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All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Panossian, H.↗
NASA NTRS2013

Issues and Strategies in Solving Multidisciplinary Optimization Problems

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya↗
NASA NTRS2015

An Analytical Solution for Yaw Maneuver Optimization on the International Space Station and Other Orbiting Space Vehicles

This paper suggests a new method for optimizing yaw maneuvers on the International Space Station (ISS). Yaw rotations are the most common large maneuvers on the ISS often used for docking and undocking operations, as well as for other activities. When maneuver optimization is used, large maneuvers, which were performed on thrusters, could be performed either using control moment gyroscopes (CMG), or with significantly reduced thruster firings. Maneuver optimization helps to save expensive propellant and reduce structural loads ‐ an important factor for the ISS service life. In addition, optimized maneuvers reduce contamination of the critical elements of the vehicle structure, such as solar arrays. This paper presents an analytical solution for optimizing yaw attitude maneuvers. Equations describing pitch and roll motion needed to counteract the major torques during a yaw maneuver are obtained. A yaw rate profile is proposed. Also the paper describes the physical basis of the suggested optimization approach. In the obtained optimized case, the torques are significantly reduced. This torque reduction was compared to the existing optimization method which utilizes the computational solution. It was shown that the attitude profiles and the torque reduction have a good match for these two methods of optimization. The simulations using the ISS flight software showed similar propellant consumption for both methods. The analytical solution proposed in this paper has major benefits with respect to computational approach. In contrast to the current computational solution, which only can be calculated on the ground, the analytical solution does not require extensive computational resources, and can be implemented in the onboard software, thus, making the maneuver execution automatic. The automatic maneuver significantly simplifies the operations and, if necessary, allows to perform a maneuver without communication with the ground. It also reduces the probability of command errors. The suggested analytical solution provides a new method of maneuver optimization which is less complicated, automatic and more universal. A maneuver optimization approach, presented in this paper, can be used not only for the ISS, but for other orbiting space vehicles.

Dobrinskaya, Tatiana↗
NASA NTRS2015

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗
NASA NTRS2013

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Chebyshev Polynomial↗
NASA NTRS1982

Optimal short-range trajectories for helicopters

An optimal flight path algorithm using a simplified altitude state model and a priori climb cruise descent flight profile was developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. In addition, a method was developed for obtaining a performance model in simplified form which is based on standard flight manual data and which is applicable to the computation of optimal trajectories. The entire performance optimization algorithm is simple enough that on line trajectory optimization is feasible with a relatively small computer. The helicopter model used is the Silorsky S-61N. The results show that for this vehicle the optimal flight path and optimal cruise altitude can represent a 10% fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability because of helicopter weight, ambient winds, and the relative cost trade off between time and fuel. In general, reasonable variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost. For fuel optimal trajectories, the optimum cruise altitude varies from the maximum (12,000 ft) to the minimum (0 ft) depending on helicopter weight.

Slater, G. L.↗
NASA NTRS1992

Experimental validation of structural optimization methods

The topic of validating structural optimization methods by use of experimental results is addressed. The need for validating the methods as a way of effecting a greater and an accelerated acceptance of formal optimization methods by practicing engineering designers is described. The range of validation strategies is defined which includes comparison of optimization results with more traditional design approaches, establishing the accuracy of analyses used, and finally experimental validation of the optimization results. Examples of the use of experimental results to validate optimization techniques are described. The examples include experimental validation of the following: optimum design of a trussed beam; combined control-structure design of a cable-supported beam simulating an actively controlled space structure; minimum weight design of a beam with frequency constraints; minimization of the vibration response of helicopter rotor blade; minimum weight design of a turbine blade disk; aeroelastic optimization of an aircraft vertical fin; airfoil shape optimization for drag minimization; optimization of the shape of a hole in a plate for stress minimization; optimization to minimize beam dynamic response; and structural optimization of a low vibration helicopter rotor.

Adelman, Howard M.↗
NASA NTRS1990

Integrated topology and shape optimization in structural design

Structural optimization procedures usually start from a given design topology and vary its proportions or boundary shapes to achieve optimality under various constraints. Two different categories of structural optimization are distinguished in the literature, namely sizing and shape optimization. A major restriction in both cases is that the design topology is considered fixed and given. Questions concerning the general layout of a design (such as whether a truss or a solid structure should be used) as well as more detailed topology features (e.g., the number and connectivities of bars in a truss or the number of holes in a solid) have to be resolved by design experience before formulating the structural optimization model. Design quality of an optimized structure still depends strongly on engineering intuition. This article presents a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated in addition to selecting shape and size dimensions. A three-phase design process is discussed: an optimal initial topology is created by a homogenization method as a gray level image, which is then transformed to a realizable design using computer vision techniques; this design is then parameterized and treated in detail by sizing and shape optimization. A fully automated process is described for trusses. Optimization of two dimensional solid structures is also discussed. Several application-oriented examples illustrate the usefulness of the proposed methodology.

Bremicker, M.↗
NASA NTRS1990

Influence of structural and aerodynamic modeling on optimization with flutter constraint

The influences of structural and aerodynamic modeling on multidisciplinary optimization in an aeroelastic environment are not well understood. Therefore, optimizations with flutter and frequency constraints were performed to investigate the effects these modeling factors have on various representative wings. To this end, the Automated Structural Optimization System (ASTROS) was used as a tool to minimize the weight of various fully built-up finite element wing models in subsonic and supersonic flow under given flutter and frequency constraints. First, the performance of the optimization module was tested against results from other codes on a straight and uniform wing widely used for optimization with flutter constraints. Then, fully built-up finite element models of various wings with different aspect ratios were investigated for the influence on the structural optimization for minimum weight of the following modeling factors: finite element selection, structural grid refinement; number of selected modes, retention of breathing modes; selection of reduced frequencies to be used in flutter analysis; aerodynamic panel size and placement; splining of the aerodynamic grid to the structural grid selection of extra points of the structural wing box for splining; and number of constraints to be retained. Knowledge of these influences as well as of the program behavior is important, since optimization can be made more efficient by the selection of reasonable initial models. Also, it was shown previously that modeling has an impact on the results of modal and aeroelastic analyses. Thus, if modeling errors can negatively affect the analyses, a minimum weight optimization can be jeopardized and result in an optimal design that is rather unreliable. In the following, selected results are presented and the influences of some modeling parameters on optimization are pointed out.

Striz, Alfred G.↗
NASA NTRS1993

Trajectory optimization for the National Aerospace Plane

The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

Lu, Ping↗
NASA NTRS1993

Optimization of contoured hypersonic scramjet inlets with a least-squares parabolized Navier-Stokes procedure

A new optimization procedure, in which a parabolized Navier-Stokes solver is coupled with a non-linear least-squares optimization algorithm, is applied to the design of a Mach 14, laminar two-dimensional hypersonic subscale flight inlet with an internal contraction ratio of 15:1 and a length-to-throat half-height ratio of 150:1. An automated numerical search of multiple geometric wall contours, which are defined by polynomical splines, results in an optimal geometry that yields the maximum total-pressure recovery for the compression process. Optimal inlet geometry is obtained for both inviscid and viscous flows, with the assumption that the gas is either calorically or thermally perfect. The analysis with a calorically perfect gas results in an optimized inviscid inlet design that is defined by two cubic splines and yields a mass-weighted total-pressure recovery of 0.787, which is a 23% improvement compared with the optimized shock-canceled two-ramp inlet design. Similarly, the design procedure obtains the optimized contour for a viscous calorically perfect gas to yield a mass-weighted total-pressure recovery value of 0.749. Additionally, an optimized contour for a viscous thermally perfect gas is obtained to yield a mass-weighted total-pressure recovery value of 0.768. The design methodology incorporates both complex fluid dynamic physics and optimal search techniques without an excessive compromise of computational speed; hence, this methodology is a practical technique that is applicable to optimal inlet design procedures.

Korte, J. J.↗
NASA NTRS1995

Displacement based multilevel structural optimization

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Striz, Alfred G.↗
NASA NTRS1996

Cascade Optimization Strategy for Aircraft and Air-Breathing Propulsion System Concepts

Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the respective merit functions. Because of the diversity of constraint types and the overall distortion of the design space, the most reliable single optimization algorithm available in COMETBOARDS could not produce a satisfactory feasible optimum solution. Some of COMETBOARDS' unique features, which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications, successfully optimized the performance of both aircraft and engines. The cascade method has two principal steps: In the first, the solution initiates from a user-specified design and optimizer, in the second, the optimum design obtained in the first step with some random perturbation is used to begin the next specified optimizer. The second step is repeated for a specified sequence of optimizers or until a successful solution of the problem is achieved. A successful solution should satisfy the specified convergence criteria and have several active constraints but no violated constraints. The cascade strategy available in the combined COMETBOARDS, FLOPS, and NEPP design tool converges to the same global optimum solution even when it starts from different design points. This reliable and robust design tool eliminates manual intervention in the design of aircraft and of air-breathing propulsion engines where it eases the cycle analysis procedures. The combined code is also much easier to use, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capability of the combined design tool through the optimization of a subsonic aircraft and a high-bypass-turbofan wave-rotor-topped engine.

Patnaik, Surya N.↗
NASA NTRS1996

Performance Trend of Different Algorithms for Structural Design Optimization

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗
NASA NTRS1996

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
NASA NTRS2001

Robust Airfoil Optimization to Achieve Consistent Drag Reduction Over a Mach Range

We prove mathematically that in order to avoid point-optimization at the sampled design points for multipoint airfoil optimization, the number of design points must be greater than the number of free-design variables. To overcome point-optimization at the sampled design points, a robust airfoil optimization method (called the profile optimization method) is developed and analyzed. This optimization method aims at a consistent drag reduction over a given Mach range and has three advantages: (a) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it allows a designer to make a trade-off between a truly optimized airfoil and the amount of computing time consumed. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.

Li, Wu↗
NASA NTRS1997

Super-optimal CO2 reduces seed yield but not vegetative growth in wheat

Although terrestrial atmospheric CO2 levels will not reach 1000 micromoles mol-1 (0.1%) for decades, CO2 levels in growth chambers and greenhouses routinely exceed that concentration. CO2 levels in life support systems in space can exceed 10000 micromoles mol-1(1%). Numerous studies have examined CO2 effects up to 1000 micromoles mol-1, but biochemical measurements indicate that the beneficial effects of CO2 can continue beyond this concentration. We studied the effects of near-optimal (approximately 1200 micromoles mol-1) and super-optimal CO2 levels (2400 micromoles mol-1) on yield of two cultivars of hydroponically grown wheat (Triticum aestivum L.) in 12 trials in growth chambers. Increasing CO2 from sub-optimal to near-optimal (350-1200 micromoles mol-1) increased vegetative growth by 25% and seed yield by 15% in both cultivars. Yield increases were primarily the result of an increased number of heads per square meter. Further elevation of CO2 to 2500 micromoles mol-1 reduced seed yield by 22% (P < 0.001) in cv. Veery-10 and by 15% (P < 0.001) in cv. USU-Apogee. Super-optimal CO2 did not decrease the number of heads per square meter, but reduced seeds per head by 10% and mass per seed by 11%. The toxic effect of CO2 was similar over a range of light levels from half to full sunlight. Subsequent trials revealed that super-optimal CO2 during the interval between 2 wk before and after anthesis mimicked the effect of constant super-optimal CO2. Furthermore, near-optimal CO2 during the same interval mimicked the effect of constant near-optimal CO2. Nutrient concentration of leaves and heads was not affected by CO2. These results suggest that super-optimal CO2 inhibits some process that occurs near the time of seed set resulting in decreased seed set, seed mass, and yield.

NASA Discipline Life Support Systems↗