Dynamic Similarity diabetes.com/Article s.asp?ID=150 Dimensionless Science.

Slides:



Advertisements
Similar presentations
Specialization in Ocean Energy MODELLING OF WAVE ENERGY CONVERSION António F.O. Falcão Instituto Superior Técnico, Universidade de Lisboa 2014.
Advertisements

Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor:
Instructor: André Bakker
1 FLOW SEPARATION Aerodynamics Bridge-Pier Design Combustion Chambers Human Blood Flow Building Design Etc. (Form Drag, Pressure Distribution, Forces and.
Convection.
Boundary Layer Flow Describes the transport phenomena near the surface for the case of fluid flowing past a solid object.
Pharos University ME 352 Fluid Mechanics II
Generalities Separated Flows Wakes and Cavities. 1.1 What is separation ? A streamline leaves the body and turns into the interior of the fluid 2D separation.
Basic bluff-body aerodynamics I
External Flows.
1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 7.
Flow Over Immersed Bodies
CE 1501 CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University,
CHE/ME 109 Heat Transfer in Electronics
Lecture 7 Exact solutions
FINAL LECTURE of NEW MATERIAL!!! (1) How to build a better model (2) Lift, Drag, Pressure forces considered together.
Flow past bluff-bodies
An Ultimate Combination of Physical Intuition with Experiments… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Boundary Layer.
Paul Drosinis UBC Phys 420. Introduction Short history on fluid dynamics Why bother studying fluid flow? Difference between Newtonian and Non-Newtonian.
Aerodynamic Forces Lift and Drag Aerospace Engineering
Pharos University ME 259 Fluid Mechanics Lecture # 9 Dimensional Analysis and Similitude.
Dimensions Dimensional Reasoning. Dimensions Dimensions and Measurements “Dimension” is characteristic of the object, condition, or event.
Dimensional analysis Drag force on sphere depends on: The velocity U
Fluid Properties: Liquid or Gas
Lesson 21 Laminar and Turbulent Flow
Introduction to Fluid Mechanics
LESSON LD04 Aerodynamics
Turbomachinery Lecture 4a Pi Theorem Pipe Flow Similarity
1 LES of Turbulent Flows: Lecture 6 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Spring 2011.
Reynolds ( ) Ernst Mach (1838 – 1916).
Dimensional Analysis A tool to help one to get maximum information from a minimum number of experiments facilitates a correlation of data with minimum.
1 MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 6: DIMENTIONAL ANALYSIS Instructor: Professor C. T. HSU.
© Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 7 Dimensional Analysis and Similitude.
Aerodynamic Forces Lift and Drag.
LES of Turbulent Flows: Lecture 2 (ME EN )
Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two Fluid dynamics Learning summary By the end of this chapter you should have learnt.
Dynamic Similarity diabetes.com/Article s.asp?ID=150
Dynamic Forces Fig. from Warrick et al Nature.
Fluid Mechanics and Applications MECN 3110
ME 101: Fluids Engineering Chapter 6 ME Two Areas for Mechanical Engineers Fluid Statics –Deals with stationary objects Ships, Tanks, Dams –Common.
Convection in Flat Plate Boundary Layers P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A Universal Similarity Law ……
Conservation of Salt: Conservation of Heat: Equation of State: Conservation of Mass or Continuity: Equations that allow a quantitative look at the OCEAN.
CE 1501 Flow Over Immersed Bodies Reading: Munson, et al., Chapter 9.
INTRODUCTION TO CONVECTION
DIMENSIONAL ANALYSIS SECTION 5.
Scales of Motion, Reynolds averaging September 22.
FLUID MECHANICS AND MACHINERY Department of Mechanical Engineering Department.
Flow Similarity and Model Testing Geometrical similarity: similar geometry. Kinematic similarity: flow pattern around the model should be similar to...
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER Recall: Fluid Mechanics.
Chapter 11 DIMENSIONAL ANALYSIS. 2 Fundamental theory preliminary expt. Dimensional analysis: ( 因次分析 ) Experiments Practical Problems analytical soln.
Lecture 27: Lift Many biological devices (Biofoils) are used to create Lift. How do these work?
IIT-Madras, Momentum Transfer: July 2004-Dec 2004 Dimensional Analysis & Similarity Uses: Verify if eqn is always usable Predict nature of relationship.
LESSON LD04 Aerodynamics
CGS Ground School Principles Of Flight Drag © Crown Copyright 2012
Martti Veuro.
Aerodynamic Forces Lift and Drag Aerospace Engineering
Chapter 7 DIMENSIONAL ANALYSIS AND MODELING
Part II. Dimensional Analysis and Experimentation
Vortex Induced Vibration in Centrifugal pump ( case study)
Physical Modeling (dimensional analysis)
Aerodynamic Forces Lift and Drag Aerospace Engineering
Heat Transfer Coefficient
LESSON LD04 Aerodynamics
Effect of Flow over a Cylinder MAE 5130 Viscous Flow Final Project
PO 2430 Applied Fluid MEchanics
LESSON LD04 Aerodynamics
Subject Name: FLUID MECHANICS
Introduction to Fluid Mechanics
Non-dimensional parameters that determine flapping wing aerodynamics.
Presentation transcript:

Dynamic Similarity diabetes.com/Article s.asp?ID=150 Dimensionless Science

Ideas needed to perform Dimensional Analysis All terms in equation must have same dimensions Terms in equation can be expressed with 3 basic dimensions: Mass, Length, Time Dimensions of these variables can be arranged in “Dimensional Matrix”

Dimensional Matrix The rank r of a matrix is the size of the largest square submatrix with non-zero determinant r = 3 Most problems in fluid mechanics Buckingham’s PI theorem: “n variables can be combined to form exactly (n-r) independent non-dimensional variables.”

inertial vs viscous Reynolds Number

Low Re High Re Flow is laminar when Re < 1000 Flow is in transition to turbulence when 100 < Re < 10 5 to 10 6 Flow is turbulent when Re > 10 6, unless the fluid is stratified

Consider an oceanic flow where U = 0.1 m/s; L = 10 km; kinematic viscosity = m 2 /s Is friction negligible in the ocean?

inertial vs pressure Froude Number

pressure vs inertial Euler Number

Great Fountain Geyser, Yellowstone National Park, USA

local vs inertial Strouhal Number f = frequency of motion; A = amplitude of motion – for flying or swimming organisms (fin or wing)

Taylor at al. (2003, Nature 425, (16 ) doi: /nature02000) “Left panels, root-flapping motion; right panels, heaving motion. Amplitude, twice wing chord; static angle of attack, 15°; flow speed, 1.5 ms -1 ; smoke wire visualizations made at end of downstroke. a, For St < 0.10, flow separates at the sharp leading-edge, but no discrete vortex forms. b, For 0.10 < St < 0.25, a leading-edge vortex forms but is shed before the downstroke ends. c, For 0.25 < St < 0.45, the leading-edge vortex is shed as the downstroke ends. d, For St > 0.45, trailing edge separation produces a characteristic mushroom- shaped wake. At higher St, the wing collides with shed vorticity on the upstroke, giving an energetically inefficient mode.”

Dynamic Similarity diabetes.com/Article s.asp?ID=150