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8th European Symposium on Aerothermodynamics for Space Vehicles
NUMERICAL STUDIES OF 3D INSTABILITIES
PROPAGATING IN SUPERSONIC
COMPRESSION-CORNER FLOW
Andrey Novikov,
Alexander Fedorov, Ivan Egorov
Central Aerohydrodynamic Institute named
after prof. N.E. Zhukovsky (TsAGI), Russia
Moscow Institute of Physics and Technology
(State University) (MIPT), Russia
Introduction
 Laminar-turbulent transition (LTT) leads to substantial increase of the surface
heating and aerodynamic drag of high-speed vehicles, and affects the
efficiency of propulsion system and control surfaces.
 LTT problem needs clarifying physical mechanisms. Holistic computation of all
LTT stages is possible only using DNS, which gives full information about 3D
disturbance field and enables to identify and study in detail different LTT
mechanisms.
 Most DNS for hypersonic boundary layers were conducted for simple
configurations like a flat plate and a cone at 0 AoA. LTT in locally separated
boundary layers is of practical interest.
 Herein DNS of artificially excited 3D instabilities propagating through the 5.5°
compression-corner flow with separation at M∞=5.373 is performed using inhouse solver “HSFlow”.
 “Young” turbulent wedge is observed in the case of low-frequency forcing.
Problem formulation
 3D Navier-Stokes equations for viscous compressible perfect gas
 2 steps calculation:
Grid:
 Laminar steady flow
• 87.5×106 nodes
 Artificial disturbances via
(2801x221x141)
suction-blowing actuator
• 120 lines in BL &
separation zone
symmetry
no-slip,
isothermal
M∞ = 5.373
Re∞1 = 14.3×106 m-1
L* = 0.316103 m
Re∞L = 5.667×106
T∞ = 74.194 K
Tw = 300.0 K = 4.043
γ = 1.4; Pr = 0.71
Freestream conditions from 2D calcs
suctionblowing
• P.Balakumar, H.Zhao, H.Atkins (2005). Stability of Hypersonic
Boundary Layers over a Compression Corner. AIAA J. 43(4)
• I.Egorov, A.Novikov, A.Fedorov (2006) Numerical Modelling of
the Disturbances of the Separated Flow in a Rounded
Compression Corner. Fluid Dynamics. 41(4)
Disturbances generator
 Periodic suction-blowing through 2 rectangular holes on the wall
Boundary condition on mass flow perturbation:
V
ρv
x1 < x < x2 ; z1 < z < z2 ; 0 < t < ∞
x1
x2
h = 0.004075 (h*=1.3 mm)
x1=0.0358 (x1*=11.3 mm); x2 = x1+2h; z1 = -h; z2 = h
Frequencies:
• ω = 450 (f* = 210.02 kHz) – typical for 2nd mode
• ω = 125 (f* = 58.37 kHz) – typical for 1st mode
Forcing amplitude:
ε = 0.001
(linear disturbances evolution)
Numerical method
 HSFlow (High-Speed Flow) in-house solver (с) TsAGI
 Navier-Stokes or Reynolds equations in dimensionless





conservative form in curvilinear coordinates
Fully implicit finite-volume shock-capturing method, 2ndorder approximation in space and time
Godunov-type scheme with Roe approximate Riemann
solver, WENO-3 reconstruction to cell edges
Newton method for system of discretized grid equations,
GMRes algorithm for linear system on each Newton step
Structured multi-block grids
Block-based parallelisation, MPI & PETSc library of linear
algebra subroutines – computations on HPC clusters
Numerical method validation
 Flat plate
 2nd-mode wave packet evolution generated by short impulse f*=313.48 kHz
 M∞ = 5.35; Re∞ = 14.3×106 m-1; T∞ = 64.32 K; Tw = 300.0 K; γ = 1.4; Pr = 0.71
 Sivasubramanian, J. & Fasel, H.F. (2011) Transition Initiated by a Localized Disturbance in a
Hypersonic Flat-Plate Boundary Layer. AIAA paper. 2011-374.
[AIAA 2011-374]
this work
Wall pressure disturbances
t = 0.017 ms
t = 0.041 ms
t = 0.291 ms
Steady laminar flow field
Computations on
HPC cluster
of Flowmodellium
Lab at MIPT using
768 CPU cores
shocklet from
reattachment region
shocklet from
separation region
bow shock
Separation &
reattachment
xsep = 0.857
xatt = 1.136
0.0010
skin friction coefficient
cf
0.0005
0.0000
x
0.2
0.4
0.6
0.8
1.0
1.2
1.4
(movie)
corner
flat plate
f*=210 kHz ,Wall pressure disturbances
 Leading wave-packet consists of 1st and 2nd unstable Mack’s mode
 Finally 2D harmonic disturbance sets in associated with 2nd mode
 Inside the separation bubble 2nd mode have lower amplitudes
as in 2D computations [P.Balakumar, H.Zhao, H.Atkins (2005) AIAA J. 43(4)], [I.Egorov, A.Novikov,
A.Fedorov (2006) Fluid Dynamics. 41(4)]
corner
t* = 0.051 ms
flat plate
f* = 210 kHz ,Wall pressure disturbances
 Leading wave-packet consists of 1st and 2nd unstable Mack’s mode
 Finally 2D harmonic disturbance sets in associated with 2nd mode
 Inside the separation bubble 2nd mode have lower amplitudes
as in 2D computations [P.Balakumar, H.Zhao, H.Atkins (2005) AIAA J. 43(4)], [I.Egorov, A.Novikov,
A.Fedorov (2006) Fluid Dynamics. 41(4)]
(movie)
corner
flat plate
f*=58.4 kHz ,Wall pressure disturbances
 Leading wave-packet and whole disturbance consists mainly of 1st unstable
Mack’s mode
 Disturbances grow rapidly inside the separation bubble and downstream the
reattachment line, so that laminar-turbulent transition begins.
corner
flat plate
f*=58.4 kHz ,Wall pressure disturbances
 Leading wave-packet and whole disturbance consists mainly of 1st unstable
Mack’s mode
 Disturbances grow rapidly inside the separation bubble and downstream the
reattachment line, so that laminar-turbulent transition begins.
f*=58.4 kHz, Skin friction distribution
cf
cf
flat plate
0.0030
0.0592 Rex-1/5
laminar
disturbed
turbulent (correlation)
0.0025
0.0020
laminar
disturbed
0.0030
0.0025
0.0020
0.0015
0.0015
transition
not finished
0.0010
0.0010
0.0005
0.0005
0.0000
0.0000
x
-0.0005
0.2
•
corner
0.0035
0.0035
0.4
0.6
0.8
1.0
1.2
cf for disturbed flow – average
through instantaneous flow fields
1.4
rapid growth
x
-0.0005
0.2
0.4
0.6
0.8
1.0
1.2
separation zone
length is reduced
f*=58.4 kHz, Spatial vorticity structures
Iso–surfaces of Q–criterion Q=100 colored with x-velocity magnitude
flat plate
spreading half-angle ≈3°
agrees with the experimental data [Fisher,
M.C. (1972). Spreading of a Turbulent
Disturbance. AIAA J. 10(7)]
corner
“young” turbulent
wedge
Conclusions
 Propagation of 3D disturbances through the 5.5° compression-corner flow and
flat plate boundary layer at M∞ = 5.373 is numerically simulated. The
disturbances are generated by periodic suction-blowing through the hole on
the wall.
 3D Navier–Stokes equations for viscous compressible perfect gas are solved
using the in-house parallel HSFlow solver on a fine grid (87.5×106 nodes).
 Unstable disturbances are excited relevant to the first and/or second mode of
instability. The instabilities evolving through the separation region exhibit
nontrivial behaviour, not captured by 2D simulations.
 “Young” turbulent wedge is observed.
 Our DNS method resolves fine structures of disturbances on the nonlinear
stage of transition. The detailed numerical solutions will be used in future for
analysis of space and time spectra as well as average characteristics of the
disturbance fields to clarify physical mechanisms of the transition process.
• This work was supported by Russian Scientific Foundation grant No.14-19-00821 in Moscow institute
of Physics and Technology (State University) (MIPT).
Ongoing activity
 DNS on longer computational domain, grid ~250 ×106 nodes
 Spectral analysis of numerical solutions
 Comparison with wind-tunnel data
flat plate
Iso–surfaces of Q–
criterion Q=100
colored with xvelocity magnitude

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