Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Chen, H. C.↗

Interlaminar stress singularities at a straight free edge in composite laminates

A quasi-three-dimensional finite-element analysis was used to analyze the edge-stress problem in four-ply, composite laminates. The seven laminates that were considered belong to the laminate family where the outer ply angle is between 0 and 90 deg. Systematic convergence studies were made to explore the existence of stress singularities near the free edge. The present analysis appears to confirm the existence of stress singularities at the intersection of the interface and the free edge. The power of the stress singularity was the same for all seven laminates considered.

Raju, I. S.↗

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

Boyd, J. P.↗

Transverse vibrations of non-uniform beams

The free vibrations of elastic beams with nonuniform characteristics are investigated theoretically by a new method. The new method is seen to combine the advantages of a finite element approach and of a Rayleigh-Ritz analysis. Comparison with the known analytical results for uniform beams shows good convergence of the method for natural frequencies and modes. For internal shear forces and bending moments, the rate of convergence is less rapid. Results from experiments conducted with a cantilevered helicopter blade with strong nonuniformities and also from alternative theoretical methods, indicate that the theory adequately predicts natural frequencies and mode shapes. General guidelines for efficient use of the method are presented.

Klein, L.↗

A diagnosis of two cyclones in the South Pacific Convergence Zone

The evolution of three cyclones which originated in the South Pacific Convergence Zone, two of which propagated into middle latitudes, are traced. The analysis is based on IR imagery from GOES-W, island meteorological station data, and estimates of heat and moisture budget residuals. A European Center for Medium-range Weather Forecasting Level III-b analysis was used to model the cyclones. The northward-propagating storms exhibited strong vertical shear of the horizontal wind, implicating baroclinic effects in the development of the storms. The processes which enhanced storm intensification are discussed. Attention is given to the spatial and temporal behavior of dynamic atmospheric components which were significant to baroclinicity and latent heat release, which the analysis demonstrates were coupled processes.

Vincent, D. G.↗

Calculation of stresses and forces between the skin and stiffener in composite panels

A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.

Hyer, M. W.↗

New insights in the numerical reliability properties of existing Kalman filter implementations

The convergence properties of Kalman filter algorithms are investigated analytically. A theoretical error analysis is performed on four types of algorithms, as defined by Anderson and Moore (1979): (1) a conventional Kalman filter, (2) a square-root (SR) covariance filter, (3) the Chandrasekhar SR filter, and (4) an SR information filter. The derivations are given in detail, and numerical results for the flight-path reconstruction problem studied by Verhaegen (1987) are presented in tables and graphs. It is shown that error propagation in algorithms (1) and (2) is sensitive to the condition number of the innovation-signal covariance matrix and the spectral norm of the filter state-transition matrix, whereas other parameters are dominant in (3) and (4). Filter (2) is found to be the most reliable for the class of problems studied.

Verhaegen, M. H.↗

DSMC and continuum analyses of low-density nozzle flow

Two different approaches, the direct-simulation Monte Carlo (DSMC) method based on molecular gas dynamics and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gas dynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothe's experimental dam, in which density and rotational temperature variations along the centerline and at various locations inside a low density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity temperature exponent, have substantial effects on the results of the DSMC method.

Chung, Chan-Hong↗

Simulation of Low-density Nozzle Plumes in Non-zero Ambient Pressures

The direct simulation Monte-Carlo (DSMC) method was applied to the analysis of low-density nitrogen plumes exhausting from a small converging-diverging nozzle into finite ambient pressures. Two cases were considered that simulated actual test conditions in a vacuum facility. The numerical simulations readily captured the complicated flow structure of the overexpanded plumes adjusting to the finite ambient pressures, including Mach disks and barrel shaped shocks. The numerical simulations compared well to experimental data of Rothe.

Chung, Chan-Hong↗

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗

Status of Axisymmetric CFD of an Eleven Inch Diameter Hybrid Rocket Motor

Current status of a steady state, axisymmetric analysis of an experimental 11 inch diameter hybrid rocket motor internal flow field is given. The objective of this effort is to develop a steady state axisymmetric model of the 11 inch hybrid rocket motor which can be used as a design and/or analytical tool. A test hardware description, modeling approach, and future plans are given. The analysis was performed with FDNS implementing several finite rate chemistry sets. A converged solution for a two equation and five species set on a 'fine' grid is shown.

Ruf, Joseph↗

Low-Density Nozzle Flow by the Direct Simulation Monte Carlo and Continuum Methods

Two different approaches, the direct simulation Monte Carlo (DSMC) method based on molecular gasdynamics, and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gasdynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothe's experimental data, in which density and rotational temperature variations along the centerline and at various locations inside a low-density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data, both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity-temperature exponent, have substantial effects on the results of the DSMC method.

Chung, Chang-Hong↗

An Investigation of the Influence of Urban Areas on Rainfall Using a Cloud-Mesoscale Model and the TRMM Satellite

A recent paper by Shepherd and Pierce (conditionally accepted to Journal of Applied Meteorology) used rainfall data from the Precipitation Radar on NASA's Tropical Rainfall Measuring Mission's (TRMM) satellite to identify warm season rainfall anomalies downwind of major urban areas. A convective-mesoscale model with extensive land-surface processes is employed to (a) determine if an urban heat island (UHI) thermal perturbation can induce a dynamic response to affect rainfall processes and (b) quantify the impact of the following three factors on the evolution of rainfall: (1) urban surface roughness, (2) magnitude of the UHI temperature anomaly, and (3) physical size of the UHI temperature anomaly. The sensitivity experiments are achieved by inserting a slab of land with urban properties (e.g. roughness length, albedo, thermal character) within a rural surface environment and varying the appropriate lower boundary condition parameters. Early analysis suggests that urban surface roughness (through turbulence and low-level convergence) may control timing and initial location of UHI-induced convection. The magnitude of the heat island appears to be closely linked to the total rainfall amount with minor impact on timing and location. The physical size of the city may predominantly impact on the location of UHI-induced rainfall anomaly. The UHI factor parameter space will be thoroughly investigated with respect to their effects on rainfall amount, location, and timing. This study extends prior numerical investigations of the impact of urban surfaces on meteorological processes, particularly rainfall development. The work also contains several novel aspects, including the application of a high-resolution (less than I km) cloud-mesoscale model to investigate urban-induce rainfall process; investigation of thermal magnitude of the UHI on rainfall process; and investigation of UHI physical size on rainfall processes.

Shepherd, J. Marshall↗

Overview of the Development for a Suite of Low-Thrust Trajectory Analysis Tools

A NASA intercenter team has developed a suite of low-thrust trajectory analysis tools to make a significant improvement in three major facets of low-thrust trajectory and mission analysis. These are: 1) ease of use, 2) ability to more robustly converge to solutions, and 3) higher fidelity modeling and accuracy of results. Due mostly to the short duration of the development, the team concluded that a suite of tools was preferred over having one integrated tool. This tool-suite, their characteristics, and their applicability will be described. Trajectory analysts can read this paper and determine which tool is most appropriate for their problem.

Kos, Larry D.↗

Effect of Distributed Patch of Smooth Roughness Elements on Transition in a High-Speed Boundary Layer

Surface roughness is known to have a substantial impact on the aerothermodynamic loading of hypersonic vehicles, particularly via its influence on the laminar-turbulent transition process within the boundary layer. Numerical simulations are performed to investigate the effects of a distributed region of densely packed, smooth-shaped roughness elements on the laminar boundary layer over a 7-degree half-angle, circular cone for flow conditions corresponding to a selected trajectory point from the ascent phase of the HIFiRE-1 flight experiment. For peak-to-valley roughness heights of 50 percent or less in comparison with the thickness of the unperturbed boundary layer, the computations converge to a stationary flow, suggesting that the flow is globally stable. Analysis of convective instabilities in the wake of the roughness patch indicates two dominant families of unstable disturbances, namely, a high frequency mode that corresponds to Mack mode waves modified by the wake and a lower frequency mode that corresponds to shear layer instabilities associated with the streaks in the roughness wake. Even though the peak growth rate of the later mode is more than 35 percent greater than the peak growth rates of the Mack modes, the latter modes achieve higher amplification ratios, and hence, are likely to dominate the onset of transition, which is estimated to occur slightly later than that in the unperturbed, i.e., smooth surface boundary layer. Additional computations are performed to investigate the effects of various roughness patch configurations on a Mach 3.5 flat plate boundary layer, to help guide an upcoming experiment in the Mach 3.5 Supersonic Low Disturbance Tunnel at NASA Langley Research Center. In this case, the cumulative reinforcement of basic state distortion over the length of the roughness patch is predicted to yield a significantly earlier transition than that over a smooth plate or a plate with a shorter length roughness patch.

Meelan Choudhari↗