natural refrigerant due to its low environmental impact—it has a GWP of 1 and 0 ODP. In order to reduce the flammability of hydrocarbons, proposals have been made to add carbon dioxide to hydrocarbons and propylene, reducing refrigerant burning speed. Multiple research projects have evaluated the refrigeration performance characteristics of HCs and carbon dioxide (CO₂) zeotropic combinations through numerical and experimental approaches. Yelishala et al. [1] analyzed the thermodynamic efficiency of a vapor compression refrigeration cycle by using combinations of HC and carbon dioxide (CO₂) refrigerants. They identified combinations that exhibit superior performance for a system with a constant temperature of energy transfer fluid. Yelishala et al. [2] later developed a temperature glide matching method for refrigerants (HCs/CO₂) mixtures and energy transfer fluids in the energy exchanger to increase the cycle performance.

Propylene, also known as propene, is an organic compound belonging to the alkene family with the chemical formula C₃H₆. It is a colorless gas with a faint petroleum-like odor. Propylene is a crucial building block in the petrochemical industry, serving as a precursor to various important chemicals.

Some common uses of propylene include:

• Polymerization: Propylene is a major feedstock to produce polypropylene, which is one of the most widely used plastics in the world. Polypropylene finds applications in packaging, textiles, automotive components, and many other areas.

• Fuel: Propylene is used as a fuel in various industrial applications, including cutting and welding processes.

• Chemical synthesis: Propylene is used as a starting material in the synthesis of various chemicals, such as propylene oxide (used in the production of polyurethane), acrylonitrile (used in the production of acrylic fibers and resins), and cumene (used in the production of phenol and acetone) [3].

Propylene is typically produced through processes such as steam cracking of hydrocarbons or through refinery operations. It is an important chemical commodity with a wide range of industrial applications.

The laminar burning speed is a fundamental property of a combustible mixture and can be used to provide information regarding the mixture's reactivity, exothermicity, and diffusivity. The laminar burning speed is influenced by various factors including chemical composition, mixture stoichiometry, temperature, and pressure. The laminar burning speed is an important parameter in combustion research and engineering, as it provides insights into the fundamental characteristics of combustion processes and influences the design and performance of combustion systems such as internal combustion engines, gas turbines, and combustors.

Laminar burning speeds are often determined experimentally using techniques such as the heat flux burner or the spherical flame method. There have been several experiments using different methods to measure the laminar burning speed of hydrocarbons such as propane, isobutane, and propylene or the mixture of hydrocarbons and carbon dioxide. Davis et al. [4] utilized the counterflow twin flame configuration to determine the laminar burning speed of propylene/air mixtures at a pressure of 1 atm and room temperature. The range of equivalence ratio is 0.7–1.4. Jomaas et al. [5] used a constant pressure method to determine the laminar burning speed of C₂–C₃ hydrocarbons, which include acetylene, ethylene, ethane, propylene, and propane. The experimental pressures for ethylene, ethane, propylene, and propane are 1, 2, and 5 atm and the temperature is room temperature. Saeed and Stone [6] measured the laminar burning speed of propylene/air mixture by using the constant volume method. The test conditions of their experiments were the initial temperatures of 293 K and 425 K, the initial pressures of 0.5, 1.0, 2.0, and 2.5 bar, and the equivalence ratios of 0.8–1.6. For their conditions, they reported laminar burning speeds at pressures up to 20 bar and unburned gas temperatures up to 650 K, but as the pressure increases in the vessel, the flame becomes cellular and assuming smooth flames predicts the wrong burning speed measurement. Burke et al. [7] with colleagues from Princeton University (PU), Texas A&M University (TAMU), Vrije Universiteit Brussel (VUB), Lund University (Lund), Université de Lorraine (LRPG) used different methods and facilities to measure laminar burning speed. Princeton's group and Texas A&M's group used the constant pressure method to measure the laminar burning speed. Both of their experiments were performed at atmospheric pressure and room temperature. The equivalence ratios for Princeton's group were from 0.8 to 1.3 and Texas A&M's group conducted a wide range of equivalence ratios from 0.7 to 1.7. Vrije Universiteit Brussel's group used the heat flux method to measure the burning speed of propylene/O₂/N₂ mixtures. The mixtures have various dilution ratios X, which are 0.18, 0.19, 0.20, 0.209 (air), where $X=(XO2)/(XO2+XN2)$⁠. Their experiments were also performed at atmospheric pressure and room temperature, and the equivalence ratios ranged from 0.7 to 1.2. Université de Lorraine's group also used the heat flux method to measure propylene/air mixtures at higher temperatures (298 K, 358 K, and 398 K) under atmospheric pressure, and the equivalence ratios are from 0.5 to 2. Wang et al. [8,9] used the constant volume method to determine the laminar burning speed of the propene/CO₂/air mixture and the isobutane/CO₂/air mixture.

As mentioned earlier, most experiments used the constant pressure method to measure the laminar burning speed of propylene and air mixtures. The main limitation of this method is that the flame radii are very small, and the stretch rate is high, which affects values of burning speed. Therefore, the stretch effect cannot be neglected. Some extrapolating relations (linear, quasi-steady nonlinear, linear model based on curvature, nonlinear model in the expansion form) [10] were used to eliminate the stretch effect and predict the unstretched laminar burning speed. The extrapolation results may be wrong. Therefore, experiments should be done with very low stretch rates where it does not affect burning speed. Another limitation of this method is that for each experiment, only one laminar burning speed can be obtained, and it is hard to measure laminar burning speed at high temperatures and pressures. In the present work, the constant volume method was used to measure laminar burning speed. The flame radii were large, resulting in low stretch rates that did not affect the measurements. Moreover, for each experiment, a series of laminar burning speeds were measured along an isentrope. Thus, laminar burning speeds were measured for a broad range of temperatures and pressures.

For these experiments, propylene/CO₂/air mixtures were burned at an initial temperature of 298 K, 350 K, and 400 K, initial pressures of 0.5, 1, and 2 atm, equivalence ratio of 0.8, 1, and 1.2, and for different CO₂ concentrations of 0–60%. The purpose of this work is to add the range of measured burning speed of propylene/air/carbon dioxide. Measurements were only made for smooth and high radii spherical flames. Laminar burning speed of propylene, air, and carbon dioxide mixtures was measured over a broad range. Also, a power-law correlation has been developed to predict laminar burning speed for temperatures range of 298 K–500 K, pressure range of 0.5 atm–4.2 atm, equivalence ratios range of 0.8–1.2, and concentrations of CO₂ range of 0–60% in the unburned mixture.

The experimental setup is made up of cylindrical combustion chamber as shown in Fig. 1. The combustion chamber is composed of a cylindrical vessel and two pieces of cylindrical fused silica glass. Band heaters are equipped in the chamber to increase the gas temperature. The cylindrical vessel is made of 316 stainless steels, and the diameter and length of the cylindrical vessel are both 13.5 cm. The fused silica windows are secured in place by two stainless steel rings that apply pressure from both sides, enabling optical access within the chamber. The glass windows can sustain the maximum pressure of 50 atm. Flames were photographed using a high-speed camera in a Z-shaped Schlieren system. The camera can capture images at a rate of 10,000 frames/s. Furthermore, images are employed to investigate the stability and instability of flames and to monitor the flame's shape. The pressure–time data were measured and utilized for determining the laminar burning speed for smooth and spherical flames. Further information regarding the experimental facilities has been addressed in earlier publications [11–14].

The multishell thermodynamic model, developed by Metghalchi and Keck [15,16], was used to determine the laminar burning speed from measured pressure of the combustion process. This model was later improved to consider the impacts of radiative and conductive energy losses to the chamber walls and conductive energy loss to the spark electrodes and influence of wall boundary layers. Figure 2 shows an illustration of this model. The combustion chamber can be partitioned into burned and unburned parts. Several assumptions are made in this setting. First, the burned and unburned gases behave as ideal gas. In addition, it is assumed that the compression of both burned and unburned gases occurs isentropically during the combustion process. Finally, it is assumed that the burned and unburned regions are separated by a preheat zone and a reaction layer of negligible thickness. The burned gas region is divided into “n” number of shells. Each shell has a different temperature, and the burned gases inside each shell remain in local chemical equilibrium. The temperature of each shell in burned gases and the mass fraction of burned gases are calculated using experimental pressure rise data, by applying volume and energy equations. The burning speed was calculated after mass fraction of burned gases, and temperatures throughout the vessel have been calculated. Further details regarding the model can be found in Refs. [8,9,12,17–21].

For given pressure, $p(t)$⁠, Eqs. (9) and (10) are solved using the Newton–Raphson method to find the values of two unknowns: the temperature of the last shell of burned gases, $Tb(t)$⁠, and mass fraction, $xb(t)$⁠.

Computational laminar burning speed was also predicted by a 1D flame code from Cantera. Chemical kinetic mechanism AramcoMech 1.3 was used in the computational calculation, which contains 124 species and 766 reactions [22].

Laminar burning speed was calculated only when the flame was smooth and spherical. Pictures of flames were taken by high-speed camera with a speed of 10,000 flames/s to study flame stability. In addition, burning speeds were calculated for flame radii larger than 40 mm, resulting in a very low stretch rate.

Figure 3 shows flame pictures captured by the Schlieren system for different CO₂ concentrations for a constant flame radius of 63 mm. The initial temperature is 400 K, and the equivalence ratio is 1. Times at which the picture is taken are shown under each picture. The pictures indicate that the flame is smooth when the initial pressure is 0.5 or 1 atm, and it becomes cellular when the initial pressure is 2 atm. Also, when CO₂ concentration increases, it inhibits the flame cellularity.

Figure 4 shows the flame pictures captured by the Schlieren system for different equivalence ratios and different initial pressures. The initial temperature was 400 K, the concentration of CO₂ is 0%, and the flame radius was 63 mm for all cases. The pictures show that pressure has a negative influence on flame stability. Reported burning speed measurements are only for smooth and spherical flames.

Figure 5 presents the stretch rate as a function of normalized flame radius with respect to vessel radius. The initial condition for this experiment was at $pi=1atm,Ti=400K$⁠, $ϕ=0.8$⁠, and $D=20%$⁠. In this research, burning speeds have been reported only for flames with normalized radii of larger than 0.6 or radii of larger than 4 cm. In these instances, the maximum stretch rate is less than 115 s⁻¹, and it diminishes as the radius of the flame increases. The impact of the stretch rate on the burning speed at such extremely low values is insignificant as proven next.

To determine the effect of low stretch rate on burning speed, experiments were made to measure burning speed for different flames having the same temperature, pressure, equivalence ratio, and concentration of carbon dioxide while having different low stretch rates. Figure 6, which is a log-log plot of unburned gas temperature versus pressure, shows starts of unburned gases during four experiments. Experiment I have the initial condition of $Ti=298K$ and $pi=0.5atm$ and final condition of $Tf=389K$ and $pf=1.34atm$⁠, having stoichiometric mixture with zero carbon dioxide in the unburned gas mixture. All points on this experiment are on the line between two blue dots of the figure. Three other experiments were done with initial conditions of $Ti=315K,330K,345K$ and $pi=0.62atm,0.72atm,0.87atm$ and final condition of $Tf=396K,419K,441K$ and $pf=1.45atm,$$1.81atm,2.20atm$⁠. The states of these experiments are on the line between two triangle points (experiment II), two square points (experiment III), and two diamond points (experiment IV). Point A with a temperature of 380 K and a pressure of 1.28 atm in this figure is followed for all four experiments. The temperature and pressure are same in all experiments but with different radius and thus resulting in different stretch rates.

The same kind of experiments were done for mixtures having 20% and 40% CO₂ concentrations, and point B and C can be also selected using the same method. Figure 7 illustrates the relationship between laminar burning speeds and varying high flame radii and low stretch rates at point A, B, and C. The circular symbols (blue) denote the condition not having carbon dioxide (CO₂), a pressure of 1.28 atm, a temperature of 380 K, and an equivalence ratio of 1. The square symbols (red) represent the second condition characterized by a CO₂ concentration of 20%, pressure of 1.29 atm, temperature of 380 K, and equivalence ratio of 1. The triangle symbols (black) represent the third condition characterized by a CO₂ concentration of 40%, pressure of 1.30 atm, temperature of 380 K, and equivalence ratio of 1. This figure shows that the laminar burning speeds are almost the same while having different stretch rates. Thus, the stretch effects on laminar burning speed are insignificant for flame radii larger than 4 cm and stretch rate of less than 115 s⁻¹. This study only provides laminar burning speeds for flames that are smooth and spherical, and flame radii of larger than 4 cm and stretch of less than 115 s⁻¹.

As mentioned earlier, since the flames are smooth and spherical, laminar burning speed can be calculated. Based on different initial conditions, laminar burning speeds were measured for temperature range of 298 K–500 K, pressures between 0.5 and 4.2 atm, equivalence ratios ranging from 0.8 to 1.2, and CO₂ concentrations of 0%, 20%, 40%, and 60%.

The constants for power-law correlation are presented in Table 1. The coefficient of determination (R²) is 0.992 showing a very good fit. The constants in this table are only valid for temperatures of $298K<Tu<500K$⁠, pressures of $0.5atm<p<4.2atm$⁠, equivalence ratios of $0.8<ϕ<1.2$⁠, and CO₂ concentration of $0%<D<60%$⁠.

Figure 8 compares experimental laminar burning speed with previous research and computational results via AramcoMech 1.3 at temperature of 298 K, pressure of 1 atm, and equivalence ratio of 1. The solid curves are present work using the power-law correlations according to Eq. (15). The dash-dotted curve is the computational results from cantera. The dashed curves represent power-law correlation of Saeed's study [6]. The square symbols represent Princeton's [7] experimental results from Burke's paper, the diamond symbols represent Jomaas's [5] experimental results, and the triangle symbols represent Davis's [4] experimental results. It is worth mentioning that results of this study and results of the study by Jomaas et al. are closely aligned with the computational results for all the cases. However, results of the studies by Burke et al. and Davis et al. exhibit greater values than the computational laminar burning speeds, particularly under rich conditions, where they are 10% higher than the computational predictions.

Figures 9–11 show measured values, predicted by Eq. (15), and computational values of burning speed of C₃H₆/CO₂/air mixtures over a wide range of temperatures, pressures, fuel air equivalence ratios, and CO₂ concentration in the fuel. The circle symbols represent the measured data, while the square symbols represent the computational results. The solid curves are the results of the power-law correlations according to Eq. (15).

Figure 9 shows the laminar burning speed of C₃H₆/CO₂/air mixtures along three isentropes with varying equivalence ratio at an initial temperature of (a) 298 K, (b) 350 K, (c) 400 K, the initial pressure of 1 atm, and the CO₂ concentration of 0%. It can be seen that $ϕ=0.8$ case has the lowest laminar burning speed in those three cases. The laminar burning speeds of fuel–air mixtures with equivalence ratios of 1 and 1.2 exhibit minimal differences. The computational predictions closely align with the experimental results for all cases, validating the reaction mechanism for this range of operation.

Figure 10 illustrates the laminar burning speed of C₃H₆/CO₂/air mixtures along four isentropes with different concentrations of CO₂, initial pressure of $pi=1atm$⁠, equivalence ratio of 1.2, and initial temperature of (a) 298 K, (b) 350 K, and (c) 400 K. It can be seen that the laminar burning speed decreases as the CO₂ concentration increases. The computational predictions exhibit lower values by 3–5% compared to experimental results across all cases.

Figure 11 shows the laminar burning speed of C₃H₆/CO₂/air mixtures along three isentropes with different initial pressures, stoichiometric mixture, CO₂ concentrations of 20%, and initial temperature of (a) 298 K, (b) 350 K, and (c) 400 K. The data shown in this figure clearly demonstrate that the laminar burning speed reduces as the initial pressure increases. The computational burning speeds are 3 cm/s lower than the measured burning speeds, which are about 5% difference.

Figures 12–14 display the laminar burning speed of C₃H₆/CO₂/air mixtures along isentropes, covering a wide range of unburned gas temperatures and pressures. These figures also consider various concentrations of CO₂. Three separate experiments were conducted to obtain the complete results of the isentropic process. The initial temperatures and pressures for these tests conform to the isentropic relation.

Figure 12 displays the laminar burning speed of C₃H₆/CO₂/air mixtures along isentropes with an equivalence ratio of 1 and CO₂ concentrations of 0%. The initial temperature and pressure of these three experiments are 298 K, 0.5 atm, 345 K, 0.87 atm, and 373 K, 1.13 atm.

Figure 13 shows the laminar burning speed of C₃H₆/CO₂/air mixtures along an isentrope with an equivalence ratio of 1 and CO₂ concentrations of 20%. The initial temperature and pressure of these three experiments are 298 K, 0.5 atm, 345 K, 0.85 atm, and 373 K, 1.15 atm. Figure 14 displays the laminar burning speed of C₃H₆/CO₂/air mixtures along isentropes with an equivalence ratio of 1 and CO₂ concentrations of 40%.

Figure 15 compares power-law correlation of this study (using Eq. (15)) with power-law correlation of Saeed and Stone’s study [6] and computational predictions of laminar burning speeds for C₃H₆/air mixtures (D = 0) along isentropes for three different equivalence ratios at an initial temperature of 298 K and initial pressure of 0.5 atm. The solid curves represent power-law correlation of this study. The dashed curves represent power-law correlation of Saeed and Stone’s study. The square symbols represent the computational predictions. From the figure, it can be noted that at $ϕ=1$⁠, both experimental results of the study by Saeed and Stone and this study are close to the computational predictions, but at $ϕ=1.2$ and $ϕ=0.8$⁠, Saeed and Stone's experimental results are 10% higher or lower than the computational predictions and experimental results of this study. Also, it can be seen that the experimental values of the current studies are very close to those of computational results.

Figure 16 compares experimental power-law correlation with computational predictions of laminar burning speed for propylene/air/CO₂ as a function of pressure at CO₂ concentration of 20% and equivalence ratios of 1. The unburned temperature is 298 K and 400 K. This figure demonstrates a close agreement between computational predictions and experimental results at a temperature of 298 K, but the computational predictions are lower than the power-law correlation at a temperature of 400 K. Also, the gap between the two results increases as the pressure rises, wondering the effect of increasing the pressure on kinetics.

Figure 17 compares experimental power-law correlation with computational predictions of laminar burning speed for propylene/air/CO₂ as a function of CO₂ concentration at a pressure of 1 atm and equivalence ratios of 1. The unburned temperatures are 298 K and 400 K. The figure shows that the computational predictions are in good agreement with the experimental results at a temperature of 298 K, but the computational predictions are 2% lower than the power-law correlation at a temperature of 400 K. Also, the difference between computational predictions and experimental results diminishes as the concentration of CO₂ rises.

Figure 18 compares experimental power-law correlation with computational predictions of laminar burning speed for three different hydrocarbon refrigerants, propylene, propane, and isobutane, at a pressure of 1 atm and an unburned temperature of 350 K. The computational results of propane and propylene were predicted by AramcoMech 1.3, and the computational results of isobutane were predicted by USC Mech II model [24]. The power-law correlation data for propane and isobutane are obtained from Wang et al. [8,9]. The figures show that laminar burning speed of propylene is almost the same as those of propane, but they are higher than the burning speed of isobutane.

In this study, laminar burning speed of propylene/CO₂/air mixtures has been measured for a temperature range of 298 K–500 K, pressure range of 0.5–4.2 atm, equivalence ratio range of 0.8–1.2, and CO₂ concentration range of 0–60% based on the different initial conditions. Measurements were done only for smooth and spherical flames having radii of larger than 4 cm with a negligible effect of stretch rate on burning speed measurements. Measured data were fit into a power-law correlation. The following conclusions were reached:

1. Propylene/air/carbon dioxide flames become cellular at about 4.2 atm pressure.

2. Addition of carbon dioxide in the unburned mixture reduces the tendency for flame to become cellular.

3. For flame radii of larger than 4 cm, the stretch effects on laminar burning speed can be negligible.

4. Increasing unburned gas temperature increases burning speed of propylene/air/carbon dioxide mixtures.

5. Increasing pressure of the mixture reduces burning speed of propylene/air/carbon dioxide mixtures.

6. Increasing concentration of carbon dioxide reduces burning speed.

7. Burning speed of propylene/air/carbon dioxide peaks about fuel/air equivalence ratio of about 1.1.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$a$ =

fitted constant

$b$ =

fitted constant

$c$ =

fitted constant

$d$ =

fitted constant

$e$ =

fitted constant

$m$ =

total mass

$p$ =

mixture pressure

$r$ =

flame radius

$t$ =

time

$D$ =

carbon dioxide mole fraction

$E$ =

standard uncertainty

$R$ =

specific gas constant

$T$ =

temperature

$V$ =

energy source volume

$cp$ =

specific heat of constant pressure

$cv$ =

specific heat of constant volume

$eb$ =

burned gas specific energy

$ebs$ =

isentropically compressed burned gas specific energy

$eu$ =

unburned gas specific energy

$eus$ =

isentropically compressed unburned gas specific energy

$mb$ =

burned gas mass

$m˙b$ =

mass burning rate

$mu$ =

unburned gas mass

$p0$ =

reference pressure

$pi$ =

initial pressure

$re$ =

electrode radius

$vb$ =

burned gas specific volume

$vbs$ =

isentropically compressed burned gas specific volume

$vu$ =

unburned gas specific volume

$vus$ =

isentropically compressed unburned gas specific volume

$xb$ =

burned gas mass fraction

$x˙b$ =

rate of burned gas mass fraction

$Ab$ =

burned gas area

$Eb$ =

burned gas energy

$Eeb$ =

electrodes boundary energy defect

$Ei$ =

initial energy

$Eph$ =

preheat zone energy defect

$Eu$ =

unburned gas energy

$Ewb$ =

wall boundary energy defect

$Qe$ =

energy loss to electrodes

$Qr$ =

radiation energy loss

$Qw$ =

energy loss to wall

$Su$ =

laminar burning speed

$Su0$ =

reference laminar burning speed

$Tb$ =

burned gas temperature

$Tbs$ =

isentropically compressed burned gas temperature

$Tf$ =

final temperature

$Ti$ =

initial temperature

$Tu$ =

unburned gas temperature

$Tus$ =

isentropically compressed unburned gas temperature

$Tu0$ =

reference temperature

$Tw$ =

chamber wall temperature

$Vb$ =

burned gas volume

$Vc$ =

chamber volume

$Ve$ =

electrodes volume

$Veb$ =

electrodes boundary displacement volume

$Vi$ =

initial volume

$Vph$ =

preheat zone displacement volume

$Vu$ =

unburned gas volume

$Vwb$ =

wall boundary displacement volume

$α0$ =

fitted constant

$α1$ =

fitted constant

$αp$ =

Planck mean absorption coefficient

$β0$ =

fitted constant

$β1$ =

fitted constant

$κ$ =

stretch rate

$σ$ =

Stefan–Boltzmann constant

$ϕ$ =

equivalence ratio