Models of gas flows with chemical and radiative effects
Physical and mathematical models of gas flows with chemical and radiative effects
MATHEMATICAL MODEL↗
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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.
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Use of a New Analytical Model To Match Production Data and Identify Opportunities To Maximize Well Productivity in the Tuscaloosa Marine Shale Reservoir
The low productivity of the oil wells in the Tuscaloosa Marine Shale (TMS) Trend, located in Louisiana and Mississippi, is a mystery. Production data from 55 wells in the TMS Trend were analyzed to identify possible means of enhancing well productivity. The -1/2 slope in a log–log plot for reservoir linear flow (RLF) was observed for some wells, but not all, and the -1 slope for boundary–dominated flow (BDF) has not been seen in the past 5 years of production. The behavior of the TMS wells is attributed to the ultralow permeability of the TMS matrix and the decline of fracture conductivity, both of which delay the BDF. On the basis of the concept of the distance of investigation, derived from the radius–of–investigation concept, the matrix permeability of the seven TMS wells was estimated to be between 34 and 65 nd, with an average of 51 nd. A new mathematical model for production decline of multifractured horizontal wells was developed taking into consideration the time–dependent fracture conductivity during the BDF period. This model fits TMS–well production data, with an average error of 6.12% and an R2 value of 0.96. Assuming constant matrix permeability, fitting the new model to the production data in the BDF period gives a rate of fracture–conductivity decline of between 0.20 and 0.74% per month. The new mathematical model reveals opportunities to optimize well completion to enhance well productivity in the TMS Trend. For a given amount of fracture proppant allocated to a well, the shortest possible fracture spacing should be used to maximize well productivity. If the number of fractures is fixed as a constraint of well completion design, well productivity is inversely proportional to the square root of fracture spacing (i.e., if the fracture spacing is shortened by fourfold, well productivity is expected to double). If the horizontal wellbore length is fixed as a constraint of well completion, well productivity is inversely proportional to fracture spacing (i.e., if the fracture spacing is shortened by 50%, well productivity is expected to double).
Engineering↗
Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)
Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.
Snell, Edward↗
Construction and simulation of a novel continuous traffic flow model
In this paper, we aim to propose a novel mathematical model for traffic flow and apply a newly developed characteristic particle method to solve the associate governing equations. As compared with the existing non-equilibrium higher-order traffic flow models, the present one is put forward to satisfy the following three conditions: 1.Preserve the equilibrium state in the smooth region. 2.Yield an anisotropic propagation of traffic flow information. 3.Expressed with a conservation law form for traffic momentum. These conditions will ensure a more practical simulation in traffic flow physics: The current traffic will not be influenced by the condition in the behind and result in unambiguous condition across a traffic shock. Through analyses of characteristics, stability condition and steady-state solution adherent to the equation system, it is shown that the proposed model actually conform to these conditions. Furthermore, this model can be cast into its characteristic form which, incorporated with the Rankine-Hugoniot relation, is appropriate to be simulated by the characteristic particle method to obtain accurate computational results. - Highlights: • The traffic model expressed with the momentum conservation law. • Traffic flow information propagate anisotropically and preserve the equilibrium state in the smooth region. • Computational particles of two families are invented to mimic forward-running and backward-running characteristics. • Formation of shocks will be naturally detected by the intersection of computational particles of same family. • A newly developed characteristic particle method is used to simulate traffic flow model equations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2
The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm.
Adams, W. M., Jr.↗
Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading
The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.
Simitses, G. J.↗
Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading
The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.
Simitses, George J.↗
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.↗
Neutron Multiplicity Counting Moments for Fissile Mass Estimation in Scatter-Based Neutron Detection Systems
Neutron multiplicity counting (NMC) techniques are widely used for nuclear materials accountability and international safeguards applications to quantitatively evaluate characteristic properties pertaining to fissile material. Mathematical models for NMC moments have been previously derived for systems that use capture-based detectors; however, these models are not applicable when scatter-based detectors are used because of “neutron cross talk.” Neutron cross talk occurs when a single neutron scatters and deposits energy above threshold into multiple detectors causing spurious increase in multiplicity counts; this, in turn, has caused fissile mass to be overestimated when not treated. In this paper, we propose new mathematical models derived from point kinetics to correct for neutron cross-talk effects up to any arbitrary order N, where N denotes the maximum number of counts a single neutron can cause. The new models were used to estimate the fissile mass of plutonium metal and oxide samples with effective 240 Pu mass ranging from 2.5 to 250 g. The adequacy of the models was confirmed using simulations of a conceptual scatter-based neutron multiplicity counter (e.g., organic scintillators) using MCNPX v2.7e with the PoliMi fission event generating extension. The fissile mass estimates with no correction for neutron cross-talk events yielded an average relative deviation from the true 240 Pu eff mass of 55.94% and 84.56% for metal and oxide samples, respectively. When neutron cross-talk events of order N = 2 are included in the model, the fissile mass estimates yielded an average relative deviation of 11.89% for metal and 13.21% for oxide samples. Accounting for neutron cross-talk events of order N = 3 resulted in fissile mass estimates with an average relative deviation of 9.58% and 10.51% for metal and oxide samples, respectively. These mass estimates were compared to a reference case (i.e., no neutron crosstalk effects) that yielded an average relative deviation of 6.81% and 4.77% for metal and oxide samples, respectively. In conclusion, the discrepancy between the estimates from the proposed model and the reference case is attributed to the assumed value of N, which sets a finite upper bound on the order of cross-talk events the model treats (i.e., the model for N = 3 assumes that a neutron will never cause more than three counts).
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach
Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.
module↗
Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics
Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.
Lightweight and high resolution optics↗
Tone excited jets. V - A theoretical model and comparison with experiment
A mathematical model of tone-excited jets is developed which consists of two major components: a mathematical description of the process by which the intrinsic instability waves of the jet are excited by the upstream tones; and the modeling of the nonlinear interaction between the mean flow of the jet, the excited large-scale instability waves or turbulence structure, and the fine scale turbulence. It is assumed that each of these jet flow components can be characterized by a few parameters, which are then related by conservation equations that are supplemented by closure models. This quasi-linear model's results are compared with experimental measurements, and good agreement is obtained over a wide range of excitation frequencies and excitation levels.
Tam, C. K. W.↗
Compositional and temporal division of labor modulates mixed sugar fermentation by an engineered yeast consortium
Abstract Synthetic microbial communities have emerged as an attractive route for chemical bioprocessing. They are argued to be superior to single strains through microbial division of labor (DOL), but the exact mechanism by which DOL confers advantages remains unclear. Here, we utilize a synthetic Saccharomyces cerevisiae consortium along with mathematical modeling to achieve tunable mixed sugar fermentation to overcome the limitations of single-strain fermentation. The consortium involves two strains with each specializing in glucose or xylose utilization for ethanol production. By controlling initial community composition, DOL allows fine tuning of fermentation dynamics and product generation. By altering inoculation delay, DOL provides additional programmability to parallelly regulate fermentation characteristics and product yield. Mathematical models capture observed experimental findings and further offer guidance for subsequent fermentation optimization. This study demonstrates the functional potential of DOL in bioprocessing and provides insight into the rational design of engineered ecosystems for various applications.
59 BASIC BIOLOGICAL SCIENCES↗
Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading
This research is performed to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.
Simitses, G. J.↗
Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading
The objective of this research is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.
Simitses, G. J.↗
Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading
The objective is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.
Simitses, G. J.↗
Nonisothermal elasto-visco-plastic response of shell-type structures
A mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is disussed. Among the system responses, which are associated with these load conditions, are thermal buckling and creep buckling. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and have been considered in the development of the mathematical model. Furthermore, this was accommodated in the solution procedures. A complete true ab-inito rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformation, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of the metric and curvature in two coordinate systems, a fixed (spatial) one and a convected (material) coordinate system. The relations between the time derivative and the covariant derivatives (gradients) have been developed for curved space and motion, so that the velocity components supply the connection between the equations of motion and the time rate of change of the metric and curvature tensors.
Simitses, G. J.↗
Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading
A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads are developed. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratcheting. Thus, geometric as well as material type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.
Simitses, G. J.↗