Data of Ch5 --Dual rotor

* Results

*Conclusion*
- little effect of rear rotor on Cp_1
- Cp1 is independent of TI
** TI effect on single-rotor, front,
| cp | ct | TI | TSR |
|    |    | 1  |     |
|    |    | 15 |     |
** Dual rotor X=4D, TI 15% -- CFD-RANS
# TI 15%, RANS results
# TSR1 TSR2/TSR1 TSR2      Cp_1      Ct_1     Cp_2    Ct_2
  5.0   0.730    3.65   0.396   0.824  -0.024  0.289
  5.0   0.600    3.00   0.397   0.829   0.010  0.284  
  5.0   0.500    2.50   0.395   0.826   0.005   0.265

TSR1 TSR2/TSR1    TSR2    Cp_1    Ct_1    Cp_2    Ct_2
5    0.733    3.665    0.394    0.82    -0.044    0.229
5    0.644    3.22    0.393    0.82    -0.02    0.218
5    0.55    2.75    0.394    0.819    -0.005    0.21
5    0.5    2.5    0.395    0.82    0.002    0.184
5    0.45    2.25    0.396    0.821    0.000    0.168
5    0.4    2    0.396    0.821    -0.004    0.153
5    0.35    1.75    0.395    0.821    -0.006    0.143
5    0.2    1    0.396    0.822    -0.004    0.09

** Dual X=4D same TSR -- BEM + Park model
 # ak, distance (norm by D)=   3.99999991E-02   4.00000000    
 # TSR1, C_T_tot, C_P_tot, omega2/omega1
   1.000000E+00   2.862664E-01   2.394140E-02   9.567473E-01
   1.250000E+00   3.237689E-01   4.581533E-02   9.503006E-01
   1.500000E+00   3.736952E-01   7.827624E-02   9.411572E-01
   1.750000E+00   4.390565E-01   1.231780E-01   9.281210E-01
   2.000000E+00   5.195406E-01   1.788598E-01   9.113323E-01
   2.250000E+00   6.136195E-01   2.441946E-01   8.893722E-01
   2.500000E+00   7.156332E-01   3.136399E-01   8.634881E-01
   2.750000E+00   8.213180E-01   3.814463E-01   8.335000E-01
   3.000000E+00   9.222423E-01   4.392351E-01   8.015752E-01
   3.250000E+00   1.001631E+00   4.755293E-01   7.784010E-01
   3.500000E+00   1.065189E+00   4.984458E-01   7.609080E-01
   3.750000E+00   1.116553E+00   5.122202E-01   7.491560E-01
   4.000000E+00   1.160889E+00   5.199742E-01   7.404510E-01
   4.250000E+00   1.196960E+00   5.233117E-01   7.338645E-01
   4.500000E+00   1.229946E+00   5.234426E-01   7.281728E-01
   4.750000E+00   1.261175E+00   5.211463E-01   7.232024E-01
   5.000000E+00   1.291180E+00   5.169932E-01   7.189118E-01
   5.250000E+00   1.313614E+00   5.118050E-01   7.153068E-01
   5.500000E+00   1.339595E+00   5.045193E-01   7.123726E-01
   5.750000E+00   1.359179E+00   4.970232E-01   7.101494E-01
   6.000000E+00   1.381723E+00   4.874390E-01   7.084185E-01
   6.250000E+00   1.399795E+00   4.772219E-01   7.073638E-01

** DONE Cp one Rear Rotor at Re 1e6 - R=0.6
*Flow Features:*
keywords:

largely stalled)
High Angle of Attack, naca0012, stall,
Goal: performance when naca0012 is stalled

C:\Users\kaiming\Documents\ZJU\naca0012_Dual_Rotor\OneRotor_Rear_1M\tsr4

| TSR | Cp      | Ct |  Re | U(m/s) | omega(rad/s) | turbulence models |
|   4 | -0.011  |    | 1e6 |    4.4 |        77.22 |   standard k-e    |
|   4 | 0.05    |    | 1e6 |    4.4 |        77.22 |   sst ko          |
| 4.5 | - 0.013 |    | 1e6 |    4.4 |        86.87 |                   |
OneRotor_Rear_1M/rear_st_tsr4_ke_7k.dat.gz
** Wake
*** TKE
refernces:
N Stergiannis CFD modelling approaches against single wind turbine wake measurements using RANS
*** velocity contour in the wake
fig.9 mycek
** wake width measurement in CFD?
iso-surface plot, set variable as: U_x

** Mean axial velocity from CFD  at a given X/D?
- wake is normal distribution, gaussian
? how to get the mean of normal distribution?

- arear averaged axial mean veolocity of wake (Mycek 2014)
  +  (rotor radius,R)

reference:
#+CAPTION:area-averaged velocity (disc diameter=1D) (fig.8b mycek 2014 dual rotor)
file:figures/post/disc_averaged_axial_velocity_mycek_2014.png

Area used in my case:
 circular, r=1.2R (radius of turbine)

How to define the edge of of wake in CFD post processing  at different X/D?
how to define the edge of wake?
U_x = 0.99U_\infty
how to define the "mean" U_x in the wake?
? is r=1R used by mycek right?

*** One Rotor Front, Eldad Blade TSR 5 TI = 1%
# One Rotor, front, eldad blade
# TSR 5, TI =1%, \theta_T = 2 deg
#X/D    X   half width,    Ux    U    Ux/U
1    0.46    0.288    0.332    0.6    0.553333333
2    0.92    0.299    0.326    0.6    0.543333333
3    1.38    0.305    0.337    0.6    0.561666667
4    1.84    0.311    0.354    0.6    0.59
5    2.3    0.318    0.374    0.6    0.623333333
6    2.76    0.326    0.394    0.6    0.656666667
7    3.22    0.332    0.409    0.6    0.681666667
8    3.68    0.341    0.437    0.6    0.728333333
9    4.14    0.35    0.457    0.6    0.761666667
10    4.59    0.352    0.464    0.6    0.773333333
*** How to the area average velocity of wake at a given X/D?

1. cacluation wake width (b) at a given X/D
create a iso-surface plot with U_o,
2. get area average in CFDpost
  + create an expression in CFD post
~areaAve(Velocity in Stn Frame w)@areaAverage~
3. change X=2D...
*** *Turbulence kinetic energy*
3e-5, 1e-2
Number of contours, 51

Velocity
0.02-0.6
Number of contours, 31

** 3D streamline
what does 3D streamline means

** k correction
calibration

| TI (%) |      k | RMS Error |
|     15 | 0.0190 |    0.0190 |
|    1   |    0.0075 |     0.0371 |

*** Bayesian Calibration
- based on exprimental data: overall power

(Rathmann 2017)
variables: hub-height wind speed, wind direction
math function: probability density function
reommmended k value: 0.06 offshore and 0.09 onshore

- Rathmann, Ole Steen, et al. "Validation of the Revised WAsP Park Model." WindEurope 2017. 2017.
-  Rathmann O., Estimation of the Wake Expansion Coefficient from Eddy Diffusivity Theory. Research note, DTU Wind Energy. (2017).
-  M.C. Kennedy, A. O’Hagan. Bayesian calibration of computer models. Journal of the Royal
Statistical Society: Series B (Statistical Methodology), 63(3), 425-464. (2001).
- Murcia, J.P. et al., Uncertainty quantification in wind farm flow models. PhD thesis, DTU Wind
Energy (2017).
- Murcia, J.P. et al., Wake Model Calibration Based On SCADA Data Considering Uncertainty In The
Inflow Conditions. Private communication (2017).
***  k vs TI

k= 0.4 TI [fn:goccmen2016wind]
k=0.04 when TI=10%
k=0.4 TI_h
- TI_h : hub height TI
k=0.4TI = 0.038 at the Sexbierum wind fams [fn:pena2016application]
[fn:pena2016application] Peña, Alfredo, Pierre‐Elouan Réthoré, and M. Paul van der Laan. "On the application of the Jensen wake model using a turbulence‐dependent wake decay coefficient: the Sexbierum case." Wind Energy 19.4 (2016): 763-776.
[fn:goccmen2016wind] Göçmen, Tuhfe, et al. "Wind turbine wake models developed at the technical university of Denmark: A review." Renewable and Sustainable Energy Reviews 60 (2016): 752-769.

*** Pyakurel's method
- based on CFD data: centre line axial mean velocity
- Eq (10) in Pyakurel 2017
- *observed* axial velocity, U_s = *centre line* velocity from CFD RANS (this value is used as experimental data)
- Predicted axial velocity, U_c = Jensen model in which Ct is also from CFD RANS
Root mean square error = (U_s - U_c )_rms
 # limit
centre line veolocity is lower than the area averaged velocity, thus low centre line velocity as baseline, k is not accurate

** Jump value of moment time history of dual rotor