The NLR7301 is a supercritical airfoil which has been modified to a two-element configuration with a non-retractable flap. This configuration and the measurements were designed for the purpose of CFD validation[1]. The measurements were taken in 1979 and includes detailed pressure distributions, transition onset locations and someboundary layer velocity profiles for the angles of attack 6° and 13.1°. These measurements have been used extensively for another viscid-inviscid interaction method[2] as well as Navier Stokes codes, e.g.[3]. There is a single measurement set available, at a Reynolds Number of 2.51E6 and a Mach Number of .185, comprising a set of 16 lift and 3 drag values.

The airfoil coordinates were derived from a grid provided on this webpage https://www.kbwiki.ercoftac.org/w/index.php?title=UFR_3-01_Description for the project ECARP[7].

import viiflow as vf
import viiflowtools.vf_tools as vft
import viiflowtools.vf_plots as vfp
import numpy as np

import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
%config InlineBackend.figure_format = 'svg'


import logging
logging.getLogger().setLevel(logging.INFO)

# Read and panel airfoil data
MAIN = vft.repanel(vft.read_selig("NLR7301MainECARP.dat"),260)[:,::-1] #180
FLAP0 = vft.repanel(vft.read_selig("NLR7301FlapECARP.dat"),260)[:,::-1] #150

The authors note an offset in the change in distance between flap and main airfoil, as well as a change in twist on the flap. This change is applied below, by shifting and rotating the flap. Such a modification was also used in the analysis in [6].

matplotlib.rcParams['figure.figsize'] = [10, 7] # Make plots bigger than default

# Rotate flap
center = np.r_[0.94,-0.011]
def rotate(deg,center,x):
    c, s = np.cos(deg*np.pi/180), np.sin(deg*np.pi/180)
    A = np.array([[c, s], [-s, c]])
    # The following transposing is done, because numpy subtracts 1x2 arrays from a Nx2 array, 
    # but not 2x1 arrays form an 2xN array.
    return ((A@((x.T-center.T).T)).T+center.T).T

FLAP = rotate(-.25,center,FLAP0)
FLAP[1,:] += 0.0025


# Plot geometry
fig,ax = plt.subplots(1,1)
ax.plot(MAIN[0,:],MAIN[1,:],'.-k')
ax.plot(FLAP[0,:],FLAP[1,:],'.-k')
ax.axis("equal");

Viiflow Parameters

All calculations have been performed with a Reynolds Number of 2.51E6 and a Mach Number of 0 or 0.185 using a Karman-Tsien correction for the pressure and lift. A critical amplification factor of 8 was used, while 11.2 seems to be recommended for the Delft low-speed wind tunnel[5]. However, the lower value agrees better with the observed transition (see the pressure distributions below).

# Settings
RE = 2.51e6
ncrit = 8
Mach = 0.0
AOArange = np.arange(-2,17,.5)

s = vf.setup(Re=RE,Ncrit=ncrit,Ma=Mach,Alpha=AOArange[0])
s.Silent = False # Do not show information on convergence and iterations
s.IterateWakes=False

# RFOIL-type shear lag fits the measurement slightly better (lower maximum lift)
s.ShearLagType = 1

results = {} # Dictionary of results
Mach_vec = [0,0.185]
res13 = {}
for val in Mach_vec:
    s.Ma = val
    
    # When using an outer loop, make sure to re-initialize the solution 
    Init = True
    
    results[val] = {}
    results[val]["AOA"] = []
    results[val]["CL"] = []
    results[val]["CLi"] = []
    results[val]["CD"] = []
    
    for alpha in AOArange:
        s.Alpha = alpha
        if Init:
            [p,bl,xn] = vf.init([MAIN,FLAP],s)
            Init = False
            

        res = None
        grad = None
        [xn,flag,res,grad,_] = vf.iter(xn,bl,p,s,res,grad)
        resi = np.sqrt(np.dot(res.T,res))
        
        if flag:
            results[val]["AOA"].append(alpha)
            results[val]["CL"].append(p.CL)
            results[val]["CLi"].append(p.CLi)
            results[val]["CD"].append(bl[0].CD)
            print('AOA %2.2f CL %f'%(alpha,p.CL))
        else:
            Init=True

Iteration 25, |res| 0.000096, lam 0.500000
AOA -2.00 CL 1.412939
Iteration 15, |res| 0.000065, lam 0.500000
AOA -1.50 CL 1.481641
Iteration 15, |res| 0.000078, lam 0.500000
AOA -1.00 CL 1.550082
Iteration 15, |res| 0.000072, lam 0.500000
AOA -0.50 CL 1.618230
Iteration 16, |res| 0.000078, lam 0.500000
AOA 0.00 CL 1.686011
Iteration 11, |res| 0.000059, lam 1.000000
AOA 0.50 CL 1.753639
Iteration 15, |res| 0.000064, lam 0.500000
AOA 1.00 CL 1.820613
Iteration 14, |res| 0.000061, lam 0.632554
AOA 1.50 CL 1.887625
Iteration 12, |res| 0.000036, lam 1.000000
AOA 2.00 CL 1.954065
Iteration 15, |res| 0.000070, lam 0.500000
AOA 2.50 CL 2.019748
Iteration 15, |res| 0.000067, lam 0.500000
AOA 3.00 CL 2.085342
Iteration 13, |res| 0.000061, lam 0.694215
AOA 3.50 CL 2.150565
Iteration 11, |res| 0.000054, lam 1.000000
AOA 4.00 CL 2.215191
Iteration 11, |res| 0.000067, lam 1.000000
AOA 4.50 CL 2.279088
Iteration 15, |res| 0.000086, lam 0.500000
AOA 5.00 CL 2.341978
Iteration 15, |res| 0.000078, lam 0.500000
AOA 5.50 CL 2.404220
Iteration 15, |res| 0.000089, lam 0.500000
AOA 6.00 CL 2.466341
Iteration 15, |res| 0.000075, lam 0.545437
AOA 6.50 CL 2.527660
Iteration 15, |res| 0.000095, lam 0.500000
AOA 7.00 CL 2.588199
Iteration 12, |res| 0.000073, lam 1.000000
AOA 7.50 CL 2.647865
Iteration 16, |res| 0.000070, lam 0.509919
AOA 8.00 CL 2.706333
Iteration 12, |res| 0.000087, lam 1.000000
AOA 8.50 CL 2.763480
Iteration 15, |res| 0.000094, lam 0.533548
AOA 9.00 CL 2.818948
Iteration 17, |res| 0.000066, lam 0.500000
AOA 9.50 CL 2.872665
Iteration 17, |res| 0.000074, lam 0.500000
AOA 10.00 CL 2.924110
Iteration 17, |res| 0.000067, lam 0.500000
AOA 10.50 CL 2.975157
Iteration 17, |res| 0.000098, lam 0.500000
AOA 11.00 CL 3.024640
Iteration 18, |res| 0.000074, lam 0.500000
AOA 11.50 CL 3.071677
Iteration 18, |res| 0.000086, lam 0.500000
AOA 12.00 CL 3.115999
Iteration 17, |res| 0.000078, lam 0.610160
AOA 12.50 CL 3.156572
Iteration 17, |res| 0.000045, lam 0.747574
AOA 13.00 CL 3.192209
Iteration 20, |res| 0.000100, lam 0.500000
AOA 13.50 CL 3.220741
Iteration 20, |res| 0.000036, lam 1.000000
AOA 14.00 CL 3.224709
Iteration 19, |res| 0.000085, lam 1.000000
AOA 14.50 CL 3.213858
Iteration 20, |res| 0.000036, lam 1.000000
AOA 15.00 CL 3.194628
Iteration 21, |res| 0.000091, lam 1.000000
AOA 15.50 CL 3.164424
Iteration 22, |res| 0.000044, lam 1.000000
AOA 16.00 CL 3.119864
Iteration 29, |res| 0.000079, lam 0.500000
AOA 16.50 CL 3.054350
Iteration 22, |res| 0.000063, lam 1.000000
AOA -2.00 CL 1.442025
Iteration 14, |res| 0.000045, lam 0.649575
AOA -1.50 CL 1.512635
Iteration 15, |res| 0.000076, lam 0.500000
AOA -1.00 CL 1.583071
Iteration 15, |res| 0.000074, lam 0.500000
AOA -0.50 CL 1.653241
Iteration 12, |res| 0.000051, lam 0.835271
AOA 0.00 CL 1.723282
Iteration 15, |res| 0.000077, lam 0.500000
AOA 0.50 CL 1.792899
Iteration 14, |res| 0.000064, lam 0.589422
AOA 1.00 CL 1.862379
Iteration 11, |res| 0.000062, lam 1.000000
AOA 1.50 CL 1.931570
Iteration 15, |res| 0.000091, lam 0.500000
AOA 2.00 CL 2.000072
Iteration 15, |res| 0.000078, lam 0.500000
AOA 2.50 CL 2.068524
Iteration 12, |res| 0.000087, lam 0.867127
AOA 3.00 CL 2.136696
Iteration 12, |res| 0.000043, lam 1.000000
AOA 3.50 CL 2.204344
Iteration 12, |res| 0.000072, lam 0.941724
AOA 4.00 CL 2.271163
Iteration 15, |res| 0.000095, lam 0.500000
AOA 4.50 CL 2.337073
Iteration 15, |res| 0.000087, lam 0.500000
AOA 5.00 CL 2.402937
Iteration 16, |res| 0.000063, lam 0.518009
AOA 5.50 CL 2.468177
Iteration 13, |res| 0.000055, lam 0.840520
AOA 6.00 CL 2.532688
Iteration 12, |res| 0.000084, lam 1.000000
AOA 6.50 CL 2.596183
Iteration 13, |res| 0.000043, lam 0.907235
AOA 7.00 CL 2.658449
Iteration 13, |res| 0.000035, lam 1.000000
AOA 7.50 CL 2.719282
Iteration 17, |res| 0.000074, lam 0.500000
AOA 8.00 CL 2.778141
Iteration 17, |res| 0.000088, lam 0.500000
AOA 8.50 CL 2.834865
Iteration 17, |res| 0.000095, lam 0.500000
AOA 9.00 CL 2.889508
Iteration 18, |res| 0.000079, lam 0.500000
AOA 9.50 CL 2.943268
Iteration 18, |res| 0.000092, lam 0.500000
AOA 10.00 CL 2.994049
Iteration 18, |res| 0.000077, lam 0.552947
AOA 10.50 CL 3.041043
Iteration 17, |res| 0.000048, lam 0.730897
AOA 11.00 CL 3.083021
Iteration 18, |res| 0.000055, lam 0.909048
AOA 11.50 CL 3.117727
Iteration 18, |res| 0.000036, lam 0.868484
AOA 12.00 CL 3.138361
Iteration 22, |res| 0.000060, lam 0.500000
AOA 12.50 CL 3.128209
Iteration 22, |res| 0.000084, lam 0.500000
AOA 13.00 CL 3.107656
Iteration 22, |res| 0.000050, lam 0.554328
AOA 13.50 CL 3.075341
Iteration 23, |res| 0.000055, lam 0.500000
AOA 14.00 CL 3.029031
Iteration 23, |res| 0.000084, lam 0.505091
AOA 14.50 CL 2.960875
Iteration 23, |res| 0.000063, lam 1.000000
AOA 15.00 CL 2.862806
Iteration 100, |res| 0.009462, lam 0.250000
Iteration 72, |res| 0.000098, lam 0.250000
AOA 16.00 CL 2.360755
Iteration 47, |res| 0.000084, lam 0.771126
AOA 16.50 CL 2.216520

# Read experimental data
EXPRES=np.genfromtxt("NLRLIFTSLOPE.csv",delimiter=",",names=True)

fix,ax = plt.subplots(1,2)
ax[0].plot(EXPRES['MEAS_X'],EXPRES['MEAS_Y'],marker=".",linestyle = 'None', color="tab:blue",label="Experimental Lift")
for val in Mach_vec:
    ax[0].plot(np.array(results[val]["AOA"]),np.asarray(results[val]["CL"]),marker=None,label="Calculation Mach %g"%val)
ax[0].plot(np.array(results[val]["AOA"]),results[val]["CLi"],marker=None,label="Inviscid Lift")

ax[0].set_xlabel('AOA')
ax[0].set_ylabel('CL')
ax[0].legend()
#ax[0].set_xlim([-2, 17])
ax[0].set_ylim([1.5, 3.5])

EXPRESD=np.genfromtxt("NLRDRAGSLOPE.csv",delimiter=",",names=True)
ax[1].plot(EXPRESD['MEAS_X'],EXPRESD['MEAS_Y'],marker=".",linestyle = 'None', color="tab:blue",label="Experimental Drag")
for val in Mach_vec:
    ax[1].plot(results[val]["AOA"],results[val]["CD"],marker=None,label="Calculation Mach %g"%val)

ax[1].set_ylim([0, 0.08]) 
#ax[1].set_xlim([-2, 17])
ax[1].set_xlabel('AOA')
ax[1].set_ylabel('CD')
ax[1].legend();

The viscous calculations accurately predict the change in lift slope compared to the inviscid calculations. Applying the Mach corrections does result in a worse prediction compared to the incompressible calculation. This seems to be in line with the results in [2], where the authors choose not to use a Mach correction for this case, but do use one for another case at the same Mach number. In the following, the pressure distributions are compared to the incompressible calculations.

# Set-up and initialize based on inviscid panel solution
s.Ma = 0.0
s.Itermax = 100

# Experimental 6° has the same lift as numerical 5.5°
s.Alpha = 6
[p6,bl6,x] = vf.init([MAIN,FLAP],s)
[x,flag,res,_,_] = vf.iter(x,bl6,p6,s,None,None)

# Experimental 13.1° has the same lift as numerical 12.6°
s.Alpha = 11.1
[p13,bl13,_] = vf.init([MAIN,FLAP],s)
[x,flag,res,_,_] = vf.iter(x,bl13,p13,s,None,None)
s.Alpha = 13.1
[x,flag,res,_,_] = vf.iter(x,bl13,p13,s,None,None)

Iteration 25, |res| 0.000076, lam 0.500000
Iteration 26, |res| 0.000073, lam 0.500000
Iteration 21, |res| 0.000047, lam 0.775109

# Shorthand for plotting all info for a single AOA from the csv dataset
def plot_cp_exp(ax,EXPRES):
    ax.plot(EXPRES['EXPMAINCP_X'],EXPRES['EXPMAINCP_Y'],marker="o",linestyle = 'None', color="tab:blue",label="Experiment")
    ax.plot(EXPRES['EXPFLAPCP_X']+.1,EXPRES['EXPFLAPCP_Y'],marker="o",linestyle = 'None', color="tab:blue")
    ax.plot(EXPRES['EXPMAINTR_X'],EXPRES['EXPMAINTR_Y'],marker="D",linestyle = 'None', color="tab:orange",label="Experimental transition region")
    ax.plot(EXPRES['EXPFLAPTR_X']+.1,EXPRES['EXPFLAPTR_Y'],marker="D",linestyle = 'None', color="tab:orange")

# Shorthand for plotting all info from the calculations for a single AOA
def plot_cp(ax,p,bl):
    # A helper index, cp is a single array of pressures over all panel nodes
    IMF = [range(0,p.foils[0].N),range(p.foils[0].N,p.foils[0].N+p.foils[1].N)]
    
    ax.plot(np.array(p.foils[0].X[0,:]),-p.cp[IMF[0]],marker="None",color="tab:blue",label="Viscous calculation")
    ax.plot(np.array(p.foils[1].X[0,:]+.1),-p.cp[IMF[1]],marker="None",color="tab:blue")
    ax.plot(np.array(p.foils[0].X[0,:]),-p.cp_inviscid[IMF[0]],':',marker="None",color="tab:green",label="Inviscid calculation")
    ax.plot(np.array(p.foils[1].X[0,:]+.1),-p.cp_inviscid[IMF[1]],':',marker="None",color="tab:green")

    for k in range(2):
        tr_lo = np.interp(bl[k].ST+bl[k].bl_fl.node_tr_lo.xi[0],p.foils[k].S,p.foils[k].X[0,:]+k*.1)
        tr_up = np.interp(bl[k].ST-bl[k].bl_fl.node_tr_up.xi[0],p.foils[k].S,p.foils[k].X[0,:]+k*.1)
        cp_up = np.interp(bl[k].ST-bl[k].bl_fl.node_tr_up.xi[0],p.foils[k].S,np.asarray(p.cp[IMF[k]]).ravel())
        cp_lo = np.interp(bl[k].ST+bl[k].bl_fl.node_tr_lo.xi[0],p.foils[k].S,np.asarray(p.cp[IMF[k]]).ravel())
        ax.plot(tr_lo,-cp_lo,'v',color="tab:red",label="Numerical transition point")
        ax.plot(tr_up,-cp_up,'v',color="tab:red")

    ax.set_xlabel('x/c')
    ax.set_ylabel('-cp')

# Read and plot data for 6° AoA
EXPRES=np.genfromtxt("NLRCP55.csv",delimiter=",",names=True)
fig,ax = plt.subplots(1,1)
plot_cp_exp(ax,EXPRES)
plot_cp(ax,p6,bl6)
ax.set_title('6° AOA')
ax.legend()

# Read and plot data for 13.1° AoA
EXPRES=np.genfromtxt("NLRCP126.csv",delimiter=",",names=True)
fig,ax = plt.subplots(1,1)
plot_cp_exp(ax,EXPRES)
plot_cp(ax,p13,bl13)
ax.set_title('13.1° AOA')
ax.legend();

[1] B. van den Berg and B. Oskam. Boundary layer measurements on a two-dimensional wing with flap and a comparison with calculations. NLR MP 79034 U

[2] Cebeci, Tuncer, Eric Besnard, and Hsun Chen. Calculation of multielement airfoil flows, including flap wells. 34th Aerospace Sciences Meeting and Exhibit. 1996.

[3] Schwamborn, Dieter, et al. Development of the DLR tau-code for aerospace applications. Proceedings of the International Conference on Aerospace Science and Technology. Bangalore, India: National Aerospace Laboratories, 2008.

[4] Guo, Chuanliang. Effects of turbulence modelling on the analysis and optimisation of high-lift configurations. Master Thesis, Cranfield University

[5] Van Ingen, J. L. The eN method for transition prediction: historical review of work at TU Delft. AIAA, 2008.

[6] Godin, P., D. W. Zingg, and T. E. Nelson. High-lift aerodynamic computations with one-and two-equation turbulence models. AIAA journal 35.2 (1997): 237-243.

[7] Haase, W. et al. ECARP - European Computational Aerodynamics Research Projects: Validation of CFD Codes and Assessment of Turbulence Models. Notes on Numerical Fluid Mechanics, Vol. 58, 1997.