Novel Approach for Computational Modeling of a Non-Premixed Rotating Detonation Engine

TLDR: In this paper, pressure gain combustion (PGC) has gained significant attention in airbreathing gas turbine applications due to its increased thermodynamic efficiency over a constant-pressure Brayton cycle.

Abstract: Pressure gain combustion (PGC) has gained significant attention in airbreathing gas turbine applications due to its increased thermodynamic efficiency over a constant-pressure Brayton cycle. Rotati...

Figures

Fig. 16 Distribution of detonation cell sizes in premixed (left) and non-premixed (right) cases

Fig. 12 Left - Streamlines drawn to extract pressure and specific volume to calculate the work done. Right - Comparison of the work done between the premixed and nonpremixed case

Fig. 21 Comparison of temperature and heat release rate as a function of local equivalence ratio between the premixed (left) and non-premixed (right) cases

Table 1 Parameters and calculations for grid independence analysis

Fig. 8 Comparison of time-averaged pressure for different grid sizes with experiment

Fig. 15 Contours of detonation cell sizes in the premixed (left) and non-premixed (right) cases

Full text

Novel Approach for Computational Modeling of a Non-
Premixed Rotating Detonation Engine
Sathyanarayanan Subramanian
Thesis submitted to the faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Science
in
Mechanical Engineering
Joseph W. Meadows - Chair
Diana N. Biaraktrova
Danesh K. Tafti
Luca Massa
28
th
of June - 2019
Blacksburg, Virginia
Keywords: Rotating Detonation Engine (RDE), Non-Premixed Combustion,
Computational Fluid Dynamics (CFD)

Novel Approach for Computational Modeling of a Non-Premixed
Rotating Detonation Engine
Sathyanarayanan Subramanian
ABSTRACT
Detonation cycles are identified as an efficient alternative to the Brayton cycles used in
power and propulsion applications. Rotating Detonation Engine (RDE) operating on a
detonation cycle works by compressing the working fluid across a detonation wave,
thereby reducing the number of compressor stages required in the thermodynamic cycle.
Numerical analyses of RDEs are flexible in understanding the flow field within the RDE,
however, three-dimensional analyses are expensive due to the differences in time-scale
required to resolve the combustion process and flow-field. The alternate two-dimensional
analyses are generally modeled with perfectly premixed fuel injection and do not capture
the effects of improper mixing arising due to discrete injection of fuel and oxidizer into the
chamber. To model realistic injection in a 2-D analysis, the current work uses an approach
in which, a Probability Density Function (PDF) of the fuel mass fraction at the chamber
inlet is extracted from a 3-D, cold-flow simulation and is used as an inlet boundary
condition for fuel mass fraction in the 2-D analysis. The 2-D simulation requires only 0.4%
of the CPU hours for one revolution of the detonation compared to an equivalent 3-D
simulation. Using this method, a perfectly premixed RDE is comparing with a non-
premixed case. The performance is found to vary between the two cases. The mean
detonation velocities, time-averaged static pressure profiles are found to be similar between
the two cases, while the local detonation velocities and peak pressure values vary in the
non-premixed case due to local pockets fuel rich/lean mixtures. The mean detonation cell

sizes are similar, but the distribution in the non-premixed case is closer due to stronger
shock structures. An analytical method is used to check the effects of fuel-product
stratification and heat loss from the RDE and these effects adversely affect the local
detonation velocity. Overall, this method of modeling captures the complex physics in an
RDE with the advantage of reduced computational cost and therefore can be used for
design and diagnostic purposes.

Novel Approach for Computational Modeling of a Non-Premixed
Rotating Detonation Engine
Sathyanarayanan Subramanian
GENERAL ABSTRACT
The conventional Brayton cycle used in power and propulsion applications is highly
optimized, at cycle and component levels. In pursuit of higher thermodynamic efficiency,
detonation cycles are identified as an efficient alternative and gained increased attention in
the scientific community. In a Rotating Detonation Engine (RDE), which is based on the
detonation cycle, the compression of gases occurs across a shock wave. This method of
achieving high compression ratios reduces the number of compressor stages required for
operation. In an RDE (where combustion occurs between two coaxial cylinders), the fuel
and oxidizer are injected axially into the combustion chamber where the detonation is
initiated. The resultant detonation wave spins continuously in the azimuthal direction,
consuming fresh fuel mixture. The combustion products expand and exhaust axially
providing thrust/mechanical energy when coupled with a turbine.
Numerical analyses of RDEs are flexible over experimental analysis, in terms of
understanding the flow physics and the physical/chemical processes occurring within the
engine. However, three-dimensional numerical analyses are computationally expansive,
and therefore demanding an equivalent, efficient two-dimensional analysis. In most RDEs,
fuel and oxidizer are injected from separate plenums into the chamber. This type of
injection leads to inhomogeneity of the fuel-air mixture within the RDE which adversely
affects the performance of the engine. The current study uses a novel method to effectively
capture these physics in a 2-D numerical analysis. Furthermore, the performance of the
combustor is compared between perfectly premixed injection and discrete, non-premixed
injection. The method used in this work can be used for any injector design and is a
powerful/efficient way to numerically analyze a Rotating Detonation Engine.

v
ACKNOWLEDGMENTS
I extend my gratitude to my research advisor, Dr. Joseph Meadows for his guidance
and support through my research project. Dr. Meadows helped me improve my problem-
solving skills and he is a source of inspiration in my professional life. I thank Dr. Danesh
Tafti, and Dr. Luca Massa for serving in my committee.
I am highly grateful to Dr. Diana Biaraktrova for providing me an opportunity to work as
a Graduate Research Assistant in her research group, ACE(D) and for serving in my
committee. Completion of my Master’s degree might not have been successful without the
support of Dr. Biaraktrova. I would also like to thank Dr. Scott Huxtable for his support in
the vObjects project. I am grateful to Dr. Srinath Ekkad who had given me the opportunity
to pursue my Master’s degree at Virginia Tech.
I thank the Advanced Research Computing (ARC) department of Virginia Tech for
providing computational resources in their cluster to run the CFD simulations. I am grateful
to Dr. Brent Rankin of the Air Force Research Laboratory (AFRL), for providing the
geometric model (CAD) used in their experiments for the current research. Special thanks
to Piyush Raj for his inputs in post-processing and to Yamini Gaur for helping me
troubleshoot my Java codes. I want to thank my lab colleagues Cody Dowd, Steven Wong,
Ashwin Kumar, and Joseph Giroux for providing me technical suggestions, and for making
our lab a conducive place to learn and fun to work.
My Master’s program wouldn’t have been a smooth sail without my friends here at VT,
Shri Hari (primarily), Sachin, RK, and Chidambaram; and friends back home: Ganesh,
Abhishek, Namitha, Pranav, Joby, Vigney, Aravind, VK, Yaseen, Ebin, Ravi, and the
entire group. I am grateful to Mr. Mahil Yadin, Mr. De’ Silva, Mr. Christopher, Dr.
Chandramouli, Dr. Pugazenthi, Dr. Rafael Ruiz, Dr. Ricard Consel, Dr. Jordi Cadafalch,
Dr. Prasad, Ms. Devi Kompella, and Mr. Les Baert for providing guidance/inspiration
through my academic and professional career, helping me to be where I am now.
I wouldn’t have come this far in my life without the love and support of my family. Thank
you, Appa, Amma, Shuba, Pranesh, and Samara. Ultimately, I bow to the creator.

Frequently asked questions

Q1. What have the authors contributed in "Novel approach for computational modeling of a non- premixed rotating detonation engine" ?

Subramanian et al. this paper used a 2D simulation of a Rotating Detonation Engine ( RDE ) to model the inhomogeneity arising from discrete fuel-air injection in 3D injection design. 

Q2. What are the future works in "Novel approach for computational modeling of a non- premixed rotating detonation engine" ?

The effect of product diluents on the wave structure, detonation cell size, and heat release using high-fidelity simulations is a part of the future work of the research group. 

Q3. What is the simplest method for calculating the energy of the fluxes?

A coupled flow, coupled energy solver with a third-order implicit, Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) [38] is used for spatial discretization of the fluxes. 

Q4. How can The authorsolve the kinetics and viscous effects at these length scales?

Resolving the kinetics and viscous effects at these length scales are computationally expensive and require high-fidelity simulation methods such as Direct Numerical Simulation with AMR, which are currently beyond the scope of this work; however, the method presented in the present study can be applied to various levels of modeling inhomogeneous fuel-oxidizer injection. 

Q5. What is the effect of the inhomogeneity of the reactant mixture?

The peak detonation pressure and detonability of the mixture are also affected by the inhomogeneity of the reactant mixture [13]. 

Q6. What is the effect of the fuel-product stratification on the detonation velocity?

The fuel-product stratification has a significant impact on the detonation velocity compared to heat loss from the RDE, as the detonation velocity drops in both these cases. 

Q7. What is the reason for the interest in using hydrogen as fuel in RDEs?

The detonation cell size of hydrogen is small compared to most hydrocarbon fuels [56], which is the primary reason for the interest in using H2 as fuel in most RDEs [57]. 

Q8. How many microns are required to resolve the chemical kinetics and viscous effects?

Powers et al [51] state that the finest length scale required to fully resolve the chemical kinetics and viscous effects is 0.1 microns. 

Q9. Who provided the computational resources to run the CFD simulations?

I thank the Advanced Research Computing (ARC) department of Virginia Tech for providing computational resources in their cluster to run the CFD simulations. 

Q10. What is the probability density function of the fuel mass fraction from a converged 3-D?

A Probability Density Function (PDF) of the fuel mass fraction from a converged 3-D, non-reacting simulation is extracted and is used as a spatially and temporally varying inlet boundary condition in the 2-D simulation. 

Q11. What is the method used in this work?

The method used in this work can be used for any injector design and is a powerful/efficient way to numerically analyze a Rotating Detonation Engine. 

Q12. What are the advantages of numerical simulations of RDE?

Numerical simulations of RDE provide additional flexibility over experiments in understanding the flow field, analyzing physical/chemical processes, and detonation wave structures which propagate at or near sonic speeds. 

Q13. How do the OH and H2O mass fractions differ with the ZND profile?

The OH and H2O mass fractions resemble the ZND profile, such that they vary linearly with local equivalence ratio up to the value of 1, beyond which the variation is gradual. 

Q14. How large is the mesh size used for further analysis?

As the simulation results obtained using a grid size of 100 microns reasonably predicts the physics such as wave structures, with values of peak pressures, and detonation wave speeds close to the theoretical conditions and satisfies the global mass balance in the domain, in addition to having a low discretization error value (Table 1), this mesh size (100 microns) is used for further analysis in this study. 

Q15. What is the effect of heat loss on the detonation velocity?

Tomeasure the effect of heat loss on the detonation velocity, a modified version of the system of equations Eqs. (14-16) is solved in which a heat loss term (Qloss) is added to Eq. (15) which then becomes Eq. (20)𝑒2 − 𝑒1 = 0.5 (𝑝22 − 𝑝1 2)𝛾2𝑝2𝜌2 − 𝑄𝑙𝑜𝑠𝑠 (20)Heat loss from the RDE also deters the detonation velocity (Fig. 23), although not as significant as fuel-product stratification. 

Q16. What was the method used to account for the mixing length?

Paxson et al [33] utilized a method in which the first few grid cells of the computational domain were made non-reacting to account for the mixing length, although the inlet mixture was perfectly premixed. 

Q17. What is the mean cell size for the non-premixed case?

The mean values measured using Shepherd’s code [58] are 3.895 mm and 3.825 mm respectively for the non-premixed and premixed cases.