16.13: PROBLEM DEFINITION
Answer each question below re: Eq (16.72) in EFM10e.
•Is the given equation in conservation form or non-conservation form? Why?
•Is the given equation in invariant form or coordinate specificform?Why?
SOLUTION
•Non-conservation form because the equation was derived by applying ΣF=ma
to a fluid particle.
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16.14: PROBLEM DEFINITION
What are the physics of the gradient of the pressure field? What are the units? What
are the primary dimensions?
SOLUTION
•Physics (intepretation #1; developed from the textbook). The gradient of the
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16.15: PROBLEM DEFINITION
What are the physics of the divergence of the shear stress tensor? What are the
units? What are the dimensions.
SOLUTION
•Physics. The divergence of the shear stress tensor gives the ratio of (net shear
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16.16: PROBLEM DEFINITION
Compare the Navier-Stokes equation to Euler’s equation (Chapter 4).
•What are the two important similarities?
•What are two important differences?
SOLUTION
•Two important similarities (there are other possibilities).
—Both are derived by applying ΣF=mato a fluid particle.
•Two important differences (there are other possibilities).
—The Navier-Stokes derivation includes the shear force (i.e. viscous force),
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16.17: PROBLEM DEFINITION
Stress, as introduced in the derivation of the Navier-Stokes equation, is a second-order
tensor. Using the internet, finds some articles on tensors and answer the following
questions:
•Why do people use tensors? What are the benefits?
•What does tensor mean? How is a tensor defined?
•What are five examples of tensors as they are applied in engineering and physics?
SOLUTION
•Benefit of using tensors (multiple possible answers; some given below)
—Compact notation.
•Meaning of a tensor.
—A mathematical entity analogous to but more general than a vector, rep-
resented by an array of components that are functions of the coordinates
of a space.
∗A zeroth order tensor (scalar) has one component.
•Examples of tensors in engineering
—Thermal conductivity (general form) is a 2nd order tensor.
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16.18: PROBLEM DEFINITION
Is someone asked you why are CFD codes useful for engineers how would you answer?
List your top three reasons in priority order.
SOLUTION
(Multiple possible answers exist; some are listed below)
•CFD provides a method when experimentation or analysis is not possible.
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16.19: PROBLEM DEFINITION
Would you prefer to write your own CFD programs or would you prefer to use codes
that have been written by others? Discuss the advantages and disadvantages of each
approach.
SOLUTION
•Advantages of writing your own code
—Understand how the code works.
•Disadvantages of writing your code
—Resources required to develop a code
∗Requires a large amount of time (years).
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16.20: PROBLEM DEFINITION
No solution provided.
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16.21: PROBLEM DEFINITION
Briefly explain the meaning of each of the following ideas.
•Grid.
•Time Step.
•Solution time for a CFD program versus the accuracy.
•Boundary condition. A condition that is specified on the spatial boundaries of
the CFD solution.
•Initial condition.
SOLUTION
•Grid. A grid which is a set of points in space at which a code solves for values
ofvelocityandothervariablesofinterest.Thegridisoftenshownwithanarray
of intersecting lines; hence the name.
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16.22: PROBLEM DEFINITION
Briefly explain the meaning of each of the following ideas.
•DNS.
•k-epsilon method.
•LES.
SOLUTION
•DNS. DNS is a way of modeling turbulent flowsthatinvolvessettingthegrid
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16.23: PROBLEM DEFINITION
Briefly explain the meaning of each of the following ideas.
•Post processor
•Verification
•Validation
SOLUTION
•Post processor. The post processor is a computer algorithm that uses the
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