Boundary Layer


Analyze wall-resolved boundary layers.


  • base: Base

    The input base.

  • coordinates: list(str)

    The physical Cartesian coordinate names.

  • bl_type: str, default= aerodynamic

    Type of boundary layer:

    • ‘aerodynamic’: aerodynamic boundary layer

    • ‘thermal’: thermal boundary layer

  • edge_crit: int, default= 7

    Criteria used for the boundary layer edge detection. Add the integer value associated to each criterion to get the chosen combination.

      1. \(dV/ds < 1\%\)

      1. Stock & Haase

      1. isentropic velocity

      1. isentropic Mach number

    if edge_crit includes 8, then the edge results from the closest point from the wall above all criteria used. Otherwise, the edge comes from the average of all edges computed independent from each criteria.

    e.g.: edge_crit = 5 means a mix between the criteria 1 and 4.

  • wall_type: str, default= resolved

    Type of wall resolution (‘resolved’ or ‘modeled’).

  • mesh_type: str in [‘2D’, ‘2.5D’, ‘3D’], default= ‘3D’

    Dimensionality of the mesh.

  • max_bl_pts: int, default= 100

    Maximum number of points in the boundary layer.

  • added_bl_pts: int, default= 2

    The number of points inside the boundary layer = number of calculated boundary layer points + added_bl_pts

  • smoothing_cycles: int, default= 0

    Number of smoothing cycles for boundary layer results.

  • families: dict(str: int) or list(str)

    Surface parts on which the boundary layer is to be computed.

    If the value is a dictionary: The key value is a family name. This family name must be refered by the boundary condition objects. The boundary condition associated to this family name will be processed. The value associated to a key is a marker of the corresponding family. Two families may have the same marker.

    As an example,

    t[‘families’] = {‘WingExt’: 3, ‘Flap’: 4, ‘WingInt’: 3}

    Both ‘WingExt’ and ‘WingInt’ families have the same marker. Then, all corresponding mesh points will be processed alltogether. They will be concatenated in the output base.

    If the value is a list, then a different marker will be assigned to each item of the list.

    As an example,

    t[‘families’] = [‘WingExt’, ‘Flap’, ‘WingInt’]

    Value 0 is special, and applied to all points that do not belong to an input family. So if you give a marker 0 to a family, then you will get all boundary conditions in the ouput base.

  • only_profiles: bool, default= False

    Only the profiles selected by profile_points will be calculated.

  • profile_points: list(list(float)), default= []

    Profiles will be plotted according to the surface points. If you give the coordinates of a point in the mesh, the boundary layer profile issued from the nearest point to the surface will be computed.

  • bl_parameters: dict, default= {}

    Dictionary with keys in [“2D_offset_vector”, “reference_Mach_number”, “reference_velocity”, “reference_pressure”, “reference_density”, “reference_temperature”, “Prandtl_number”, “gas_constant_gamma”, “gas_constant_R”]

  • offsurf: int, default= -1

    Distance from the wall. To get values on a surface lying at this distance from the wall.

  • eps_Mis: float, default= 0.01

    Threshold on the isentropic Mach number for edge_crit = 8.

  • variables: list(str), default= [‘density’, ‘x_velocity’, ‘y_velocity’, ‘z_velocity’, ‘pressure’]

    Names of the input primitive variables (density, velocity components, static pressure).

  • nb_zone_passingthrough: int, default= 50

    Maximum number of zone a vector could pass through. When the maximum is reached, the process will stop to propagate the vector (will be cut before the end).

  • keep_interpolation_data: bool, default= False

    Allow intermediary results (interpolation coefficients, C objects to remain instantiated in the treatment, in order not to be recomputed in a further call of the same treatement. Warning, the mesh must remain the same.

  • instant_selection: int or str, default= 0

    Instant name (or index) to execute in the base.

  • change_input_data_type: bool, default= False

    C routines need to have a specific type for the provided variables. Mostly float64 for float, and int32 for int. And C ordered tables. If the provided base does not have the correct type and ordering, a retyped/ordered copy is performed. To save memory, this copy could replace the input variable. This will avoid to keep both tables instantiated at the same time, but may increase the memory used in the initial base (as new copies will mostly use a bigger type size). This copy will only apply to coordinates and retrieved variables.


Zones must be unstructured.

Input flow field values must be dimensionalized. The standard variables named density, x_velocity, y_velocity, z_velocity and pressure must be given in instants.

If edge_crit >= 8, then the variables total_temperature and Mach_number must also be given.


Three output bases.

If you give the coordinates of a point in the mesh, it will compute the boundary layer profile issued from the nearest point to the surface.

A profile is a line issued from a point (mesh point) on a surface that is perpendicular to this surface. The points along the boundary layer profile are computed from the volume grid points. A point along the boundary layer profile is the result of the intersection between the normal and a face of a volume element.


import antares
myt = antares.Treatment('Bl')
myt['base'] = base
myt['coordinates'] = ['points_xc', 'points_yc', 'points_zc']
myt['families'] = {'Slat': 2, 'Flap': 4, 'Main': 3}
myt['mesh_type'] = '2.5D'
myt['max_bl_pts'] = 50
myt['added_bl_pts'] = 2
myt['smoothing_cycles'] = 0
myt['only_profiles'] = False
myt['bl_type'] = 'aerodynamic' # 'aerodynamic' 'thermal'
myt['offsurf'] = 0.5
myt['profile_points'] = [[1.0 , 1.0 , 0.0],]
t['bl_parameters'] = {'2D_offset_vector': 2, 'gas_constant_R': 287.0,
                      'reference_Mach_number': 0.1715, 'reference_velocity': 36.4249853252,
                      'reference_pressure': 101325.0, 'reference_density': 3.14466310931,
                      'reference_temperature': 112.269190122, 'gas_constant_gamma': 1.4,
                      'Prandtl_number': 0.72, }
res_base, profbase, offsurfbase = t.execute()

Main functions

class antares.treatment.codespecific.boundarylayer.TreatmentBl.TreatmentBl

This class is used to analyze boundary layers.

The treatment is divided in many parts. Some of them are developed in C language to get CPU performance. C routines are made available in python with the module ‘ctypes’.

  1. read results and user parameters

  2. build a volume element connectivity structure

  3. compute the surface normals

  4. interpolate the flow field values to the surface normals

  5. compute the boundary layer edge see file calculate_boundary_layer_edge.c

  6. define the local (s, n) coordinate system

  7. compute the boundary layer values in the (s, n) coordinate system see file calculate_boundary_layer.c

  8. modify the boundary layer edge

  9. define the local (s, n) coordinate system

  10. compute the boundary layer values in the (s, n) coordinate system

static asvoid(arr)

View the array as dtype np.void (bytes).

Based on, 2013-06) The items along the last axis are viewed as one value. This allows comparisons to be performed which treat entire rows as one value.


Compute normal vectors and interpolation coefficients.

compute_interzonetopo(base, cstzone, zone_loc_bnds)

Create additional boundary to consider elements coming from other zone when doing normal vector calculation.


Analyze the boundary layer.


the base containing the results

Return type:



Set the constant part.

Only needed once (both global then cstzone)


Merge prism layer layer between additional vector and main one.


Indices \(\displaystyle \delta\) and \(\displaystyle \infty\) are used respectively for the boundary layer edge and for the free stream conditions.

‘s’ denotes the coordinate of the streamwise direction, and ‘n’ the coordinate of the normal to the streamwise direction. ‘s’ and ‘n’ form the (s, n) streamline-oriented coordinate system. This coordinate system is curvilinear, orthogonal and attached to the surface.

Boundary layer profile (normal to the wall):

If asked, the profiles are output in a formated ascii file containing:

  • a first section (header) with free stream conditions (given as parameters):


Mach number

\(\displaystyle M_\infty\)



\(\displaystyle p_\infty\)



\(\displaystyle \rho_\infty\)




Velocity modulus

\(\displaystyle V_\infty\)


Pressure coefficient


Total pressure


Dynamic pressure

  • a section that is repeated as long as there are profiles:

Profile number


Requested coordinates of the profile origin


True coordinates of the profile origin. Profiles are computed at surface grid points

Normal vector

Normal unit vector at the profile origin

then come the integral values:


Boundary layer thickness


Displacement thickness [s-dir]


Displacement thickness [n-dir]


Thermal boundary layer thickness approximation


Momentum thickness [s-dir]


Momentum thickness [n-dir]


Incompressible shape factor

then the wall values:

FirstLayer height





Pressure coefficient

cfsI, cfnI

Skin friction coefficients [s, n dirs], \(\displaystyle V_\infty\)


Resulting skin friction coefficient, \(\displaystyle V_\infty\)

cfsD, cfnD

Skin friction coefficients [s, n dirs], \(\displaystyle V_\delta\)


Resulting skin friction coefficient, \(\displaystyle V_\delta\)






Dynamic viscosity


Kinematic viscosity


Shear stress component [s-dir]


Shear stress component [n-dir]


Resulting shear stress

then the edge values:

Prism height

Total height of the prism layer


Velocity modulus


Mach number


Total pressure


Pressure coefficient

finally, come different values along the profile:


Distance to the wall


adimensionalized distance to the wall

Vx, Vy, Vz

Cartesian velocity components


Velocity modulus normalized by the free stream velocity modulus


s normalized velocity component


n normalized velocity component


Skew angle


logarithm of the nondimensional wall distance


Velocity modulus normalized by the shear stress velocity modulus


Velocity modulus normalized by the shear stress velocity modulus based on a flow over a flat plate (theory)




Static pressure coefficient


Dynamic pressure coefficient


Total pressure


Total pressure loss




Total temperature


to be defined


Isentropic velocity modulus


Isentropic velocity modulus - velocity modulus


Mass flow


Turbulent Kinetic Energy


ratio of viscosities


Eddy viscosity


Mach number


Isentropic Mach Number

Boundary layer surface:

A surface contains in the mesh can be divided in many parts. A marker is a set of triangular and quadrilateral faces.

All the surfaces of a computation may be defined as families (or markers).

It can return a 2D field on the surface (or selected markers) with the following boundary layer quantities:

X, Y, Z

Cartesian coordinates of the surface point

VecNx, VecNy, VecNz

Cartesian coordinates of the surface normal vector

VxSurf, VySurf, VzSurf

Cartesian velocity components close to the wall [first grid layer] for wall streamlines

VxEdge, VyEdge, VzEdge

Cartesian velocity components at the boundary layer edge for inviscid streamlines

Vs, Vn

s, n velocity components close to the wall


Profile skew angle between wall and boundary layer edge in the s, n coordinate system


Nondimensional wall distance


Boundary layer thickness, \(\displaystyle \delta\)


Displacement thickness [s-dir] based on the velocity at the boundary layer edge, \(\displaystyle \delta^{*}_s\)


Displacement thickness [n-dir] based on the velocity at the boundary layer edge, \(\displaystyle \delta^{*}_n\)


Thermal boundary layer thickness, \(\displaystyle \delta_T\) (approximation)


Kinetic energy thickness [s-dir]


Kinetic energy thickness [n-dir];


Momentum thickness [s-dir], \(\displaystyle \theta_{ss}\)


Momentum thickness [n-dir], \(\displaystyle \theta_{nn}\)


Incompressible shape factor. A shape factor is used in boudary layer flow to determine the nature of the flow. The higher the value of H, the stronger the adverse pressure gradient. A large shape factor is an indicator of a boundary layer near separation. A high adverse pressure gradient can greatly reduce the Reynolds number at which transition into turbulence may occur. Conventionally, H = 2.59 (Blasius boundary layer) is typical of laminar flows, while H = 1.3 - 1.4 is typical of turbulent flows.


Total pressure


Pressure coefficient


Mach number at the boundary layer edge

CfsInf, CfnInf

Skin friction coefficients [s, n dirs], \(\displaystyle V_\infty\)


Resulting skin friction coefficient, \(\displaystyle V_\infty\)

CfsDel, CfnDel

Skin friction coefficient [s, n dirs], \(\displaystyle V_\delta\)


Resulting skin friction coefficient, \(\displaystyle V_\delta\)


Maximum eddy viscosity along the profile


Wall temperature


Temperature at the boundary layer edge


Temperature at the boundary layer edge, TO BE DETAILED


Profile tag


Index of the point in the array of grid points


Total height of the prism layer


Number of prism layers


(delta - heightPrismLayers)/delta*100


Height of the first prism layer


1 if the number of profile points is close to the maximum number of boundary layer points given as input, NOT YET AVAILABLE


100 tells that the boundary layer edge is found


Transition Laminar/Turbulent


Number of points in the boundary layer

The mathematical definitions are given below:

Displacement thicknesses (based on the velocity at the boundary layer edge):

\(\displaystyle \delta^{*}_s = \int_0^\delta (1-\frac{\rho}{\rho_\delta}\frac{V_s}{V_\delta}) ds\) (deltas), \(\displaystyle \delta^{*}_n = -\int_0^\delta (1-\frac{\rho}{\rho_\delta}\frac{V_n}{V_\delta}) ds\) (deltan)

Momentum thicknesses:

\(\displaystyle \theta_{ss} = \int_0^\delta \frac{\rho}{\rho_\delta}\frac{V_s}{V_\delta}(1-\frac{V_s}{V_\delta}) ds\) (thetass), \(\displaystyle \theta_{nn} = \int_0^\delta \frac{\rho}{\rho_\delta}\frac{V_n}{V_\delta}(1-\frac{V_n}{V_\delta}) ds\) (thetann)

Kinetic energy thicknesses:

\(\displaystyle \theta_{es} = \int_0^\delta \frac{\rho}{\rho_\delta}\frac{V_s}{V_\delta}(1-\frac{V_s^2}{V_\delta^2}) ds\) (deltaes), \(\displaystyle \theta_{en} = \int_0^\delta \frac{\rho}{\rho_\delta}\frac{V_n}{V_\delta}(1-\frac{V_n^2}{V_\delta^2}) ds\) (deltaen)

Shape factors:

\(\displaystyle H12 = \frac{\delta^{*}_s}{\theta_{ss}}\), \(\displaystyle H22 = \frac{\delta^{*}_n}{\theta_{nn}}\)

Pressure coefficients:

\(\displaystyle Cp = \frac{p - p_{\infty}}{\frac{1}{2}\rho_{\infty} V_{\infty}^2}\) (cp_static), \(\displaystyle Kp = \frac{p_{tot} - p_{\infty}}{\frac{1}{2}\rho_{\infty} V_{\infty}^2}\) (cp_dyn)

Skin friction coefficients:

\(\displaystyle Cf_{\delta} = (\mu_w + \mu_t) \frac{{\frac{\partial V}{\partial w}}_{|_w}}{\frac{1}{2}\rho_w V_\delta^2}\), \(\displaystyle Cf_{\infty} = (\mu_w + \mu_t) \frac{{\frac{\partial V}{\partial w}}_{|_w}}{\frac{1}{2}\rho_\infty V_\infty^2}\)

\(\displaystyle Y^+ = Y \frac{V^\star}{\nu}\)

Velocity normalized by the shear stress velocity:

\(\displaystyle V^+ = \frac{V}{V^\star}\)

Shear stress at the wall:

\(\displaystyle \tau_w = \mu_w \frac{\partial u}{\partial y}\)

Shear stress velocity (friction velocity) at the wall:

\(\displaystyle V^\star = \sqrt{\frac{\tau_w}{\rho_w}}\)

Total pressure loss:

\(\displaystyle \frac{\Delta P_t}{P_t} = \frac{P_t - {P_t}_\infty}{{P_t}_\infty}\) (PtotLoss)

Skew angles:

\(\displaystyle \beta = \gamma - \gamma_\delta\), \(\displaystyle \beta_w = \gamma_w - \gamma_\delta\)

Users must keep in mind the following restrictions when analyzing their results.



There are two types of regions where an exact boundary layer edge can not be found:

  1. The velocity component Vs becomes very small or zero:
    1. Stagnation point regions

      At a stagnation point, Vs=0. Then, there is no boundary layer thickness. Near stagnation points, it is also difficult to find a boundary layer thickness accurately.

    2. Trailing edge regions

      In thick trailing edge regions, Vs becomes very small.

  2. The surface normals do not leave the boundary layer:
    1. Intersection regions (wing-body, body-tail, etc)
      1. The surface normal does not leak from the boundary layer.

      2. The surface normal passes the boundary layer from another component first.

      3. The surface normal hits another surface.

    No accurate boundary layer edge can be found in these cases.


The best situation is when the boundary layer edge lies in the prism layer. In this case, the difference between the true boundary layer edge and the grid point laying on the profile that is upper (or lower) than this true edge is small.

If the boundary layer edge lies outside the prism layer, then the diffence may be more important. Of course, that depends on the mesh quality, but, in general, mesh cell ratio increase quite fast outside the prism layer. In this case, the computed boundary layer thickness can be overestimated, and the step between two successive points on the profile can be large. Then, it is necessary to check the displacement (or momentum) thickness to check the lower pointsand the upper point (respective to the boundary layer edge).

Boundary layer edge:

The edge of the boundary layer is detected with the following multistage algorithm.

A first guess of the boundary layer edge is made with four different methods (see input parameter edge_crit) (function calculate_boundary_layer_edge()):

  1. the first derivative of the boundary layer profile velocity is smaller than the 1% and the step between one derivative and the previous one is smaller than the 0.01%. (function edge_velocity_slope())

  2. \(\displaystyle \delta = \epsilon y_{max}\) with \(\displaystyle y_{max}\) is the wall distance for which the diagnostic function \(\displaystyle y^a |\frac{\partial u}{\partial y}|^b\) is maximum. The first 10 points are omitted from this maximum search. The constants for a turbulent boundary layer are evaluated from Coles velocity profiles: \(\displaystyle a=1, b=1, \epsilon = 1.936\). The constants for a laminar boundary layer come from quasi-similar compressible solutions including heat transfer effects: \(\displaystyle a=3.9, b=1, \epsilon = 1.294\). The reference is [STOCKHAASE].

  1. the relative difference between the isentropic velocity and the velocity of the profile is smaller than a threshold.

    \(\displaystyle V_r = \sqrt{V_x^2 + V_y^2 + V_z^2}\) and \(\displaystyle V_i = V_{\infty} \sqrt{\frac{2}{(\gamma-1)*M_{\infty}^2} *(1-(0.5*\frac{2*(P-P_{\infty})}{\rho_{\infty}*V_{\infty}^2}*\gamma*M_{\infty}^2 + 1)^{(\gamma-1)/\gamma}) + 1}\) and

    The edge is the first point giving \(\displaystyle \frac{| V_r - V_i|}{Vr} < \epsilon_{V_i}\) with \(\displaystyle \epsilon_{V_i} = 2.5 \, 10^{-3}\)

    If none, then the edge is given by \(\displaystyle \min{\frac{| V_r - V_i|}{Vr}}\)

  1. hypothesis: the isentropic Mach number is constant in the boundary layer. Comparing with the Mach number gives the edge. \(\displaystyle P_{t_{is}} = P_{ref} (T_t/T_{ref})^{\gamma/(\gamma-1)}\), \(\displaystyle T_{t_{is}} = (P_{t_{is}}/P)^{(\gamma-1)/\gamma}\), \(\displaystyle M_{is} = \sqrt{2 |T_{t_{is}}-1| / (\gamma-1)}\)

    \(\displaystyle \delta M = M_{is} - M\), \(\displaystyle \delta M_{min} = \min(\delta M)\), \(\displaystyle M_{is_{cor}} = M_{is} - \delta M_{min}\).

    The edge is the first point giving \(\displaystyle | M - M_{is_{cor}}| / M_{is_{cor}} < \epsilon_{M_{is}}\) with \(\displaystyle \epsilon_{M_{is}} = 0.01\) by default.

The boundary layer edge is at the position where the first derivative of “V+” becomes approximately zero.

Start defining a range for the edge search. This range, stored in “points”, will be the 160% of the first guess of the boundary layer edge.

The first step is to search the first maximum of the first derivative of “V+” and then, starting from this maximum, search where the first derivative is smaller than two. Once this first edge is found, the next maximum is compared to the first one. If it is bigger, search again the boundary layer edge starting from this new maximum.

When the final edge is found, perform two checks. If the thickness of the boundary layer is greater than two, move the edge back to the last maximun or minimum of the first derivate of “V+” before the distance to the wall is two.

The second check is done using the isentropic velocity. Search for the point where the isentropic velocity meets the profile velocity but only until three points below the current boundary layer edge. If the point is found, average it with the current edge to get the final and corrected boundary layer edge.


The interpolation of the CFD values to the normal (profile) is done with a polynomial expansion of the form \(\displaystyle G^i = a + b x + c y\), which represents a linear variation of G in both x and y directions within a triangular element. The three constants a, b, and c are computed with the three triangle points. more details can be found in [CHUNG].


Sutherland law for molecular viscosity: \(\displaystyle \mu = \frac{C_1 \sqrt{T_w}}{1+\frac{S}{T_w}}\) with \(\displaystyle C_1 = 1.46 10^{-6} kg.m^{-1}.s^{-1}.K^{-1/2}\) and \(\displaystyle S = 112. K\) (functions Skinfric() of calculate_boundary_layer.c and bl_profile(), clear_values() of calculate_boundary_layer_edge.c)


Function \(\displaystyle U^+\) versus \(\displaystyle y^+\):

linear part: \(\displaystyle U^+ = y^+\) for \(\displaystyle y^+ < 11.63\)

log part: \(\displaystyle U^+ = 5.75 * \log(y^+) + 5.5\) for \(\displaystyle y^+ > 11.63\)


if not given, T_wall is computed with the equation of state of perfect gas: \(\displaystyle T_w = \frac{\gamma}{(\gamma-1)C_p} \frac{P}{\rho}\) where \(\displaystyle C_p = 1,003.41^{-1}.K\) is here the specific heat at constant pressure (at T = 250 K), and \(\displaystyle \gamma = \frac{C_p}{C_v}\) given as input, with \(\displaystyle C_v\) the specific heat at constant volume


The boundary layer thickness \(\displaystyle (\delta)\) is the average of a numerical value (distance of the boundary layer edge from the wall) and a correlation value coming from the shape factor (function Thickness() of calculate_boundary_layer.c).

\(\displaystyle \delta = \frac{\delta_{sf}+\delta_{num}}{2}\)

\(\displaystyle \delta_{sf} = \delta^{*I} * (\frac{\theta_s^{I}}{\delta_s^{*I}} H_{1}+1)\) where the superscript I means that the incompressible formula is used and with \(\displaystyle H_{1}\) the mass flow shape factor computed with a correlation of Green [GREEN].


\(\displaystyle \delta_T\) (deltat) is the E. Polhausen approximation of the thermal boundary layer thickness for Prandtl number greater than 0.6

\(\displaystyle \delta_T = \frac{\delta}{{Pr}^{1/3}}\)


Numerical values that are not available as inputs are computed with:

\(\displaystyle M_a = \frac{V}{\sqrt(\gamma*R*T)}\)

\(\displaystyle P_{tot} = (1+.2*M_a*M_a)^{3.5} * P\) (so \(\displaystyle \gamma = 1.4\))


PROCUREMENT EXECUTIVE MINISTRY OF DEFENCE AERONAUTICAL RESEARCH COUNCIL REPORTS AND MEMORANDA no 3791 Prediction of Turbulent Boundary Layers and Wakes in Compressible Flow by a Lag-Entrainment Method By J. E. GREEN, D. J. WEEKS AND J. W. F. BRODMAN, Aerodynamics Dept., R.A.E, Farnborough


Hans W. Stock and Werner Haase. “Feasibility Study of e^N Transition Prediction in Navier-Stokes Methods for Airfoils”, AIAA Journal, Vol. 37, No. 10 (1999), pp. 1187-1196.


Computational Fluid Dynamics. T. J. Chung. Cambridge University Press, 2002. pp 273–275


import os
if not os.path.isdir('OUTPUT'):

import antares

r = antares.Reader('netcdf')
r['filename'] = os.path.join('..', 'data', 'BL', 'EUROLIFT_2D', '')
base =

r = antares.Reader('netcdf')
r['base'] = base
r['filename'] = os.path.join('..', 'data', 'BL', 'EUROLIFT_2D', 'sol_Local_Sweep_ETW1.pval.30000')

t = antares.Treatment('Bl')
t['base'] = base
t['coordinates'] = ['points_xc', 'points_yc', 'points_zc']
t['families'] = {'Slat_2': 2, 'Flap_4': 4, 'Main_3': 3}
t['mesh_type'] = '2.5D'
t['max_bl_pts'] = 50
t['added_bl_pts'] = 2
t['smoothing_cycles'] = 0
t['only_profiles'] = False
t['bl_type'] = 'thermal' # 'aerodynamic' 'thermal'
t['bl_type'] = 'aerodynamic' # 'aerodynamic' 'thermal'
t['offsurf'] = 0.5
t['profile_points'] = [[1.0 , 1.0 , 0.0],
                       [2.0 , 1.0 , 0.0],
                       [3.0 , 1.0 , 0.0],
                       [5.0 , 1.0 , 0.0],
                       [7.0 , 1.0 , 0.0],
                       [9.0 , 1.0 , 0.0],
                       [10.0, 1.0,  0.0],
                       [15.0, 1.0,  0.0]
t['bl_parameters'] = {'2D_offset_vector': 2, 'gas_constant_R': 287.0,
                      'reference_Mach_number': 0.1715, 'reference_velocity': 36.4249853252,
                      'reference_pressure': 101325.0, 'reference_density': 3.14466310931,
                      'reference_temperature': 112.269190122, 'gas_constant_gamma': 1.4,
                      'Prandtl_number': 0.72, }
res_base, profbase, offsurfbase = t.execute()

w = antares.Writer('bin_tp')
w['base'] = res_base
w['filename'] = os.path.join('OUTPUT', 'ex_blsurf.plt')

if offsurfbase:
    w = antares.Writer('bin_tp')
    w['base'] = offsurfbase
    w['filename'] = os.path.join('OUTPUT', 'ex_offblsurf.plt')