Euler Turbine Equation

Slides:

Advertisements

Similar presentations

Velocity Triangle for Turbo-machinery

Advertisements

Basic Thermodynamics and Fluid Mechanics

Creation of A Better Energy Harvester !!!?!?!?! P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Harvesting of the Useful Energy.

FUNDAMENTALS OF FLUID MECHANICS

Aerofoil as A Turbine Blade

Introduction to Fluid Mechanics

Moment of Momentum Equation (1) Moment of a force → Torque Moment of force represents the magnitude of force applied to a rotational system at a distance.

Chapter 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS

The Ultimate Importance of Invariant Property : Rothalpy

A Mathematical Frame Work to Create Fluid Flow Devices…… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Conservation Laws for.

Fluid Dynamic Characterization of Turbo-machinery P M V Subbarao Professor Mechanical Engineering Department Understanding the Role of Vectorial analysis.

Fluid Mechanics –For Civil Engineers is all about SMU Storing– Moving– Using ( Incompressible fluids - water) To design and manage these systems we need.

Test 3 today, at 7 pm and 8:15 pm, in Heldenfels 109 Chapters

The Centrifugal Pump.

Chapter 5 Finite Control Volume Analysis

Similarity Laws for Turbo-machinery P M V Subbarao Professor Mechanical Engineering Department From Inception to Utilization….

Chapter 6: Momentum Analysis of Flow Systems

Analysis of A Disturbance in A Gas Flow P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Search for More Physics through.

© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

Flow inside turbomachines

Lecture 6.3: C-Angular Momentum and Turbomachines

PTT 204/3 APPLIED FLUID MECHANICS SEM 2 (2012/2013)

Turbomachinery Lecture 5a Airfoil, Cascade Nomenclature

MAE 4261: AIR-BREATHING ENGINES Velocity Triangles Example April 12, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology.

Introduction Compressor is a device used to produce large pressure rise ranging from 2.5 to 10 bar or more. A single stage compressor generally produce.

Chapter 7: Linear Momentum Along with conservation of energy, we will now include other conserved quantities of linear and angular momentum. Linear momentum.

An Exclusive Conservation Equation for Ideal Turbo-machines P M V Subbarao Professor Mechanical Engineering Department Invention of New Property for CVs.

Model to Schedule A Flow Path through A Turbo-machine P M V Subbarao Professor Mechanical Engineering Department Description of the Journey is More Important.

CE 1501 CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University,

Pharos University ME 259 Fluid Mechanics Lecture # 5 Dr. A. Shibl Momentum Equation.

Wind power Part 3: Technology San Jose State University FX Rongère February 2009.

Chapter 14 SYSTEMS OF PARTICLES The effective force of a particle P i of a given system is the product m i a i of its mass m i and its acceleration a i.

© Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

LINEAR MOMENTUM APPLICATIONS AND THE MOMENT OF MOMENTUM 1.More linear momentum application (continuing from last day) Fluid Mechanics and Hydraulics.

1 Work in Rotational Motion Find the work done by a force on the object as it rotates through an infinitesimal distance ds = r d  The radial component.

Selection of Stator-Rotor Combinations

Chapter 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS

Creation of A Better Energy Harvester !!!?!?!?! P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Harvesting of the Useful Energy.

A Design Philosophy through Accounting/Balancing/ Conservation …. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Rothalpy Based.

Parametric Study of Turbine Cascades P M V Subbarao Professor Mechanical Engineering Department Identification of New design Variables.……

First Law of Thermodynamics applied to Flow processes

Turbomachinery Lecture 5 Airfoil, Cascade Nomenclature

Chapter 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS

SNS COLLEGE OF ENGINEERING Coimbatore-107 Subject: Thermal Engineering

Betz Theory for A Blade Element

Blade Design for Modern Wind Turbines

TURBOMACHINES Chapter 1 INTRODUCTION

Fluid Dynamic Principles to Generate Axial Induction

Turbomachine principles, Velocity triangles

Euler’s Vision of Newton’s Laws of Motion

Design Evolution of Wind Turbines

Identification of Fundamental Design Parameter for A Wind Turbine

FLUID FLOW TYPICAL ENGINEERING PROBLEMS:

Performance of Centrifugal Pumps

Design Analysis of Axial Flow Gas Turbines

Initial Designs of Turbines

Analysis of Multi Stage Steam Turbines

Power Plant Steam Turbines

Control volume approach (검사체적 방법)

Eulerization of Betz Theory : Wind Turbines

The thermodynamic Variations

Fans, Compressors & Turbines for Jet Engines

MAE 5350: Gas Turbine Engines

Analysis of Large Turbines

Mechanical Engineering Department

Introduction to Fluid Mechanics

Dual Induction theory for Wind Turbines

Eulerization of Betz theory: Wind Turbines

EXAMPLE: SEE SECTION 8.2 FROM H&P

Presentation transcript:

Euler Turbine Equation P M V Subbarao Professor Mechanical Engineering Department I I T Delhi An Important Engineering Form of Newton's Laws!!!?!?!?!

Simple Turbine : Harvester of Useful Fluid Energy out T

Macro Analysis of A Turbine Fluid in Fluid out

Cartesian View of Momentum Equation This is a vector equation and will have three components in x, y and z Directions. X – component of momentum equation:

X – component of momentum equation: Y – component of momentum equation: Z – component of momentum equation:

Axial Momentum Equations A turbomachine cannot tolerate this force doing any work. The axial force should be completely absorbed by a thrust bearing. Any remaining traces of this force can cause mechanical or aerodynamic damages.

Concurrent Designs for Minimum Axial Thrust

Normal Momentum Equations Resultant radial Force: The radial force component has little do with steady state aerodynamic performance of a turbo-machine. Special Casings are designed to reduce this force. The remaining force is normally absorbed in a journal type bearing.

Pump Impeller and casing

Radial Force on Impeller

Best Efficiency Point (B. E. P Best Efficiency Point (B.E.P.): The point on a pump's performance curve that corresponds to the highest safe efficiency. At this point, the impeller is subjected to minimum radial force promoting a smooth operation with low vibration and noise.

Euler’s Version of Newton’s Second Law In turbo-machines much useful information is obtained by employing Newton’s second law in the form where it applies to the moments of forces. This form is of central importance in the analysis of the energy transfer process in turbo-machines.

Euler’s Statement for Second Law For a system of mass m, the vector sum of the moments of all external forces acting on the system about some arbitrary axis A--A fixed in space is equal to the time rate of change of angular momentum of the system about that axis, i.e.

Euler Theory: Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid = t Angular momentum is moment of linear momentum of angular velocity, Vq Define, L as Angular momentum :

The Boeing 747 Cruising at an Altitude of 10 km

Turbo-jet Engine

Even for a steady flow through a turbo-machine: Inlet rate of angular momentum : Exit rate of angular momentum at exit: Change in Rate of angular momentum: