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In order to perform simulations,
we use our existing high fidelity computational aeroacoustics (CAA) code
that solves the fully two- and three-dimensional Navier-Stokes equations
in Cartesian block-structured geometries. The method utilizes 6th-order-accurate
compact finite difference schemes and explicitly 4th-order Runge-Kutta
time advancement. Optional boundary conditions include accurate inflow/outflow,
nonreflecting, symmetric, isothermal and adiabatic walls, as well as periodic
conditions. The code is fully parallelized using MPI. The algorithm introduces
very little numerical dissipation and is able to efficiently resolve complex,
unsteady flow physics, including acoustic wave generation and propagation.
The algorithm and code has been developed, validated, and successfully
implemented in studies of sound radiation from mixing layers, jets, vortex
rings, and flow/acoustic instabilities in flows over open cavities. (see
Ref. 4. For more details, please visit our Cavity
flows webpage.)
It is known that the most unstable
waves at hypersonic flow conditions are two-dimensional [2], but typical
UAC coatings consist of regular or random patterns of cylindrical/rectangular
pores (see figure 4). It is not expected that the flow physics associated
with three-dimensional (circular) pores are dramatically different than
those that would exist in two-dimensional slots. Thus we consider strictly
2D (slot) porosity.
Figure 4: Ceramic UAC
samples from the material group of Teledyne (former Rockwell Scientific
Company).
Left: Ceramic composites
bonded to tile insulation. Right: Details of the porous coating.
We develop simulations following
a building block approach wherein simpler configurations are used to bracket
the types of flow phenomena that exist in the more complex geometries,
and to gain confidence in the numerical method and modeling approach:
1. In a first phase, we perform
DNS with a standard no-slip wall in order to validate the use of the temporally-evolving
assumption on both the mean hypersonic boundary layer and instability
wave development. The existing spatially-evolving linear instability theory
[2] is also reformulated as a temporally-evolving instability in order
to assess possible discrepancies in wave phase-speeds and growth rates.
We first considered a calorically perfect gas with temperature independent
properties, and obtain results in good agreement with the linear theory.
The existing DNS code is currently being modified to include temperature-dependent
properties suitable for (shock-free) hypersonic flow (AIAA paper 2008-4337).
2. In a second phase, we consider
the acoustic scattering problem (no boundary-layer flow) from single slot
and arrays of slots (2D). For typical UAC parameters, we investigate the
range of frequencies corresponding to the ultrasonic frequency band, which
is sufficient to capture the frequency of the most amplified second-mode
instability waves observed in experiments and numerical simulations, including
those in our first phase. Comparisons with theoretical predictions show
excellent agreement with the DNS results, and a complete parametric study
of the geometrical factors (cavity aspect ratio, porosity) and flow conditions
effects (Reynolds number, angle of incidence of acoustic waves) is performed.
Guidelines for the choice of these parameters are also suggested (AIAA
paper 2008-3903).
3. Finally, we will add flow
in the slot configuration and investigate UAC performance under both linear
and transitional (nonlinear) conditions. Under 2D conditions, run times
are expected to be short enough to allow extensive parametric investigations
of geometrical factors (pore size, aspect ratio, spacing, and number of
pores per wavelength) and flow parameters (free-stream velocity and temperatures,
boundary layer thickness, Reynolds number).
With this approach, our numerical
results will be used to propose improvements to existing models to extend their range
of validity and generalize their use as a tool for robust design and implementation
of UAC in applications.
[1] Rasheed, A.,
Hornung, H.G., Fedorov, A.V., and Malmuth, N.D., “Experiments on
Passive Hypervelocity Boundary Layer Control Using a Ultrasonically Absorptive
Surface,” AIAA Journal, Vol. 40, No. 3, pp. 481-489.
[2] Fedorov, A.V.,
Shiplyuk, A., Maslov, A., Burov, E., and Malmuth, N.D., “Stabilization
of a Hypersonic Boundary Layer Using an Ultrasonically Absorptive Coating,”
J. Fluid Mech., Vol. 479, 2003, pp. 99-124.
[3] Fedorov, A.V.,
Malmuth, N.D., Rasheed, A., and Hornung, H.G., “Stabilization of
Hypersonic Boundary Layers by Porous Coatings,” AIAA Journal,
39, No. 4, April 2001, pp. 605-610.
[4] Brès, G.A. and Colonius T.,
“ Three-Dimensional
Instabilities in Compressible Flow over Open Cavities,”J. Fluid Mech., vol. 599,
2008, pp. 309-339.
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