This article focuses on the fact that using computational fluid dynamics (CFD) and design of experiments (DOE) software, researchers are in pursuit of aircraft fluidics thrust control without moving component parts. Fluidics’ performance is dictated by complex interactions among approximately two dozen geometric and fluid properties. These complex interactions probably proved overwhelming to early researchers seeking a stable, reliable rocket flight control system. A major advantage of DOE is that it allows all the parameters to vary simultaneously. A single permutation, on the other hand, varies one parameter at a time and cannot deal with interactions among the fixed parameters. There is still more development work to be done, but indications are that CFD and DOE are leading Lockheed Martin to a promising design. Physical testing reinforces the belief that a fluidic nozzle can achieve the performance levels required. The technology that never got off the ground in the early rocket era may find itself flying high in the next generation of high-performance tactical aircraft.
Fluidics thrust control, born and then left to languish during the nation 's early space efforts, is being resuscitated, thanks to advances in research tools. Using computational fluid dynamics (CFD) and design of experiments (DOE) software, researchers are in pursuit of aircraft thrust control without moving parts. The payoff could be dramatically reduced weight and cost in tomorrow's high-performance military aircraft.
Simply put, fluidics alters the mass flow and direction of a main fluid stream by the introduction of small control jets. Small disturbances created by the control jets at points along the flow produce large responses in the main stream.
While functionally easy to describe, fluidics' performance is dictated by complex interactions among approximately two dozen geometric and fluid properties. These complex interactions probably proved overwhelming to early researchers seeking a stable, reliable rocket flight control system.
Lockheed Martin Tactical Aircraft Systems of Fort Worth, Texas, working collaboratively with General Electric Aircraft Engines in Evendale, Ohio, has attacked fluidic design using DOE and CFD techniques that were unavailable to research predecessors decades ago. The resulting design advances have brought the technology to the threshold of a full-scale engine demo.
While planning the next-generation tactical aircraft, Lockheed Martin, which is also lea d developer of the F-22, began scrutinizing each component for weight-slashing opportunities. In the propulsion area, the multifunction exhaust nozzle, accounting for 30 percent of the total engine weight, became the prime candidate.
"The way to get the weight out is to reduce or eliminate the actuation systems and moving surfaces associated with today's variable geometry exhaust systems," said Daniel Miller, Lockheed Martin 's principal investigator.
"Fluidics allows you to do this without losing any afterburning or thrust vectoring functionality."
Eliminating moving parts reduces parts count, increases reliability, and potentially chops 30 to 50 percent from the exhaust system cost. In addition, a fixed nozzle can be easily shaped for reduced drag and signature, with the latter yielding significant stealth benefits.
A fixed nozzle can be fabricated from a wider range of materials. This would allow one of the most replaced items on fighter aircraft, the nozzle internal flap (the area between the exhaust nozzle throat and exit) to be designed based on thermal rather than mechanical constraints.
"The exhaust system is a very expensive component," Miller said. " For a fleet of 3,000 planes, fluidic nozzles could potentially save hundreds of millions of dollars."
Inside a Fluidic Nozzle
Turbofan engine features, such as thrust vectoring and afterburning, require complex controls for manipulating exhaust angle and exhaust nozzle geometry. During afterburning, fuel is sprayed directly into the exhaust duct where it is burn ed. Afterburning dramatically increases thrust as well as exhaust temperature. To maintain constant flow and backpressure, the exhaust nozzle throat area must increase 50 to 100 percent over its normal cruise operation size.
This thrust vectoring and afterburn control system is a complex mechanical maze of hundreds of parts-hinges, seals, hydraulic actuators, bearings, flaps, etc.-that must slide, pivot, extend, and retract while maintaining tight tolerances under extreme temperature and pressure variations.
In a fluidic nozzle, effective throat area is controlled via tiny injectors symmetrically located around the nozzle throat. Depending on the configuration, injection angle, and pressure, these injectors can throttle the main exhaust stream as much as 50 percent between afterburning and normal cruise operation.
Thrust vectoring .is a technique for turning an aircraft by diverting the exhaust stream using movable flaps or paddles. In fluidic thrust vectoring, a second set of injectors is symmetrically located around the nozzle flap, but the injectors are individually activated, as needed, to skew the sonic plane, the section of the exhaust where the flow reaches a speed of Mach 1.
Control flows for choking and vectoring are bled from the compressor stage or some other high-pressure source in the engine.
Fluidic nozzle performance depends on parameters such as injector location, shape, size, and flow rate; nozzle flap length; and control pressure. Manipulating these parameters can be a daunting task. For example, to investigate eight parameters with three levels each would require 38, or 6,561 experiments, to handle all the possible combinations.
"When faced with this situation, engineers run a few experiments and rely on their experience to pick the levels for best performance," Miller said. "They could, of course, go to the other extreme and do a full permutation but, in reality, no one can afford that."
Design of experiments uses regression analysis to identify statistically significant subsets of the full factorial from which the user can pick for his experiments. There is some sacrifice in accuracy, but the results usually trend in the right direction.
A variation of DOE, known as the Taguchi method, is widely used in the automotive processing industry. However, in the R&D community, the technique has had limited use.
A major advantage of DOE is that it allows all the parameters to vary simultaneously. A single permutation, on the other hand, varies one parameter at a time and cannot deal with interactions among the fixed parameters.
Lockheed Martin uses a program called DOE Pro, from Air Academy Associates of Colorado Springs, Colo. It uses an Excel spreadsheet as the user interface.
Building A DOE/CFD Solution
DOE starts with a prescreening exercise and a baseline configuration. The baseline will not meet all the design criteria. If it did, the analysis wouldn't be necessary in the first place.
A figure of merit is established for comparing results. For fluidic nozzle throttling, the figure of merit is the nozzle discharge coefficient, which directly correlates to effective throat area. For thrust vectoring, the figure of merit is primarily jet thrust vector angle and gross thrust coefficient.
The prescreening exercise is much like a typical analysis: Design parameters are varied one at a time to determine which have the greatest effect on the figure of merit. Lockheed Martin used CFD for the screening.
A CAD model of each nozzle/injector shape is built using an internally developed CAD program. TIllS model is discretized using semi-automated gridding software called Gridgen from Pointwise of Fort Worth, Texas, and analyzed using CFD software called Falcon, developed by Lockheed Martin.
The models are initially culled using two-dimensional CFD analysis. If the results look favorable, then the more time-consuming three-dimensional CFD calculation is performed.
Based on CFD results, parameters are winnowed down to the three or four that produced the greatest response, and at least three levels are assigned to each parameter.
"If only two levels were used, we wouldn't know whether the resulting points represented a straight line or whether there was a peak in between," Miller pointed out. "You need at least three levels to determine if there is a curvature in the design space."
Even with only four variables and three levels for each one, a full permeation is 34, or 81 experiments. Here is where the power of DOE comes to the rescue.
Design of experiments takes the full factorial and develops subsets. In the case of81 combinations, two common subsets are 9 and 27, between which the user can pick, depending on the amount of risk he is willing to take.
"The more combinations you run through CFD, the more accurate the results, but also the greater the expense," Miller said.
Miller's preference is to run between a quarter and a third of the full factorial of experiments. He believes that range delivers the best tradeoff among time, cost, and accuracy. He feels that with anything less you have to be really careful in interpreting the results.
"DOE will produce some combinations of design variables that either seem strange or are ones that you know won't give you the best solution;' he reported, "but this is all part of determining the design sensitivity."
The subset combinations are processed first through 2-D CFD to weed out unlikely candidates and then further analyzed with 3-D.
These results are post-processed by DOE to develop design sensitivities-for instance, to see if a parameter could be longer or shorter, higher or lower, to improve response. Knowing this information, the researcher can develop a "paper champ," as Miller puts it, the parameter combination expected to deliver the best performance. This paper champ is then verified with CFD to ensure that DOE has, indeed, produced a promising combination. If it passes the analytical test, the design is ready for wind tunnel testing.
"When we go into the wind tunnel, it is no longer a matter of whether it will work, but will it work as well as CFD predicts," Miller asserted.
For nozzle discharge coefficient and thrust efficiency, the CFD results are typically within 1 and 2 percent of the physical experiments' results, while vectoring effectiveness has been within 1 and 2 degrees.
For its CFD analysis, Lockheed Martin relies on its home-grown code, Falcon, which Miller prefers to commercially available packages. Falcon is a Reynolds-averaged Navier-Stokes code that uses an approximate lower-upper implicit solver.
Falcon allows boundary conditions inside the grid, an important feature when a researcher is looking at an injector port that sits inside the grid. The software also allows the problem to be cut into chunks so that the pieces can be run in parallel on different supercomputers.
"Most importantly, we've been developing and using it for more than 10 years, and have had good agreement with wind tunnel results on a wide variety of problems," Miller noted.
Calculating these complex CFD problems, some with almost two million grid points, demands hefty computing power. For one million grid points or fewer, Miller uses a Silicon Graphics Octane, a high-performance Unix-based graphics workstation with multiple RISC processors and one gigabyte of RAM. A one million grid point problem will take about three full days to run.
For problems with more than one million grid points, Miller taps one of Lockheed Martin's supercomputers, a Cray J90, HP V-class, or Silicon Graphics Origin.
"The beauty of DOE is that it lays out all your experiments in advance, so you don't have to wait for one to be done before you do the next," Miller explained. "Using a supercomputer, we can run three or four at the same time, and we can knock out a whole DOE study in three to four weeks."
Miller heartily recommends that DOE users have a statistician at hand.
"The statistician does not do the work; in fact, he would be the wrong person because he doesn't know how to interpret the results," Miller explained. "However, you need a statistician looking over your shoulder to make sure that you are applying DOE correctly, or you might end up with design sensitivities that are erroneous. A statistician will look at things such as residuals to determine how good the regression was."
Lockheed Martin has found that design of experiments has slashed the number of analytical experiments, and computational fluid dynamics has eliminated innumerable wind tunnel tests. A typical wind tunnel test alone costs $250,000 to $500,000. After six years of development work (not unusual when you realize military aircraft have a 10- to 15-year developmental cycle), the techniques have cut millions of dollars from development costs, a fact that has made the development work economically feasible.
The analytical approach is gradually winning customer support, as well. Denis P. Mrozinski, program manager for advanced nozzle technology with the Air Force Research Laboratory at Wright-Patterson AFB in Ohio, noted, "The biggest challenge facing developers is to show that a concept works. This is difficult to do without actual test data. And if you can't show that something works, then you don't get money to produce the data. It's sort of a Catch-22.
"Fortunately, analytical solutions carry more weight than they did in the past," Mrozinski added, "so that analytical work is a good way to start. A lot of analytical work has been done with fluidic nozzles and that has helped to capture funding for testing."
There is still more development work to be done, but indications are that CFD and DOE are leading Lockheed Martin to a promising design. Physical testing reinforces the belief that a fluidic nozzle can achieve the performance levels required. The technology that never got off the ground in the early rocket era may find itself flying high in the next generation of high-performance tactical aircraft.