Army case study: Using DOE to reduce time required to optimize complex designStory
June 24, 2008
Dan Cler at U.S Army BenEt Laboratories is using Design of Experiments (DOEs) to drive a series of computer simulations in designing a new generation of muzzle brakes. DOE saves time by reducing the number of simulations required and makes it possible to optimize the design with a higher level of certainty.
The traditional approach to optimizing a product or process using computer simulation is to evaluate the effects of one design parameter at a time. Then after it has been optimized, the analyst moves to the next variable. The problem with this approach is that interactions between design factors and second order effects mean that it is likely to lead down a blind alley. It will result in a locally optimized design that will provide far less performance than the global optimum. Another problem is that many types of simulation take a considerable amount of time, even days, to evaluate a single design iteration. So there is only time to evaluate a small subset of the design space.
For these reasons, a number of analysts have begun using Design of Experiments (DOEs) via Response Surface Methods (RSMs) to drive the design process. DOE/RSM can be used to develop experiments that examine first order, second order, and multiple factor effects simultaneously with relatively few simulation runs.
Dan Cler, Senior Mechanical Engineer for the U.S. Army Armament Research, Development and Engineering Center (ARDEC) - BenEt Laboratories, Watervliet, New York, is using DOE to design a new generation of muzzle brakes with a far higher level of certainty and in much less time than the traditional approach. BenEt Laboratories is a Department of the Army research, development, and engineering facility recognized worldwide as a Center of Excellence for gun design, structural and dynamic analysis, application of advanced materials and composites, and laboratory simulations.
Optimizing design over many variables
One of the centerpieces of the Army's Future Combat Systems (FCS) program is the development of new combat vehicles that are only about one-fourth to one-half the weight of the Army's current vehicles, yet capable of mounting guns as powerful as the older vehicles' guns. To meet this goal, the new lighter vehicles require muzzle brakes that redirect part of the gun's propellant flow backwards to reduce the gun's recoil. But this redirection must be accomplished while keeping the blast overpressure on the vehicle itself low enough to prevent vehicle damage and injury to nearby soldiers. (See article header photo on this page, depicting a Howitzer with a muzzle brake.)
Testing proposed muzzle brake designs is very expensive and time consuming. The engineers at the Army's BenEt Laboratories are therefore using a new generation of Computational Fluid Dynamics (CFD) software to model the gun's recoil forces and blast pressures for different muzzle brake designs to provide a design with low recoil force and acceptable blast overpressure. They face the challenge that there are many possible design parameters that can affect the performance of the muzzle brakes, and evaluating just one combination of design parameters can take a considerable amount of time because of the complexity of the analysis task.
BenEt is addressing this challenge by using designed experiments that require a relatively small number of simulation runs. Each simulation run uses a simplified two-dimensional model to explore the entire design space. This method identifies the area of optimal design; then Cler builds a more detailed three-dimensional model and explores this small area without having to pay attention to the vast areas that DOE/RSM has ruled out.
Figure 1 shows the design parameters, or factors in DOE/RSM terminology, for a typical muzzle brake. As depicted, the muzzle vane is connected to the barrel through the opening A. The combustion gases move from the barrel through opening A and are reversed in direction by passing through the curved passageway in the muzzle brake. Dimensions B, C, D, and E define the geometry of the curved passageway. Cler selected a D-optimal design to provide an ideal set of experimental combinations for fitting a cubic predictive model with a minimum number of design points.
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Simplifying the DOE/RSM method
BenEt Laboratories used Design-Expert DOE/RSM software from Stat-Ease, Inc., Minneapolis, Minnesota, to design the experiment and perform the analysis. Design-Expert provides a wide range of experimental designs and statistical analyses such as mixture-in-mixture, Box-Behnken, D-optimal, and many other designs that go far beyond what is offered by general statistical packages. Design-Expert also greatly simplifies DOE/RSM by making it easy for a user without statistical background to design an experiment and analyze the results.
The experiment created by Design-Expert focuses on the edges of the design space while also including some points in the middle. Each point represents a different run, and each run is a simulation. The different colors represent blocks that define the sequence of experiments. First the black runs are completed, then the green, then the red. The numbers 4, 5, and 6 indicate there are 4, 5, and 6 runs at those points. Additionally, the points tend to be evenly spaced in order to reduce colinearity.
An important characteristic of physical experiments is that they are subject to natural process variations so they are not deterministic. Numerical simulations, on the other hand, generally provide exactly the same answer every time. A designed experiment based on physical experiments includes repeat runs to estimate the error, but this is not applicable to the simulation world. Ben√©t added extra design points to compensate for the absence of error points.
BenEt Laboratories uses FLUENT CFD software from ANSYS to simulate the operation of the muzzle brake. FLUENT uses static adaption to change the density of the mesh throughout the domain so that shocks in the muzzle brake are properly resolved. Comparing 3-D simulation predictions to physical testing has shown that CFD (Figure 2) accurately predicts forces generated on the muzzle brake during blow-down of the propellant gases after the projectile leaves the gun barrel. For the 2-D simulations utilized in the 51-run design, complete convergence was not possible in all cases due to flow instabilities in some of the configurations. This is one of the difficulties in performing designed experiments. Often the design points selected do not always provide acceptable results.
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DOE results expedite optimization of design
Cler used two key responses in this designed experiment. Axial momentum is the product of the axial velocity and the density of the gas. Essentially, it determines the change in direction provided by the muzzle brake. The other response is the mass flux ratio or the mass flux through the vane of the muzzle brake divided by the mass flux through the barrel. Physically, this represents the proportion of the flow emitted by the barrel that is redirected by the muzzle brake.
The design objective is to maximize both responses in order to reduce recoil. Figure 3 shows the Analysis of Variance (ANOVA) results for first and second order two-factor interaction effects of each factor on the mass flux ratio. The ANOVA results separate the factors that have the greatest impact from those that have a minimal impact on the responses. In this case, the opening width has the greatest impact while the shape factor appears to be insignificant.
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Design-Expert calculated the optimal values for each factor in this application. The true power of DOE/RSM resides in its ability to optimize a design across many variables. The response surface method explores the entire design space and so avoids the common problem of getting stuck in a local optimum by not taking second order and multiple factor interactions into account. In this case, DOE/RSM quickly and efficiently zeroed in on the area of the design space containing the optimum. It also provided expected values as well as confidence intervals for the responses with the factors optimized.
The next step was to manually perform a more detailed and time-consuming analysis of this small area of the design space. DOE has proven to be a very effective method for exploring the complex design space of our products. DOE does not replace the judgment and experience of the engineer. But by eliminating the vast majority of the design space from consideration, DOE enables the engineer to focus his or her attention on the critical areas where he or she can have the most impact.
Dan Cler joined the U.S. Army BenEt Laboratories in 2001, where he performs both CFD analysis and experimental testing of large-caliber gun systems and muzzle brakes. He worked at NASA Langley Research Center from 1990 to 2001 as a research and test engineer in the 16-Foot Transonic Tunnel. He graduated from Purdue University in 1990 with a bachelor's degree in Aeronautical and Astronautical Engineering. He can be reached at [email protected].
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