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Large eddy simulation of aircraft wake vortex with self-adaptive grid method

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Abstract

A self-adaptive-grid method is applied to numerical simulation of the evolution of aircraft wake vortex with the large eddy simulation (LES). The Idaho Falls (IDF) measurement of run 9 case is simulated numerically and compared with that of the field experimental data. The comparison shows that the method is reliable in the complex atmospheric environment with crosswind and ground effect. In addition, six cases with different ambient atmospheric turbulences and Brunt V¨ais¨al¨a (BV) frequencies are computed with the LES. The main characteristics of vortex are appropriately simulated by the current method. The onset time of rapid decay and the descending of vortices are in agreement with the previous measurements and the numerical prediction. Also, secondary structures such as baroclinic vorticity and helical structures are also simulated. Only approximately 6 million grid points are needed in computation with the present method, while the number can be as large as 34 million when using a uniform mesh with the same core resolution. The self-adaptive-grid method is proved to be practical in the numerical research of aircraft wake vortex.

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Abbreviations

A :

ratio of maximum and minimum grid spacing

b 0 :

initial vortex spacing

E(k):

energy density spectrum

F(f):

function valued from 0 to 1

g :

gravitation acceleration

i :

grid point index

J :

Jacobi determinant

K :

stiffness of spring

k i :

wave number component in spectral space

k kol :

Kolmogorov wave number, (ε/ν3)1/4

k p :

wave number of peak spectrum value

L x(y,z) :

size of simulation domain in x(y, z)- direction

N :

Brunt Väisälä (BV) frequency

N u :

grid speed refresh cycle

N x :

total grid number in x-direction

P rt :

turbulent Prandtl number

p :

pressure

r :

distance from vortex center

r c :

radius of vortex core

t :

time

t 0 :

time scale

t 2 :

onset time of rapid decay phase

Δt :

timestep

u :

velocity component in x-direction

u g :

lateral velocity of grid point

v :

velocity component in axial direction

v g :

axial velocity of grid point

v tan :

tangential velocity

w :

velocity component in vertical direction

w g :

vertical velocity of grid point

w 0 :

initial descend speed of vortex

x :

lateral coordinate

x ′ i :

equilibrium position of ith grid point in lateral direction

Δx :

grid spacing in x-direction

Δy :

grid spacing in y-direction

Δz :

grid spacing in z-direction

x ξ :

partial derivative \(\frac{\partial x}{\partial \xi}\)

y η :

partial derivative \(\frac{\partial y}{\partial \eta}\)

z ς :

partial derivative \(\frac{\partial z}{\partial \zeta}\)

x τ :

partial derivative \(\frac{\partial x}{\partial \tau}\)

y τ :

partial derivative \(\frac{\partial y}{\partial \tau}\)

z τ :

partial derivative \(\frac{\partial z}{\partial \tau}\)

y :

axial coordinate

z :

vertical coordinate

ε:

turbulence dissipation rate

Γ0 :

initial circulation of vortex

ν:

molecular viscosity

ν t :

sub-grid-scale eddy viscosity

θ:

potential temperature

θ0 :

reference temperature

ρ:

density

ξ, η, ς:

space coordinates in computation domain

τ:

time coordinate in computation domain.

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Authors and Affiliations

  1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100010, China

    Mengda Lin, Guixiang Cui & Zhaoshun Zhang

Authors
  1. Mengda Lin
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  2. Guixiang Cui
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  3. Zhaoshun Zhang
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Corresponding author

Correspondence to Guixiang Cui.

Additional information

Project supported by the Boeing-COMAC Aviation Energy Conservation and Emissions Reduction Technology Center (AECER)

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Lin, M., Cui, G. & Zhang, Z. Large eddy simulation of aircraft wake vortex with self-adaptive grid method. Appl. Math. Mech.-Engl. Ed. 37, 1289–1304 (2016). https://doi.org/10.1007/s10483-016-2132-9

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  • DOI: https://doi.org/10.1007/s10483-016-2132-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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