Development of a fan-stirred constant volume combustion chamber and turbulence measurement with PIV

Abstract

A fan-stirred combustion chamber is deve-loped for spherically expanding flames, with P and T up to 10 bar and 473 K, respectively. Turbulence characteristics are estimated using particle image velocimetry (PIV) at different initial pressures (P = 0.5–5 bar), fan frequencies (ω = 0–2000 r/min), and impeller diameters (D = 100 and 114 mm). The flame propagation of methanol/air is investigated at different turbulence intensities (u′=0–1.77 m/s) and equivalence ratios (φ = 0.7–1.5). The results show that u′ is independent of P and proportional to ω, which can be up to 3.5 m/s at 2000 r/min. L_T is independent of P and performs a power regression with ω approximately. The turbulent field is homogeneous and isotropic in the central region of the chamber while the inertial subrange of spatial energy spectrum is more collapsed to –5/3 law at a high Re_T. Compared to laminar expanding flames, the morpho-logy of turbulent expanding flames is wrinkled and the wrinkles will be finer with the growth of turbulence intensity, consistent with the decline of the Taylor scale and the Kolmogorov scale. The determined S_L in the present study is in good agreement with that of previous literature. The S_L and S_T of methanol/air have a non-monotonic trend with φ while peak S_T is shifted to the richer side compared to S_L. This indicates that the newly built turbulent combustion chamber is reliable for further experimental study.

Graphical abstract

Keywords

fan-stirred combustion chamber / turbulence characteristics / particle image velocimetry (PIV) / methanol / turbulent expanding flames

1 Introduction

In practical engine applications, the combustion process usually occurs at an intense turbulence which is coupled by the complex interactions between fluid dynamics, thermodynamics, and chemical reactions. To investigate these complex interactions and clarify these factors separately, many experimental apparatuses have been developed such as Bunsen burner [1–5] and the combustion chamber [6–9]. For Bunsen burner and other jet flames, it is easier to measure the species and temperature with advanced laser diagnostics. The problem is that high mean flow velocity is required to achieve a strong turbulence and to stabilize high laminar burning velocity flames. In addition, it is difficult to control the uniform turbulent field because the downstream can be decayed by the boundary layer of burner wall. Comparatively, the fan-stirred turbulent combustion chamber is advantageous because it is easier to achieve a strong turbulence by adjusting fan frequency. Besides, the uniformity of turbulent field is better in the central region due to the elimination of boundary layer. Moreover, it can achieve high initial pressures at a low cost and can reduce fuel consumption [10].

Since the turbulent field is generated by rotation of fans in combustion chamber, it is necessary to estimate turbulence characteristics, especially turbulence intensity and integral length scale, which are usually the two most important parameters to characterize a turbulent field. Turbulent field contains a variety of vortexes, which are in a broad range of temporal and spatial scales. Based on this, it is essential to characterize the turbulent field by means of spatial spectral analysis. At the same time, the ideal turbulent field for combustion chamber is homogeneous and isotropic (HIT). The homogeneous and isotropic turbulence is considered as the simplest form of turbulence and is often used as the benchmark to study the physical nature of turbulence. Under HIT conditions, the inherently random characteristics of a practical turbulent field can be simplified, leading to an easier understanding of the fluid dynamics of turbulent combustion [11]. Thus, it is also necessary to test the homogeneity and isotropy of the turbulent field.

Up to the present, the diagnostic technique usually used for turbulent field has been hot wire anemometry (HWA), laser Doppler velocimetry (LDV), and particle image velocimetry (PIV). The first two techniques are for single point measurement while the last one can measure the instantaneous velocity of 2D fields. Although HWA is generally used for turbulence measurement due to its convenience and high temporal resolution, it cannot be applied in experimental devices with no mean flow, which is usually the case in the fan-stirred combustion chamber. Therefore, the turbulent field in the combustion chamber is commonly investigated by using LDV or PIV. Table 1 is an overview of the turbulence characterization in fan-stirred combustion chamber, in which the dash indicates that the data are not provided in the literatures. The effects of diagnostic techniques and initial conditions such as pressure and temperature have been extensively investigated. Sick et al. [12] investigated the turbulence scale at ambient temperature and pressure using PIV and found that turbulence intensity had a linear relationship with rotational fan frequency. Weiß et al. [13] compared the turbulence characteristics at ambient temperature and pressure between PIV and LDV, and found that turbulence fluctuations determined by PIV were up to 30% smaller than that determined by LDV. Galmiche et al. [14] measured the turbulence statistics by utilizing standard PIV, time-resolved PIV, and LDV in a wide temperature (300–473 K) and pressure (1–10 bar) range, and found that gas temperature and pressure had no significant effect on integral length scale, but the evolutions of RMS velocity fluctuations were related to the ratio between gas kinetic viscosity and square of Taylor microscale. Xu et al. [15] extended the initial pressures up to 30 bar, measured three sheet scales to overcome the limitation of 2D-PIV, and found that turbulence intensity was still independent of pressure but positively proportional to fan frequency. In addition, the impeller was redesigned and the numerical simulation was also introduced to investigate the turbulent field. Ravi et al. [16] studied the effects of impeller geometric features on turbulence statistics and established the mechanism to independently vary the intensity level and integral length scale, where turbulence intensity was dependent on fan frequency and integral length scale was decreased with blade pitch angle. Ge et al. [10] evaluated two calculation models by measuring the flow motion driven by two fans, and found the body force model was more reasonable than the sliding mesh model for the combustion chamber. Except for cold flow field, Chaudhuri et al. [17] achieved a simultaneous measurement of flame location and turbulent field using high speed PIV, and quantified flame-turbulence interaction in a centrally ignited constant pressure combustion chamber.

The above review indicates that the maximum turbulence intensity of most combustion chambers is in the range of 1.5–4 m/s and achieved by a high fan frequency, which would increase the electric motor load and experimental risk. Therefore, there is a need to design a safer combustion chamber which could obtain the same turbulence intensity at a lower rotational speed. Besides, the effects of high pressure, high temperature, impeller number, and blade pitch angle on turbulence characteristics have been studied, while the effects of sub-atmospheric pressure and impeller size has not been investigated yet. It is known that the sub-atmospheric pressure condition is also important and usually appears in practical engines, such as aircraft engine in high altitude. And the impeller size is another important geometric parameter of impeller which may have a significant effect on turbulent field.

On the other hand, many studies have been conducted on turbulent expanding flames, which mainly concentrated on gas fuels, such as hydrogen [21–24], methane [25,26], syngas [27,28] and ammonia [29,30]. However, due to the complexity of heating system and experimental procedure, there are only a few work concentrated on liquid fuels [31–38]. Besides, most of these studies are about iso-octane [34–37] while much less studies are about alcohols [31–33], which, as an alternative or additive to gasoline and diesel, are very important due to its potential of less emission and independence of fossil fuel. Especially for methanol, it has been advanced as a most promising alternative and used both as blending component and pure fuel in methanol engines. Thus, more fundamental investigations of methanol/air turbulent flame propagation are necessary for its further applications.

The objective of this study is to report a high-pressure high-temperature fan-stirred combustion chamber and investigate the methanol/air turbulent expanding flames. To provide a reference, a systematic measurement and analysis of turbulence characteristics has been conducted for the combustion chamber, including turbulence intensity, integral length scale, homogeneity, isotropy, and spatial energy spectrum. Moreover, the effects of pressures, impeller sizes, and fan frequency on turbulence characteristics are also investigated. Furthermore, to validate this newly built apparatus, the laminar and turbulent flame propagations of methanol/air mixture are captured in a wide range of conditions. The morphology and burning velocity of methanol/air mixture are determined and the effects of turbulence intensity and equivalence ratio are analyzed in detail.

2 Experimental apparatus and methods

2.1 Fan-stirred combustion chamber

The schematic of the newly built fan-stirred combustion chamber is demonstrated in Fig. 1(a). The volume of the chamber is 22.6 L, with a 305 mm inner diameter and a 310 mm inner length. Two quartz windows with a diameter of 150 mm are equipped on each side of the chamber for optical access. Four fans are mounted in diagonal positions which are coupled to electric motors (whose maximum speed can reach up to 10000 r/min with a precision of ±10 r/min) with independent frequency controllers. Two electrodes of 1 mm in diameter are located on the chamber wall symmetrically and used for the ignition of gas mixture. The ignition energy is supplied by a high-tension coil of about 10000 V and the charge duration can be adjusted between 1 and 99 ms. A heating wall is embedded in the chamber to heat the gas mixture to the target temperature, which is monitored by an Omega thermocouple and the temperature uncertainty can be controlled in ±2°C. Two pressure transmitters are mounted on the chamber, one for monitoring introduced gas pressure (Rosemount), and the other for measuring transient explosion pressure (Kistler 6125C).

It is worth pointing out that the turbulent chamber is a high-pressure high-temperature vessel, whose initial pressure and temperature can reach up to 10 bar and 473 K, respectively. Due to the large inner diameter and optical window, a wider flame radius range (about 10–45 mm) can be used for obtaining target parameters, such as turbulent burning velocity, thus reducing the experimental uncertainty from ignition process and chamber confinement. Except for high pressures, the spherically expanding flames can also be measured at sub-atmospheric pressure because of its good vacuum and high-energy ignition system.

Besides, there is also a heating tank connected with the turbulent combustion chamber mainly for conducting the experiments of liquid fuels. The tank and connected tubes will be heated to the same target temperature with the chamber, and the liquid fuel will be injected into the tank and vapored. After that, the vapored fuel will be introduced into the chamber. In this way, it can make sure that the liquid fuels introduced into chamber have been vaporized. Additionally, the gases such as gas fuel, oxygen, and nitrogen will come from gas cylinder and be introduced into the chamber directly through the precision pin valve.

2.2 PIV system

The schematic of PIV system is exhibited in Fig. 1(b), which mainly consists of a dual-head Nd:YAG laser and a CCD camera. The wavelength of the laser is 532 nm and the energy is 100 mJ/pulse, with a duration shorter than 10 ns. The initial laser beam is about 10 mm, coming into the chamber through a hole where the electrode is located preciously, and is then transferred into a 1.0 mm thin fan-shaped sheet using a cylindrical concave lens. In the present study, the field of view (FOV) is rectangular with an area of 80 mm× 50 mm, which is large enough for the measurement of turbulent burning velocity. Prior to the estimation of turbulence characteristics, a calibration is placed at the center of the FOV, allowing the laser sheet to be aligned with the center plane of the chamber and in parallel with the camera image plane. The digital resolution is approximately 21 pixels/mm estimated from the calibration plate.

Olive oil is used as the seeding particle with a diameter of about 1.0 μm, which is produced by a particle generator and carried into the chamber by nitrogen. When the particles have reached a quasi-stationary state, the fans will be activated about 30 s, and then the data acquisition process will be initiated, with a frequency of 10 Hz. For each condition, seven sets of 80 image pairs have been obtained and a total of 560 image pairs have been collected, which are enough for an accurate estimation of the turbulent field. The velocity vector fields are processed through a cross-correlation of particle images using the Davis 7.2 software. The interrogation window is fixed at 16 × 16 pixels and the final vector spacing is 0.76 mm, resulting in 107 × 66 vector grids in FOV.

2.3 Experimental conditions

The experimental conditions of turbulence characterization are listed in Table 2. To investigate the effects of impeller size, two impellers are chosen for turbulence characterization with a diameter of 114 and 100 mm, respectively. Keeping the initial temperature at 298 K, the initial pressure is varied from 0.5 to 5 bar to cover a sub-atmosphere range. The fan frequency is increased from 500 to 2000 r/min to create different turbulence intensities. Besides, the turbulent expanding flames of methanol/air mixtures are investigated at different turbulence intensities and equivalence ratios, which are presented in Table 3. The initial temperature is heated to 353 K to make sure that the methanol has been vapored completely. Three loops are conducted for laminar conditions while five loops are repeated for turbulent conditions because of its larger random and scatter.

3 Results and discussion

3.1 Mean velocity and turbulence intensity

The original data of PIV measurement are the velocity vector fields in different image pairs. The average velocity components \overline{u}(x,y) and \overline{v}(x,y) in the two orthogonal directions (x,y) can be determined as

\overline{u}(x,y)={\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{j=\mathrm{1}}^n{u}_j(x,y)},

(1)\overline{v}(x,y)={\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{j=\mathrm{1}}^n{v}_j(x,y)},

where n is the number of image pairs and equal to 560 in the present work.

The total velocity is evaluated by

(2)\overline{U}(x,y)=\sqrt{\overline{u}{(x,y)}^{\mathrm{2}}+\overline{v}{(x,y)}^{\mathrm{2}}}.

The root mean square (RMS) of velocity fluctuation is determined by

u_{\mathrm{RMS}}(x,y)=\sqrt{{\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{j=\mathrm{1}}^n{u}_{\mathrm{f}}{(x,y,t)}^{\mathrm{2}}}},

(3)v_{\mathrm{RMS}}(x,y)=\sqrt{{\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{j=\mathrm{1}}^n{v}_{\mathrm{f}}{(x,y,t)}^{\mathrm{2}}}},

where u_{\mathrm{f}}(x,y,t)=u(x,y,t)-\overline{u}(x,y) and v_{\mathrm{f}}(x,y,t)=v(x,y,t)-\overline{v}(x,y) is the velocity fluctuation in x direction and y direction, respectively.

The single point turbulence intensity is defined as

(4)u\text{'}(x,y)=\sqrt{{\displaystyle \frac{u_{\mathrm{RMS}}{(x,y)}^{\mathrm{2}}+v_{\mathrm{RMS}}{(x,y)}^{\mathrm{2}}}{\mathrm{2}}}}.

To assess the distribution of the mean velocity and turbulence intensity directly, the maps of mean velocity and turbulence intensity field at d = 114 mm, P = 1.0 bar, and ω = 1000 r/min are shown in Fig. 2 which indicates that the mean velocity in the diagonal region is lower than that in other regions, due to the fact that the four fans are equipped in this region and the gas is affected by a balance force at this location. On the contrary, the gas far away from the diagonal region is not balanced by a pair of opposite forces and the mean velocity is a little higher. For the turbulence intensity field, it performs an approximate circular stratified distribution and the turbulence intensity is increased from the center to the outside. It is easy to understand this because the location outside is closer to the fans, thus obtains a stronger turbulence intensity. Besides, due to the circular distribution of the turbulent field, it can be inferred that the four fans are very uniform and perform at the same rotational speed. It is worth noting that the results in all conditions nearly have the same distribution as those in this example.

A spatial average is conducted on the turbulent field and the total turbulence intensity can be obtained under different conditions, as displayed in Table 4 and Fig. 3. The turbulence intensity is proportional to the fan frequency which is consistent with Refs. [12,15,16]. It is worth pointing out that the turbulence intensity is independent of the initial pressure not only under high pressure conditions [15], but also under the sub-atmospheric pressure condition in the present study. The maximum value of the turbulence intensity can reach up to 3.5 m/s, which is roughly equivalent to that of others [13,16]. However, it corresponds to a lower fan frequency of 2000 r/min, suggesting that the newly developed turbulent combustion chamber is much safer for experiment. Comparing Figs. 3(a) and 3(b), it is found that the turbulence intensity of the two impellers is almost identical, but this does not mean that the turbulence intensity is not affected by the impeller size. As is known, a larger impeller will produce a higher linear velocity at the same frequency, which can lead to a more intense turbulence intensity. In the authors’ opinion, the difference in impeller size (114 mm and 100 mm) is not enough. The inadequate difference cannot cause an evident turbulence intensity discrepancy and will be covered up by the uncertainty of experiments and post-processing. In fact, the turbulence intensity of a large impeller is slightly higher than that of a small impeller, which can be judged by the slope of fitting lines.

3.2 Integral length scale

Integral length scale is another important parameter for turbulence characterization, which physically represents the mean size of large eddies in a turbulent flow. Concerning the evaluation of integral length scale, a few methods have been proposed in Refs. [18,39]. In consideration of the spatial advantages of PIV, integral length scale is determined by integrating the fluctuation velocity correlation coefficient obtained as a function of the distance between two points,

(5)L_{\mathrm{u}x}={\displaystyle {\int }_{\mathrm{0}}^{\infty }{R}_{\mathrm{uu}}(\mathrm{\Delta }x,\mathrm{0})}\mathrm{d}\left(\mathrm{\Delta }x\right),

(6)R_{\mathrm{uu}}\left(\mathrm{\Delta }x\right)={\displaystyle \frac{\langle u_{\mathrm{f}}(x,y,t)u_{\mathrm{f}}(x+\mathrm{\Delta }x,y,t)\rangle }{u_{\mathrm{f}}^{\text{'}}{\left(t\right)}^{\mathrm{2}}}},

where L_{\mathrm{u}x} is the longitudinal integral length scale in the x direction, R_{\mathrm{uu}}\left(\mathrm{\Delta }x\right) is the fluctuation velocity correlation coefficient, and u_{\mathrm{f}}^{\text{'}}\left(t\right) is the RMS of fluctuation velocity in the whole spatial field at a given moment. Equations (5) and (6) give the expressions for the evaluation of the longitudinal integral length scale in x direction, and the integral length scale in other directions can be estimated in a similar method. Figure 4 depicts the four correlations of fluctuating velocities for a large impeller at P = 1.0 bar and ω = 1000 r/min. It can be observed that with the increase of spatial lag, the correlation coefficients will decrease gradually. They will reduce to zero at a critical distance where the two points are no longer related to each other. It should be mentioned that the lateral correlation coefficients can reduce to zero in the range of FOV, thus the corresponding integral length scale are evaluated directly through an integration of them. However, for the longitudinal correlation coefficients, their values will perform an evident fluctuation and even have an increasing trend at a large spatial lag, which is evidently contrary to common sense in physics. Thus, a decaying exponential fitting has been applied to the points within the 40 mm spatial lag, and the integral length scale is evaluated by integrating the fitting function.

Figure 5 shows the results of integral length scale under different conditions. It can be observed that integral length scale is not affected by pressure even in sub-atmosphere, but increases with fan frequency and approximately performs a power law relationship, which is consistent to that of Refs. [20,40]. However, there are also many studies indicating that integral length scale is not affected by fan frequency, such as Bradley et al. [33], Weiß et al. [13] and Galmiche et al. [14]. In the authors’ opinion, there is no contradiction between these results. In the present study, the maximum fan frequency is 2000 r/min, which is far lower than others. As a result, the power law between integral length scale and fan frequency is evident. But when fan frequency is very high, just like the conditions of other studies, the variation between integral length scale and fan frequency is negligible. Besides, the results of Xu et al. [15] also indicate that integral length scale is increased with fan frequency when it is lower than 2000 r/min. In fact, when fan frequency is zero, the integral length scale is also zero. Thus, it can be inferred that integral length must vary with fan frequency. At the same time, the longitudinal integral length scale is not equal to lateral integral length scale, but about twice of it. According to the relative theory, the lateral integral length scale is just half of the longitudinal integral length scale in isotropic turbulence [41], thus, to some extent, the present experiment reflects the isotropy of turbulent field. Comparing the integral length scale of a large and a small impeller, it can be found that the integral length scale of a large impeller is apparently higher than that of a small impeller, although the turbulence intensity of both of them are nearly identical to each other. This indicates that integral length scale is not only affected by blade pitch angle [16], but also very sensitive to impeller size. By using different impellers, the integral length scales can be controlled independent of turbulence intensity, thus the effects of integral length scale can be studied separately.

Turbulent flows are characterized by many length scales. Besides the integral length scale representing the large eddy size, the Taylor and Kolmogorov length scale are also two important parameters, which represent the intermediate length scale and smallest length scale, respectively. Especially, the Kolmogorov length scale is representative of the dimension at which the dissipation of turbulent kinetic energy to fluid internal energy occurs and kinetic viscosity is significant. According to the theoretical derivation [42], the Taylor length scale λ and the Kolmogorov length scaleη can be evaluated by

(7){\displaystyle \frac{\lambda }{L_{\mathrm{T}}}}\sim \sqrt{{\displaystyle \frac{\mathrm{15}}{R{e}_{\mathrm{T}}}}},

(8){{\displaystyle \frac{\eta }{L}}}_{\mathrm{T}}\sim R{e}_{\mathrm{T}}^{-\mathrm{3}/\mathrm{4}},

where L_T is the integral length scale, Re_T is the turbulent Reynolds number and defined by R{e}_{\mathrm{T}}={\displaystyle \frac{u^{\text{'}}{L}_{\mathrm{T}}}{\nu }}, and \nu is the kinetic viscosity. As shown in Fig. 6, both the Taylor length scale and the Kolmogorov length scale are decreased with pressure and fan frequency. The kinetic viscosity is reduced with pressure, while the turbulence intensity is increased with fan frequency. Both of these will increase the turbulent Reynolds number. According to Eqs. (7) and (8), the Taylor length scale and the Kolmogorov length scale are inversely related to the turbulent Reynolds number, thus will have a downward trend as well.

3.3 Homogeneity and isotropy

Another feature of the ideal turbulent field in the turbulent combustion chamber is homogeneity and isotropy. The homogeneity ratio is introduced here to estimate the homogeneity, which is defined as the ratio of local RMS velocity to the spatially averaged RMS velocity in the same direction,

H_{\mathrm{u}}={\displaystyle \frac{u_{\mathrm{RMS}}(x,y)}{\overline{u_{\mathrm{RMS}}}}},

(9)H_{\mathrm{v}}={\displaystyle \frac{v_{\mathrm{RMS}}(x,y)}{\overline{v_{\mathrm{RMS}}}}},

where H_u, H_v is the homogeneity ratio in the x and y direction, respectively.

Similar to homogeneity, the isotropy ratio is used to estimate the isotropy of the turbulent field and is defined as the ratio of local RMS velocities in two vertically crossed directions,

(10)I={\displaystyle \frac{u_{\mathrm{RMS}}(x,y)}{v_{\mathrm{RMS}}(x,y)}},

where I is the isotropy ratio.

Figure 7 is the homogeneity and isotropy of turbulent field for the baseline condition (large impeller, P = 1.0 bar, ω = 1000 r/min), and the similar results can be obtained for other conditions. It can be seen that the homogeneity appears to have a nearly circular distribution from the center to the outside, which is similar to the distribution of the turbulence intensity. The homogeneity ratio is about 1.0 in the central region of the turbulent field, which indicates a good homogeneity in this zone. Although the maximum value of homogeneity can be up to 1.8, it occurs only on a very few points close to the fans, where there is a larger RMS velocity. Moreover, this zone will not be used for the determination of the turbulent burning velocity. As for the isotropy, the right side of the FOV is better than that of the left side, and the maximum value of the isotropy ratio in the whole FOV is no more than 1.3, indicating that the turbulent filed can be considered as isotropy. The analysis based on the maps of homogeneity and isotropy is qualitative, and in order to quantitatively conduct a more detailed analysis, the histograms and cumulative distribution functions (CDFs) are also derived, as shown in Fig. 8. It can be seen that most homogeneity ratios are in the range of 0.8–1.2, indicating that the spatial uniformity of the whole FOV is reasonable, although very few extreme points exist near the fans. At the same time, the majority of isotropy ratios are in the range of 0.9–1.1, reflecting that the current turbulent field is isotropic.

3.4 Spatial energy spectrum

To estimate the turbulent kinetic energy distribution of different scale eddies in the turbulent field, one-dimensional spatial energy spectrum has been calculated using the method of discrete Fourier transform in space [43],

(11)E_{ii}({\kappa }_i,y,t)={\displaystyle \frac{L}{\mathrm{2}\mathrm{\pi }{N}^{\mathrm{2}}}}{\displaystyle \sum _n{F}_i({\kappa }_i,y,t)}{F}_i^{\ast }({\kappa }_i,y),

(12)F_i({\kappa }_i,y,t)={\displaystyle \sum _n{u}_{\mathrm{f}}(x_n,y,t)}\exp (-j{\kappa }_i{x}_n),

where E_{ii}\left({\kappa }_i,y,t\right) is the longitudinal energy density in the x direction, F_i\left({\kappa }_i,y,t\right) is the discrete Fourier transform function, L is the domain length, and N is the points number. It should be mentioned that \kappa is the wavenumber which can be calculated by \kappa \mathrm{=}{\displaystyle \frac{\mathrm{2}\mathrm{\pi }}{L}}\cdot n, n=\mathrm{1},\mathrm{2},\mathrm{...},N, which is similar to the frequency in time Fourier transform. Equations (11) and (12) are the expressions of the energy density in the x-direction while the energy density in the y-direction can be evaluated by utilizing a similar expression. Figure 9 is the spatial energy spectrum at different turbulent Reynolds numbers. The smallest wavenumber corresponds to the domain length of FOV, while the largest wavenumber is the cutoff wavenumber which is estimated as {\kappa }_{\mathrm{c}}=\mathrm{2.8}/\mathrm{\Delta }, where \mathrm{\Delta } is the interrogation size. It can be seen that the turbulent kinetic energy is deduced with the smaller eddy size. When the wavenumber is small and medium, there is a linear region denoted as the inertial subrange. But with the wavenumber increasing over a critical value, a rapid decline range appears, which is called the viscous dissipation range. According to the Kolmogorov theory [41], in every flow at a sufficiently high Reynolds number, the inertial range of energy spectrum conforms to the –5/3 law. From Figs. 9(a) and 9(b), it can be noticed that when the turbulent Reynolds number is about 500 and 1250, the inertial range does not correspond to the –5/3 reference line very well, indicating that the Reynolds number is not high enough at this time. With the turbulent Reynolds number increasing, the inertial range approaches to the –5/3 reference line, which is shown in Figs. 9(c) and 9(d). Especially when the turbulent Reynolds number is about 12500, it performs a good correspondence to the –5/3 law. Thus, the current experiment results effectively demonstrate the Kolmogorov theory. Further, for an ideal isotropic turbulent field, there is a relationship between the lateral and the longitudinal spectrum,

(13)E_{ii}\left({\kappa }_i\right)={\displaystyle \frac{\mathrm{3}}{\mathrm{4}}}{E}_{jj}\left({\kappa }_i\right),

where E_{ii}\left({\kappa }_i\right), E_{jj}\left({\kappa }_i\right) is the longitudinal and lateral energy density, respectively.

The longitudinal energy density and the 3/4 lateral energy density is plotted together in Fig. 9. A satisfaction coincidence can be observed, which indicates again that the current turbulent field can be considered as isotropy.

3.5 Spherically expanding flames of methanol/air mixtures

To validate the reliability of the current turbulent combustion chamber, the spherically expanding flames of methanol/air mixtures are investigated in a wide range of conditions. Figure 10 shows the shadow pictures of methanol/air flames at φ = 1.0 and P = 1 bar. Under the laminar condition, the flame surface nearly stays smooth in the observation domain, due to the lack of flame intrinsic instability. Besides, the tiny cracks on the surface are mainly caused by the disturbance of ignition. However, under turbulent conditions, the flame surface does not stay smooth anymore and plenty of wrinkles appear on the surface, which are caused by the stretch of turbulence vortexes. With the growth of turbulence intensity, the wrinkles on the flame surface become more refined, which is consistent with the decline of the Taylor scale and the Kolmogorov scale. Because of the randomness of the turbulence, the morphology of turbulent expanding flames is not as regular as that under the laminar condition, sometimes even skewness occurs. However, the direction of skewness is irregular, indicating the uniformity of turbulent field.

Figure 11 is the flame propagation velocity of methanol/air mixtures at different turbulence intensities and equivalence ratios. With the turbulence intensity increasing, the stretch of turbulence vortex is strengthened, leading to a larger propagation velocity. In addition, the scatter of data becomes larger with the turbulence intensity, mainly due to the randomness of the turbulence itself. At a fixed turbulence intensity of 1.77 m/s, the flame propagation velocity appears to be a non-monotonic variation with the equivalence ratio, whose peak value corresponds to the equivalence ratio of about 1.3. It should be mentioned that, the flame propagation velocity of turbulent expanding flames is always increased with flame radius, demonstrating a self-similar acceleration phenomenon. Moreover, with the growth of the turbulence intensity, the acceleration is strengthened correspondingly. Different from laminar expanding flames, the acceleration of turbulent expanding flames is induced by the coupling effect of turbulence stretch and flame intrinsic instability. Thus, the propagation of turbulent expanding flames does not appear to be distinguished stages just like that under the laminar condition, but follows a self-similar acceleration in the observation domain.

Figure 12 is the laminar and turbulent burning velocity of methanol/air flames corresponding to unburned gas, while the error bar is the standard deviation of many loops. The error bar of laminar burning velocity is also calculated but it is too small to be covered by the experimental points. Laminar burning velocity is nonlinear extrapolated by {\displaystyle \frac{\mathrm{d}R}{\mathrm{d}t}}-\kappacurves according to the study of Kelley and Law [44]. Due to the acceleration of turbulent expanding flames, it is difficult to determine the specific value of turbulent burning velocity. Therefore, various methods have been proposed [25,35,38]. In the present study, turbulent burning velocity is obtained by an average of the flame propagation speed in the radius range of 10–45 mm and then divided by the thermal expansion ratio. According to the study of Bradley et al. [33], the turbulent burning velocity obtained by shadow method approximately corresponds to the progress variable \overline{c}\approx \mathrm{0.1}. As shown in Fig. 12(a), it is more evident that the laminar and turbulent burning velocity displays a non-monotonic trend with the equivalence ratio. Although all peak values of burning velocity correspond to equivalence ratios between 1.2 and 1.3, it can still be noticed that it gradually shifts to the richer side with the turbulence intensity increasing. In other words, furl-rich turbulent burning velocities somewhat do not follow the trend expected on the basis of laminar burning velocity. The interpretation of this phenomenon can be referred to Lawes et al. [32]. On the other hand, the laminar burning velocities in this study are compared with the results of Veloo et al. [45], and the latter is at the temperature of 343 K, which is a little lower than the present study. Considering the uncertainty in experiments, the experimental data in the present study are in good agreement with the results in literature, indicating that the newly built combustion chamber is reliable and can be used for further investigation. Figure 12(b) shows the normalized turbulent burning velocity at different equivalence ratios and turbulence intensities. It appears that the ratio of S_T/S_L is the largest in the fuel leanest condition, and after that it declines with the equivalence ratio. Until φ = 1.2, S_T/S_L declines to the lowest value and then gradually increases with the equivalence ratio. This may be related to the Karlorvitz number, which reflects the effects of the turbulence stretch. Even so, a further interpretation is still needed to clarify this interesting phenomenon.

4 Conclusions

A fan-stirred constant volume combustion chamber is developed for further study of turbulent flame propagation, whose initial pressure and temperature can reach up to 10 bar and 473 K, respectively. The turbulence characteristics of the combustion chamber have been systematically measured and estimated by PIV. Besides, the reliability of the new combustion chamber and turbulence characteristics have been validated by methanol/air expanding flames.

Specifically, turbulence intensity is proportional to the fan frequency but independent of the initial pressure, and can reach up to 3.5 m/s at 2000 r/min. The integral length scale is increased with fan frequency and sensitive to impeller size, while not affected by initial pressure. Most homogeneity ratios are in the range of 0.8–1.2, revealing that the turbulent field is homogeneous. Most isotropy ratios are between 0.9 and 1.1, which reflects a reasonable isotropy of the turbulent field. The turbulent kinetic energy is reduced with smaller eddies, and the inertial range corresponds very well to the –5/3 law at a high turbulent Reynolds number, validating the Kolmogorov theory. A 3/4 relationship is obtained between the lateral and the longitudinal energy density, which also indicates a reasonable isotropy of the turbulent field.

The morphology of turbulent methanol/air expanding flames is wrinkled by the stretch of the turbulence, and the wrinkles become more refined with the growth of the turbulence intensity, which is consistent with the decline of the Taylor scale and the Kolmogorov scale. Turbulent expanding flames follow a self-similar acceleration propagation in the observation domain. The turbulent burning velocity of methanol/air flames is increased with the turbulence intensity, while appears to be a non-monotonic trend with the equivalence ratio. In addition, the laminar burning velocity in the present study appears to have a good agreement with the results in literature. All above indicate that the newly developed combustion chamber and turbulence characteristics are reliable. Based on these, more subsequent studies of turbulent flame propagation can be conducted in the future.

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