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Aerodynamic drag
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Introduction
Aerodynamic drag refers to the retarding force on moving aerodynamic bodies acting in the direction of the freestream flow. From the body perspective (near-field approach), the drag comes from forces due to pressure distributions over the body surface, symbolized , and forces due to skin friction, which is a result of viscosity, denoted .
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Introduction
Aerodynamic drag refers to the retarding force on moving aerodynamic bodies acting in the direction of the freestream flow. From the body perspective (near-field approach), the drag comes from forces due to pressure distributions over the body surface, symbolized , and forces due to skin friction, which is a result of viscosity, denoted . Alternatively, calculated from the flowfield perspective (far-field approach), the drag force comes from three natural phenomena: shock waves, vortex sheet and viscosity.
The pressure distribution over the body surface exerts normal forces which, summed and projected into the freestream direction,
represent the drag force due to pressure . The nature of these normal forces combines shock wave effects, vortex system
generation effects and wake viscous mechanisms all together.
When the viscosity effect over the pressure distribution is considered separately, the remaining drag force is called pressure
(or form) drag. In the absence of viscosity, the pressure forces on the vehicle cancel each other and, hence, the
drag is zero. Pressure drag is the dominant component in the case of vehicles with regions of separated flow, in which the pressure
recovery is fairly ineffective.
The friction drag force, which is a tangential force on the aircraft surface, depends substantially on boundary layer configuration and
viscosity. The calculated friction drag utilizes the x-projection of the viscous stress tensor evaluated on each
discretized body surface.
The sum of friction drag and pressure (form) drag is called viscous drag. This drag component takes into account the influence of
viscosity. In a thermodynamic perspective, viscous effects represent irreversible phenomena and, therefore, they create entropy. The
calculated viscous drag use entropy changes to accurately predict the drag force.
When the airplane produces lift, another drag component comes in. Induced drag, symbolized , comes about due to a modification on the pressure distribution due to the trailing vortex system that accompanies the lift production. Induced drag tends to be the most important component for airplanes during take-off or landing flight. Other drag component, namely wave drag, , comes about from shock waves in transonic and supersonic flight speeds. The shock waves induce changes in the boundary layer and pressure distribution
over the body surface. It is worth noting that not only viscous effects but also shock waves induce irreversible phenomena and, as a
consequence, they can be measured through entropy changes along the domain as well. Figure \ref is a summary of the
various aspects previously discussed.
Theoretical Aspects of Far-Field/Near-Field Balance
The drag force calculation can be performed using the integral of force balance in the freestream direction as
which surrounds the body represents the union of two unconnected surfaces,
where is the airplane surface, is the outlet surface and represents both the lateral and inlet surfaces. In general, the far-field control volume is located in the boundaries of the domain and its choice is user-defined. In Subsection \ref, further considerations concerning to the correct selection of the far-field boundary are given, allowing for desired flow characteristics.
Equation (\ref) can be decomposed into two surface integrals, yielding
The right-hand side integral in Eq.\ (\ref) represents the reaction forces of the airplane. The left-hand side integral in Eq.\
(\ref) represents the total force exerted by the fluid. Mathematically, these two integrals are equivalent. However, the
numerical integration of these terms will hardly lead to the same result, because the solution is approximated. In the terminology of
Computational Fluid Dynamics (CFD), when the integration is performed using the left-hand side integral in Eq.\ (\ref), the
near-field method is employed. On the other hand, when the integration of the right-hand side in Eq. (\ref) is computed,
the far-field method is considered.
The drag force balance is assured mathematically by Eq.\ (\ref), that is, the resultant drag force evaluated using the
near-field approach must be equal to the drag force extracted by the far-field approach. The correct drag breakdown considered in this
work is
See also
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