# 338-0525/01 – Finite Volume Method (MKO)

 Gurantor department Department of Hydromechanics and Hydraulic Equipment Credits 4 Subject guarantor prof. RNDr. Milada Kozubková, CSc. Subject version guarantor prof. RNDr. Milada Kozubková, CSc. Study level undergraduate or graduate Requirement Choice-compulsory Year 1 Semester summer Study language Czech Year of introduction 2004/2005 Year of cancellation 2016/2017 Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
BOJ01 doc. Ing. Marian Bojko, Ph.D.
KOZ30 prof. RNDr. Milada Kozubková, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+4

### Subject aims expressed by acquired skills and competences

Students will learn the theory of laminar and turbulent flow and simulations in applications where there are equipment and machinery, which contain liquid, or use it for their activities. They will build the CFD simulations for the basic cases iffluid mechanics. They will apply knowledge of drawing in higher CAD systems, deal with the quality of the grid, select the turbulence models and define appropriate boundary conditions. Students will interpret the results of simulations and analyze the flow. Based on the simulation results will be used for prediction of important parameters. Students will become familiar with the possibilities of CFD simulations, and their areas of application and will be able to solve basic problems in fluid mechanics.

Lectures
Tutorials

### Summary

The course deals with the turbulence, mathematical models of laminar and turbulent flow with heat transfer and incompressible compressible gases. For solution the software product ANSYS-CFX is applied, which uses finite volume integration method. The mathematical model is complemented by boundary and initial conditions. In detail the classic k-eps model is derived and other models are used, for example LES, SAS, DES models. To create geometry the data transfer between CAD - ANSYS-Workbench will be used. The theory is applied to examples of the basic fluid mechanics, buoyancy, natural convection and heat transfer.

### Compulsory literature:

ANSYS CFX- ANSYS CFX RELEASE 11.0, Theory Guide, Tutorials. Southpointe: ANSYS, Inc., 2006.

### Recommended literature:

ANSYS CFX- ANSYS CFX RELEASE 11.0, Theory Guide, Tutorials. Southpointe: ANSYS, Inc., 2006.

no .

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. P.: Introduction, numerical modelling of flow – software for solution of fluid flow, ANSYS CFX, Implementation of CFX in Workbench, type of tasks. (C): Workstation SUN, operating system based on LINUX, introduction ANSYS CFX 2. P.: Coordinate system, Navier-Stokes equation (laminar flow), Einstein summation theorem, examples, flow in domain with step (C): Sketch of geometry in ANSYS Workbench, philosophy of modification of geometry and its modification, creating of computation grid, step by step process, comparison of mesh for FEM and CFD. 3. P.: Turbulence phenomena (C): CFD model of geometry with step, laminar flow regime. Import of mesh, types of readable mesh. 4. P.: Mathematical model of turbulence, N-S equation, the equation of continuity, the Reynolds stress, time averaging, Reynolds rules, Boussinesq hypothesis, two-equation turbulence model: evaluation of the result. (C): Simulation of laminar flow in the domain with a step. The creation of the evaluation equation of the drop coefficient in postprocessor. 5. p.: General equations of conservation, for example, the equation of heat conduction + peripheral and initial conditions, the numeric methods of solutions (the differential method, the method of the final volumes), (C): Calculation of non isothermal flow in natural convection, different variants. 6. P.: Integration method of definitive volumes for one dimension equation of continuity and motion equation iteration cycle, interpolation scheme, convergence (residual), folding, currents, definition of matter-multiphase models (C): Determination of local losses in the area, with a sudden enlargement, testing the effects of turbulence model on the value of the loss factor. Define the boundary conditions function, the measured data. Export data from the postprocessor, an evaluation of the data in Excel. 7. P.: Boundary conditions, the conditions of inlet and outlet, symmetry conditions, periodic terms, conditions, on the wall, the wall of the heat transfer with time-dependent task C: Modelling the dispersion of matter, Lagrange definition. 8. P.: Flow of solid particles and drops, the ingredients and their definitions. Definition of drag and lift coefficient of droplets, solid particles. (C): Modelling of pollutant dispersion (left over) 9. P.: Methods of solution of differential equations Solver LGS, multigrid. (C): Modelling of dispersion of matter, Euler's approach, multiphase a mixture of water-air 10. P.: a brief overview of turbulence models available in CFX, zero-equation model, k-model, RNG k-RSM (model, model, and models of the LES, SAS, and DES. (C): Modelling of heat transfer and heat conduction in solid wall. 11. P.: The Flow of real liquids, the law of conservation of mass, momentum, energy flow for compressible fluid. (C).: Example of a combined FEM-CFD calculation. FSI (Fluid-Solid Interaction). 12. P.: Specifying individual seminar work, (C): solution of individual seminar work: Special settings in the program CFX, multidomain, (C) Solution of individual seminar work 13. P.: Integration of CFX in Workbench, a general procedure in the design and calculation of machine parts (C): Solution of individual seminar work

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2010/2011 Summer semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
Exercises evaluation Credit 35 (35) 0 3
Project Project 35  0 3
Examination Examination 65 (65) 0 3
Oral Oral examination 65  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2012/2013 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

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