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At least 1,135 records · Page 63

Computerized reduction of elementary reaction sets for combustion modeling

If the entire set of elementary reactions is to be solved in the modeling of chemistry in computational fluid dynamics, a set of stiff ordinary differential equations must be integrated. Some of the reactions take place at very high rates, requiring short time steps, while others take place more slowly and make little progress in the short time step integration. The goal is to develop a procedure to automatically obtain sets of finite rate equations, consistent with a partial equilibrium assumptions, from an elementary set appropriate to local conditions. The possibility of computerized reaction reduction was demonstrated. However, the ability to use the reduced reaction set depends on the ability of the CFD approach in incorporate partial equilibrium calculations into the computer code. Therefore, the results should be tested on a code with partial equilibrium capability.

Wikstrom, Carl V.↗

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

Chang, F.-C.↗

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗

Simulation of Oxygen Disintegration and Mixing With Hydrogen or Helium at Supercritical Pressure

The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.

Bellan, Josette↗

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Moin, P.↗

The stability of motion of satellites with cavities partially filled with liquid

The stability and time dependent motion of a spinning satellite, simulated by a rigid body with a cavity partially filled with liquid is examined. The problem formulation, consisting of the boundary-value problem for the liquid and moment equations for the entire system is presented. Because of large Reynold's numbers involved, viscosity effects are negligible everywhere except for a thin boundary layer near the wetted surface. Using a boundary-layer analysis, the effect of the boundary layer is replaced by modified boundary conditions for the liquid. The solution of the differential equations for the inviscid problem is solved in closed form. A semi-analytical numerical solution of the inviscid equations subject to the viscous boundary condition has proved unsucessful.

Nayfeh, A. H.↗

Template Matching Approach to Signal Prediction

A new approach to signal prediction and prognostic assessment of spacecraft health resolves an inherent difficulty in fusing sensor data with simulated data. This technique builds upon previous work that demonstrated the importance of physics-based transient models to accurate prediction of signal dynamics and system performance. While models can greatly improve predictive accuracy, they are difficult to apply in general because of variations in model type, accuracy, or intended purpose. However, virtually any flight project will have at least some modeling capability at its disposal, whether a full-blown simulation, partial physics models, dynamic look-up tables, a brassboard analogue system, or simple hand-driven calculation by a team of experts. Many models can be used to develop a predict, or an estimate of the next day s or next cycle s behavior, which is typically used for planning purposes. The fidelity of a predict varies from one project to another, depending on the complexity of the simulation (i.e. linearized or full differential equations) and the level of detail in anticipated system operation, but typically any predict cannot be adapted to changing conditions or adjusted spacecraft command execution. Applying a predict blindly, without adapting the predict to current conditions, produces mixed results at best, primarily due to mismatches between assumed execution of spacecraft activities and actual times of execution. This results in the predict becoming useless during periods of complicated behavior, exactly when the predict would be most valuable. Each spacecraft operation tends to show up as a transient in the data, and if the transients are misaligned, using the predict can actually harm forecasting performance. To address this problem, the approach here expresses the predict in terms of a baseline function superposed with one or more transient functions. These transients serve as signal templates, which can be relocated in time and space against the signal background. One then has the ability to reconstruct a signal regardless of the precise timing of the transients. During operation, one applies the actual start times of spacecraft activities as they occur, and produces a reconstructed, accurate predict in real-time. This general approach is valid under two important conditions. First, the transients themselves must be time-invariant. Second, the transients must be reasonably consistent with respect to different operating points. Both of these assumptions are generally valid, but in the case of a complicated system with numerous types of overlapping transients, this approach may not be effective. Fortunately, there tend to be few transients in spacecraft telemetry of sensor quantities or low-level health and status information because these signals rarely reflect multiple different types of operation. Furthermore, if the predict is at least reasonably close to actual operation, the shift either in time, or in the operating point when the transient occurs - is likely to be small. The proposed approach considers three ways to recognize a transient. The first and most reliable is to use a different signal that identifies operating mode - often the transient will be correlated to a change in operating mode, and this change can usually be detected positively from discrete signals in spacecraft telemetry. If there is no useful mode signal, the second option is to identify the transient template by hand, and detect the onset of the transient using a curve-fitting approach. Finally, if one elects not to choose by hand, there is an option for automatic selection. This technique has been applied to sensor data from several JPL missions and industrial applications, demonstrating an improvement in accurate prediction of future behavior and early detection of system problems. This technique is applicable to practically any time-varying, quantitative sensor measurement.

Mackey, Ryan↗

Development of MCAERO wing design panel method with interactive graphics module

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Hawk, J. D.↗

Towards sub-optimal stochastic control of partially observable stochastic systems

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

Ruzicka, G. J.↗

Fluid System Stability Analysis Techniques

Fluid systems, or networks, consist of multiple components that work together to achieve some desired thermofluid state. For any generic application, this fluid state can be a combination of the fluid pressure, flow rate, enthalpy, or species concentration. Fluid system components, such as pumps and valves, are often governed by nonlinear differential equations, resulting in complex component-to-component interactions. System-level fluid network stability occurs when the flow through the system can maintain a steady-state solution in the presence of small perturbations, which depends on these component interactions. System instability, however, can go undetected until issues arise during integrated system testing. This presentation explores a method for system designers to think of the fluid network as an assembly of components, each with their own thermofluid surfaces of partial stability, called nullclines. The intersections of all nullclines yields system-level solutions, called equilibrium points. When designers define operating points, they are tuning system parameters so that these equilibrium points move to the desired location in the thermofluid state plane. However, linearization theory shows us that the dynamic behavior around these points can be unstable. The local stability of these equilibrium points can be assessed analytically with eigen-analysis, or numerically by propagating state-plane samples to construct a phase portrait. Investigating a phase portrait can help designers gain a qualitative understanding of a system’s dynamic performance. This understanding can then help inform requirement definitions, component selection, and operational procedures. This presentation includes an example of the phase portrait technique on a system featuring a centrifugal pump and a back-pressure regulator (BPR). Numerical modeling of this system suggests that equilibrium points on the left-hand side of the pump curve are dynamically unstable.

Fluid System↗

Fluid System Stability Analysis Techniques

Fluid systems, or networks, consist of multiple components that work together to achieve some desired thermofluid state. For any generic application, this fluid state can be a combination of the fluid pressure, flow rate, enthalpy, or species concentration. Fluid system components, such as pumps and valves, are often governed by nonlinear differential equations, resulting in complex component-to-component interactions. System-level fluid network stability occurs when the flow through the system can maintain a steady-state solution in the presence of small perturbations, which depends on these component interactions. System instability, however, can go undetected until issues arise during integrated system testing. This presentation explores a method for system designers to think of the fluid network as an assembly of components, each with their own thermofluid surfaces of partial stability, called nullclines. The intersections of all nullclines yields system-level solutions, called equilibrium points. When designers define operating points, they are tuning system parameters so that these equilibrium points move to the desired location in the thermofluid state plane. However, linearization theory shows us that the dynamic behavior around these points can be unstable. The local stability of these equilibrium points can be assessed analytically with eigen-analysis, or numerically by propagating state-plane samples to construct a phase portrait. Investigating a phase portrait can help designers gain a qualitative understanding of a system’s dynamic performance. This understanding can then help inform requirement definitions, component selection, and operational procedures. This presentation includes an example of the phase portrait technique on a system featuring a centrifugal pump and a back-pressure regulator (BPR). Numerical modeling of this system suggests that equilibrium points on the left-hand side of the pump curve are dynamically unstable.

Fluid System↗

Towards sub-optimal stochastic control of partially observable stochastic systems

The paper deals with a class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in n dimensions is proved.

Ruzicka, G. J.↗

Chromospheric models for Altair (A7 IV-V)

The star, Altair (A7 IV-V), is clearly shown to have Lyman-alpha emission of chromospheric origin, while no evidence is found for the Mg II emission reported in previous investigations. We present non-Local Thermodymanic Equilibrium (non-LTE) semiempirical models incorporating partial redistribution of the chromosphere of Altair that reproduce the observed Lyman-alpha emission and the Mg II resonance absorption at 2800 A. We unambiguously establihed that chromospheres exist at spectral types as early as A7 on the main sequence, and we also demonstrate that it very unlikely that the observed emission originates in a corotating expanding wind. This result represents a new challenge for chromospheric heating theories. It may indicate that both differential rotation and convection layers, at least near the equator, exist in this fast rotating (v sin i = 220 km/s) star.

Ferrero, R. Freire↗

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗

Origin, evolution and present thermal state of the moon

The relative absence of lunar volcanism in the last 3 b.y. and the Apollo 15 heat flow measurement suggest that present-day temperatures in the moon are approximately steady state to depths of 100 km. An exponential distribution of heat sources with depth is scaled by equating the surface heat flow to the integrated heat production of this exterior shell. Presumed present-day interior temperatures and the present-day surface heat flow of 30 ergs/cm2-sec are obtained. The estimated homogeneous concentrations of U, the chemistry of the lunar surface material and inferences to modest depth, and the short accretion time of the moon necessary to provide large-scale differentiation at 4.6 AE suggest that the moon had its origin in the rapid accretion of compounds first condensing from the protoplanetary nebula. The present thermal state of the moon may involve at least some partial melting through all the lunar interior deeper than 200 km. Such a thermal configuration is inconsistent neither with temperatures inferred from electrical conductivity studies nor with the nonhydrostatic shape of the moon.

Hanks, T. C.↗

Diffusion effects on the helium abundance of the solar transition region and corona

The diffusion of helium in the solar transition region is studied by solving the mass and momentum conservation equations for a hydrogen-helium plasma given a representative temperature profile. Steady state solutions show that two distinct atmospheres may result. In cases where the thermal force on alpha-particles is balanced by the partial pressure gradient force, helium is the dominant coronal species. On the other hand, if it is the frictional force between protons and alpha-particles which balances the thermal force on alpha-particles then hydrogen is the major coronal component. In order to explore which of these solutions are attainable within reasonable time scales, the time-dependent equations are solved, starting from an initial state with a uniform helium abundance of 10 percent. The atmosphere as a whole is close to hydrostatic equilibrium, but due the thermal forces the individual elements are not. This force inbalance leads to a differential flow between species. It is found that this differential flow leads to a significant enhancement of the coronal helium abundance. Even for the relatively shallow temperature gradient used the helium abundance in the lower corona increases to 30 percent over a 24 hr period.

Hansteen, Viggo H.↗

Generalized Functions for the Fractional Calculus

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Lorenzo, Carl F.↗