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The Multi-point Optimization of Shock Control Bump with Constant-Lift Constraint Enhanced with Suction and Blowing for a Supercritical Airfoil

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Abstract

Both shock control bump (SCB) and suction and blowing are flow control methods used to control the shock wave/boundary layer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. A SCB uses a small local surface deformation to reduce the shock-wave strength, while suction decreases the boundary-layer thickness and blowing delays the flow separation. Here a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of SCB and suction and blowing. These flow control methods are used separately or together on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of all devices. It is shown that the simultaneous application of blowing and SCB (hybrid blowing/SCB) improves the average aerodynamic efficiency at off-design conditions by 18.2 % in comparison with the clean airfoil, while this increase is only 16.9 % for the hybrid suction/SCB. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.

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Abbreviations

A T :

Jacobian of convective flux

c :

Speed of sound

C B /l B :

Bump degree of symmetry

Cd p :

Pressure drag coefficient

Cd t :

Airfoil drag coefficient

Cd v :

Viscous drag coefficient

C f :

Skin friction coefficient

Cl :

Airfoil lift coefficient

C p :

Pressure coefficientt

C Q :

Non-dimensional mass flow

ds :

Surface element

E :

Total energy per unit mass

f :

Hicks-Henne Sine-function

F :

Cost function

f inv :

Inviscid flux vector

f vis :

Viscous flux vector

G :

Gradient vector of cost function

H :

Total enthalpy

h B :

Maximum bump height

K :

Turbulent kinetic energy

l B :

Bump length

L/D :

Aerodynamic efficiency

M −T :

Transition matrix of non-conservative variables

\(M_{\infty }\) :

Free stream Mach number

n x ,n y :

Component of the unit normal vector

p :

Static pressure

p t a r :

Static pressure target on airfoil surface

P 0 :

Total Pressure

\(P_{\infty }\) :

Free stream pressure

q k :

Heat flux

r :

Penalty function parameter

Rey \(_{\infty }\) :

Free stream Reynolds number

S :

The control volume surface

S n :

Normal distance from the airfoil surface

S w :

The airfoil surface

t :

Bump slope parameter

T :

Static temperature

\(U_{\infty }\) :

Free stream velocity

U :

Vector of flow variable

u,v :

Cartesian velocity component

V :

Contra variant velocity

x,y :

Cartesian coordinate system

x 0 :

Beginning of bump

Y+ :

Non-dimensional wall coordinate

α :

Airfoil angle of attack (AoA), deg

γ :

Ratio of specific heat coefficient

δ k m :

Kronecker symbol

κ :

Thermal diffusivity coefficient

λ :

Second viscosity coefficient

μ :

Dynamic viscosity coefficient

μ t :

Turbulent viscosity coefficient

τ :

Shear stress across the control volume surface

τ k m :

Component of viscous stress tensor

ρ :

Density

ω :

Turbulent specific dissipation rate

ψ :

Vector of adjoint variable

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Authors and Affiliations

  1. Center of Excellence in Aerospace Systems, Sharif University of Technology, Tehran, Iran

    K. Mazaheri & A. Nejati

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  1. K. Mazaheri
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  2. A. Nejati
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Mazaheri, K., Nejati, A. The Multi-point Optimization of Shock Control Bump with Constant-Lift Constraint Enhanced with Suction and Blowing for a Supercritical Airfoil. Flow Turbulence Combust 96, 639–666 (2016). https://doi.org/10.1007/s10494-015-9671-8

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