VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION

LHCB 2003120 “THE VALIDATION CARD FOR THE CALORIMETER TRIGGERS”
VALIDATION TEST PLAN RUNNING [SOFTWARE PRODUCT] ON VMWARE
2 NOM PRENOM VALIDATION DES ACQUIS DE

3 OPEN UNIVERSITY VALIDATION SERVICES OPEN UNIVERSITY AWARDING BODY
40 TIMBER VOLUME ESTIMATOR HANDBOOK CHAPTER 40 VALIDATION
6TH MARCH 2012 PAGE 66 VALIDATION REPORT

AIRFLOW DISTRIBUTIONS IN THE FILLET SPACES OF A TIMBER STACK

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION AND EVAPORATION OF DROPLETS WITHIN A SPRAY

Nijdam, J.J.1, Guo, B.2, Fletcher, D.F.1, Langrish, T.A.G.1

1. Department of Chemical Engineering, University of Sydney, Australia

2. School of Materials Science and Engineering, University of New South Wales, Australia

Keywords and Phrases: spray drying; computational fluid dynamics; CFD; particle drying

ABSTRACT

The accuracy of the Lagrangian approach for predicting droplet trajectories and evaporation rates within a simple spray has been addressed. The turbulent dispersion and overall evaporation rates of droplets are modelled reasonably well, although the downstream velocity decay of the larger droplets is under-predicted, which is attributed to a poor estimate of the radial fluctuating velocity of these droplets at the inlet boundary. Qualitative agreement is found between the predicted and experimental evolution of the droplet size distribution downstream of the nozzle. These results show that smaller droplets evaporate preferentially to larger droplets, because they disperse more quickly towards the edge of the jet, where the entrainment of fresh air from the surroundings produces a significant evaporative driving force. Droplet dispersion and evaporation rates are highly influenced by the rate of turbulence generation within the shear layer. This work demonstrates the potential of the Lagrangian approach for analysing particle trajectories and drying within the more complex spray dryer system.

INTRODUCTION

Spray drying is the process of atomising a liquid that contains dissolved solids within a flow of hot air, where moisture is progressively evaporated from the droplets until dried particles are produced. This process is normally carried out within a drying chamber, which is specially designed to provide sufficient droplet/particle residence times for a given heat load so that the powder collected at the exit point of the chamber achieves the desired moisture content without experiencing any heat degradation. As an illustration, where low air temperatures are necessary for heat-sensitive products, moisture evaporation from droplets is slow, and thus long droplet/particle residence times are required in order to produce powder with the desired moisture content, which calls for a drying chamber of great height. The droplet/particle residence time within the drying chamber also affects the functional properties of the powder, such as the solubility and bulk density, which are essentially related to the size and morphology of individual particles. Long residence times enable particles to agglomerate and increase in size during their passage through the spray dryer, provided the particles are sufficiently tacky to stick together after a collision, and the particle number concentration is sufficiently high to result in frequent collisions. Clearly, the droplet/particle residence time is an important consideration when designing spray dryers, and a method is required to predict this quantity before any attempt can be made to choose an appropriate dryer configuration and size for a given application. Masters (1976) has described various methods for evaluating the droplet/particle residence time, which involve piecewise methods to predict the droplet/particle trajectories in different regions of the drying chamber. However, numerous simplifications and assumptions are often associated with these methods, since the airflow patterns and the interaction of the spray and airflow turbulence are very complex.

Recently, the more rigorous Computational Fluid Dynamics (CFD) method has been employed by various workers (Huang et al., 2004; Langrish et al., 2004; Oakley, 2004; Verdurmen et al., 2004) to investigate different aspects of the flow within a spray dryer, with the ultimate aim of providing a validated CFD code that accurately predicts droplet/particle trajectories and residence times, and the extent of particle drying and agglomeration within the spray dryer, so that information can be gained on the likely properties of the dried powder. Langrish et al. (2004) and Harvie et al. (2001) have demonstrated good agreement between experiment and CFD predictions of the swirling motion and transient nature of airflow within short-form and tall-form spray dryers, respectively. In addition, Nijdam et al. (2004) and Rüger et al. (2000) have shown that the turbulent dispersion of droplets/particles within a simple spray is predicted accurately using a Lagrangian droplet/particle tracking model, a feature of many commercially-available CFD codes. This set of papers has illustrated the potential of CFD to accurately predict both the airflow patterns and the interaction of the airflow and the discrete phase within a spray dryer, which should allow droplet/particle trajectories and residence times to be estimated with a higher degree of precision in the near future.

Nijdam et al. (2004) have also demonstrated good qualitative agreement between experiment and Lagrangian predictions of droplet coalescence. Moreover, they have shown that the Lagrangian predictions of coalescence are consistent with a rigorous multi-phase Eulerian calculation, which lends support to the validity of the Lagrangian approach for modelling both droplet coalescence and particle agglomeration. These workers have provided a rough estimate of the coalescence constant that appears in the Lagrangian model of droplet coalescence; however, the particle agglomeration constant, which is a function of the stickiness of particles, must also be estimated before predictions of both droplet coalescence and particle agglomeration within a spray dryer are feasible. Rüger et al. (2000) have also shown good agreement between Lagrangian predictions and experiments of droplet coalescence in a water spray.

Particle stickiness is related to the surface moisture content and temperature of individual particles, which implies that moisture evaporation from the discrete phase must also be modelled before any particle-agglomeration predictions are possible. Harvie et al. (2002) have demonstrated that the Lagrangian particle-tracking approach can be used to model such moisture evaporation from droplets and particles. The underlying assumption used in their drying model is that the discrete phase experiences two distinct stages of drying. During the first drying stage, which is generally called the constant-rate period, the surface of the droplet/particle is saturated with water, and only the resistance of the droplet/particle boundary layer to heat and mass transfer influences the evaporation rate. The second drying stage, known as the falling-rate period, begins once sufficient moisture has been removed from the particle such that surface saturation can no longer be maintained, which results in the formation of a dry outer layer that progressively thickens, impeding the transport of moisture from the core to the surface of the particle, so that the drying rate falls steadily. Harvie et al. (2002) have shown reasonable agreement between the predicted and measured moisture content of powder at the exit point of a spray dryer, although no comparisons were made between predictions and experiment at any locations within the spray dryer.

The aim of this paper is to continue the validation work of Harvie et al. (2002) by comparing experimental data with Lagrangian predictions of moisture evaporation from the discrete phase during the so-called constant-rate period. The experimental data of Nijdam et al. (2004) for the evaporation of acetone droplets, which contain no solids to otherwise impede the drying rate, are used for this purpose. Rüger et al. (2000) have also modelled evaporation within a spray using the Lagrangian approach, although they used water rather than acetone, such that the evaporation of droplets was negligible compared with the coalescence of these droplets. We neglect droplet coalescence in this work, since evaporation is the dominant phenomenon in the dilute acetone spray investigated here. This work is more rigorous than the earlier study of Harvie et al. (2002), because experimental and predicted droplet evaporation rates are compared at various locations throughout a spray, so that the ability of the model to accurately predict the influence of airflow turbulence on droplet evaporation can be ascertained. In addition, the validity of the Lagrangian model for predicting the turbulent dispersion of droplets within an evaporating spray is assessed in this paper, which should reveal the potential of this approach for accurately modelling trajectories and residence times of evaporating droplets and drying particles within the more complex spray dryer system.

THEORY

In the Lagrangian droplet-tracking approach, the spray is modelled as a gas-flow carrying a large number of discrete droplet parcels, with each parcel consisting of a number of physical droplets of similar size. The gas flow-field is computed using the Eulerian continuum equations, while the droplet-parcel trajectories within the gas-flow are calculated by solving the Lagrangian equations of mass and momentum. The effect of turbulence on the droplet motion is simulated by the stochastic approach of Gosman and Ioannides (1983), in which the fluctuating velocity of the droplet parcels is randomly sampled from a Gaussian distribution, whose standard deviation is a function of the local turbulence kinetic energy of the air. The droplet evaporation rate VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is modelled using the following equation,

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION (1)

where VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is the diameter of the droplet, VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION are the vapour molar fractions at the surface of the droplet and in the gas phase, respectively, and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION are the molecular weights of the vapour and the gas mixture in the continuous phase, respectively. The diffusivity of vapour in the gas is given by VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION , while the Sherwood number VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is estimated from the empirical correlation of Ranz and Marshall (1952), as follows:

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION (2)

which is applicable for Reynolds numbers (VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION ) of up to 200. The energy balance for an evaporating droplet, assuming that the temperature throughout the droplet VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is uniform, is given by the following expression:

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION (3)

where VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is the temperature of the gas, VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION are respectively the mass of the droplet and heat capacity of the liquid, VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is the thermal conductivity of the gas, and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is the latent heat of vaporisation of the liquid. The Nusselt number VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is calculated from a correlation analogous to Equation (2), in which the Prandtl number (VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION ) replaces the Schmidt number (VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION ). The vapour mole fraction at the surface of the droplet VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is calculated from the following equation,

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION (4)

where VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION , VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION are empirically-determined constants in the Antoine equation, and VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is the total pressure. Equations (1) to (4) allow the size and temperature of droplets within each parcel to be calculated as they progressively evaporate. Two additional transport equations for enthalpy and mass fraction are required in addition to the gas momentum, continuity and any turbulence equations, in order to calculate the temperature VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION and vapour mole fraction VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION of the gas, as described in the CFX4.4 manual (ANSYS).

EXPERIMENTAL DESCRIPTION AND NUMERICAL ASPECTS

The predictions of the Lagrangian model are compared with droplet evaporation, velocity and spreading rate measurements of the acetone round-jet spray investigated experimentally by Nijdam et al. (2004). The experimental apparatus consisted of a wind tunnel and a nozzle (a long thin tube, 9.8mm in diameter, located centrally at the exit plane of wind tunnel, as shown in Figure 1), which generated a round air jet within a co-flow of air with velocities of approximately 23 m/s and 2.4 m/s, respectively. The air jet was laden with a dispersion of acetone droplets in the size range from 1 to 90 m, which were produced by an ultrasonic nebulizer located upstream of the nozzle. A phase-Doppler anemometer (PDA) was used to measure the axial velocity and volume flux of the droplets within the jet at various locations downstream of the nozzle. These experimental measurements are presented in detail in the paper of Nijdam et al. (2004). Note that we compare only the experimental and predicted axial velocities in this work, because the radial velocity component was not measured in order to improve the accuracy of the droplet volume flux measurement, as discussed by Nijdam et al. (2004). Nevertheless, the dispersion of droplets in the jet downstream of the nozzle can be adequately described by the decay in the axial velocity profile and the evolution of the droplet volume flux profile.

Evaporative cooling of the acetone droplets within the nozzle ensured that the air and droplet temperatures at the exit of the nozzle were well below the ambient room temperature. Due to the considerable length of the nozzle (24 nozzle diameters), we assumed that the air and droplet temperatures reached an equilibrium value of 0 °C at the exit of the nozzle. This temperature was estimated from the ideal gas law by determining the density of the air at the exit of the nozzle from a mass balance over the nozzle, which was based on the known air flow and temperature entering the nozzle and the PDA-measured airflow exiting the nozzle. The total acetone droplet flow at the exit of the nozzle was 1.7 ml/min. The temperature of the air co-flow was measured at 16 °C.

The simulations presented in this paper are performed using CFX4.4 (ANSYS), a commercial CFD code, which uses a finite-volume discretisation method. Turbulence is modelled using the standard VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION - VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION model described by Launder and Sharma (1974), with the turbulence parameter VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION taking on a value of 1.55 in these simulations, which is different from the value of 1.6 found by McGuirk and Rodi (1979) for a round jet. McGuirk and Rodi (1979) have explained that VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is an empirical constant, which does not take on a universal value for every type of flow. They have stated that the value for VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION of 1.6 is only applicable for round jets well away from any potential core and for jets issuing into stagnant surroundings. However, the jet investigated in this work has a top-hat axial mean velocity profile at the exit of the nozzle, which indicates the presence of a potential core, and the jet issues into a co-flow. We have found that a value of 1.55 for VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION is appropriate in the case of such a jet in order to match the experimental and predicted decay of the centreline axial mean velocities of the gas and droplets. Clearly, the VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION -VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION turbulence model lacks generality, and more sophisticated gas-flow turbulence models are needed to resolve this. However, such complex turbulence models are likely to be computationally very expensive, and simpler formulations are preferable when other phenomena, such as droplet evaporation and turbulent dispersion, are the main focus of an investigation.

The acetone parcels of droplets are tracked using the Lagrangian particle-tracking feature of CFX4.4 and the turbulent dispersion model of Gosman and Ioannides (1983). The following values were used for the properties of acetone: liquid density, 790 kg/m3; latent heat of vaporisation, 543 kJ/kg; liquid and vapour heat capacities, 2180 and 1466 J/kg K, respectively; diffusivity of vapour in air, 1.09×10-5 m2/s. The coefficients A, B and C in the Antoine Equation (see Equation 4) took the values 21.695, 3021.6, and 240.705, respectively. Note that a transient three-dimensional simulation is required in order to properly model the movement of droplet parcels throughout time and space, although we have observed in practice that the jet was in fact steady and axisymmetric (two dimensional). The evaporation of the acetone droplets is simulated by employing the spray drier model incorporated within CFX4.4, which models heat and mass transfer between the discrete and gas phases, as described above. The turbulent Prandtl number is set to 0.7 for both the enthalpy and vapour mass fraction equations (Antonia and Bilger, 1976). The grid used was a three-dimensional, non-uniform, block-structured grid, which was refined in regions of high-velocity gradient. A sensitivity analysis has been conducted to ensure that the converged solution is independent of the number of parcel tracks used to represent the acetone droplet flow (40,000) and the grid mesh size (105 nodes); doubling the number of droplet parcels and grid nodes lead to a minor change in the droplet volume mean diameter (D30) at the exit of the flow domain of less than 2%. Further details of the Lagrangian modelling approach can be found in the CFX4 documentation.

RESULTS AND DISCUSSION

A typical axial mean velocity profile within a fully-developed jet is similar in appearance to a Gaussian distribution, with a peak axial mean velocity at the centreline, and a tapering axial mean velocity with increasing radial distance from the centreline, down to the co-flow velocity at the edge of the jet. Downstream of the nozzle, the centreline axial mean velocity progressively decreases (or decays) as the jet spreads radially outwards. Figure 2 compares the experimental and predicted centreline axial mean velocity decay rates with axial distance from the nozzle exit for different sized droplets. The decay of the centreline axial mean velocity for the smallest droplets (5 m) is predicted reasonably accurately, while the decay of the centreline axial mean velocity for the largest droplets (85 m) is predicted rather poorly. The smallest droplets are sufficiently small to behave as tracers for the airflow. Therefore, the good agreement between the predicted and experimental decay of the centreline axial mean velocity for the smallest droplets indicates that the turbulence constant VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION of 1.55 is appropriate to properly model the spread of air momentum in this jet. However, the spread of momentum of the larger droplets is under-predicted by the Lagrangian model. This discrepancy is probably due to the incorrect assumption that the radial fluctuating velocities of these droplets at the inlet boundary of the simulation region, which is located close to the nozzle exit, are zero. The initial spread of momentum of the larger droplets is likely to be sensitive to these inlet radial fluctuating velocities, which were not measured during the experiments.

The droplet volume flux profile within a fully-developed jet is also similar to a Gaussian distribution, featuring a peak at the centreline and a tapering volume flux in the radial direction, which reduces down to zero towards the edge of the jet where droplets are relatively sparse. The volume-flux profile also decays and spreads downstream of the nozzle as individual droplets interact with airflow turbulence, which drags them radially outwards. The half-radius of the volume-flux profile, which is defined as the radius of the Gaussian-shaped volume-flux profile corresponding to half the total height of this profile, is a measure of the extent of this turbulent spread or dispersion. A small half-radius indicates that the droplets have not dispersed outwards significantly and that they are concentrated near the axis of the jet, whereas a relatively large half-radius indicates that the droplets have been dispersed by their own inertia or airflow turbulence away from the jet axis. Figure 3 shows that the turbulent dispersion rate of droplets downstream of the nozzle appears to be predicted reasonably accurately, although some caution is required in this interpretation, since the turbulent dispersion of the droplets is linked to the spread of momentum, so that improperly modelling one (as has been demonstrated by the poor momentum predictions of the larger droplets, shown in Figure 2) will inevitably affect the validity of the other. Nevertheless, the overall trends are clearly reasonable. Figure 3 implies that smaller droplets disperse radially more rapidly than larger droplets downstream of the nozzle. This is physically reasonable because small droplets have relatively low inertia such that they readily follow the turbulent fluctuations of the airflow, which tends to disperse the droplets radially outwards. On the contrary, larger droplets have relatively high inertia, so that they are less affected by airflow turbulent fluctuations, being more inclined to continue along the axially-directed trajectories imparted to them at the nozzle exit, and thus spreading very little in the radial direction. Very little spreading of droplets occurs in any droplet size class within the first 10 cm of the nozzle exit, because insufficient airflow turbulence has diffused from the shear layer, near the edge of the jet where this turbulence is generated, towards the centre of the jet to disperse the droplets radially outwards. It is this diffusion of airflow turbulence into the core of the jet that is responsible for the dispersion of droplets beyond 10 cm of the nozzle exit.

Figure 4 compares the experimental and predicted axial evolution of the total volume flow of droplets. Two different extremes for the value of the acetone vapour mass fraction at the nozzle exit are tested in these simulations - no vapour mass fraction and saturated vapour mass fraction - since this value was not measured during the experiments. The true mass fraction of acetone vapour lies between these extremes. In the simulation that assumes no acetone vapour at the nozzle exit, the flow of acetone droplets reduces immediately on emerging from the nozzle, since there is a significant driving force for evaporation within the core of the jet. In the simulation that assumes vapour-saturated airflow at the nozzle exit, very little evaporation of acetone droplets occurs within the first 10 cm from the nozzle exit, because insufficient fresh air from the co-flow has been transported (via turbulence) to the core of the jet to reduce the vapour mass fraction below the saturated value. Acetone droplets begin to evaporate only when the vapour-imbued airflow within the core of the jet is diluted with sufficient fresh air, entrained from the co-flow, to provide a significant driving force for evaporation. The predicted axial evolution of droplet volume flow assuming saturated acetone vapour at the nozzle exit gives the best agreement with the experimental data, which suggests that the airflow was close to vapour saturation at the nozzle exit during the experiments. Nevertheless, the predicted droplet evaporation rate with distance from the nozzle exit is similar irrespective of the acetone vapour fraction adopted at the nozzle exit, and in good agreement with the experimental data, which demonstrates the accuracy of the Lagrangian approach for modelling the overall droplet evaporation rate. These simulations highlight the significant effect of fresh-air entrainment on the evaporation rate of droplets within the jet.

The accuracy of the model for predicting the evolution of the droplet size distribution due to evaporation downstream of the nozzle is evaluated in Figure 5. It appears that the Lagrangian model predicts the correct qualitative trends, although a quantitative comparison shows mixed agreement. Both predictions and experiment imply that there is a gradual shift in the droplet size distribution towards the larger droplet size classes, which suggests that smaller droplets evaporate more quickly than larger droplets. This is expected given that small droplets disperse outwards more readily than large droplets, and thus move more quickly into the outer regions of the spray where fresh air entrained from the co-flow ensures that the vapour mass fraction is relatively low. Nijdam et al. (2004) have shown that the shift in droplet size distribution towards the larger droplet size classes is also due in part to the collision and subsequent coalescence of droplets, although this effect is likely to be small in comparison with the evaporative effect for the dilute sprays investigated here. The discrepancy between the experimental results and the Lagrangian predictions is difficult to resolve without information regarding the evolution of the experimental acetone vapour-fraction field, which would otherwise allow a more detailed analysis of the spray evaporation simulations.

CONCLUSIONS

The decay of the centreline axial mean velocity of the smallest droplets is predicted reasonably accurately, while the centreline axial mean velocity decay for the larger droplets is under-predicted, which we attribute to a poor estimate of the radial fluctuating velocity of these droplets at the inlet boundary. The turbulent dispersion and overall evaporation rates of droplets within the simple spray are modelled reasonably well, which illustrates the potential of the Lagrangian approach for accurately modelling droplet/particle trajectories (and hence residence times) and evaporation within the more complex spray dryer system. However, the evolution of the droplet size distribution is not modelled properly, although there is reasonable qualitative agreement between experiment and predictions. A more detailed experimental investigation of the effect of vapour mass fraction on the evaporation rates of droplets in different size classes is required in order to resolve this discrepancy. Nevertheless, these simulations show that smaller droplets evaporate more quickly than larger droplets, because they disperse more readily towards the outer regions of the jet, where the evaporative driving force is greatest. The importance of turbulence generation within the shear layer on the rate of droplet dispersion and evaporation within the jet has been demonstrated.

ACKNOWLEDGMENTS

This work has been supported by the New Zealand Foundation for Research, Science and Technology under contract UOSY0001, and an Australian Research Council Large Grant.

NOMENCLATURE


VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION heat capacity of liquid (J/kgK)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION droplet diameter (m)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION nozzle diameter (m), or diffusion coefficient (m2/s)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION latent heat of vaporisation (J/kg)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION gas thermal conductivity (W/mK)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION droplet mass (kg)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION droplet evaporation rate (kg/s)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION molecular weight (kg/mol)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION half the width of the volume-flux profile at half the maximum volume flux (mm)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION total gas pressure (Pa)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION temperature (K, °C)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION mean axial velocity (m/s)

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION mole fraction

VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION density (kg/m3)

REFERENCES

Antonia, R.A., Bilger, R.W., 1976, The heated round jet in a co-flowing stream, AIAA J., 14 (11): 1541-1547.

Gosman, A.D., Ioannides, E., 1983, Aspects of computer simulation of liquid-fuelled combustors, J. Energy, 7(6): 482-490.

Harvie, D.J.E., Langrish, T.A.G., Fletcher, D.F., 2001, Numerical simulation of gas flow patterns within a tall-form spray dryer, Trans. I. Chem. E., Part A, 79: 235-248.

Harvie, D.J.E., Langrish, T.A.G., Fletcher, D.F., 2002, A Computational Fluid Dynamics study of a tall-form spray dryer, Trans. I. Chem. E. , Part C, 80: 163-175.

Huang, L., Kumar, K., Mujumdar, A.S., 2004, Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computational fluid dynamic model, Drying Technology, 22(6):1489-1515.

Langrish, T.A.G., Williams, J., Fletcher, D.F., 2004, Simulation of the effects of inlet swirl on gas flow patterns in a pilot-scale spray dryer, Trans. I. Chem. E., Part A, 82(7): 821-833.

Launder, B.E., Sharma, B.T., 1974, Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disk, Lett. Heat and Mass Transfer, 1: 131-138.

Masters, K., 1976, Spray Drying, 2nd ed., John Wiley and Sons, New York.

McGuirk, J.J, Rodi, W, 1979, The calculation of three-dimensional turbulent free jets, in Turbulent Shear Flows (edited by Durst et al.), Springer-Verlag, 1: 71-83.


Nijdam, J.J., Stårner, S.H., Langrish, T.A.G., 2004, An experimental investigation of droplet evaporation and coalescence in a simple jet flow, Experiments in Fluids, 37: 504-517.

Nijdam, J.J., Guo, B., Fletcher, D.F., Langrish, T.A.G., 2004, Challenges of simulating droplet coalescence within a spray, Drying Technology, 22(6): 1463-1488.

Oakley, D.E., 2004, Spray dryer modelling in theory and practice, Drying Technology, 22(6): 1371-1402.


Ranz, W.E., Marshall, W.R., 1952, Evaporation from droplets, Chem. Eng. Prog., Vol. 48, no. 3, pp. 141-146.

Rüger, M., Hohmann, S., Sommerfeld, M., Kohnen, G., 2000, Euler/Lagrange calculations of turbulent sprays: the effect of droplet collisions and coalescence, Atomization and Sprays, 10: 47-81.


Verdurmen, R.E.M., Menn, P., Ritzert, J., Blei, S., Nhumaio, G.C.S., Sorensen, T., Gunsing, M., Straatsma, J., Verschueren, M., Sibeijn, M., Schulte, G., Fritsching, U., Bauckhage, K., Tropea, C., Sommerfeld, M., Watkins, A.P., Yule, A.J., Schonfeldt, H., 2004, Simulation of agglomeration in spray drying installations: the EDECAD Project, Drying Technology, 22(6):1403-1461.


VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION


















Figure 1. Spray nozzle configuration (not to scale).

FVALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION
igure 2. Centreline axial velocity VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION for different size classes at various axial locations from the nozzle exit: experiment (EX) and Lagrangian model (LM).

FVALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION
igure 3. The half-radii VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION of the radial profiles of droplet volume flux for different droplet size classes at various axial locations from the nozzle exit: experiment (EX) and Lagrangian model (LM).

Figure 4. The axial evolution of the total flowrate of droplets: comparison between experiment and two model predictions; one prediction assumes no acetone vapour at the nozzle exit, while the other prediction assumes acetone vapour saturation at the nozzle exit.VALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION


FVALIDATION OF THE LAGRANGIAN APPROACH FOR PREDICTING TURBULENT DISPERSION
igure 5. Comparison of experiment and model predictions of the droplet size distribution at various axial locations from the nozzle exit.



A CROSS VALIDATION OF CONSUMERBASED BRAND EQUITY (CBBE) WITH
A DATA MODEL VALIDATION APPROACH FOR RELATIONAL DATABASE DESIGN
A VALIDATION STUDY ON STATUS AND AGE OF NATURAL


Tags: approach for, lagrangian approach, approach, turbulent, validation, lagrangian, predicting, dispersion