Source code for RCAIDE.Library.Methods.Aerodynamics.Common.Drag.parasite_drag_fuselage
# RCAIDE/Library/Methods/Aerodynamics/Common/Drag/subsonic_parasite_drag_fuselage.py
# (c) Copyright 2023 Aerospace Research Community LLC
#
# Created: Jun 2024, M. Clarke
# ----------------------------------------------------------------------------------------------------------------------
# IMPORT
# ----------------------------------------------------------------------------------------------------------------------
# RCAIDE import
import RCAIDE
from RCAIDE.Framework.Core import Data
from RCAIDE.Library.Methods.Aerodynamics.Common.Drag.compressible_turbulent_flat_plate import compressible_turbulent_flat_plate
from RCAIDE.Library.Methods.Utilities import Cubic_Spline_Blender
# python imports
import numpy as np
# ----------------------------------------------------------------------------------------------------------------------
# Parasite Drag Fuselage
# ----------------------------------------------------------------------------------------------------------------------
[docs]
def parasite_drag_fuselage(state,settings,fuselage):
"""
Computes the parasite drag coefficient for a fuselage or boom accounting for compressibility effects.
Parameters
----------
state : Data
Flight conditions containing:
- conditions.freestream.mach_number : float
Freestream Mach number [unitless]
- conditions.freestream.temperature : float
Freestream static temperature [K]
- conditions.freestream.reynolds_number : float
Freestream Reynolds number per unit length [unitless/m]
settings : dict
Aerodynamic analysis settings containing:
- fuselage_parasite_drag_form_factor : float
Form factor for fuselage parasite drag [unitless]
- supersonic.fuselage_parasite_drag_begin_blend_mach : float
Mach number at which supersonic blending begins [unitless]
- supersonic.fuselage_parasite_drag_end_blend_mach : float
Mach number at which supersonic blending ends [unitless]
fuselage : Data
Fuselage geometry containing:
- tag : str
Unique identifier for the fuselage
- areas.front_projected : float
Front projected area [m²]
- areas.wetted : float
Wetted area [m²]
- lengths.total : float
Total length of fuselage [m]
- effective_diameter : float
Effective diameter of fuselage [m]
Returns
-------
None
Results are stored in state.conditions.aerodynamics.coefficients.drag.parasite[fuselage.tag]
Notes
-----
This function calculates the parasite drag coefficient for a fuselage or boom using
compressible turbulent flat plate theory with form factor corrections. The calculation
accounts for compressibility effects through Mach number-dependent form factors and
uses cubic spline blending for the transonic regime.
**Major Assumptions**
* Fully turbulent boundary layer over the entire fuselage
* Cylindrical body approximation for form factor calculations
* Compressible turbulent flat plate skin friction correlation
* Cubic spline blending smooths transition between subsonic and supersonic regimes
* Form factor accounts for pressure drag due to body shape
**Theory**
The fuselage Reynolds number is:
:math:`Re_{fus} = Re \\cdot l_{fus}`
where :math:`Re` is the freestream Reynolds number per unit length and :math:`l_{fus}` is the fuselage length.
The skin friction coefficient is calculated using compressible turbulent flat plate theory:
:math:`C_f = f(Re_{fus}, M, T)`
The diameter-to-length ratio is:
:math:`d/l = \\frac{d_{fus}}{l_{fus}}`
For subsonic flow (M ≤ 1.0), the form factor parameters are:
:math:`D = \\sqrt{1 - (1-M^2)(d/l)^2}` for M < 0.95
:math:`D = \\sqrt{1 - (d/l)^2}` for M ≥ 0.95
:math:`a = \\frac{2(1-M^2)(d/l)^2(\\text{arctanh}(D)-D)}{D^3}` for M < 0.95
:math:`a = \\frac{2(d/l)^2(\\text{arctanh}(D)-D)}{D^3}` for M ≥ 0.95
The maximum velocity perturbation is:
:math:`\\frac{\\Delta u_{max}}{u_{\\infty}} = \\frac{a}{(2-a)\\sqrt{1-M^2}}` for M < 0.95
:math:`\\frac{\\Delta u_{max}}{u_{\\infty}} = \\frac{a}{2-a}` for M ≥ 0.95
The form factor is:
:math:`k_{fus} = (1 + FF \\cdot \\frac{\\Delta u_{max}}{u_{\\infty}})^2`
where :math:`FF` is the user-specified form factor.
For supersonic flow, the form factor is calculated using cubic spline blending between
subsonic and supersonic correlations.
The parasite drag coefficient is:
:math:`C_{D,parasite} = k_{fus} \\cdot C_f \\cdot \\frac{S_{wet}}{S_{ref}}`
**Definitions**
'Parasite Drag'
Drag component caused by viscous effects and pressure forces on the aircraft surface.
'Form Factor'
Multiplier accounting for the increase in drag due to body shape compared to a flat plate.
'Compressibility Effects'
Changes in aerodynamic characteristics due to compressible flow effects at high Mach numbers.
References
----------
[1] Stanford AA241 Course Notes
See Also
--------
RCAIDE.Library.Methods.Aerodynamics.Common.Drag.compressible_turbulent_flat_plate
RCAIDE.Library.Methods.Utilities.Cubic_Spline_Blender
"""
# unpack inputs
Sref = fuselage.areas.front_projected
Swet = fuselage.areas.wetted
l_fus = fuselage.lengths.total
d_fus = fuselage.effective_diameter
form_factor = settings.fuselage_parasite_drag_form_factor
low_cutoff = settings.supersonic.fuselage_parasite_drag_begin_blend_mach
high_cutoff = settings.supersonic.fuselage_parasite_drag_end_blend_mach
Mach = state.conditions.freestream.mach_number
T = state.conditions.freestream.temperature
Re = state.conditions.freestream.reynolds_number
# Reynolds number
Re_fus = Re*(l_fus)
# skin friction coefficient
cf_fus, k_comp, k_reyn = compressible_turbulent_flat_plate(Re_fus,Mach,T)
d_d = d_fus/l_fus
if np.all((Mach<=1.0) == True):
# compute form factor for cylindrical bodies
D = np.zeros_like(Mach)
D[Mach < 0.95] = np.sqrt(1 - (1-Mach[Mach < 0.95]**2) * d_d**2)
D[Mach >= 0.95] = np.sqrt(1 - d_d**2)
a = np.zeros_like(Mach)
a[Mach < 0.95] = 2 * (1-Mach[Mach < 0.95]**2) * (d_d**2) *(np.arctanh(D[Mach < 0.95])-D[Mach < 0.95]) / (D[Mach < 0.95]**3)
a[Mach >= 0.95] = 2 * (d_d**2) *(np.arctanh(D[Mach >= 0.95])-D[Mach >= 0.95]) / (D[Mach >= 0.95]**3)
du_max_u = np.zeros_like(Mach)
du_max_u[Mach < 0.95] = a[Mach < 0.95] / ( (2-a[Mach < 0.95]) * (1-Mach[Mach < 0.95]**2)**0.5 )
du_max_u[Mach >= 0.95] = a[Mach >= 0.95] / ( (2-a[Mach >= 0.95]) )
k_fus = (1 + form_factor*du_max_u)**2
fuselage_parasite_drag = k_fus * cf_fus * Swet / Sref
else:
# supersonic condition
D_low = np.zeros_like(Mach)
a_low = np.zeros_like(Mach)
du_max_u_low = np.zeros_like(Mach)
D_high = np.zeros_like(Mach)
a_high = np.zeros_like(Mach)
du_max_u_high = np.zeros_like(Mach)
k_fus = np.zeros_like(Mach)
low_inds = Mach < high_cutoff
high_inds = Mach > low_cutoff
D_low[low_inds] = np.sqrt(1 - (1-Mach[low_inds]**2) * d_d**2)
a_low[low_inds] = 2 * (1-Mach[low_inds]**2) * (d_d**2) *(np.arctanh(D_low[low_inds])-D_low[low_inds]) / (D_low[low_inds]**3)
du_max_u_low[low_inds] = a_low[low_inds] / ( (2-a_low[low_inds]) * (1-Mach[low_inds]**2)**0.5 )
D_high[high_inds] = np.sqrt(1 - d_d**2)
a_high[high_inds] = 2 * (d_d**2) *(np.arctanh(D_high[high_inds])-D_high[high_inds]) / (D_high[high_inds]**3)
du_max_u_high[high_inds] = a_high[high_inds] / ( (2-a_high[high_inds]) )
spline = Cubic_Spline_Blender(low_cutoff,high_cutoff)
h00 = lambda M:spline.compute(M)
du_max_u = du_max_u_low*(h00(Mach)) + du_max_u_high*(1-h00(Mach))
k_fus = (1 + form_factor*du_max_u)**2
fuselage_parasite_drag = k_fus * cf_fus * Swet / Sref
# Store data
state.conditions.aerodynamics.coefficients.drag.parasite[fuselage.tag] = Data(
wetted_area = Swet ,
reference_area = Sref ,
total = fuselage_parasite_drag ,
skin_friction = cf_fus ,
compressibility_factor = k_comp ,
reynolds_factor = k_reyn ,
form_factor = k_fus ,
)
return
