Anna Bulińska, Zbigniew Buliński. A CFD analysis of different human breathing models and its influence on spatial distribution of indoor air parameters. CAMES 2015 (22)

The computational fluid dynamics (CFD) analysis of the indoor environment in buildings requires numerical modelling of a human being (computer simulated person - CSP). There are two crucial aspects in developing reliable CSP models: the CSP geometry and the breathing model. This paper focuses on the analysis of different breathing models for application in the CFD modelling. Three breathing models were analysed: first model was restricted to constant exhalation, second model, the so-called full breathing, included constant rate inhalation, constant rate exhalation and pause period, and in the third model temporal variation of flow rate was represented by sinusoidal function. The main findings from this work show that all three models compared with experimental data gave reliable results. The spatial distribution of CO_{2} concentration and velocity showed only small differences among the models in the vicinity of the mouth and above the person. It was shown that a simplified constant exhalation model can be effectively used for the CFD analysis of the indoor air quality (IAQ). However, a detailed simulation of micro-environment in the room and transport of contaminants should include complete breathing.

*Keywords:* breathing models, metabolic carbon dioxide, indoor air quality (IAQ), computer simulated
person (CSP), CFD.

Michael Harris, Alain Kassab, Eduardo Divo. Application of an RBF blending interpolation method to problems with shocks. CAMES 2015 (22)

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices.
The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high conditioning number for the interpolation matrix, rendering the RBF smooth [1-10]. However, this strategy fails for a problem with a shock or sharp discontinuity. Instead, in such cases the conditioning number must be kept small. The focus of this work is then to demonstrate the use of RBF interpolation in the approximation of sharp
gradients or shocks by use of a RBF blending interpolation approach. This RBF blending interpolation approach is used to maintain the optimum shape parameter depending on the field. The approach is able to sense gradients or shocks in the field and adjust the shape parameter accordingly to keep excellent accuracy. Presented in this work, is an explanation of the RBF blending interpolation methodology and testing of the RBF blending interpolation approach by solving the Burger's equation using the virtual
finite difference method.

*Keywords:* meshless methods, radial basis functions, multiquadrics, shape parameter, shocks.

Marek Jaszczur, Inga Polepszyc, Michał Dudek. An analysis of the boundary conditions model influence on the ground temperature profile determination. CAMES 2015 (22)

In this work, the influence of boundary conditions model (environmental model) on the ground temperature profile is analyzed. A numerical model for transport phenomena in the area above the top ground surface and below in the ground is presented. The results of simulation- ground temperature profile and mean seasonal temperature which estimate the energy potential of the ground are presented. In addition, the results of implementation of five different environmental models for the area above the top ground surface
are presented. It is found that none of the models is able to reproduce the temperature variation similar to the reference (most complex) model accuracy. On the other hand, it is found that with a slight error a similar result for low ground depth can be obtained using the simplest Model 1.

*Keywords:* heat transfer, ground heat transport, ground temperature profile, ground source heat pump.

Iwona Nowak, Grzegorz Nowak. Real ant colony optimization as a tool for multi-criteria problems. CAMES 2015 (22)

This paper presents a population-based heuristic method - a real ant colony optimization (RACO) as a tool for multi-criteria optimization problems. The idea of multi-criteria optimization is discussed and the necessary modifications of RACO are proposed. These modifications made possible to use the method to simultaneously search many Pareto-optimal solutions. The method was numerically tested in problems of benchmark-type and used for solving simple engineering problems. This article presents and discusses
all results obtained in tests, and two different approaches to multi-criteria optimization are additionally compared (search then decision and decision then search).

*Keywords:* multi-objective optimization.

Krzysztof Rogoziński, Grzegorz Nowak. Numerical simulations of a conceptual blade cooling with a working medium. CAMES 2015 (22)

The development of steam power units aims to increase the working steam parameters as they are the main factors that determine the efficiency of energy conversion. Most state of the art units are designed for supercritical steam parameters. However, the temperature level of steam feeding the turbine is limited by thermal strength of the material used to make the machine components. In this situation, using nickel alloys or cooling the elements exposed to the impact of high temperatures could be the appropriate
solution. The former is rather expensive and the latter - technically difficult. The cooling option would require that the cooled element should be fed by a steam with a very high pressure and with a lower temperature than the temperature in the machine flow system. This paper presents the concept of using working steam as the cooling medium after it is expanded in a convergent-divergent nozzle. In such a case, the cooling system is very simple and the performed simulations indicate, for example, that the turbine
blades may be cooled in this way.

*Keywords:* blade cooling, convergent-divergent nozzle, Laval nozzle, shock wave.

Wit Stryczniewicz, Andrzej J. Panas. Numerical data processing from a laser flash experiment on thin graphite layer. CAMES 2015 (22)

In this paper, the methodology for determination of the out-of-plane thermal diffusivity (TD) of a thin graphite layer deposited onto a substrate of known properties is presented. The developed methodology resulted in combined experimental-numerical procedure enabling investigation of the properties of thin layer deposits. The procedure involves the experimental data acquisition during the laser flash tests, and next the numerical processing of the collected data using the heat conduction problem solution and the
nonlinear least square parameter identification approach. Two last steps produce a certain inverse heat conduction problem that is formulated and numerically solved for a three-layer specimen. The procedure has been successfully tested while processing the real experimental data from investigation of flake graphite layers. This proved the effectiveness of the methodology in providing quantitative data on the TD of thin layers of relatively poor conductors deposited onto a highly conductive substrate.

*Keywords:* inverse analysis, finite element method (FEM), multilayer heat transfer, thin layer diffusivity, laser flash data processing.

Shiting Wen, Kai Wang, Rizwan Zahoor, Ming Li, Bozidar Šarler. Method of regularized sources for two-dimensional Stokes flow problems based on rational or exponential blobs. CAMES 2015 (22)

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary,
i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity is obtained from the analytical solution due to the action of the Dirac delta- type force. Instead of Dirac delta force, a non-singular function called blob, with a free parameter epsilon is employed, which is limited to Dirac delta function when epsilon is limited to zero. The analytical expressions for related Stokes flow pressure and velocity around such regularized
sources have been derived for rational and exponential blobs in an ordered way. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions.A numerical example for two-dimensional (2D) driven cavity and a flow between parallel plates are chosen to assess the properties of the method. The results of the posed method of regularized sources (MRS) have been compared with the results obtained by the fine-grid second-order classical finite difference method (FDM) and analytical solution. The results converge with finer discretisation; however, they depend on
the value of epsilon. The method gives reasonably accurate results for the range of epsilon between 0.1 and 0.5 of the typical nodal distance on the boundary. Exponential blobs give slightly better results than the rational blobs; however, they require slightly more computing time. A robust and efficient strategy to find the optimal value of epsilon is needed in the perspective.

*Keywords:* Stokes flow, regularized sources, rational blobs, exponential blobs, meshless method, driven cavity problem, convergence study.