Elsevier

Combustion and Flame

Volume 219, September 2020, Pages 425-436
Combustion and Flame

Experimental investigation of the evaporation of suspended mono-sized heptane droplets in turbulence intensities approaching unity

https://doi.org/10.1016/j.combustflame.2020.06.007Get rights and content

Abstract

For decades, experimental investigations of turbulent droplet evaporation have generally followed one of two distinct paths: wind tunnel experiments, which generate significant mean flow but low turbulence intensity, and stirred chamber configurations, which yield the opposite characteristics. The present study bridges the gap between these two established techniques by modifying a fan-stirred spherical chamber to incorporate a controllable mean flow while retaining the attributes of highly-energetic homogeneous and isotropic turbulence. Heptane droplets with a fixed initial diameter, d0, of 500 ± 10 µm are suspended on the intersection of two microfibers and evaporated in pockets of high-intensity turbulence (27% < Tu < 103%) at small mean flow droplet Reynolds numbers, Red, of 10 and 50. A rigorous series of particle image velocimetry (PIV) tests mapped the homogeneous and isotropic turbulent flow regions for various combinations of fan speed, and a two-dimensional translating fiber support system allowed the precise spatial placement of the droplet for subsequent evaporation studies. PIV results indicate the generation of isotropic flow regions that satisfy 0.9 ≤ urms/vrms ≤ 1.1 with a minimum diameter of 20d0 at each test condition. The steady-state droplet evaporation rate, K, increases quasi-linearly with turbulence intensity at both Reynolds numbers, with steeper improvement associated with higher Red. A comparison with zero-mean flow data reveals that the mean velocity component remains a significant contributor to the droplet evaporation rate at both tested Reynolds numbers over the explored range of turbulence intensity. Subsequent analysis indicates that the mean flow attenuates the effect of turbulence. The findings are of fundamental and practical interest, as vaporization in high turbulence intensity is a plausible scenario for small droplets subject to a moderate slip velocity.

Introduction

Turbulence is the rule rather than the exception in most fluid flows of engineering significance. This statement is undoubtedly true for spray combustion applications which rely on turbulence to positively influence the multiphase system properties, including mass and energy transport phenomena, to increase performance and improve efficiency. The level of ambient turbulence affects the critical balance between droplet vaporization and dispersion (e.g., [1]) and, due to the importance of these two processes, it cannot be neglected in any comprehensive spray combustion analysis. Fuel droplets suddenly introduced into a moving gas stream, a scenario typical of injection, will experience both the bulk convective effects resulting from the slip velocity, along with a cascade of variably-sized turbulent eddies. The turbulence intensity, Tu, quantifies the relative strength of these two mechanisms and is generally defined as the characteristic root mean square velocity of the fluctuating component over the mean velocity and expressed as a percentage. The turbulence intensity, along with the specific magnitudes of its constituent parameters, are quantities of great interest in the analysis of turbulent droplet evaporation.

The exposure of droplets to high Tu occurs if the relative velocity between the droplets and flow is small to moderate, or if the flow itself is extremely turbulent. The conditions under which the former scenario is realized are examined within, but presently it suffices to state that small droplets and rapid evaporation are favorable in promoting this regime. Warnica et al. [2] state that the relative turbulence intensity experienced by a droplet in a turbulent spray combustion environment can exceed 100%. The latter possibility, in which the flow itself is dominated by strong turbulent fluctuations, has ample supporting evidence in the literature. For instance, consider the flow field conditions that exist in various internal combustion engine applications at the instant when fuel is introduced, atomized, and evaporated – the early intake stroke for port injection and homogeneous charge direct injection, and late compression stroke for stratified charge operation such as diesel. As discussed by Tabaczynski [3], the early intake and late compression phases of an engine are favorable to the development of high turbulence intensity on the order of unity due to the shear produced at the intake valve(s) and the squish band influence as the piston approaches top dead center (TDC), respectively. Mean in-cylinder velocities near TDC of the compression stroke can be negligible prior to ignition (e.g., [4]), a trend which is relatively independent of intake processes and modifications (e.g., [5]). More recent full-field investigations (e.g., [6,7]) confirm the likelihood of encountering very high Tu flows in engines. The evolution of single droplet vaporization studies to include flow fields with turbulence intensities approaching 100% is, therefore, one of practical necessity.

The effect of freestream turbulence intensity was first applied to the spherical geometry via large metallic or ceramic spheres in wind tunnels. With rare exception (e.g., [8,9]), the established consensus is one of agreement that freestream turbulence intensity significantly increases the rate of heat and mass transfer from spheres to the flowing gas. The turbulence effect is summarized in a series of review papers by Galloway and Sage [10], [11], [12] who compiled the results of published studies and, based on their subsequent analysis, support the inclusion of a turbulence intensity parameter in adapting Nusselt, Nu, and Sherwood, Sh, correlations to turbulent flows. Although the spheres in these studies were large and, further noting that spheres lack specific heat and mass transfer processes routinely found in liquid drops (internal circulation, for example, as mentioned in [13]), there are certain results which may retain relevance at the smaller scale of fuel droplets. Of particular interest is the repeated finding that turbulence intensity is more impactful at high Reynolds number, Red (e.g., [14]), and that a certain threshold of Tu must be crossed before key transport parameters (e.g., Nu and Sh) begin to rapidly increase (e.g., [15]). It's unclear how these findings translate to small fuel droplets, which are limited in realistic application to Red ~ 100 (e.g., [16]). At very low Red, the flow is approximately creeping in nature and the complex processes of boundary layer instability, separation, turbulent reattachment, and wake formation, which are crucial in relating flow turbulence to transport phenomena for large spheres (e.g., [17]), are presumably minimized.

Early experimental studies concerned with the effect of Tu on droplet evaporation rates are marked by discrepancy. Ohta et al. [18] found no influence on the evaporation rate of isooctane or benzene for Tu up to 21%. However, the number and range of conditional variations, including Red, gas temperature, fuel vapor relative humidity, initial diameter, and suspension method (porous sphere versus captive droplet), combined with the limited presentation of parametric results and lack of detailed turbulence characterization gives pause to accepting this conclusion completely. For instance, Yearling and Gould [13,19] found that heat and mass transfer rates of droplets and porous spheres increased by 30–50% over laminar cases when subjected to even minor turbulent intensities of 5–10%. Gökalp et al. [20] analyzed large suspended droplets of heptane and decane in wind tunnel grid turbulence at intensities up to 44% and Red of 100–450. Most significantly, they determined that turbulence was effective in increasing the evaporation rate of decane whereas heptane, the more volatile fuel, was unaffected. This finding is explained using the framework of a vaporization Damköhler number, Dav, defined as the ratio of the characteristic turbulent flow over vaporization time scales. Gökalp et al. [20] surmise that only flow-droplet combinations yielding small Dav are affected by turbulence. Wu et al. [21,22] confirmed the applicability of the Damköhler approach for similar fuels and Reynolds numbers in a highly isotropic turbulent flow field with intensities up to 60%, and proposed a well-fitted correlation of the form K/KL = C1DavC2. In contrast to Gökalp et al. [20], Wu et al. [21,22] present a clear influence of turbulence intensity on heptane, although the consensus that less volatile fuels (e.g., decane) are more affected is agreed upon. A set of elevated temperature experiments performed by Hiromitsu and Kawaguchi [23] raised questions regarding the applicability of the Damköhler correlation in hot environments, and the authors suggest the potential importance of the Kolmogorov scale eddies in breaking down the vapor boundary layer and thereby increasing the driving gradient for mass transfer. The theory that the smallest scales of turbulence can influence turbulent droplet vaporization is directly contradicted by Eckartsberg and Kapat [24] who conclude from their experimental investigations that there is negligible turbulence enhancement if the initial droplet diameter is smaller than the Taylor microscale. In the most recent experimental study, Marti et al. [25] examined the evaporation of large suspended heptane droplets in a wind tunnel with a switchable active grid at Reynolds numbers of 260 and 700. A slight improvement in K was noted in both cases when switching from passive (Tu < 4%) to active (20% < Tu < 26%) grid modes.

Aside from the multiple points of contention above, there are several aspects of turbulent droplet vaporization which the aforementioned studies have not addressed. First, the maximum Tu obtained in an experimental setup is 60% [21,22], with the remaining apparatuses capable of far less. The scarcity of data at high intensities relevant to spray combustion was noted in a 1983 review paper by Faeth [26], with only modest increases in achievable Tu reported since that time. Although numerical studies are not bound by the same intensity limitations imposed by experiment, the few such studies that pertain directly to the matter at hand (e.g., [27], and a series of studies by Abou Al-Sood and Birouk beginning chronologically with [28]) do not report results beyond Tu = 60%, despite showing continual improvement in K, potentially due to the absence of validation data. Second, the integral length scale, L, is typically varied, often as a consequence of manipulating other parameters, such that L ~ d0 in certain test cases. In realistic combustor applications, L >> d0 (e.g., [29]). Third, initial droplet diameters are universally large (900–3500 µm) which shifts the droplet Reynolds numbers to an unrealistically high range. Consequently, data for Red < 100 is lacking. Finally, the initial diameter may be varied without regard to the probable influence of d0 on the steady-state evaporation rate. The present study seeks to address these four issues through the following primary objectives:

  • 1)

    Modify a fan-stirred, zero-mean flow turbulence chamber to incorporate a significant mean velocity component while maintaining the characteristics of isotropy and homogeneity.

  • 2)

    Evaluate the evaporative effect of turbulence intensities approaching unity on mono-sized suspended droplets of the reference fuel heptane at discrete mean flow Reynolds numbers.

  • 3)

    Assess the suitability of existing correlations, developed exclusively using experimental data for large Reynolds numbers and low turbulence intensities, for predicting the present case of droplets evaporating in a flow field where the mean and turbulent fluctuations have approximately equal strength.

Section snippets

Experimental setup and methodology

Droplet evaporation investigations are performed in a 29-l fan-stirred spherical chamber. Although the general layout of the test rig remains consistent with the description provided in [30], there are several important alterations to both the physical setup and experimental procedure that warrant a detailed description. Section 2.1 outlines the specific test conditions and illustrates the data collection process, while Section 2.2 provides an overview of the apparatus. Sections 2.3 and 2.4

Characterization of the turbulent flow field

When operated alone, the axial fan produces a jet-like flow structure with an isotropic band surrounding the high-velocity core. This configuration, depicted in Fig. 6(a) and (c), is utilized to produce the smallest Tu values for both Red considered in this study. Interestingly, the turbulence intensity in both Red cases is approximately equal to the theoretical centerline value, 25%, for a fully developed round turbulent jet [34]. However, unlike the idealized round jet in which the axial RMS

Evaluation of published correlations

Multiple studies have attempted to quantify the impact of pure turbulence by calculating the difference between the normalized evaporation rates in a turbulent and laminar flow (e.g., [20,23]):KT=KTKLK0

The success of Eq. (3) rests on whether KT is independent of the mean flow. Stated a different way, if KT is a characteristic measure of the droplet evaporation improvement due to pure turbulence, it should be a function of the evaporation rate in zero-mean flow turbulence only. Although the

Conclusions

Until now, experimental droplet evaporation studies focusing on the effect of turbulence in the presence of a mean flow have been unable to generate turbulence intensities beyond approximately 60%. However, a thorough literature review revealed that spray combustion applications, particularly internal combustion engines, generate flow fields that match or exceed 100% intensity. To fill the gap between low intensity wind tunnels and zero-mean flow apparatuses, a fan was added to an existing

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).

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