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NASA NTRS2008

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

NASA NTRS2008

Thermal Capacitance (Slug) Calorimeter Theory Including Heat Losses and Other Decaying Processes

A mathematical model, termed the Slug Loss Model, has been developed for describing thermal capacitance (slug) calorimeter behavior when heat losses and other decaying processes are not negligible. This model results in the temperature time slope taking the mathematical form of exponential decay. When data is found to fit well to this model, it allows a heat flux value to be calculated that corrects for the losses and may be a better estimate of the cold wall fully catalytic heat flux, as is desired in arc jet testing. The model was applied to the data from a copper slug calorimeter inserted during a particularly severe high heating rate arc jet run to illustrate its use. The Slug Loss Model gave a cold wall heat flux 15% higher than the value of 2,250 W/sq cm obtained from the conventional approach to processing the data (where no correction is made for losses). For comparison, a Finite Element Analysis (FEA) model was created and applied to the same data, where conduction heat losses from the slug were simulated. The heat flux determined by the FEA model was found to be in close agreement with the heat flux determined by the Slug Loss Model.

Hightower, T. Mark↗

NASA NTRS2008

Geometric Modeling of Inclusions as Ellipsoids

Nonmetallic inclusions in gas turbine disk alloys can have a significant detrimental impact on fatigue life. Because large inclusions that lead to anomalously low lives occur infrequently, probabilistic approaches can be utilized to avoid the excessively conservative assumption of lifing to a large inclusion in a high stress location. A prerequisite to modeling the impact of inclusions on the fatigue life distribution is a characterization of the inclusion occurrence rate and size distribution. To help facilitate this process, a geometric simulation of the inclusions was devised. To make the simulation problem tractable, the irregularly sized and shaped inclusions were modeled as arbitrarily oriented, three independent dimensioned, ellipsoids. Random orientation of the ellipsoid is accomplished through a series of three orthogonal rotations of axes. In this report, a set of mathematical models for the following parameters are described: the intercepted area of a randomly sectioned ellipsoid, the dimensions and orientation of the intercepted ellipse, the area of a randomly oriented sectioned ellipse, the depth and width of a randomly oriented sectioned ellipse, and the projected area of a randomly oriented ellipsoid. These parameters are necessary to determine an inclusion s potential to develop a propagating fatigue crack. Without these mathematical models, computationally expensive search algorithms would be required to compute these parameters.

Bonacuse, Peter J.↗

NASA NTRS1961

Flight Performance Handbook for Orbital Operations: Orbital Mechanics and Astrodynamics Formulae, Theorems, Techniques, and Applications

This handbook provides parametric data useful both to the space vehicle designer and mission analyst. It provides numerical and analytical relationships between missions and gross vehicle characteristics as a function of performance parameters. The effects of missile constraints and gross guidance limitations plus operational constraints such as launch site location, tracking net location, orbit visibility and mission on trajectory and orbit design parameters are exhibited. The influence of state-of- the-art applications of solar power as compared to future applications of nuclear power on orbit design parameters, such as eclipse time, are among the parameters included in the study. The principal aim, however, is in providing the analyst with useful parametric design information to cover the general area of earth satellite missions in the region of near-earth to cislunar space and beyond and from injection to atmospheric entry and controlled descent. The chapters are organized around the central idea of orbital operations in the 1961-1969 era with emphasis on parametric flight mechanics studies for ascent phase and parking orbits, transfer maneuvers, rendezvous maneuver, operational orbit considerations, and operational orbit control. The results are based almost entirely on the principles of flight and celestial mechanics. Numerous practical examples have been worked out in detail. This is especially important where it has been difficult or impossible to represent all possible variations of the parameters. The handbook contains analytical formulae and sufficient textual material to permit their proper use. The analytic methods consist of both exact and rapid, approximate methods. Scores of tables, working graphs and illustrations amplify the mathematical models which, together with important facts and data, cover the engineering and scientific applications of orbital mechanics. Each of the five major chapters are arranged to provide a rapid review of an entire astrodynamic subject. By the use of compact graphical and tabular presentation the full scope of the material is made available in an easy-to-use style. Throughout the volume the analyst is shown, by means of suitable introductions, notes, authoritative examples, and cross-references the vital interrelation of the various orbital mechanics topics in the general field of earth satellites and satellite rendezvous. The handbook is designed to give the analyst rapid, reliable access to the mathematics of orbital mechanics needed for virtually any working requirements.

Ambrosio, Alphonso↗

NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗

NASA NTRS2009

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

NASA NTRS2009

Ultrasonic Apparatus and Method to Assess Compartment Syndrome

A process and apparatus for measuring pressure buildup in a body compartment that encases muscular tissue. The method includes assessing the body compartment configuration and identifying the effect of pulsatible components on compartment dimensions and muscle tissue characteristics. This process is used in preventing tissue necrosis, and in decisions of whether to perform surgery on the body compartment for prevention of Compartment Syndrome. An apparatus is used for measuring pressure build-up in the body compartment having components for imparting ultrasonic waves such as a transducer, placing the transducer to impart the ultrasonic waves, capturing the imparted ultrasonic waves, mathematically manipulating the captured ultrasonic waves and categorizing pressure build-up in the body compartment from the mathematical manipulations.

Yost, William T.↗

NASA NTRS2009

Efficient Model-Based Diagnosis Engine

An efficient diagnosis engine - a combination of mathematical models and algorithms - has been developed for identifying faulty components in a possibly complex engineering system. This model-based diagnosis engine embodies a twofold approach to reducing, relative to prior model-based diagnosis engines, the amount of computation needed to perform a thorough, accurate diagnosis. The first part of the approach involves a reconstruction of the general diagnostic engine to reduce the complexity of the mathematical-model calculations and of the software needed to perform them. The second part of the approach involves algorithms for computing a minimal diagnosis (the term "minimal diagnosis" is defined below). A somewhat lengthy background discussion is prerequisite to a meaningful summary of the innovative aspects of the present efficient model-based diagnosis engine. In model-based diagnosis, the function of each component and the relationships among all the components of the engineering system to be diagnosed are represented as a logical system denoted the system description (SD). Hence, the expected normal behavior of the engineering system is the set of logical consequences of the SD. Faulty components lead to inconsistencies between the observed behaviors of the system and the SD (see figure). Diagnosis - the task of finding faulty components - is reduced to finding those components, the abnormalities of which could explain all the inconsistencies. The solution of the diagnosis problem should be a minimal diagnosis, which is a minimal set of faulty components. A minimal diagnosis stands in contradistinction to the trivial solution, in which all components are deemed to be faulty, and which, therefore, always explains all inconsistencies.

Fijany, Amir↗

NASA NTRS2010

Shifting the Inertial Navigation Paradigm with MEMS Technology

Why don t you use MEMS? is one of the most common questions posed to navigation systems engineers designing inertial navigation solutions in the modern era. The question stems from a general understanding that great strides have been made in terrestrial MEMS accelerometers and attitude rate sensors in terms of accuracy, mass, and power. Yet, when compared on a unit-to-unit basis, MEMS devices do not provide comparable performance (accuracy) to navigation grade sensors. This paper will propose a paradigm shift where the comparison in performance is between multiple MEMS devices and a single navigation grade sensor. The concept is that systematically, a sufficient number of MEMS sensors may mathematically provide comparable performance to a single navigation grade device and be competitive in terms power and mass allocations when viewed on a systems level. The implication is that both inertial navigation system design and fault detection, identification, and recovery could benefit from a system of MEMS devices in the same way that swarm sensing has benefited Earth observation and astronomy. A survey of the state of the art in inertial sensor accuracy scaled by mass and power will be provided to show the specific error in MEMS and navigation graded devices, a mathematical comparison of multi-unit to single-unit sensor errors will be developed, and preliminary applications to Constellation vehicles will be explored.

Crain, Timothy↗

NASA NTRS2009

Improved Method of Design for Folding Inflatable Shells

An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One particularly difficult problem is that of mathematically defining fold lines on a gore pattern in a double- curvature region. Moreover, because the fold lines in a double-curvature region tend to be curved, there is a practical problem of how to implement the folds. Another problem is that of modifying the basic gore shapes and sizes for the various layers so that when they are folded as part of the integral structure, they do not mechanically interfere with each other at the fold lines. Heretofore, it has been a common practice to design an inflatable shell to be assembled in the deployed configuration, without regard for the need to fold it into compact form. Typically, the result has been that folding has been a difficult, time-consuming process resulting in a An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One particularly difficult problem is that of mathematically defining fold lines on a gore pattern in a double- curvature region. Moreover, because the fold lines in a double-curvature region tend to be curved, there is a practical problem of how to implement the folds. Another problem is that of modifying the basic gore shapes and sizes for the various layers so that when they are folded as part of the integral structure, they do not mechanically interfere with each other at the fold lines. Heretofore, it has been a common practice to design an inflatable shell to be assembled in the deployed configuration, without regard for the need to fold it into compact form. Typically, the result has been that folding has been a difficult, time-consuming process resulting in a

Johnson, Christopher J.↗

NASA NTRS2009

System and method for deriving a process-based specification

A system and method for deriving a process-based specification for a system is disclosed. The process-based specification is mathematically inferred from a trace-based specification. The trace-based specification is derived from a non-empty set of traces or natural language scenarios. The process-based specification is mathematically equivalent to the trace-based specification. Code is generated, if applicable, from the process-based specification. A process, or phases of a process, using the features disclosed can be reversed and repeated to allow for an interactive development and modification of legacy systems. The process is applicable to any class of system, including, but not limited to, biological and physical systems, electrical and electro-mechanical systems in addition to software, hardware and hybrid hardware-software systems.

Hinchey, Michael Gerard↗

NASA NTRS2010

Turbulence and the Stabilization Principle

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Zak, Michail↗

NASA NTRS2010

Shifting the Intertial Navigation Paradigm with the MEMS Technology

"Why don't you use MEMS?" is of the most common questions posed to navigation systems engineers designing inertial navigation solutions in the modern era. The question stems from a general understanding that great strides have been made in terrestrial MEMS accelerometers and attitude rate sensors in terms of accuracy, mass, and power. Yet, when compared on a unit-to-unit basis, MEMS devices do not provide comparable performance (accuracy) to navigation grade sensors in several key metrics. This paper will propose a paradigm shift where the comparison in performance is between multiple MEMS devices and a single navigation grade sensor. The concept is that systematically, a sufficient number of MEMS sensors may mathematically provide comparable performance to a single navigation grade device and be competitive in terms power and mass allocations when viewed on a systems level. The implication is that both inertial navigation system design and fault detection, identification, and recovery could benefit from a system of MEMS devices in the same way that swarm sensing has benefited Earth observation and astronomy. A survey of the state of the art in inertial sensor accuracy scaled by mass and power will be provided to show the scaled error in MEMS and navigation graded devices, a mathematical comparison of multi-unit to single-unit sensor errors will be developed, and preliminary application to an Orion lunar skip atmospheric entry trajectory will be explored.

Crain, Timothy P., II↗

NASA NTRS2007

Designing Rolling-Element Bearings

Bearing Analysis Tool (BAT) is a computer program for designing rolling-element bearings for cryogenic turbomachines. BAT provides a graphical user interface (GUI) that guides the entry of data to develop mathematical models of bearings. The GUI breaks model data into logical subsets that are entered through logic-driven input screens. The software generates a threedimensional graphical model of a bearing as the data are entered. Most dataentry errors become immediately obvious in the graphical model. BAT provides for storage of all the data on a shaft/bearing system, enabling the creation of a library of proven designs. Data from the library can be transferred to subsequent projects by use of simple cut-and-paste routines. BAT includes a library of temperature- dependent cryogenic bearing-material properties for use in the mathematical models. BAT implements algorithms that (1) enable the user to select combinations of design and/or operating-condition parameters, and then (2) automatically optimize the design by performing trade studies over all of the parameter combinations. This feature enables optimization over a large trade space in a fraction of the time taken when using prior bearingmodel software.

Moore, James D., Jr.↗

NASA NTRS2007

POD Model Reconstruction for Gray-Box Fault Detection

Proper orthogonal decomposition (POD) is the mathematical basis of a method of constructing low-order mathematical models for the "gray-box" fault-detection algorithm that is a component of a diagnostic system known as beacon-based exception analysis for multi-missions (BEAM). POD has been successfully applied in reducing computational complexity by generating simple models that can be used for control and simulation for complex systems such as fluid flows. In the present application to BEAM, POD brings the same benefits to automated diagnosis. BEAM is a method of real-time or offline, automated diagnosis of a complex dynamic system.The gray-box approach makes it possible to utilize incomplete or approximate knowledge of the dynamics of the system that one seeks to diagnose. In the gray-box approach, a deterministic model of the system is used to filter a time series of system sensor data to remove the deterministic components of the time series from further examination. What is left after the filtering operation is a time series of residual quantities that represent the unknown (or at least unmodeled) aspects of the behavior of the system. Stochastic modeling techniques are then applied to the residual time series. The procedure for detecting abnormal behavior of the system then becomes one of looking for statistical differences between the residual time series and the predictions of the stochastic model.

Park, Han↗

NASA NTRS2007

Noncoherent DTTLs for Symbol Synchronization

Noncoherent data-transition tracking loops (DTTLs) have been proposed for use as symbol synchronizers in digital communication receivers. [Communication- receiver subsystems that can perform their assigned functions in the absence of synchronization with the phases of their carrier signals ( carrier synchronization ) are denoted by the term noncoherent, while receiver subsystems that cannot function without carrier synchronization are said to be coherent. ] The proposal applies, more specifically, to receivers of binary phase-shift-keying (BPSK) signals generated by directly phase-modulating binary non-return-to-zero (NRZ) data streams onto carrier signals having known frequencies but unknown phases. The proposed noncoherent DTTLs would be modified versions of traditional DTTLs, which are coherent. The symbol-synchronization problem is essentially the problem of recovering symbol timing from a received signal. In the traditional, coherent approach to symbol synchronization, it is necessary to establish carrier synchronization in order to recover symbol timing. A traditional DTTL effects an iterative process in which it first generates an estimate of the carrier phase in the absence of symbol-synchronization information, then uses the carrier-phase estimate to obtain an estimate of the symbol-synchronization information, then feeds the symbol-synchronization estimate back to the carrier-phase-estimation subprocess. In a noncoherent symbol-synchronization process, there is no need for carrier synchronization and, hence, no need for iteration between carrier-synchronization and symbol- synchronization subprocesses. The proposed noncoherent symbolsynchronization process is justified theoretically by a mathematical derivation that starts from a maximum a posteriori (MAP) method of estimation of symbol timing utilized in traditional, coherent DTTLs. In that MAP method, one chooses the value of a variable of interest (in this case, the offset in the estimated symbol timing) that causes a likelihood function of symbol estimates over some number of symbol periods to assume a maximum value. In terms that are necessarily oversimplified to fit within the space available for this article, it can be said that the mathematical derivation involves a modified interpretation of the likelihood function that lends itself to noncoherent DTTLs. The proposal encompasses both linear and nonlinear noncoherent DTTLs. The performances of both have been computationally simulated; for comparison, the performances of linear and nonlinear coherent DTTLs have also been computationally simulated. The results of these simulations show that, among other things, the expected mean-square timing errors of coherent and noncoherent DTTLs are relatively insensitive to window width. The results also show that at high signal-to-noise ratios (SNRs), the performances of the noncoherent DTTLs approach those of their coherent counterparts at, while at low SNRs, the noncoherent DTTLs incur penalties of the order of 1.5 to 2 dB.

Simon, Marvin↗

NASA NTRS2010

Tuning Parameters in Heuristics by Using Design of Experiments Methods

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

Arin, Arif↗

NASA NTRS2010

Simulation of Propellant Loading System Senior Design Implement in Computer Algorithm

Propellant loading from the Storage Tank to the External Tank is one of the very important and time consuming pre-launch ground operations for the launch vehicle. The propellant loading system is a complex integrated system involving many physical components such as the storage tank filled with cryogenic fluid at a very low temperature, the long pipe line connecting the storage tank with the external tank, the external tank along with the flare stack, and vent systems for releasing the excess fuel. Some of the very important parameters useful for design purpose are the prediction of pre-chill time, loading time, amount of fuel lost, the maximum pressure rise etc. The physics involved for mathematical modeling is quite complex due to the fact the process is unsteady, there is phase change as some of the fuel changes from liquid to gas state, then conjugate heat transfer in the pipe walls as well as between solid-to-fluid region. The simulation is very tedious and time consuming too. So overall, this is a complex system and the objective of the work is student's involvement and work in the parametric study and optimization of numerical modeling towards the design of such system. The students have to first become familiar and understand the physical process, the related mathematics and the numerical algorithm. The work involves exploring (i) improved algorithm to make the transient simulation computationally effective (reduced CPU time) and (ii) Parametric study to evaluate design parameters by changing the operational conditions

Bandyopadhyay, Alak↗