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Advanced Spray and Combustion Modelling
[Thesis]. Manchester, UK: The University of Manchester; 2011.
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Abstract
Abstract Advanced Spray and Combustion Modelling Ahmed Abed Al-Kadhem Majhool, 2011 Doctor of Philosophy, The University of ManchesterThe first attempt at modelling a fully Eulerian model for poly-disperse nature of the spray flowwithout using droplet size classes was proposed by Beck and Watkins [2003a]. The parametersused to describe the distribution of droplet sizes are the moments of the droplet size distributionfunction. Transport equations for only some moments of the spray distribution function arederived and solved through classical Eulerian schemes. The velocities to be used in the twotransport equations are obtained by defining moment-average quantities and constructing furthertransport equations for the relevant moment-average velocities. The continuous distribution ofdroplets is approximated using an analytically integrable function to use as a number distributionwas sought such that the volume distribution it produced was a reasonable approximation to aRosin-Rammler distribution. The new form of the continuous function was later revised by Yueand Watkins [2004], who implemented the Gamma distribution whose parameters were obtainedfrom the transport equations for second, third and fourth moments. This permits the form ofthe two parameter number size distribution to be totally calculated and to all predictions ofchanges to the distribution in space and time. Hydrodynamics submodels were implementedin Jones [2009] with higher order of numerical tools. The model is implemented in a new codebased on current numerical methods detailed in Ferziger and Peri ́ [2002], so as to make use of chigh resolution differencing schemes for the transportation of the moments and enable improvedresolution of the solution by using an unstructured grid topology.The thesis presents work across three different subjects of investigations into the modelling ofspray development and its interaction with non-reactive and reactive flow. The first part ofthis research is aimed to create a new and robust family of convective scheme to capture theinterface between the dispersed and the carrier phases without the need to build up the interfaceboundary. The selection of Weighted Average Flux (WAF) scheme is due to this scheme beingdesigned to deal with random flux scheme which is second-order accurate in space and time. Theconvective flux in each cell face utilizes the WAF scheme blended with Switching Technique forAdvection and Capturing of Surfaces (STACS) scheme for high resolution flux limiters. Howeverin the next step, the high resolution scheme is blended with the scheme to provide the sharpnessand boundedness of the interface by using switching strategy. The proposed scheme is tested on capturing the spray edges in modelling hollow cone type sprays without need to reconstructtwo-phase interface. A test comparison between TVD scheme and WAF scheme using the sameflux limiter on convective flow on hollow cone spray is presented. Results show that the WAFscheme gives better prediction than the TVD scheme. The only way to check the accuracy of thepresented models are evaluations according to physical droplets behaviour and its interactionwith air. In the second part, due to the effect of evaporation the temperature profile in thereleased fuel vapour has been proposed. The underlying equation utilizes transported vapourmass fraction. It can be used along with the solution of heat transfer inside a sphere. Afterapplying boundary conditions, the equation can provide a solution of existing conditions atliquid-gas interface undergoing evaporation and it is put in a form similar to well-known one-third rule equation. The resulting equation is quadratic type that gives an accurate prediction forthe thermo-physical properties due to the non-linear relation between measured properties andtemperature. Comparisons are made with one-third rule where both equations are implementedin simulating hollow cone spray under evaporation conditions. The results show the presumedequation performs better than one-third rule in all comparisons.The third part of this research is about a conceptual model for turbulent spray combustionfor two combustion regimes that has been proposed and tested for n-heptane solid cone spraytype injected into a high-pressure, high-temperature open reactor by comparing to the availableexperimental data and to results obtained using two well known combustion models named theCombined Combustion Model (CCM) and the unsteady two-dimensional conditional momentclosure (CMC) model. A single-zone intermittent beta-two equation turbulent model is sug-gested to characterise the Lumped zone. This model can handle both unburned and burnedzones. Intermittency theory is used to account for the spatially non-uniform distribution ofviscous dissipation. The model suggests that the Lumped zone can be identified by using theconcept of Tennekes and Kuo-Corrsion of isotropic turbulence that suggests that dissipativeeddies are most probably formed as vortex tubes with a diameter of the order of Kolmogorovlength scale and a space of the order of Taylor length scale. Due to the complexity of mixturemotion in the combustion chamber, there exist coherent turbulent small scale structures con-taining highly dissipative vortices. The small size eddies play an important role in extinguishinga diffusion spray flame and have an effect on the combustion reaction at molecular scale becausesmall scales turbulence increase heat transfer due to the dissipation. A common hypothesis inconstructing part of the model is if the Kolmogorov length scale is larger than the turbulentflame thickness. The Lumped strategy benefits from capturing small reactive scales information provided by numerics to improve the modelling and understand the exact implementation of theunderlying chemical hypothesis. The Lumped rate is estimated from the ratio of the turbulentdiffusion to reaction flame thickness. Three different initial gas temperature test cases are im-plemented in simulations. Lumped spray combustion model shows a very good agreement withavailable experimental data concerning auto-ignition delay points.