Introduction to Computational Fluid Dynamics

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Introduction to Computational Fluid Dynamics

• Course Notes (CFD 4)

Karthik Duraisamy Department of Aerospace
Engineering University of Glasgow
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Contents

• Introduction (1.5)
• Classification of PDE, Model equations (1.5)
• Finite difference methods
• ? Spatial discretization (3)
• ? Temporal discretization (2)
• ? Convergence, Consistency, Stability (2)
• Grids/Boundary conditions (1)
• Euler equations (1)
• RANS Equations and Turbulence modeling (2)
• DNS/LES (1)
• Best practices in CFD (1)
• Case studies/Demonstrations (3)

(.) Approximate number of lectures
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• CASE STUDIES

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Best practices in CFD

• Selection of Problem/model/numerical method
• Feasibility study of computation
• Identifying physics and required resolution in
  different parts of the mesh
• Grid convergence
• Time step convergence (unsteady)
• Verification/Validation
• COMMENT YOUR CODE!!! ?

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What do you plot?

• Line graphs (x vs Cp)
• Contours (Velocity magnitude in a section)
• Iso-surfaces (Vorticity magnitude)
• Streamtraces (Streamlines)
• Spectra (Energy spectra)

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• CASE STUDY 1

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Fixed wing validation

• M0.15, Re4.5x106, a10o, AR0.75, rounded tip.
• Extensive mean and turbulence measurements by
  Chow et. al. 1997
• Surface (pressure tabs) and wake measurement
  (pressure probes and hot wires) up to 0.68c.
• Resolution good enough to compare flow viz with
  numerics.

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Surface pressure distribution
y/c0.667
y/c0.583
f45o
f90o
f
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Axial Velocity (x/c-0.394)
Computation
Experiment
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Axial Velocity (x/c-0.114)
Experiment
Computation
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Axial Velocity (x/c0.005)
Experiment
Computation
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Axial Velocity (x/c0.678)
Computation
Experiment
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RANS/Inviscid Comparison
Swirl velocity
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• CASE STUDY - 2

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Why study tip vortices?
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Application of Spanwise blowing

• Baseline test case of Heyes et al. (Imperial
  college)
• AR1, NACA0012 wing section, a7.5o, M0.1,
  Re2.2x105.
• Spanwise blowing Velocity measurements x/c1
  downstream of trailing edge.
• Blowing co-efficient

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Validation Baseline case, x/c1
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Blowing test cases
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Validation Blowing case C1, x/c1
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Physics of control
Axial Vorticity
x/c0.21 (from l.e.)
Freestream direction
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Case C1 x/c-0.95
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Case C1 x/c-0.85
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Case C1 x/c-0.75
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Case C1 x/c-0.45
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Case C1 x/c-0.25
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Case C1 x/c-0.1
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Case C1 x/c1.0
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Blowing case C1
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Blowing case C1
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Different blowing rates
Core radius
Peak swirl velocity
Effectiveness of blowing weak function of
blowing angle
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• CASE STUDY -3
• Some thoughts from 30 years of Development and
  Application of CFD at Boeing
• - Johnson et al., Computers and Fluids.

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Role of CFD

• CFD has joined wind tunnel and flight testing as
  primary tool
• Flight testing Too expensive, but real data
• Wind tunnel Good flight envelope, accurate, but
  low Re, but effect of mounting, walls, not enough
  detail
• CFD Inexpensive, used in optimization,
  extrapolation of tunnel data to flight conditions
  and detailed understanding, but somewhat
  inaccurate.
• CFD Very useful in design of high speed cruise
  configuration of full transport aircraft

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Well..
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Role of CFD
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Contribution of CFD in 777 design
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Use of CFD