| dc.description.abstract | During lift-off of launch vehicles jets from nozzles impinge on a wedge deflector which
directs the jet away from the rocket along passages. As a high Reynolds number turbulent
flow the whole region has a broad spectrum of intense pressure
fluctuations which can
damage the launch vehicle. The deflected jet emerges from the passages and can emit
acoustic radiation that can damage the payload. The low frequency unsteadiness requires
a suitable method such as large eddy simulation (LES) for its prediction.
LES is a viable method for the study of this
flow due to its capacity to accurately
compute the large scale unsteadiness at much lower computational expense than direct
numerical simulation (DNS). Though DNS can provide accurate solutions, it becomes
computationally prohibitive for problems of practical interest. RANS (Reynolds-averaged
Navier-Stokes) methods are computationally less intensive but can sometimes yield qual-
itatively incorrect solutions, especially when there is separation and/or large scale, low
frequency unsteadiness. Since the jets are supersonic, LES of such
flows require a method
that can handle shocks. In the presence of shocks typical computations can acquire oscil-
lations in the solution leading to blow-up especially when higher order methods are used,
unless suitable methods are employed to mitigate this problem.
The first contribution of this thesis is the development of filter order adaptation in
the vicinity of shocks as a method for handling shocks. Although there have been many
proposals for shock capturing for inviscid
flows which have also been applied to RANS,
since these are low-order methods, typically 2nd or 3rd order in general, falling to 1st-
order at the shock, there is a need to design methods that complement the higher-order
(4th to 8th order), high-resolution scheme used for DNS/LES. Filter-order adaptation
allows the underlying numerical scheme for integrating the Navier-Stokes equations to
remain the same spatial high-order everywhere. It is also a minor modifi cation of the
explicit fi ltering approach to LES which requires a high resolution fi lter to be applied after
every time step. In this adaptive fi ltering approach the spatial discretization remained the
same everywhere and was 6th-order. The order of the spatial fi lter was reduced from 10 in
smooth regions to 2 at gridpoints where a shock was detected. Filter order was increased
in steps at neighboring gridpoints. To minimise dissipation due to fi lter adaptation, fi lter
was adapted in coordinate directions which were almost normal to shock surface. This
was achieved by adapting the lter along a coordinate direction i if ^xi rM=jrMj or
^xi r =jr j > 1=
p
3 at that point, where ^xi is the unit vector along the ith coordinate
direction.
A requirement of the explicit filtering LES is to compute spatial derivative using
high resolution schemes. A bi-diagonal split system for a 6th-order compact scheme was
derived and its characteristics were con firmed by showing the error fall rate with grid
re finement. The anisotropy of error of the numerical scheme was investigated in terms
of numerical phase and group speeds and was observed that the anisotropy error was
negligibly small for the resolved scales of the LES.
The solver was made parallel for distributed memory platform using message passing
interface (MPI) with the help of 2DECOMP&FFT library. The scalability of the solver
was performed using the supercomputer Cray-XC40 which showed good results.
The present approach for LES was validated extensively on several
flows with and
without shocks. The problems taken for
flows without shock are 1-d linear wave prop-
agation, 2-d acoustic scattering, vortex advection in curvilinear grid, viscous/inviscid
Taylor-Green vortex, and turbulent subsonic jets. These test cases were chosen to demon-
strate the effectiveness of the LES method for smooth
flows where the shock sensor did
not activate fi lter adaptation at any time unintentionally. Test cases of
flows with shock
include Riemann problems, interaction of 1-d and 2-d plane waves with shocks, underex-
panded, overexpanded, and impinging round jets. These cases demonstrate the efficacy
of the present method to capture shock at right location and strength without adding
extra dissipation in the smooth regions.
When turbulent
fluctuations traverse a shock, they undergo changes in structure,
intensity and length scales. At the same time the shock also becomes undulated due
to the incoming turbulence. Before using the adaptive filtering method for LES it is
necessary to understand how it performs for
flows with shocks. A canonical problem
is the interaction of homogeneous isotropic turbulence (HIT) with a normal shock. The
second contribution of this thesis is the study of explicit filtering LES of shock turbulence
interaction with the adaptive fi ltering. Homogeneous isotropic turbulence was computed
in a precursor simulation for the study of the interaction. Interaction of this turbulence
with a normal shock of M=1.5 was studied in another domain where one realization of
the turbulence
fluctuations was injected at the in
flow. Two LES with different transverse
grid resolutions and a DNS were performed keeping same axial resolution of the grid for
all the cases. The shock drifted slightly faster in LES grids. The jump in pressure across
the shock was lower than the corresponding Rankine-Hugoniot jump, similar to findings
by other researchers. The pressure jump across the shock in LES and DNS agreed closely.
Though there were some differences in the axial Reynolds stresses and vorticity variance,
the SPL of pressure
fluctuations was same for all the LES and DNS solutions. The
pressure spectrum downstream of a shock for LES was in good agreement with the DNS
for a large range of large scales which implies LES should be adequate for predicting low
frequency content.
The third contribution of this thesis is the application of the method developed to
study an ideally expanded supersonic jet at M=1.5 and Re=105 impinging on a wedge
mounted on a
at plate. Two impingement distances Hj=W(1 and 4) where Hj and
W represent the distance between nozzle exit to wedge tip and width of the nozzle,
respectively, and two wedge angles (90 and 20 ) were considered. Attached and de-
tached shock waves were seen for the large and small angle wedges, respectively, near the
wedge tip. A turbulent boundary layer developed on the wedge with the larger vertex
angle whereas
flow separated quickly with the small angle wedge. The interaction of the
shock/expansion fan with the boundary layer was evident. The maximum pressure
fluctuations were higher for the wedge with small angle. Lighthill sources were dominant in
the jet and wall jet regions. Acoustic waves generated at the wedge tip for the large angle
wedge with large impingement distance propagated and steepened to form a train of weak
shock waves which were propagating sources. The time series of pressure at a location,
where these waves pass by, shows the N-shaped variations which is a signature of crackle.
As the wave steepened the contribution from the viscous sources became dominant. Low
frequency high amplitude peaks were observed for larger separation jets.
In summary a new method for LES of
flows with shocks was proposed, and tested
systematically on a variety of problems. Its suitability was examined by simulating a
turbulent
flow passing through a nominally normal shock. Next, it was applied to a new
type of
flow at high Reynolds number, typical of applications where shocks interacting
with structures give rise to potentially damaging low frequency unsteadiness. The method
shows excellent promise for predictions needed in high speed
flow applications. | en_US |
