<p>Combustion instability,
a complex phenomenon observed in combustion chambers is due to the coupling
between heat release and other unsteady flow processes. Combustion instability
has long been a topic of interest to rocket scientists and has been extensively
investigated experimentally and computationally. However, to date, there is no
computational tool that can accurately predict the combustion instabilities in
full-size combustors because of the amount of computational power required to
perform a high-fidelity simulation of a multi-element chamber. Hence, the focus
is shifted to reduced fidelity computational tools which may accurately predict
the instability by using the information available from the high-fidelity
simulations or experiments of single or few-element combustors. One way of
developing reduced fidelity computational tools involves using a reduced
fidelity solver together with the flame transfer functions that carry important
information about the flame behavior from a high-fidelity simulation or
experiment to a reduced fidelity simulation.</p>
<p> </p>
<p>To date, research has
been focused mainly on premixed flames and using acoustic solvers together with
the global flame transfer functions that were obtained by integrating over a
region. However, in the case of rockets, the flame is non-premixed and
distributed in space and time. Further, the mixing of propellants is impacted
by the level of flow fluctuations and can lead to non-uniform mean properties
and hence, there is a need for reduced fidelity solver that can capture the gas
dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler
equations have all the required capabilities and are at the bottom of the list
in terms of the computational cost among the solvers that can solve for mean
flow and allow multi-dimensional modeling of combustion instabilities. Hence,
in the current work, nonlinear Euler solver together with the spatially
distributed local flame transfer functions that capture the coupling between
flame, acoustics, and hydrodynamics is explored.</p>
<p> </p>
<p>In this thesis, the
approach to extract flame transfer functions from high-fidelity simulations and
their integration with nonlinear Euler solver is presented. The dynamic mode
decomposition (DMD) was used to extract spatially distributed flame transfer
function (FTF) from high fidelity simulation of a single element non-premixed
flame. Once extracted, the FTF was integrated with nonlinear Euler equations as
a fluctuating source term of the energy equation. The time-averaged species destruction
rates from the high-fidelity simulation were used as the mean source terms of
the species equations. Following a variable gain approach, the local species
destruction rates were modified to account for local cell constituents and
maintain correct mean conditions at every time step of the nonlinear Euler
simulation. The proposed reduced fidelity model was verified using a Rijke tube
test case and to further assess the capabilities of the proposed model it was
applied to a single element model rocket combustor, the Continuously Variable
Resonance Combustor (CVRC), that exhibited self-excited combustion
instabilities that are on the order of 10% of the mean pressure. The results
showed that the proposed model could reproduce the unsteady behavior of the
CVRC predicted by the high-fidelity simulation reasonably well. The effects of
control parameters such as the number of modes included in the FTF, the number
of sampling points used in the Fourier transform of the unsteady heat release,
and mesh size are also studied. The reduced fidelity model could reproduce the
limit cycle amplitude within a few percent of the mean pressure. The successful
constraints on the model include good spatial resolution and FTF with all modes
up to at least one dominant frequency higher than the frequencies of interest.
Furthermore, the reduced fidelity model reproduced consistent mode shapes and
linear growth rates that reasonably matched the experimental observations,
although the apparent ability to match growth rates needs to be better
understood. However, the presence of significant heat release near a pressure
node of a higher harmonic mode was found to be an issue. This issue was
rectified by expanding the pressure node of the higher frequency mode. Analysis
of two-dimensional effects and coupling between the local pressure and heat
release fluctuations showed that it may be necessary to use two dimensional
spatially distributed local FTFs for accurate prediction of combustion
instabilities in high energy devices such as rocket combustors. Hybrid
RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use
Flame Describing Function (FDF) to capture the growth of pressure fluctuations
to limit cycle when Navier-Stokes solver is used.</p>
<p> </p>
<p>The main objectives of
this thesis are:</p>
<p>1. Extraction of
spatially distributed local flame transfer function from the high fidelity
simulation using dynamic mode decomposition and its integration with nonlinear
Euler solver</p>
<p>2. Verification of the
proposed approach and its application to the Continuously Variable Resonance
Combustor (CVRC).</p>
<p>3. Sensitivity analysis
of the reduced fidelity model to control parameters such as the number of modes
included in the FTF, the number of sampling points used in the Fourier
transform of the unsteady heat release, and mesh size.</p>
<p> </p>
<p>The goal of this thesis
is to contribute towards a reduced fidelity computational tool which can
accurately predict the combustion instabilities in practical systems using
flame transfer functions, by providing a path way for reduced fidelity
multi-element simulation, and by defining the limitations associated with using
flame transfer functions and nonlinear Euler equations for non-premixed flames.</p>
<p> </p><br>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/8290184 |
| Date | 02 August 2019 |
| Creators | Gowtham Manikanta Reddy Tamanampudi (6852506) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/REDUCED_FIDELITY_ANALYSIS_OF_COMBUSTION_INSTABILITIES_USING_FLAME_TRANSFER_FUNCTIONS_IN_A_NONLINEAR_EULER_SOLVER/8290184 |
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