### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Foundations of Fluid Mechanics I M E 521

Penn State

GPA 3.79

### View Full Document

## 7

## 0

## Popular in Course

## Popular in Mechanical Engineering

This 0 page Class Notes was uploaded by Chester Goldner III on Sunday November 1, 2015. The Class Notes belongs to M E 521 at Pennsylvania State University taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/233073/m-e-521-pennsylvania-state-university in Mechanical Engineering at Pennsylvania State University.

## Similar to M E 521 at Penn State

## Reviews for Foundations of Fluid Mechanics I

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/01/15

Detailed Outline M E 522 Foundations of Fluid Mechanics II Prepared by Professor J M Cimbala Penn State University Latest revision 02 January 2008 continued from M E 521 VII Laminar Boundary Layers F 2D Laminar Free Shear Layers 1 Introduction 2 2D laminar jet a integral CV analysis b differential analysis c similarity solution 1 example problem e discussion G AXisymmetric Boundary Layers 1 Introduction 2 AXisymmetric boundary layer equations 3 The Mangler transformation a introduction b derivation c example 4 General axisymmetric boundary layers a introduction b axisymmetric BL equations 5 The thin axisymmetric jet H ThreeDimensional Boundary Layers 1 Introduction 2 Boundary layer equations 3 How to choose a 3D coordinate system a developable surface b intrinsic coordinates c computer generation 4 Summary Why 3D BLs are harder than 2D BLs a outer ow b coordinate system c BL equations 1 secondary ow 5 Secondary ow a de nition b example problem at plate with transverse pressure gradient c class demonstration the teacup experiment 1 practical application of secondary ow the cyclone separator I Numerical Solutions b unstructured c hybrid 3 Convergence a residuals b underrelaxation factors c grid adaption VIII Instability A Introduction 1 Examples of instability a ball on the wall b unstable ows 1 pipe ow 2 jets 3 Blasius boundary layer 4 ow over a circular cylinder 5 freely rotatable cylinder with splitter plate 6 thermal instability 7 surface tensiondriven Benard convection 8 TaylorCouette ow 9 KelvinHelmholtz instability 2 Notation B Linear Stability Theory 1 De nition 2 Procedure for linear stability analysis 3 Simple example C Method of Normal Modes 1 Introduction 2 Thermal instability the Benard problem 3 Other examples a centrifugal instability D Stability of Locally Parallel Flows 1 Introduction 2 Linear stability analysis 3 Squire s threorem 4 OrrSommerfeld equation a derivation b boundary conditions c solutions and examples 5 The Rayleigh equation a derivation b conditions for instability c typical solutions d example far wake of a circular cylinder E Transition IX Turbulence The Final Frontier A Introduction What is Turbulence 1 De nition of turbulence 2 Characteristics of turbulence a randomness or irregularity b nonlinearity c diffusivity d 3D uctuating vorticity at wide range of scales e dissipation 3 Other features of turbulence a turbulence is a continuum phenomenon b turbulence is a property of uid ows not of uids B Notation and Terminology 1 Notation 2 Types of averages a time average b ensemble average c phase average 3 Other de nitions and rules a the ensemble average of any uctuating component is zero b commutative rules for ensemble averages c commutative rules do not work for multiplication of uctuations d statistical de nitions e turbulence intensity f turbulent kinetic energy tke g intermittancy h homogeneous turbulence i isotropic turbulence j inhomogeneous turbulence C Equations of Motion for Turbulent Flow 1 NavierStokes equations 2 Reynolds decomposition 3 Comparison of laminar and turbulent mean ows 4 Some comments about the Reynolds stress tensor a it is a 9component tensor b it is symmetric c sign of the normal components d special case isotropic turbulence e eg turbulent shear ow f notation 5 The closure problem a mean ow quantities b Reynolds stress transport equation 6 Mean and turbulent kinetic energy equations a mean kinetic energy equation b turbulent kinetic energy equation c comments about the tke equation D Order of Magnitude Analysis of Turbulence 1 Introduction a notation b example laminar at plate boundary layer 2 Eddy scales and the energy cascade a largest eddies b intermediatesized eddies c smallest eddies 3 Kolmogorov s contribution a Kolmogorov s universal equilibrium hypothesis b Kolmogorov microscales 4 How to estimate the turbulent dissipation rate a order of magnitude estimate b some examples 5 The turbulent Reynolds number a de nition b examples 6 Can turbulent ows be solved exactly E Turbulence Models 1 Introduction a Why do we need turbulence models b equations of motion c desired attributes of a turbulence model d classi cation of turbulence models 1 zeroequation models 2 oneequation models 3 twoequation models 35 algebraic stress models ASM 4 Reynolds stress models RSM 5 large eddy simulation LES 2 The eddy Viscosity a eddy Viscosity for 2D boundary layer ows b eddy Viscosity for general 3D ows 3 Closure for algegraic zeroeq turbulence models a how to nd the mixing length b examples of mixing length models 1 free shear ows 2 wallbounded shear ows 3 von Karman s mixing length 4 BaldwinLomax Model c summary of zeroequation eddy Viscosity mixing length turbulence models 3a Closure for halfequation turbulence mode s 4 Closure for oneequation turbulence models a introduction b the modeled tke equation 5 Closure for twoequation turbulence models a introduction b exact transport equation for dissipation rate c modeled transport equation for dissipation rate d the near wall region 6 Closure for Reynolds stress turbulence models a introduction b equations c summary of RSM F Turbulent Flow Solutions 1 Turbulent channel ow a analytical analysis b approximate analysis using layers c wall functions d solutions using turbulence models 2 Free shear ows a introduction b equations of motion c turbulent jets d turbulent far wake

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.