# Spray evaporation in turbulent flow

## Best Practice Advice for the AC

### Key Fluid Physics

The spray evaporation in a heated turbulent air stream was studied experimentally.

The flow configuration was a pipe expansion with an expansion ratio of three, where heated air entered through an annulus with the hollow cone spray nozzle being mounted in the centre.

In the experiments isopropyl-alcohol was used as a liquid due to its high evaporation rates.

Measurements were taken for different flow conditions, such as air flow rate, air temperature, and liquid flow rate in order to provide a set of reliable data.

The two-phase flow is characterised by heat, mass and momentum transfer between the phases. Hence two-way coupling is important for this AC.

The key assessment parameters are, the profiles of air and droplet velocities along the test section and the evolution of the integrated droplet mass flow rate along the test section.

### Application Uncertainties

Summary of measurement uncertainties:

• The air flow rate was determined from the integration of the axial velocity profile at the inlet and the associated mass flow rate was determined by multiplication with the air density resulting from the average inlet temperature. Hence an accuracy of ±10% can be estimated.

• The liquid flow rate could be adjusted within ±5% by using a flow meter.

• The velocity measurements of the gas phase were performed by sampling 2,000 signals at each measurement location. Therefore, a high degree of confidence is given.

• The droplet phase properties were obtained from 20,000 samples over the entire size spectrum ensuring statistical reliable data for the mean properties and the associated rms-values.

• The droplet mass flux could be measured with an accuracy of ±10% since the spray was rather symmetric.

### Computational Domain and Boundary Conditions

The numerical calculations of the turbulent spray should be performed by the Eulerian/Lagrangian approach for the gas and droplet phase by accounting for two-way coupling.

• The standard k-ε turbulence model with wall functions was found to give reasonable results.

• The geometry of the test facility was axi-symmetric and the spray nozzles were selected to provide a symmetric spray. Therefore, the flow computations may be performed on the basis of the two-dimensional, axi-symmetric form of the conservation equations. The dispersed phase should be treated by a Lagrangian approach using the Cartesian form of the equations in order to avoid the singularity for r → 0 at the centre-line.

• A length of 1.2 m for the computational domain is sufficient to allow the application of outflow boundary conditions without affecting the result in the region where the spray is evaporating (i.e. up to about 0.5 m).

• The inflow boundary conditions for the air flow (annular jet) should be specified according to the measurements. Profiles of the axial mean velocity and mean temperature are available. The radial and tangential mean velocity can be assumed to be zero. The turbulent kinetic energy can be calculated from the measured three components of the rms values. The dissipation rate should be determined in the standard way using a length scale of 0.41ž0.012 m.

• The inlet conditions for the spray droplets should be specified according to the measurements. For the droplet phase, size distributions are provided at several radial positions 3 mm downstream of the nozzle holder. Additionally, the size velocity correlations are given.

• At the walls no-slip boundary conditions should be used for the air velocity. The wall temperature along the test section may be specified according to the measurements.

### Discretisation and Grid Resolution

• The set of gas-phase conservation equations was solved by using a finite-volume discretization scheme and applying an iterative solution procedure based on the SIMPLE algorithm. The convective terms were discretised by a flux correction method (a combination of upwind and central differencing) and the diffusive terms were discretised by second central differences.

• Four different numerical grids were used with 13 x 22, 24 x 42, 46 x 82 and 90 x 162 cells in the radial and axial direction (i.e. 0.1 m x 1.5 m). A grid-independent result may be obtained with 90 x 162 cells.

• The computations were performed on an equidistant grid in the radial direction and continuously expanded in the axial direction with the finest mesh near the inlet.

• For calculating the droplet trajectories a first order Euler approach was found to be sufficient.

• The droplet size spectrum should be resolved by about 20 classes having a width of no more than 5 mm.

• In order to get statistically reliable results at least 40,000 parcel trajectories should be calculated for each coupling iteration. With an under-relaxation factor of 0.1 about 50 coupling iterations are recommended.

### Physical Modelling

• The Euler/Lagrange approach with two-way coupling (mass, momentum, energy and turbulence) should be used due to the importance of the droplet size distribution.

• The well-known k-ε turbulence model employing the standard constants is sufficient to obtain reasonable predictions of the single-phase flow.

• Three-dimensional droplet tracking by accounting for drag and gravity (transverse lift forces are negligible) is suggested.

• A random walk approach was found to satisfactorily predict the droplet turbulent dispersion (i.e. generation of the instantaneous fluid velocity along the droplet trajectories).

• The gas-side heat and mass transfer may be described by an extended film theory introduced by Abrahamson and Sirignano. For the liquid side the infinite conductivity model was found to be sufficient.

### Recommendations for Future Work

Further improvements of the numerical predictions may be possible by the following:

• Application of a full Reynolds stress turbulence model together with a more advanced droplet dispersion model (e.g. Langevin model).

• Further improvement of the droplet evaporation model (e.g. temperature distribution inside the droplet, non-equilibrium model).

• Consideration of droplet coalescence.

• Multi-component spray evaporation.