# 338-0546/02 – Modeling of fluid flow with heat transfer (MPsPT)

 Gurantor department Department of Hydromechanics and Hydraulic Equipment Credits 4 Subject guarantor doc. Ing. Marian Bojko, Ph.D. Subject version guarantor doc. Ing. Marian Bojko, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language English Year of introduction 2013/2014 Year of cancellation Intended for the faculties FS, USP Intended for study types Follow-up Master
Instruction secured by
BLE02 doc. Ing. Tomáš Blejchař, Ph.D.
BOJ01 doc. Ing. Marian Bojko, Ph.D.
KOZ30 prof. RNDr. Milada Kozubková, CSc.
MAR0476 Ing. Patrik Marcalík
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

In this course, students will learn in detail the basic concepts of modeling fluid flow and heat transfer, ie conduction and convection. They will also gain knowledge about mathematical models of multiphase flow with phase change (eg cavitation), optimization of geometry in terms of hydraulic quantities and the possibility of modeling time-dependent vortex structures. They will learn to solve selected problems using available software.

Lectures
Tutorials

### Summary

The subject deals with the physical meaning of turbulence and mathematical models of laminar and turbulent flow with heat transfer. The mathematical model is defined by a system of partial differential equations and supplemented by boundary and initial conditions. In addition to normal hydraulic flow conditions, wall conditions, heat transfer through the wall, time-dependent boundary conditions, and conditions for multi-phase flow are also taken into account. Classical models of turbulence are defined in detail. The theory is applied to examples solving bypassing of obstacles, buoyancy force, natural convection, heat transfer through the wall, etc. For the solution is applied software product Ansys-Fluent, which uses the finite volume method.

### Compulsory literature:

[1] ANSYS Fluent User’s Guide (Release 18.2). 2017. [2] INCROPERA, P. F., DEWITT, P. D., BERGMAN, L. T., LAVINE, S. A. Fundamentals of Heat and Mass Transfer. 997 s. ISBN 978-0-471-45728-2.

### Recommended literature:

[1] ANSYS Fluent Theory Guide (Release 18.2). 2017. [2] ANSYS Fluent Tutorial Guide (Release 18.2). 2017.

### Way of continuous check of knowledge in the course of semester

Zápočet se skládá z hodnocení dvou testů (1. a 2. test jsou stejně hodnoceny, tj. min. 5 bodů, max. 8 bodů) v průběhu výuky a seminární práce (min. 15. bodů, max. 19 bodů). Zápočet: min. 25 bodů max. 35 bodů Zkouška: min. 26 bodů max. 65 bodů Zkouška bude probíhat kombinovanou formou.

### Other requirements

List of exam questions 1. Continuum hypothesis 2. Methods of solution of heat, mass and momentum transfer 3. Physical properties of solids and liquids 4. Dimensionless criteria 5. Convective transition, diffusion transition, balance equation of transition 6. Boundary conditions 7. Numerical methods, difference method, finite volume method 8. Creation of geometry, mesh elements, convergence and residuals, acceleration of convergence, relaxation 9. Conduction heat transfer equations, boundary conditions 10. Laminar flow, mass and momentum transfer (continuity equation, Navier-Stokes (moment, motion) equation) 11. Boundary and initial conditions on inlet, outlet and wall 12. Theory of laminar flow with heat transfer, solution of conduction and convection in laminar flow, boundary conditions 13. Turbulence, Reynolds time averaging, k-ε two-equation model of turbulence 14. Boundary conditions for k-ε turbulent model, ie mass flow, turbulent quantities, inlet pressure, outlet pressure, Outflow 15. Wall functions, possibilities of refinement of calculation, influence of mesh quality on choice of wall function for various turbulence models, selection of turbulent model for refinement of calculation 16. Conduction and convection solution in turbulent flow, heat transfer in turbulent flow around the cylinder, boundary conditions 17. Analysis of heat exchangers, basic types of heat exchangers and their description, heat output and pressure drop of heat exchanger 18. Time-dependent solution, time-dependent boundary conditions 19. Multi-phase flow, principle of cavitation and water hammer 20. Optimization of shape in terms of hydraulic quantities

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Introduction, physical properties of fluids, balance transfer equation 2. Differential method, network types, finite volume method, relaxation, residuals 3. Conduction, heat conduction in a plate, time-dependent solution 4. Laminar flow, application to water flow between plates, boundary conditions, calculation of velocity profile 5. Conduction and convection in laminar flow, evaluation of thermal quantities, reference values 6. Turbulence, calculation and evaluation of turbulent quantities, boundary conditions for turb. quantities, 7. Accuracy of wall turbulence calculation according to gradient, RSM, LES, DNS methods, flow around cylinder 8. Conduction and convection in turbulent flow, single pipe wrapping, cross pipe wrapping and in-line, temperature-dependent physical properties 9. Heat exchangers in general, co-current, counter-current, physical properties of gas, kinetic theory, example of a tube heat exchanger, spiral heat exchanger 10. Time-dependent flow, boundary conditions of time-dependent solution, FFT-examples 11. Optimization of flow geometry (elbow) 12. Multiphase flow, physical properties of mixture, flow of gas mixture, gravity 13. Cavitation flow, porous medium flow - nozzle application, 14. Vectors in flow theory, discussion

### Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 35  25
Examination Examination 65  26
Mandatory attendence parzicipation: full-time study - 80% attendance part-time study - 50% attendance

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2027/2028 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2026/2027 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2025/2026 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2024/2025 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2023/2024 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2022/2023 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2021/2022 (N0715A270034) Applied Mechanics P English Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2018/2019 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2017/2018 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2016/2017 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2016/2017 (N2301) Mechanical Engineering (2302T006) Energy Engineering P English Ostrava 1 Compulsory study plan
2015/2016 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Master Studies 2021/2022 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Master Studies 2020/2021 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Master Studies 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Master Studies 2018/2019 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Master Studies 2017/2018 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Master Studies 2016/2017 Full-time English Choice-compulsory 301 - Study and International Office stu. block