Exam 1 Review

 

Lecture:	Topic:
8/27	Introduction to the Class
8/27-29	First Exercise of our Modeling Tools
8/27-29	More Experience with SNAP
9/5	The Basics of Two-Phase Flow
	Acronyms
	Nomenclature
	Void Fraction Estimates
9/5	The Basic Model Equations
9/7	Intro. to Finite Volume and Finite Difference Methods
	Some Standard Difference Equations
9/7	Conservative Finite Volume Equations
9/10-12	Verification and Validation
9/12-14	Work on Richardson Error Analysis
9/17	Error Analysis for Difference Equations
9/19-21	Heated Flow Exercise
9-24	Solving the Difference Equations
	Simple Newton's Method
	Newton's Method for More than One Equation
9-26	Modeling Pumps
9-28	The TEE and its Relatives, Momentum Conservation

Highlights

Introduction

• Why are computer simulations important to reactor safety
• What is the difference between Best Estimate and Conservative calculations.

First Exercises

• Estimation of reasonable transient time  to reach steady state.
• Use of Bernoulli Equation with loss coefficients
• Qualitative feeling for numerical diffusion

Basics of Two Phase Flow

• Three tasks of numerical simulation
• Any Acronyms that have been used regularly in class
• Key nomenclature (void fraction, mean density, 3 flavors of quality, mean velocity ...)
• Basic flow regime map and horizontally stratified flow.
• Ability to do simple geometric calculations to obtain expressions for void fraction or relate such things as droplet spacing to void fraction

The Base Model Equations

• Know the basic assumptions and  number and type of mass, momentum, and energy equations associated with each model
• Know what area averaging  is and what it can do to you.
• Be able to identify important individual terms in the equations: mass, energy, and momentum fluxes, pressure work, interfacial friction, wall friction, interfacial heat transfer, wall heat transfer

Finite Volume Equations

• Know how to apply Gausses theorem
• Know meaning of Fully Explicit (Forward), Fully Implicit (Backward), Semi-Implicit time level methods
• How do thiese methods affect numerical diffusion?
• What does numerical instability look like?
  
• For the above methods when (if at all) is stability a problem?
  
• Know upwind (or donor cell) differencing
• Understand a staggered mesh and where mass, energy, and momentum equations are evaluated on that mesh.
• Given a differential equation, be able to write a finite volume implementation of any of the above time level methods using a staggered mesh.
• What is a conservative form of a flow equation, and how does it impact the finite volume implementation?
• Mass concervation errors due to void fraction cut-off.
• When can the non-conservative form of the energy equation cause serious problems with results from simulations?
  

Verification and Validation

• Reading Assignment
• Definitions: verification, validation, error, uncertainty, calibration
• Two major authors on V&V
• Sources of error
• Richardson error analysis
• Grid convergence index
  
• Key components of QA
• What is the Method of Manufactured solutions?
  
• What is the PIRT process?  What are its key components?
  
• Systematic (bias) and Stochastic error in experiments

Taylor Series Truncation Error analysis

• How do you choose the point to evaluate error?
• Given the difference form of a differential operator or differential equation, be able to evaluate truncation error.
• What is order of accuracy?
• What penalty do you pay for use of higher order methods?

Heated Flow

• Be able to apply the steady state form of a mixture energy equation to relate inlet and outlet conditions to power added.

Equation Solution

• Be able to do simple linearization (single Newton iteration). and obtain updated values for variables.
• Be able to apply the linearization process to more than one equation with more than one unknown.
  
• Understand basic properties of a Newton iteration (e.g. quadratic convergence, radius of convergence)
  
• How do you decide when to quit an iteration?
  

Pumps

• What are the primary types of pumps, and their characteristics?
• Understand head curves.
• How many curves define the full range of pump behavior?
• What is the independent variable associated with each curve?
• What  quantity does each curve give you?

Tee Momentum sources and Momentum Conservation

• Be able to use simple conservation of momentum arguments to estimate pressure changes in simple situations.
• Have a common sense feel for impact of side flows on pressure in flows