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


1
Calculation of the Efficiency of Integrated
Cross-Flow Fan by K-e Turbulence model

• Sameer P. Kadhikhaye MAE 741
• April 19 2006

2
Agenda

• Comparison of Turbulence models
• Overview of standard k-e model
• The grid generation for integrated cross-flow 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 k-e Model

• The equation governing turbulence kinetic energy
  k is obtained by multiplying the N-S 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/k(Gk C3eGb) C2ee2/k Se

6
Transport Equations for the Standard k-e 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 ßgi(µt/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)
8
Complete Grid for CFF domain
9
CFF grid
Grid for a blade of CFF
10
Velocity Contours from simulation
11
Reference Joseph D. Kummer and Thong Q. Dang
High-Lift Propulsive Airfoil with Integrated
Cross-Flow Fan

• Calculation of Total Efficiency from simulation
• t QPt/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 k-e model is
  consistent for Cross-flow fan simulations.