338-0513/04 – Applied Fluid Mechanics (AplMT)
| Gurantor department | Department of Hydromechanics and Hydraulic Equipment | Credits | 4 |
| Subject guarantor | doc. Dr. Ing. Lumír Hružík | Subject version guarantor | doc. Dr. Ing. Lumír Hružík |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2020/2021 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The aim of the course is to acquaint students with the mathematical models, numerical methods and programs for the solution of unsteady flow in fluid systems. They will gain knowledge about the possibilities, advantages, and limitations of using various mathematical models, numerical methods and programs, especially for hydraulic systems with a long hydraulic pipeline. Students gain experience in the field of experimental determination of dynamic properties of fluid systems. Transient and frequency responses of long hydraulic pipelines will be evaluated. They will gain practical experience in numerical modeling of hydraulic system dynamics with a long hydraulic pipeline in Matlab Fluids.
Teaching methods
Lectures
Tutorials
Experimental work in labs
Project work
Summary
In the course of Applied Fluid Mechanics, students learn about mathematical models, numerical methods and programs for solving unsteady fluid flow. They will learn experimental methods of dynamic properties evaluation in fluid systems. They will learn the effects of various parameters on the dynamics of fluid systems. Transient and frequency responses of hydraulic lines will be evaluated.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Credit: during the semester will be enter 2 programs for which it is possible to get up to 35 points. Minimum for obtaining credit is 18 points, max. 35 points.
Examination: oral exam - 2 questions, each for max 25 points, defense of programs for max. 15 points.
E-learning
The following study materials are available on the department website:
http://www.338.vsb.cz/studium/studijni-opory/
Other requirements
List of questions to examination
1. Unsteady flow in a long pipeline. Pulsating flow in pipelines - magnitude and phase responses of pipelines. The shape of pipeline oscillation.
2. Mathematical model of a segmented pipeline with lumped parameters, composition, and definition of R, H, D resistances.
3. One-dimensional pipeline model with continuously distributed parameters - quasi-stationary velocity profile. Motion equation and continuity equation.
4. Basic dynamic parameters of hydraulic lines. Wave propagation constant in hydraulic lines. Wave resistance.
5. Laplace transform method for a pipeline with continuously distributed parameters. Matrix notation of pipeline model. Matrix solution of chain dynamics of hydraulic components.
6. Dynamic resistance. Mathematical models of discrete elements - Laplace transform method - matrix notation.
7. Method of characteristics for the solution of pipelines with continuously distributed parameters.
8. Bulk modulus of liquid- air mixture: computational equations, possibilities of mixture definition in the modeling of hydraulic systems dynamics.
9. Experimental determination of fluid bulk modulus and pipe (hose) modulus of elasticity.
10. Methods for determining the amount of air in the liquid.
11. Experimental evaluation of hydraulic shock in pipeline. Speed of sound determination in the pipeline. System structure, measurement methodology, sensors, measuring device.
12. Eigenfrequency of hydraulic lines - the influence of boundary conditions and other parameters.
13. Dynamics of hydraulic system with hydraulic cylinder, mass load, long hydraulic pipeline. Influence of pipeline parameters, dimensions of hydraulic cylinder and mass load.
14. Experimental determination of pipeline pressure frequency responses. System structure, measurement methodology, sensors, measuring device.
15. Influence of accumulator in the pipeline during pulsating flow.
16. Simulation of unsteady flow in hydraulic systems with a long pipeline in Flowmaster software. Options, mathematical model, numerical method. Advantages and disadvantages.
17. Simulation of unsteady flow in hydraulic systems with a long pipeline in Matlab Fluids software. Options, mathematical model, numerical method. Advantages and disadvantages.
18. Simulation of unsteady flow in hydraulic systems with a long pipeline, Laplace transform method, software Hydroobvod. Options, mathematical model, numerical method. Advantages and disadvantages.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
The program of lectures
1. Overview of mathematical models, numerical methods and programs for solving fluid systems dynamics. One-dimensional pipeline model with lumped parameters - segmented pipeline, program Matlab - Fluids.
2. One-dimensional pipeline model with continuously distributed parameters - quasi-stationary velocity profile, unsteady velocity profile.
3. Method of characteristics and Laplace transform method for solving pipeline with continuously distributed parameters. Software Flowmaster, Circuit and F-achar.
4. Modulus of elasticity of hydraulic lines: calculation equations, the effect of fluid compressibility, pipe walls, amount of air bubbles. Bulk modulus for liquid and gas mixture. Experimental determination of liquid bulk modulus and hose modulus of elasticity.
5. Methods for determination of air content in the liquid. The speed of sound in the hydraulic line. Evaluation of wave runtime. Industrial tomograph.
6. Eigenfrequency of hydraulic system with a long pipeline. Influence of line elasticity module, line length, boundary conditions and liquid viscosity on dynamics. Pulsating flow.
7. Experimental evaluation of the frequency and transient response of long pipeline. Method of measurement and evaluation variables, the frequency spectrum of the measured signal.
8. Simulation of transient and frequency responses of the hydraulic system with a long pipeline in the software Fluids. Modeling of hydraulic systems with proportional directional control valves and hydraulic cylinders with a mass load.
9. Influence of accumulator in the pipeline during pulsating flow. Comparison of numerical models and software for modeling unsteady fluid flow in a long pipeline.
Program of exercises and seminars
1. Hydraulic system for measurement of transient and frequency response of a long pipeline. Structure, control of the proportional directional control valve in the software Matlab. Used sensors, measuring device. Project assignment Measurement and numerical simulation of frequency responses of the hydraulic system with a long pipeline.
2. Transient responses measurements of hydraulic shock in a long pipeline. Frequency response measurement in the long pipeline with throttle valve at its end.
3. Evaluation of measured dynamic properties of a long pipeline. Numerical modeling of the hydraulic system with a long pipeline in software Matlab Fluids. Segmented pipeline model, proportional directional control valve and throttle valve.
4. Numerical modeling of the hydraulic system with a long pipeline in software Matlab Fluids. Numerical simulation of the dynamic properties of hydraulic system with a long pipeline in software Matlab Fluids - comparison of simulated time dependencies of pressure with an experiment.
5. Simulation of the influence of individual parameters (pipeline length, viscosity, amount of air bubbles) on dynamics of hydraulic system – time dependencies of pressure for the simulated hydraulic system. Project assignment Measurement and numerical simulation of long pipeline and hydraulic cylinder with mass load.
6. Hydraulic system with proportional directional control valve and hydraulic cylinder. Structure of hydraulic system, measuring device, sensors. Measurement of time dependencies of pressure and position of a hydraulic cylinder.
7. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve.
8. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve. Comparison of simulated time dependencies of position and pressure with experiment. Influence of piston diameter and mass load on time responses of pressure and position.
9. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve. Credit.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction