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Title: Extension of spray flow modelling using the drop number size distribution moments approach
Author: Alqurashi, Faris
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2015
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This work is an extension to the spray model of Watkins and Jones (2010). In their model, the spray is characterized by evaluating the three moments Q_2, Q_3 and Q_4 of general gamma number size distribution from their transport equations. The sub-models of drop drag, drop break-up and drop collisions were simulated in terms of gamma distributions. The model is considered as non-vaporising and compared with cases which have low ambient gas temperature and also is strict to a particular set of sub-models for drop drag and break up which they are applicable to produce integrable functions. In this work the model is adjusted to allow a variety of sub-models to be implemented. Three models (TAB, ETAB, DDB) are considered for drop breakup which have been basically introduced to be used with the Droplet Discrete Method (DDM) approach. So in order to implement these models with the model of Watkins and Jones the source terms of the breakup are calculated by grouping the droplets in each cell into parcels which contain a certain number of droplets with similar physical properties (size, velocity, temperature ...). The source terms of each parcel are calculated and multiplied by the number of droplets in these parcels and a numerical integration is then used to obtain the resultant effect of the drop breakup in each cell. The number of drops in each cell is determined from the gamma size distribution. Also three hybrid breakup models (KH-RT, Turb-KH-RT, Turb-TAB) which include two distinct steps: primary and secondary break up model are implemented. The Kelvin- Helmholtz (KH) and the turbulence induced breakup (Turb) models were used to predict the primary break up of the intact liquid core of a liquid jet while the secondary break up is modelled using the TAB model and competition between the KH and the RT models. Both models are allowed to work simultaneously. However it is assumed that if the disintegration occurs due to the RT the KH break up does not occur. In case of drag sub-model, a dynamic drag model is introduced which accounts for the effects of drop distortion and oscillation due to the effects of high relative velocity between the liquid and the surrounding gas. In this model the drag coefficient is empirically related to the magnitude of the drop deformation. The magnitude of drop deformation was calculated by using the TAB model. In this work, the effects of mass and heat transfer on the spray are modelled. An additional equation for the energy of the liquid is solved. The mass transfer rate is evaluated using the model of Godsave (1953) and Spalding (1953) while the Faeth correlation (1983) is used to model heat transfer between the two phases. For all equations of heat and mass transfer between phases, the drop Nusselt and Sherwood number are calculated by using the correlation of Ranz and Marshall. In this model also the liquid surface-average temperature T_l2 which is calculated by Watkins (2007) is used to determine the heat and mass transfer between phases instead of liquid volume-average temperature. It was derived by assuming a parabolic temperature profile within individual drops. All the equations are treated in Eulerian framework using the finite volume method. The model has been applied to a wide range of sprays and compared to a number of experiments with different operating conditions including high liquid injection pressure and high ambient gas density and temperature. A reasonable agreement is found by the ETAB model with most of the data while the TAB and the DDB models continually underestimate the penetration and drop sizes of the spray. The hybrid breakup models perform well and show better agreement with the available experimental data than the single breakup models. In term of high temperature cases, the model correctly captures the effect of evaporation on the different spray properties especially with hybrid break up model.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: spray ; gamma distribution ; breakup ; drag ; and heat transfer