Modeling & Simulation

Combustion Stability

The emergence of resonant acoustic waves in large combustors stands as arguably the single most debilitating obstacle reported in the developmental stages of new propulsive systems.  Their appearance signals the presence of combustion instabilities, which commonly manifest as high-amplitude pressure oscillations.  In some cases, acoustic pressure amplitudes exceeding 100% of the mean chamber pressure are measured.  These may lead to severe structural vibrations, increased heat transfer, or outright catastrophic failure.

GTL is a recognized leader in modeling and analysis of combustion instabilities.  Their Universal Combustion Device Stability (UCDSTM) framework is an energy-based approach developed to quantify the physical processes leading to the emergence of combustion instabilities.  This multi-faceted framework can be applied to provide rapid predictions of combustion systems instabilities, maximum insight from computational and experimental data, and directly motivate engineering design.

Tangential and Longitudinal Acoustic Modes in the RD-170

Multiphysics Modeling

GTL offers a range of modeling tools to address real engineering problems.  These include acoustics simulation and analysis tools, heat transfer, structural vibrations, reacting flow CFD, and customizable multi-physics modeling packages.  These packages are all built on the same unstructured, finite volume, computational framework so that new capabilities can be quickly deployed.


GTL’s RESONANCETM software quickly identifies the natural acoustic frequencies and mode shapes experienced in complex fluid dynamical systems.  RESONANCETM integrates with structured Plot3D or TecPlot formatted grid and CFD solution data to address complex geometries and sophisticated flow conditions.  It has been validated against a variety of benchmark experiments to ensure accuracy and reliability.  Moreover, it fully supports distributed, high-performance computing architectures to provide the scalability needed to address sophisticated engineering challenges.

Figure 1 RESONANCETM Solution Modeling a Tangential Acoustic Mode in a Liquid Rocket Engine with Resonators

Figure 2 RESONANCETM Solution Modeling a Longitudinal Acoustic Mode in a 5-Segment Solid Rocket Booster

Time-Dependent Acoustic Wave Modeling

Beyond RESONANCETM, GTL offers alternative acoustic modeling and simulation tools.  In fact, the formation and transmission of sound waves are valuable to a wide market.  Both GTL’s time-dependent Convected-Wave, and Linearized Navier-Stokes solvers offer insight into the formation and propagation of sound waves.  Solving acoustics problems in the time domain easily allows for a variety of acoustic sources to be included.  This flexibility lets the user define sound sources ranging from simple pulses and sirens, to more sophisticated models involving moving boundaries, aeroacoustic, or thermal-acoustic sound models.

Convected-Wave Solutions

For fast solutions that quickly show wave propagation and reflection, GTL’s convected wave solver is the answer.  This approach is applicable to systems with complex geometries with subsonic flow and well-defined thermodynamic profiles.  This solver is perfectly suited for acoustics engineering, noise pollution modeling, sound suppression engineering, forensic acoustics, and other similar endeavors.

Figure 3 GTL’s Convected Wave Solver applied to a Baffled Sound-Suppression System

Figure 4 Sound Waves Reflecting in an Urban Landscape

Linearized Navier-Stokes

When an acoustics model needs a bit more sophistication, GTL’s Linearized Navier-Stokes Solver is the right choice.  This approach makes no assumptions.  Rather, it directly solves the entire acoustic field – including pressure, velocity, density, and temperature – directly.  Therefore, this can be applied to both subsonic flows, supersonic flows, and reacting flows with strong thermodynamic variations.  Moreover, this approach allows greater flexibility when incorporating sound source models.  Just like the convected wave solver, sources can include pulses and sirens.  However, it also can include thermal sources and moving walls.  It couples with GTL’s aeroacoustics module to provide simulation capabilities for turbulent noise sources.  Lastly, nonlinear effects can be included when acoustic harmonics are important.

Figure 5 Comparison of the Sound Generated by Mach 0.695 Flow over a 0.1×0.2-inch Cavity

Figure 6 Snapshot of First Tangential Acoustic Mode Emerging from Broadband Noise in a Liquid Rocket Engine

Elastic Solids

GTL addresses the problem of elastic waves by employing a custom-built solid mechanics solver that can calculate the propagation of displacements in solids.  The solver uses a time-dependent finite volume scheme to solve the Navier-Cauchy equation of motion.  Since this is a single linear vector equation, it is computationally efficient and can be solved very quickly.  This solver captures both compressive and shear waves over homogeneous or non-homogeneous materials.  Both wave types can be important when assessing impact damage, fatigue, structural vibrations, and seismic activity.  This type of model has wide applicability in structural engineering analysis and can be coupled with time-dependent acoustic models to model structural vibrations stemming from fluid/structure interactions.

Figure 7 Comparison of GTL’s Elastic Wave Solver and Experimental Displacement

Computational Fluid Dynamics

Modern computational fluid dynamics packages provide a powerful framework for addressing a range of engineering-based fluid dynamics problems.  However, a need arises for custom computational algorithms with additional flexibility and customization.  Built on a consistent, unstructured, finite-volume framework, GTL offers an in-house computational fluid dynamics software.  This package allows great flexibility with custom physics modules or boundary conditions are easily added and ubiquitous across GTL’s other computational software.  It allows for tightly controlled methods and approaches that would be difficult to implement within other commercial or externally developed algorithms.

Figure 8 Demonstrations of GTL’s In-House CFD Framework. a) Bow Shock Pressure b) Subsonic Thermal Air Jet, c) Acoustic Waves in a Transonic Cavity

Incorporation of a reacting flow module expands the power of this algorithm greatly.  Chemical reaction modeling is a challenging for several reasons.  Firstly, the reaction mechanism must be sophisticated enough to handle detonations.  This is very important when modeling any transitions from high-amplitude waves in deflagration combustion to fully detonation waves.  Computationally, though, sophisticated reaction models can introduce hundreds or even thousands of equations that must be solved simultaneously.  Moreover, the computational requirements must be managed since the time-scales related to detonation reactions are small.  This requires careful considerations with respect to grid quality, cell type, and density pared with effective time integration schemes.  GTL has developed a custom suite of chemical reaction modeling tools to address this problem directly.  Figure 9 shows the GTL’s solution for the heat release and pressure profiles at an instance in time for a detonation wave forming in a narrow tube.

Figure 9 Two-Dimensional Detonation Wave for a Propane/Oxygen Reaction in Narrow Tube


Since each physics model is built upon a consistent computational framework, coupling fluid dynamics to thermal or structural models is relatively straightforward.  First GTL identified a need to couple acoustic oscillations to structural vibrations.  This was expanded upon to define an extensible, two-way coupled, approach to interface any existing GTL physics models.  This latest offering from GTL has demonstrated coupling of conduction heat transfer into solid structures, computational fluid dynamics, and chemical combustion in real aerospace applications.  The figure shows GTL’s multi-physics model simulating a propane heater.  The simulation is modeling a fully reacting flow with conjugate heat transfer to couple the solid and gas domains.  The two-dimensional slice shows nine propane jets along the steel tube.  The flame heats a copper plate.  The plate heats air flowing from left to right in the upper domain.

Figure 10 A Demonstration Model of GTL’s Reacting Flow/Conjugate Heat Transfer Module Simulating a Propane Heater