The main subjects of the present study are the computational and the accompany-ing theoretical investigations of flow induced by saccompany-ingle-drop impacts. The objective is to assess the capabilities of the computational procedure for interface capturing based on the VOF-method and to improve the overall understanding of the under-lying physical mechanisms. The following characteristic flows pertinent to spray impingement are identified, computed and analyzed:
• drop collisions, comprising collision with a shallow liquid layer, binary drop collision, and collision with a dry wall,
• drop impact onto a heated wall with the simultaneous heat transfer in the wall and
• drop impact onto a porous substrate.
All the flows studied are treated as laminar, although this might eventually represent an approximation for some of the configurations. The numerical code used is appropriately extended to account for the advancing and receding contact angles, the nonisothermal free-surface flow and simultaneous heat transfer in the solid and for fluid penetration in the porous substrate.
The formation and evolution of the crater formed upon the drop impact on a liquid layer are investigated. Based on the results obtained by numerical simulations, the crater penetration and the formation of the residual liquid film on the substrate are theoretically described. The investigation of the flow generated by normal drop collision with a rigid substrate or by collision with another drop enables the dynamics of the expansion of the spreading lamella to be described. The existing results, commonly based on the energy balance approach, are examined. The early stages of the drop initial deformation and spreading are computed numerically providing the database of results required for the theoretical modeling which are presently not available in the literature. Modeling the complicated wall effects is avoided in the simulation of binary drop collision.
Drop impact onto a heated wall is examined with respect to the developing temperature distribution in the spreading lamella and simultaneously in the wall.
Coupled numerical simulations of the nonisothermal free-surface flow above and the conjugate heat transfer in the wall are performed, utilizing temperature-dependent thermophysical properties. The numerical simulation enables the temporal distri-butions of the wall temperature and the removed heat flux to be determined.
Drop impact on a porous substrate is computed using two approaches. In the first approach, the computational model for interface capturing is extended and the combined model is formulated including both the external flow for the spreading and the flow of the absorbed fluid in the porous substrate. In the second approach, drop spreading on the porous surface is numerically simulated by computing only the external flow generated by the drop impact and the existence of the porous surface is accounted for by formulating an appropriate boundary condition for the permeable wall. The capabilities of both approaches are analyzed.
In the introductory part, Chapter 1, a short background in drop and spray impact is given outlining some of the important perspectives which were the basic motivation for this work. The main phenomenological aspects of the flow are delin-eated and main computational strategies for free-surface flows are revised. A brief overview of some of the previously published research related to the present study is given.
In Chapter 2 the numerical code and the computational procedure relying on the finite-volume method are described.
The subsequent chapters comprise the analysis and results of the studied flow configurations. The computational models are validated using the common test cases from the existing literature. The governing equations and the main considerations for the specific flow are given, followed by the presentation of the results obtained by the numerical simulations and the theoretical models. Chapter 3 presents the investigation of the flow generated by drop collisions, including collision with a shallow liquid layer, binary drop collision and collision with a dry wall. In Chapter 4
the results of the investigation of the nonisothermal drop impact onto a dry heated wall with the simultaneous heat transfer within the wall are presented. Chapter 5 deals with the investigation of drop spreading on and absorbtion in the porous substrate.
General conclusions are presented in Chapter 6 with the accompanying recom-mendations for future work.
In this Chapter the numerical code used for the simulation is briefly described and the basic discretization techniques applied in the framework of the finite-volume numerical method are outlined. The discretization practice and the solution tech-nique are applied to the generic transport equation, which has the same general form taken by the transport equations governing the studied flows. These governing equations form equation systems describing the flows and consist of the equations for the conservation of mass, phase fraction (indicator function) and linear momentum, including the energy conservation equation in the nonisothermal flow. The gov-erning equations pertinent to the specific flow are introduced in the corresponding subsequent Chapters where also some additional numerical features and the details of the implementation are presented.
2.1 Description of the Open Source CFD Toolbox OpenFOAM
All numerical simulations were performed using OpenFOAM (Open Field Opera-tion And ManipulaOpera-tion), a free-source CFD-toolbox produced by OpenCFD Ltd.
It is based on the finite-volume numerical method with the co-located variable ar-rangement for solving systems of transient transport equations on arbitrary un-structured meshes in three-dimensional space. The software consists of a number of pre-compiled libraries and solvers, accompanied by the corresponding open-source codes written in C++ programming language in an object-oriented manner suitable for solving problems in Computational Continuum Mechanics (CCM). Using the object-oriented programming approach creation of data types (fields) closely mim-icking those of mathematical field theory is enabled, and the feature of operator overloading in C++ allows mathematical symbols to be applied on scalar, vector and tensor fields very similar to those in ordinary mathematics (vector and tensor products or differential operators). Contrary to numerical codes written in procedu-ral languages (like FORTRAN) that require implementation of transport equations and models at a low programming level, this task is accomplished at the highest coding level (top user level) in OpenFOAM, resembling closely the standard tensor notation. It is utilized by the OpenFOAM programming language which is generic, making extensive use of C++ class and function templates and the principle of class inheritance (Weller et al. [129]).
For the finite-volume discretization, a variety of discretization practices are im-plemented for the temporal, convection, diffusion and source terms in the transport equations. All numerical schemes are run-time selectable and can be used
indepen-dently of the geometry of the cases studied. Coupling between equations is handled in a segregated fashion, by formulating and solving equations for each variable sep-arately and iterating over the equations’ system until the predefined convergence criteria are satisfied. From the implementation point of view boundary conditions are treated as an integral part of the overall tensor field, rather than being extra added. Available are basic conditions, including fixed value, zero gradient, fixed gra-dient, symmetry and cyclic, and a number of derived boundary conditions combining the basic ones. A number of iterative solvers for linear systems of equations is avail-able and run-time selectavail-able, including conjugate gradient, algebraic and geometric multigrid solvers.
For the code parallelization OpenFOAM uses the domain decomposition method, where the computational domain is split into a number of subdomains, one for each processor. At run-time each processor receives a separate copy of the compiled code to be run on each subdomain. For the communication between processors the Message Passing Interface (MPI) is used. The inter-processor communication is im-plemented at the level of field classes (representing scalar, vector or tensor fields), thereby enabling any new code written at the higher user level for solving partial differential transport equations to be automatically parallelized.