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].

In [1]:
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 notebook
%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"),220)[:,::-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].

In [2]:
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).

In [3]:
# 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

# 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))
Iteration 19, |res| 0.000093, lam 0.500000
AOA -2.00 CL 1.419525
Iteration 7, |res| 0.000071, lam 1.000000
AOA -1.50 CL 1.488510
Iteration 10, |res| 0.000093, lam 0.500000
AOA -1.00 CL 1.557110
Iteration 10, |res| 0.000051, lam 0.540243
AOA -0.50 CL 1.625587
Iteration 6, |res| 0.000007, lam 1.000000
AOA 0.00 CL 1.693837
Iteration 9, |res| 0.000061, lam 0.500000
AOA 0.50 CL 1.761443
Iteration 8, |res| 0.000075, lam 0.500000
AOA 1.00 CL 1.829074
Iteration 7, |res| 0.000004, lam 1.000000
AOA 1.50 CL 1.896493
Iteration 5, |res| 0.000026, lam 1.000000
AOA 2.00 CL 1.963505
Iteration 10, |res| 0.000067, lam 0.500000
AOA 2.50 CL 2.029928
Iteration 10, |res| 0.000084, lam 0.500000
AOA 3.00 CL 2.094737
Iteration 10, |res| 0.000087, lam 0.500000
AOA 3.50 CL 2.160381
Iteration 8, |res| 0.000058, lam 0.500000
AOA 4.00 CL 2.225588
Iteration 7, |res| 0.000093, lam 0.584005
AOA 4.50 CL 2.290247
Iteration 7, |res| 0.000086, lam 0.500000
AOA 5.00 CL 2.354415
Iteration 8, |res| 0.000007, lam 0.981072
AOA 5.50 CL 2.417950
Iteration 8, |res| 0.000055, lam 0.500000
AOA 6.00 CL 2.480735
Iteration 5, |res| 0.000038, lam 1.000000
AOA 6.50 CL 2.542897
Iteration 6, |res| 0.000013, lam 1.000000
AOA 7.00 CL 2.604265
Iteration 9, |res| 0.000069, lam 0.500000
AOA 7.50 CL 2.664719
Iteration 5, |res| 0.000097, lam 1.000000
AOA 8.00 CL 2.724403
Iteration 10, |res| 0.000087, lam 0.569421
AOA 8.50 CL 2.783003
Iteration 10, |res| 0.000077, lam 0.514730
AOA 9.00 CL 2.840273
Iteration 12, |res| 0.000056, lam 0.500000
AOA 9.50 CL 2.896353
Iteration 14, |res| 0.000058, lam 0.500000
AOA 10.00 CL 2.936402
Iteration 7, |res| 0.000066, lam 0.500000
AOA 10.50 CL 2.988272
Iteration 8, |res| 0.000056, lam 0.500000
AOA 11.00 CL 3.037719
Iteration 7, |res| 0.000090, lam 0.500000
AOA 11.50 CL 3.084842
Iteration 7, |res| 0.000090, lam 0.500000
AOA 12.00 CL 3.128700
Iteration 7, |res| 0.000084, lam 0.500000
AOA 12.50 CL 3.168065
Iteration 7, |res| 0.000094, lam 0.500000
AOA 13.00 CL 3.201428
Iteration 8, |res| 0.000076, lam 0.500000
AOA 13.50 CL 3.220530
Iteration 9, |res| 0.000094, lam 0.587627
AOA 14.00 CL 3.206833
Iteration 9, |res| 0.000082, lam 0.622621
AOA 14.50 CL 3.181222
Iteration 9, |res| 0.000062, lam 0.652364
AOA 15.00 CL 3.140461
Iteration 11, |res| 0.000076, lam 0.500000
AOA 15.50 CL 3.075679
Iteration 11, |res| 0.000071, lam 0.679716
AOA 16.00 CL 2.963714
Iteration 18, |res| 0.000090, lam 0.555618
AOA 16.50 CL 2.516397
Iteration 20, |res| 0.000072, lam 0.500000
AOA -2.00 CL 1.449025
Iteration 8, |res| 0.000067, lam 0.717978
AOA -1.50 CL 1.519983
Iteration 9, |res| 0.000080, lam 0.500000
AOA -1.00 CL 1.590698
Iteration 6, |res| 0.000080, lam 0.500000
AOA -0.50 CL 1.661279
Iteration 9, |res| 0.000081, lam 0.500000
AOA 0.00 CL 1.731389
Iteration 8, |res| 0.000083, lam 0.547081
AOA 0.50 CL 1.801742
Iteration 5, |res| 0.000052, lam 0.793141
AOA 1.00 CL 1.871700
Iteration 9, |res| 0.000082, lam 0.500000
AOA 1.50 CL 1.941393
Iteration 7, |res| 0.000057, lam 0.758890
AOA 2.00 CL 2.010873
Iteration 14, |res| 0.000075, lam 0.500000
AOA 2.50 CL 2.078471
Iteration 8, |res| 0.000076, lam 0.500000
AOA 3.00 CL 2.147065
Iteration 10, |res| 0.000076, lam 0.500000
AOA 3.50 CL 2.215306
Iteration 6, |res| 0.000079, lam 0.500000
AOA 4.00 CL 2.283348
Iteration 6, |res| 0.000028, lam 0.937570
AOA 4.50 CL 2.350748
Iteration 8, |res| 0.000096, lam 0.500000
AOA 5.00 CL 2.417489
Iteration 9, |res| 0.000088, lam 0.500000
AOA 5.50 CL 2.483803
Iteration 6, |res| 0.000007, lam 1.000000
AOA 6.00 CL 2.549346
Iteration 9, |res| 0.000077, lam 0.500000
AOA 6.50 CL 2.613832
Iteration 7, |res| 0.000067, lam 1.000000
AOA 7.00 CL 2.677474
Iteration 7, |res| 0.000082, lam 0.607065
AOA 7.50 CL 2.739834
Iteration 10, |res| 0.000070, lam 0.517859
AOA 8.00 CL 2.800812
Iteration 11, |res| 0.000064, lam 0.500000
AOA 8.50 CL 2.859940
Iteration 14, |res| 0.000076, lam 0.500000
AOA 9.00 CL 2.903010
Iteration 8, |res| 0.000063, lam 0.500000
AOA 9.50 CL 2.956740
Iteration 7, |res| 0.000087, lam 0.500000
AOA 10.00 CL 3.007710
Iteration 7, |res| 0.000097, lam 0.500000
AOA 10.50 CL 3.054246
Iteration 7, |res| 0.000078, lam 0.500000
AOA 11.00 CL 3.094966
Iteration 8, |res| 0.000065, lam 0.500000
AOA 11.50 CL 3.126726
Iteration 9, |res| 0.000084, lam 0.500000
AOA 12.00 CL 3.131922
Iteration 10, |res| 0.000059, lam 0.500000
AOA 12.50 CL 3.108852
Iteration 9, |res| 0.000085, lam 0.708979
AOA 13.00 CL 3.072093
Iteration 9, |res| 0.000092, lam 0.500000
AOA 13.50 CL 3.016233
Iteration 12, |res| 0.000074, lam 0.519065
AOA 14.00 CL 2.924172
Iteration 18, |res| 0.000079, lam 0.703780
AOA 14.50 CL 2.720816
Iteration 14, |res| 0.000076, lam 0.598524
AOA 15.00 CL 2.428571
Iteration 12, |res| 0.000097, lam 0.603142
AOA 15.50 CL 2.325921
Iteration 27, |res| 0.000098, lam 0.500000
AOA 16.00 CL 1.615937
Iteration 12, |res| 0.000092, lam 0.500000
AOA 16.50 CL 1.516377
In [4]:
# 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.

In [5]:
# Set-up and initialize based on inviscid panel solution
s.Ma = 0.0

# 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 = 13.1
[p13,bl13,_] = vf.init([MAIN,FLAP],s)
[x,flag,res,_,_] = vf.iter(x,bl13,p13,s,None,None)
Iteration 15, |res| 0.000070, lam 0.500000
Iteration 20, |res| 0.000079, lam 0.500000
In [6]:
# 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('Main Airfoil 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.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.