Isotropic Turbulent Flow Field Research Articles

Background vapor effect on droplet evaporation in a turbulent flow at elevated pressure

Investigation of the evaporation of single droplets holds a significant importance as it emulates the diluted spray region and helps improve the accuracy of numerical modelling. In the present study, a fan-stirred spherical chamber was employed to generate a homogeneous and isotropic turbulent flow field with negligible mean velocity. This setup was used to investigate the effect of background vapor on the vaporization of a 500 µm pentane droplet in a turbulent flow at elevated pressure and room temperature. Turbulence intensity and pressure were varied, respectively, from stagnant to 1.5 m/s and from 1 to 5 bar. Additionally, the background pentane vapor was altered (on molar basis) from 0 % up to 40 %. The results show that the d2-law is valid throughout all explored test conditions, including in the presence of background vapor. The findings indicated that the presence of background vapor around the evaporating droplet diminishes the droplet vaporization rate under both stagnant and turbulent flow scenarios, with a more pronounced impact at elevated pressure conditions. Furthermore, turbulence is observed to enhance the vaporization rate in the presence of background vapor, with its influence being more substantial at elevated pressure levels and higher concentrations of background vapor. Finally, the experimental data was used to correlate the coupled effect of ambient background vapor, turbulence, and pressure on the vaporization of a pentane droplet in terms of the flow turbulent Reynolds number.

Experimental study of butanol droplet evaporation in a turbulent, high-pressure environment

An experimental investigation is conducted to study the vaporization behavior of butanol droplets in a turbulent environment at elevated pressure. A single droplet of butanol, with a diameter of 500 µm, is suspended at the intersection point of two micro-fibers positioned in the center of a fan-stirred spherical chamber. The latter is equipped with eight axial fans to generate an isotropic and homogeneous turbulent flow field with nearly zero-mean velocity. In this experiment, turbulence intensity and ambient pressure were varied from 0 to 1.5 m/s and from 1 to 10 bar, respectively, while ambient temperature was kept at room conditions. The experimental findings revealed that the butanol droplet squared diameter exhibited a linear relationship with time for the majority of the droplet lifetime. This observation suggests that the d2-law is applicable across all the test conditions explored in this study. Results showed that the vaporization rate of a butanol droplet decreases with ambient pressure and increases with turbulence intensity. The vaporization rate of butanol falls between that of heptane and decane, with closer proximity to decane. Furthermore, the comparison of these fuels indicates that the influence of turbulence on the vaporization rate is more significant for fuels with lower vapor mass diffusivity. Finally, published correlations based on Damköhler and Reynolds numbers are verified and found to hold for the butanol droplet vaporization data.

Turbulent droplet breakage in a von Kármán flow cell

Droplet dispersion in liquid–liquid systems is a crucial step in many unit operations throughout the chemical, food, and pharmaceutic industries, where improper operation causes billions of dollars of loss annually. A theoretical background for the description of droplet breakup has been established, but many assumptions are still unconfirmed by experimental observations. In this investigation, a von Kármán swirling flow device was used to produce homogeneous, low-intensity turbulence suitable for carrying out droplet breakage experiments using optical image analysis. Individual droplets of known, adjustable, and repeatable sizes were introduced into an isotropic turbulent flow field providing novel control over two of the most important factors impacting droplet breakage: turbulence dissipation rate and parent droplet size. Introducing droplets one at a time, large data sets were gathered using canola, safflower, and sesame oils for the droplet phase and water as the continuous phase. Automated image analysis was used to determine breakage time, breakage probability, and child droplet size distribution for various turbulence intensities. Breakage time and breakage probability were observed to increase with increasing parent droplet size, consistent with the classic and widely used Coulaloglou–Tavlarides breakage model (C–T model). The shape of the child drop size distribution function was found to depend upon the size of the parent droplet.

Effect of fluctuation on heat transfer enhancement of a spherical particle

Heat transfer of a particle in turbulent flows is essential, while the study on the effect of turbulent fluctuation on the heat transfer enhancement of a spherical particle is rarely reported. In this work, a 4.4 mm copper particle with a small Biot number was subject to a near homogenous and isotropic turbulent flow field to investigate the heat transfer behaviors. The detailed flow characteristics were measured with the Particle Image Velocimetry (PIV). As the fan speed increases, both the fluctuating velocity (urms) and the time-averaged velocity (uave) increase quickly at first and then slowly. When the furnace temperature increases, both urms and uave barely change. For all conditions, urms is apparently larger than uave. As for the particle heating experiment, the heating rate increases with the fan speed and the furnace temperature. Based on the measured results of the flow field and the particle temperature, a modified correlation for predicting Nusselt number was proposed to describe the effect of the turbulent fluctuation on the heat transfer of a single spherical particle. The newly proposed correlation was further validated by particle heating experiments of a 2 mm copper sphere in this work and direct numerical simulation results from the literature.

An experimental assessment of the enhancement of fuel droplet vaporization in a very high turbulence intensity environment

A zero-mean flow fan-stirred chamber is used to gather data on suspended fuel droplet evaporation at turbulence intensities, q1/2, approaching 4.30 m/s. This research is driven by the oft-cited but unconfirmed belief that the droplet evaporation rate, K, eventually plateaus with increasing turbulence kinetic energy. Further motivation comes from numerous real-world examples, including combustion systems, where droplets are exposed to turbulence intensities far beyond the experimental capabilities reported in the literature to date. Decane, ethanol, and heptane fuels are selected and grouped into two categories based on the similarity of their vapor pressures, Pv, and mass diffusivity coefficients, DAB, in an effort to discern which thermophysical properties are important to vaporization enhancement, or lack thereof, in high turbulence. Individual droplets with constant initial diameters, d0, of 500 µm are placed in the central region of a highly homogeneous and isotropic turbulent flow field using a novel multi-fiber intersection technique. Neither alkane fuel exhibits any sign of reduced effect of turbulence, as K/K0 remains a strongly linear function of turbulence intensity throughout the test conditions. Conversely, the normalized evaporation rate of ethanol begins to plateau at the higher levels of intensity. Although equalizing the vapor pressures of ethanol and heptane was sufficient to match K/K0 values at low intensity, their divergence as q1/2 increases implies that the thermodynamically-predicted vapor quantity at the droplet surface does not enforce an upper limit on turbulence effectiveness at moderately elevated temperatures. This is confirmed by decane, which has the lowest volatility and yet experiences the greatest improvement in evaporation rate at the highest levels of turbulence.

Experimental investigation of the effect of droplet size on the vaporization process in ambient turbulence

This paper presents the results of an experimental investigation of the effect of droplet size on the fuel vaporization process in a turbulent atmosphere at standard ambient conditions. Single droplets of n-heptane and n-decane are formed and evaporated at the intersection point of two micro-fibers placed in the center of a fan-stirred spherical vessel which is maintained at room temperature and pressure. The droplet initial diameter varies in the range between 145 and 730µm. A controlled isotropic and homogeneous turbulent flow field with nearly zero mean velocity and intensity ranging between 0.25 and 1.5m/s is generated inside the vessel by means of eight axial fans. The results indicate that the droplet normalized squared diameter varies quasi-linearly with time, suggesting the applicability of the d2 law at all examined conditions. More importantly, the results reveal that the droplet initial diameter becomes a significant contributing factor in determining the evaporation rate in a turbulent environment, as the rate of vaporization is found to increase with both turbulent intensity and droplet size. However, droplet size produces no effect on the vaporization rate in quiescent (no flow) surroundings. The results also emphasize that as the ratio of the Kolmogorov length scale over droplet initial diameter approaches unity, the effect of turbulence becomes negligible, illustrating the importance of the small-scale eddies, and their relation to droplet size, in the transport/transfer of mass. The coupled effect of droplet size and turbulence on the vaporization rate is correlated in terms of either a turbulent Reynolds number or a vaporization Damköhler number.

A time-dependent Eulerian model of droplet diffusion in turbulent flow

Industrial sprays are common in many operations where liquid application to surfaces is required. Maximization of the spray process efficacy depends on accurate simulation of spray characteristics and surrounding flow conditions. Traditionally, droplet modeling has been performed using a Lagrangian approach which requires tracking a sufficient number of droplets to form statistical estimates of droplet deposition. Alternatively for this study, an Eulerian-based flow and droplet transport model using the Direct Quadrature Method of Moments (DQMOM) is applied to spray modeling and is coupled with the Reynolds Averaged Navier Stokes (RANS) equations and Shear Stress Transport (SST) turbulence model. A new turbulent diffusion model is developed for droplet transport which accounts for inertia and time-limit effects and covers a wide range of operational parameters associated with aerial spraying. The model is based on a full parametric study using Lagrangian particle tracking in a uniform, homogeneous and isotropic turbulent flow field and is subsequently implemented within the Eulerian DQMOM framework and compared to: 1) Lagrangian tracking predictions of a log-normal particle size distribution injected into a homogeneous, isotropic turbulent flow field, and 2) full-scale experimental wind tunnel measurements in the anisotropic, non-homogeneous wake of a hollow cone hydraulic nozzle.

Stochastic dispersion of ellipsoidal fibers in various turbulent fields

In this study dispersion and deposition of fibers of various sizes in fully developed turbulent pipe and duct flows were analyzed for a range of flow Reynolds numbers. Fibers translational and rotational equations of motion were solved using the Lagrangian approach assuming one-way interaction. The influences of turbulent fluctuations were included using appropriate stochastic models for fluctuating velocity and velocity gradient components. Performance of the stochastic model was evaluated for several test cases including dispersion of fibers in a synthesized isotropic homogenous turbulent flow field, inhomogeneous turbulent flow field, and fully developed turbulent pipe and duct flows. The simulation results were compared with earlier numerical and experimental studies for flow statistics and deposition velocity and good agreements were observed. It was shown that using appropriate stochastic models leads to satisfactory evaluation of dispersion and deposition of fibers in turbulent flows.

Development of a two zone turbulence model and its application to the cycle-simulation

The development of a two zone k-? turbulence model for the cycle-simulation software is presented. The in-cylinder turbulent flow field of internal combustion engines plays the most important role in the combustion process. Turbulence has a strong influence on the combustion process because the convective deformation of the flame front as well as the additional transfer of the momentum, heat and mass can occur. The development and use of numerical simulation models are prompted by the high experimental costs, lack of measurement equipment and increase in computer power. In the cycle-simulation codes, multi zone models are often used for rapid and robust evaluation of key engine parameters. The extension of the single zone turbulence model to the two zone model is presented and described. Turbulence analysis was focused only on the high pressure cycle according to the assumption of the homogeneous and isotropic turbulent flow field. Specific modifications of differential equation derivatives were made in both cases (single and two zone). Validation was performed on two engine geometries for different engine speeds and loads. Results of the cyclesimulation model for the turbulent kinetic energy and the combustion progress variable are compared with the results of 3D-CFD simulations. Very good agreement between the turbulent kinetic energy during the high pressure cycle and the combustion progress variable was obtained. The two zone k-? turbulence model showed a further progress in terms of prediction of the combustion process by using only the turbulent quantities of the unburned zone.

Modelling of aggregate restructuring in a weakly turbulent flow

An aggregate may undergo a restructuring that leads to a change of its porosity. The cause of this morphology change is not only the colloidal forces between the primary particles but also the interaction between the primary particles and the flowing fluid. We investigate in this paper the restructuring of the aggregates with Van der Waals forces between the primary particles in the presence of the Brownian motion and a weakly turbulent flow. The motion of all the primary particles constituting the aggregate is studied thanks to a 1-D model based on the work of G. Narsimhan [Model for drop coalescence in a locally isotropic turbulent flow field, J. Colloid Interface Sci., 272 (2004) 197–209]. A shrinking rate law, i.e. aggregate porosity versus time, is proposed after a transition to a 3-D model. Its characteristic time depends on the initial porosity, the number of primary particle and a characteristic time at the scale of the primary particle.

A model for predicting the acceleration variance of arbitrary-density finite-size particles in isotropic turbulence

The paper concerns the effects of particle inertia, density, and size on acceleration statistics. A simple analytical model for estimating the acceleration variance of particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of qualitative describing the particle acceleration variance over the entire range of the particle-to-fluid density ratio. Comparisons of model predictions with numerical simulations and experimental data are presented.

Acceleration of heavy particles in isotropic turbulence

The paper concerns the effect of particle inertia on acceleration statistics. A simple analytical model for predicting the acceleration of heavy particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of describing the influence of both Stokes and Reynolds numbers on the particle acceleration variance. Comparisons of model predictions with numerical simulations are presented.

Assessment of a flame surface density-based subgrid turbulent combustion model for nonpremixed flames of wood pyrolysis gas

A flame surface density (FSD) model for closing the unresolved reaction source terms is developed and implemented in a large eddy simulation (LES) of turbulent nonpremixed flame of wood pyrolysis gas and air. In this model, the filtered reaction rate ω¯α of species α is estimated as the product of the consumption rate per unit surface area mα and the filtered FSD Σ¯. This approach is attractive since it decouples the complex chemical problem (mα) from the description of the turbulence combustion interaction (Σ¯). A simplified computational methodology is derived for filtered FSD Σ¯, which is approximated as the product of the conditional filtered gradient of mixture fraction and the filtered probability density function. Two models for flamelet consumption rate mα are proposed to consider the effect of filtered scalar dissipation rate. The performance of these models is assessed by direct numerical simulation (DNS) database where a laminar diffusion flame interacts with a decaying homogeneous and isotropic turbulent flow field. The chemistry is modeled by a four-step reduced mechanism that describes the oxidization process of gaseous fuel released from high temperature pyrolysis of wood occurring in a wildland fire. Two-dimensional (2D) and 3D LES computations based on the FSD models are conducted for the same conditions as the DNS. The comparative assessments confirm the applicability of the proposed FSD model to describe the filtered reaction rate and the time evolution of temperature and species concentration in the turbulent nonpremixed flame.

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

AbstractThe mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.

Model for drop coalescence in a locally isotropic turbulent flow field

The proposed model views drop coalescence in a turbulent flow field as a two-step process consisting of formation of a doublet due to drop collisions followed by coalescence of the individual droplets in a doublet due to the drainage of the intervening film of continuous phase under the action of colloidal (van der Waals and electrostatic) and random turbulent forces. The turbulent flow field was assumed to be locally isotropic. A first-passage-time analysis was employed for the random process of intervening continuous-phase film thickness between the two drops of a doublet in order to evaluate the first two moments of coalescence-time distribution of the doublet. The average drop coalescence time of the doublet was dependent on the barrier for coalescence due to the net repulsive force (net effect of colloidal repulsive and turbulent attractive forces). The predicted average drop coalescence time was found to be smaller for larger turbulent energy dissipation rates, smaller surface potentials, larger drop sizes, larger ionic strengths, and larger drop size ratios of unequal-sized drop pairs. The predicted average drop coalescence time was found to decrease whenever the ratio of average turbulent force to repulsive force barrier became larger. The calculated coalescence-time distribution was broader, with a higher standard deviation, at lower energy dissipation rates, higher surface potentials, smaller drop sizes, and smaller size ratios of unequal drop pairs. The model predictions of average coalescence-rate constants for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) in a high-pressure homogenizer agreed fairly well with the inferred experimental values as reported by Narsimhan and Goel (J. Colloid Interface Sci. 238 (2001) 420–432) at different homogenizer pressures and SDS concentrations.

Pair dispersion and preferential concentration of particles in isotropic turbulence

The objective of the paper is to present a statistical model for predicting pair dispersion and preferential concentration of particles suspended in an isotropic homogeneous turbulent flow field. This model is based on a kinetic equation for the probability density function of the relative velocities of two particles. The model developed is applied to predict the pair relative velocity statistics and the accumulation effect of heavy particles in a steady-state suspension. The effect of particle inertia on the predicted Eulerian two-point particle velocity correlations is demonstrated and compared with known results of numerical simulation.

An experimental correlation of turbulent burning velocities for premixed turbulent methane-air combustion

This paper is devoted to the general correlation of turbulent burning velocities in terms of straining rates for premixed flames propagating in intense turbulence. This problem was investigated by the Leeds group led by Professor Bradley and many other researchers. We present here a new methodology based upon a downward propagating premixed CH4–air flame through a nearly isotropic turbulent flow field with a pair of specially designed ion probes for quantitative measurements of turbulent burning velocities. The improvements are that the flame propagation is not influenced by the ignition source and the unwanted turbulence from walls, effects of buoyancy and pressure rise due to burning are minimized, and a greater parameter range than hitherto is covered. The results show that both the turbulent burning velocity bending and the vitality of turbulent premixed flames are certain and surprising. Logarithmic plots of turbulent burning velocities S T/ S L – 1 against the turbulent intensities u '/ S L reveal a transition, where S L is the laminar burning velocity. Across the transition, the slope n changes from positive to negative when values of u '/ S L and/or Karlovitz number are greater than some critical values. This transition seems to correspond to the Klimov–Williams criterion that separates corrugated flamelets from distributed reaction zones. Interestingly, no global quenching of premixed turbulent flames is observed, even at u ' S L ≊ 40, a value significantly higher than in most previous measurements. At a fixed u '/ S L, values of the S T/ S L data vary with the equivalence ratio ϕ. This indicates that the common expression of the form S T/ S L = 1 + C ( u '/ S L) n cannot be applicable generally, because values of the constant C are different for different mixture compositions. It is found that all of the present data with different values of ϕ can be approximated by a simple expression, ( S T – S L)/ u ' ≊ 0.06 Da 0.59, where Da is the Damkohler number. Hence a better correlation of turbulent burning velocities in terms of straining rates for premixed turbulent (methane–air) combustion is proposed.

On the Development of a Distributed Reaction Zones Model for Turbulent Premixed Flame of Lean Mixtures in a Closed Vessel

Turbulent premixed flame propagation in a closed spherical vessel with a homogeneous and isotropic turbulent flow field is modelled using the one-point transport equation for the probability density function (pdf) in the thermodynamic space. The pdf equation is discretized using the control volume formulation on a one-dimensional spherical grid. Then the discretized equation is solved using the Monte Carlo method to follow particles with variable volumes on a grid moving with the expansion radial velocity. The mixing term is modelled using the Curl model, and the modified Curl model. The source term is simulated delerministically using a one-step chemical reaction mechanism. Transient solutions are obtained for spherical benzene-air flames using frozen turbulent flow. The pressure rise, the mass fraction burned, the flame speed, the entrainment speed, the burning speed, and the burned gas speed are calculated. The calculated entrainment speeds are compared with the ones reported in Bradley et al (1992) for KLc>5.3 where distributed reaction zones are assumed to govern the flame propagation. The effects of different turbulent flow field (uvS1) and the effect of the product (KLe) are discussed.

The structure of two-phase grid turbulence in a rectangular channel: an experimental study

Measurements in two-phase, water–air bubble, grid turbulence have been conducted in a vertical water channel of square cross section. The water flow was directed upwards. A 30 mm mesh grid located at the entrance of the test section generated, in the absence of the dispersed phase, a nearly isotropic turbulent flow field occupying the central part of the channel. Air bubbles were injected in the flow from the grid. Velocity measurements of the liquid phase were obtained using Laser Doppler Velocimetry. The measured flow characteristics included mean velocity and statistical quantities such as turbulence intensity, probability distribution function, skewness and flatness factors, autocorrelation, macroscale and power spectra, for both the longitudinal and transverse velocity components. Local void fraction was measured with an optical probe as well as with hot film anemometry. Bubble velocity and size were estimated with photographic techniques. Presented measurements illustrate the upwards development of void fraction distribution at successive cross sections of the channel. The observed distributions indicate the presence of a mechanism responsible for capturing and redistributing the bubbles. Accordingly, physical mechanisms possibly responsible for the observed phenomenon such as a Segre–Silberberg effect, modified for deformable bubbles in the presence of buoyancy, or the action of large eddies present in the flow are discussed. The velocity field has been obtained on a cross-section at a distance of 30 mesh from the grid at a constant water volumetric flow rate. Based on the obtained experimental results, the influence of the dispersed phase on the initially isotropic turbulence field is identified and the physical processes responsible for the observed changes are discussed. The presence of the second phase appears to introduce inhomogeneities in the void fraction and flow property distributions leading to the emergence of two spatial regions controlled by different physical processes. Also, two distinct regimes in the measured quantities are observed, corresponding to low and high values of gas flow rate ratio. The described changes result in a significant departure from initial isotropy, followed by a tendency towards returning to a state characterised by nearly normal probability distributions and scales close to that of grid turbulence as the gas flow rate increases. Finally, the measured autocorrelation and power spectra offer information regarding the nature of the energy exchanging mechanism occurring between the liquid and dispersed phase.

Experimental analysis of flame surface density modeling for premixed turbulent combustion using aqueous autocatalytic reactions

In the flamelet framework for premixed turbulent combustion, a transport equation for the flame surface density, commonly known as the Σ-equation, can be formulated but requires closure assumptions. We have applied an aqueous autocatalytic reaction, which produces a self-propagating chemical surface (liquid flame) with characteristics closely matching many of those assumed by flamelet models to extract full spatial statistics relating to the Bray-Moss-Libby model. The present work reports, for the first time, measurements of some unclosed terms in the Σ-equation using liquid flames in a nearly isotropic turbulent flow field. The three-dimensional form of nearly stationary isotropic turbulence was generated near the core region between a pair of vibrating grids in a chemical tank, as verified by laser-Doppler velocimetry. Visualization of propagating surfaces is via a high-speed, successive planar chemically reacting, laser-induced fluorescence technique to extract flame surface density, vector normal to the front, and curvature. Unlike gaseous flames, liquid flames with essentially constant laminar propagating (burning) velocity are approximately free of thermal expansion and heat loss effects and thus may be useful for developing a very basic understanding of the interrelationship between production by hydrodynamic straining and destruction by propagating effects in the Σ-equation, relevant to flamelet models. It is found that the propagation term is negligible and the curvature term has three different modes across the turbulent front brush, respectively (1) mainly negative, (2) positive/negative: production at the reactant side/destruction at the product side, and (3) mainly positive. The first two modes constitute nearly 90% of all possible modes found for a typical aqueous propagating front, indicating that the curvature behavior is more complicated than that generally assumed by flamelet models (mode 1 only) and that of direct numerical simulation and gaseous V flame results (mode 2 only). Two simple schemes are included to explain these results. Finally, measurements of the total propagating surface area production (flame stretching) suggest that the collisions or reconnections of flamelets may be important for the coexistence of these three different curvature modes.