First-principles Modeling of Modern Jet-Engine Combustors with Petascale Computations: Real Jet Fuels, Real Jet-Engine Conditions
This post was adapted from an article, which appeared in the Fall 2016 issue of the HPC Insights Magazine.
Few physical processes are as fundamental to the functioning of modern society as combustion – energy extraction from a fuel through rapid, highly exothermic chemical reactions. Indeed, virtually all of us rely daily on turbulent flames inside the automotive and aircraft engines for transportation, in gas-turbine power plants for energy production, or in countless industrial settings for chemical processing, manufacturing, etc.
In recent years, the growing awareness of the environmental effects associated with fossil fuels has created a powerful momentum to replace them with alternative energy sources in the automotive and power-generation industries. At the same time, presently there is virtually no alternative to hydrocarbon (and hydrogen) combustion for aircraft and rocket propulsion – two areas of critical importance for the mission of the Department of Defense.
This does not mean that alternative energy sources are not being explored. At the time of the writing of this article, we have been witnessing a remarkable aviation milestone as the aircraft Solar Impulse 2 is preparing for the last leg of the bid to circumnavigate the Earth for the first time by a fixed-wing solar-powered aircraft. Despite this achievement, major scientific and engineering breakthroughs will be required in the future before alternative energy sources become capable of providing performance comparable to modern jet and rocket engines in terms of thrust, specific impulse, etc. This aspect is particularly crucial for defense applications, in which gains in environmental impact cannot come at the expense of combat characteristics.
Historically, development of combustion systems proceeded through an empirical “trial-and-error” approach, without necessarily an in-depth understanding of all aspects of the highly complex reacting flow inside a combustor. Such an “agnostic” approach, while costly, still allowed conventional aircraft and rocket engines to reach a remarkable level of perfection. In recent years, however, both the advances in traditional combustion systems, e.g., turbine jet engines, as well as the emergence of more novel designs, e.g., scramjet engines for hypersonic flight, have been pushing reacting flows into ever more extreme conditions characterized by higher pressures, faster flow speeds, and leaner, more premixed mixtures. Such novel combustion regimes are far less understood, they are more difficult to diagnose experimentally, and it is far more costly to design engines for them through simple trial-and-error. The “agnostic” approach of the past is no longer sufficient to enable the revolutionary advances in propulsion, which require an in-depth understanding of the combustion dynamics for real fuels and realistic engine conditions.
This has led to the emergence of computational modeling as one of the key tools both for the fundamental combustion research and for the design of practical systems. Numerical models can be used to probe the flame dynamics and understand the behavior of a reacting flow both during stable operation and, more importantly, in off-design regimes. Such insights often cannot be obtained through modern experimental techniques, and they are invaluable for guiding the development of stable, reliable systems providing major savings both in time and cost.
Virtually all existing computational approaches face one major hurdle, which is often referred to as the “tyranny of scales”. This is illustrated in Fig. 1. A typical modern high-bypass turbofan jet engine has a fan diameter of under 3 m and an overall length of around 5 m (upper left panel), while typical combustors have sizes on the order of 10 cm (upper right and middle panels). On the other hand, characteristic scales of physical processes inside a combustor can be vastly smaller. For instance, the typical width of a flame which is folded inside a complex turbulent-flame structure (lower panel) varies with pressure, and can range from hundreds of microns under atmospheric conditions to just a few tens of microns at high pressures present in modern turbine engines.
Such vast dynamical range of spatial (and, consequently, temporal) scales is further complicated by the rich, multi-physics nature of the reacting flow, which can involve complex chemical reactions, molecular transport processes, radiation, multiple phase states, etc., all evolving in a highly dynamic, turbulent flow field. All computational approaches face the challenge of capturing that complexity. In general, this cannot be done entirely from first principles without a multitude of simplifying assumptions, which ultimately leads to an obvious question: How accurate are modern computational models, and how robust is their predictive capability?
The main compromise that must typically be made is the decision to focus on either large or small scales of the flow. In particular, when the temporal dynamics of the flow cannot be ignored, this gives rise to the two major classes of approaches known as Large-Eddy (LES) and Direct Numerical (DNS) simulations. LES are intended to model the entire flow field inside a combustor taking proper account of an infinite diversity of realistic combustor geometries, inlet and outlet conditions, boundaries, etc., while not resolving small scales explicitly. DNS, on the other hand, aim to provide the highest possible physical fidelity on small scales at the expense of not capturing the large-scale flow dynamics. Ultimately, these two complementary approaches are intended to form a synergy: DNS allows one to probe in detail the small-scale flow physics, which can then be distilled into accurate, efficient, and universal models. Such models, subsequently, can be used in LES to capture the effects of the unresolved small scales.
The field of turbulent combustion has largely inherited this paradigm from its counterpart focused on studies of nonreacting turbulent flows. Relative simplicity of the underlying physical picture in the latter case has led to a great success of this approach, even though work still continues actively in the community aimed at improving the LES small-scale (also known as “subgrid-scale”) models.
At the same time, recent studies by us, as well as other groups, of a broad range of turbulent combustion regimes are starting to form a picture of reacting turbulence, which is profoundly different from its nonreacting counterpart. In high-speed regimes, such as found in scramjet engines or in modern high-pressure jet-engine combustors, turbulence is sufficiently strong to be an important, and potentially dominant, factor shaping the resulting flame dynamics. We found that high-speed flames can be highly unstable, exhibiting large variability of the burning speed even under the most idealized upstream conditions. Somewhat paradoxically, highly subsonic reacting turbulence can also spontaneously produce shocks and even transition to a supersonic detonation without any external assistance of walls or obstacles – a phenomenon, which has no analog in nonreacting turbulence. Furthermore, combustion can also generate significant amounts of turbulence, far in excess of what can be ascribed to the upstream turbulent flow. Such energy is injected on small scales and is redistributed to larger scales, which can lead to the acceleration of the overall turbulent flame producing, in a sense, a self-propelling system.
These findings have demonstrated the existence of a rich variety of phenomena in reacting turbulence, which are dynamically important and which are not captured in modern LES subgrid-scale models. Furthermore, they point to a much more complex coupling between small and large scales than a traditional LES-DNS paradigm can account for. The fact that small scales can energize the entire turbulent flow field shows that they become an important, or sometimes even the main, driving force controlling the flow dynamics and turbulence-flame coupling. This is contrary to the traditional logic of the LES approach, which assigns such role to large scales. All this points to the need to re-examine the LES framework carefully in the context of high-speed turbulent reacting flows. More specifically, it is important to assess the validity of various assumptions fundamental to LES, first of all concerning the nature of the interplay between small scales and all other scales of the flow.
From a computational point of view, this means that we need to attempt to relax all such assumptions and instead capture all relevant scales explicitly in a calculation. In other words, we need to extend the DNS beyond its traditional realm of small scales to model a realistic combustion system in its entirety. Is this possible?
Due to the “tyranny of scales” as well as the physical complexity of a reacting flow discussed above, a traditional answer would be – No! As will be shown below, in a general sense, that is still indeed true. At the same time, in certain cases, recent advances in physical models, numerical tools, and high-performance computing platforms place this seemingly impossible goal within reach.
Consider a flame in a mixture of vaporized jet fuel and air. Under atmospheric conditions, a typical flame thickness is ~0.4 mm. In our code, Athena-RFX, grid resolution of ~16 cells per flame width is generally sufficient to capture the flame dynamics accurately. This means that a computational grid with 2,048 ´ 2,048 x 8,192 cells (32 billion cells) would represent a domain with a size of 5 ´ 5 ´ 20 cm. This starts to approach a size of a realistic combustor. Figure 1 (lower panel) shows an example of a DNS of a similar size (32 billion cells in a 1,024 ´ 1,024 x 16,384 domain) performed by us on 65,536 computational cores on Cray XE6 (Garnet) at the ERDC DSRC.That calculation used simplified single-step reaction kinetics. It is important to emphasize, however, that it is not sufficient to focus only on achieving a realistic range of scales representative of a typical jet-engine combustor. It is equally important to provide also a comparable level of realism of a physical model and, in particular, of the description of chemical reactions for a realistic jet fuel. Recent advances in the understanding of chemical kinetics of heavy hydrocarbons have resulted in a new generation of reduced reaction-kinetics models, which are sufficiently compact (< 30 species) and efficient to allow their use in DNS calculations.
The emergence of such reaction models has allowed us in the last two years, in the course of the ongoing Frontier project, to carry out the first systematic study of turbulent flame properties for realistic jet fuels (dodecane and Jet-A) under flow conditions representative of realistic jet-engine combustors, i.e., high pressures (30 atm) and high temperatures (700 K), for a broad range of turbulent intensities – from relatively low to ultra-high. Figure 2 shows an example of such turbulent flame in a jet-fuel/air mixture.
From a physical standpoint, this survey has uncovered a number of surprising effects in terms of the flame structure and dynamics, which are characteristic of higher hydrocarbon fuels undergoing pyrolysis, and which are not present in lighter fuels, such as methane. On the other hand, from a practical point of view, it has demonstrated that it is computationally feasible to model realistic jet-fuel chemistry in large-scale DNS. For instance, this survey included 30 DNS calculations with the largest domain size of 1 billion cells, and it required a total of ~ 100 million CPU hours on the HPCMP Excalibur and Thunder platforms at the ARL and AFRL DSRCs. In particular, the observed code performance with a stiff reaction-kinetics solver and mixture-averaged molecular transport model was ~30,000 cells/core/s (or 33 ms/cell) both on Cray XC40 and SGI ICE-X platforms. We currently estimate that ongoing code modifications aimed at better vectorization, as well as improvements in the hybrid parallelization will increase performance on the HPCMP platforms by a factor of 2-3 on conventional CPUs without any assistance from external accelerators pushing a 100,000 cells/core/s (10 ms/cell) mark.
Let us now revisit the question that we posed above: is DNS of an entire, realistic combustor possible? Figure 2 shows that the largest scales accessible today in a DNS at high-pressure conditions do not exceed 1 mm. Therefore, at high pressures, a DNS of a system with a size of ~10 cm would require a domain ~106 times bigger than shown in Fig. 2, or approximately 1000 trillion cells. This means that in our quest for a full realism – realistic combustor scales, realistic jet fuels, and realistic flow conditions, i.e., pressure, – all three conditions cannot be satisfied simultaneously in a DNS. At the same time, the first two criteria are certainly within reach of DNS on the petascale-class platforms available in the DoD HPCMP program. For instance, a system with a size of 10 ´ 10 ´ 20 cm, would require a domain with ~128 billion cells. With a notional code performance of 10 ms/cell discussed above, this will translate into ~14 s per computational time-step on a 100,000-core-class platform, which is suitable for practical computations.
Such large-scale DNS of an entire realistic combustor, while obviously computationally expensive, would allow one for the first time to explore the dynamics of reacting turbulence over a realistic range of scales from first principles with minimal model assumptions. As was discussed above, reacting turbulence can be profoundly different from its nonreacting counterpart, exhibiting a remarkable wealth of unexpected physical phenomena. Increasing the level of realism of DNS calculations will open a path to deepen our understanding of how those physical effects manifest themselves in realistic systems, to compare those findings directly with experiments, and ultimately to enable the development of a new generation of more accurate and reliable LES subgrid-scale models.