Calculation of the Efficiency of Integrated CrossFlow Fan by Ke Turbulence model


1
Calculation of the Efficiency of Integrated
CrossFlow Fan by Ke Turbulence model

• Sameer P. Kadhikhaye MAE 741
• April 19 2006

2
Agenda

• Comparison of Turbulence models
• Overview of standard ke model
• The grid generation for integrated crossflow fan
• Calculation of the efficiency by simulation
• Agreement of the simulation efficiency with the
  plot in reference paper.

3
Comparison of the various Turbulence Models
4
Comparison of the various Turbulence Models
5
Transport Equations for the Standard ke Model

• The equation governing turbulence kinetic energy
  k is obtained by multiplying the NS equations
  by ui time averaging all the terms and
  subtracting the kinetic energy of the mean flow
  we get
• ?/?t?k ?/?xi?kui ?/?xj[µ
  µt/sk?k/?xj] Gk
• Gb
  ?e YM Sk
• . And the rate of dissipation e is obtained
  from
• ?/?t?e ?/?xi?eui ?/?xj[µ
  µt/se?k/?xj]
• 
  C1ee/kGk C3eGb C2e?e2/k Se

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Transport Equations for the Standard ke Model

• The constants are evaluated as follows
• Turbulent viscosity µt ?Cµk2/e
• The model constants have the following default
  values
• Cµ 0.09 C1e
  1.44 C2e 1.92
• sk 1 se
  1.3
• The generation of kinetic energy due to mean
  velocity
• gradients Gk µtS2 where S 2Sij Sij
• The generation of kinetic energy due to buoyancy
  is given by
• Gb ßgiµt/Pt?T/?xi
  where Pt 0.85 and
• The coefficient of thermal expansion is
• ß 1/???/?T

7
Grid generation for integrated CFF Flow domain
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Complete Grid for CFF domain
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CFF grid
Grid for a blade of CFF
10
Velocity Contours from simulation
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Reference Joseph D. Kummer and Thong Q. Dang
HighLift Propulsive Airfoil with Integrated
CrossFlow Fan

• Calculation of Total Efficiency from simulation
• ?t Q?Pt/O?
• where Q flow rate Area of tunnel
  velocity of air
• 
  1.550.313
• 0.485
  m3/sec.
• where velocity of air in tunnel can be
  found out as follows
• We have this set up for Flow coefficient f
  0.3
• f Q/DLUf
• where D
  Fan diameter 0.333 ft
• L Fan
  length for calculation its unit length
• Uf fan
  tip speed OR 314.151/6 52.35
• Therefore flow coefficient can be given as
• f
  heighttunnvelocitytunn/ DUf

12
Calculation of Total Efficiency from simulation

• Plugging in values of f heighttunn D Uf we
  get Velocitytunn.
• Velocitytunn
  0.313 m/sec
• Now from simulation we get
• total pressure difference ?Pt 300 N/m2
• and
  torque T 0.7195 Nm
• Again plugging in values of ?Pt T Q and O in ?t
  we get
• ?t
  64 from simulation.

13
Total Efficiency from plot of inline housing fan
performance

• From plot we can see at
• f 0.3
• ?t 64
• which is same as ?t from simulation. It was
  found that for all other values of f the
  efficiencies are same. Thus simulation and plot
  are in agreement showing that ke model is
  consistent for Crossflow fan simulations.