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This file contains a compilation of BHT data from oil wells in southwestern New Mexico. Surface temperature is calculated using the collar elevation. An estimate of geothermal gradient is calculated using the estimated surface temperature and the uncorrected BHT data.
A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties
A method for the accurate calculation of the horizontal pressure gradient acceleration in hydrostatic atmospheric models is presented which is especially useful in situations where the isothermal surfaces are not parallel to the vertical coordinate surfaces. The present method is shown to be exact if the potential temperature lapse rate is constant between the vertical pressure integration limits. The technique is applied to both the integration of the hydrostatic equation and the computation of the slope correction term in the horizontal pressure gradient. A fixed vertical grid and a dynamic grid defined by the significant levels in the vertical temperature distribution are employed.
The viscous airfoil design analysis code XFOIL was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique used was the Steepest Descent method applied to a Penalty Function. The gradients of the aerodynamic variables with respect to the design variables were cheaply calculated as by-products of XFOIL's integral boundary layer Newton solver. The speed of the optimization process further increased by updating the Newton system boundary layer variables after each optimization step using the available gradient information. Two examples are presented.
Abstract not provided.
Gravity alters local blood pressure within the body so that arterial pressures in the head and foot are lower and higher, respectively, than that at heart level. Furthermore, vascular responses to local alterations of arterial pressure are probably important to maintain orthostatic tolerance upon return to the Earth after space flight. However, it has been difficult to evaluate the body's arterial pressure gradient due to the lack of noninvasive technology. This study was therefore designed to investigate whether finger arterial pressure (FAP), measured noninvasively, follows a normal hydrostatic pressure gradient above and below heart level during upright posture and 30 deg head down tilt (HDT). Seven healthy subjects gave informed consent and were 19 to 52 years old with a height range of 158 to 181 cm. A Finapres device measured arterial pressure at different levels of the body by moving the hand from 36 cm below heart level (BH) to 72 cm above heart level (AH) in upright posture and from 36 cm BH to 48 cm AH during HDT in increments of 12 cm. Mean FAP creased by 85 mmHg transitioning from BH to AH in upright posture, and the pressure gradient calculated from hydrostatic pressure difference (rho(gh)) was 84 mmHg. In HDT, mean FAP decreased by 65 mmHg from BH to AH, and the calculated pressure gradient was also 65 mmHg. There was no significant difference between the measured FAP gradient and the calculated pressure gradient, although a significant (p = 0.023) offset was seen for absolute arterial pressure in upright posture. These results indicate that arterial pressure at various levels can be obtained from the blood pressure at heart level by calculating rho(gh) + an offset. The offset equals the difference between heart level and the site of measurement. In summary, we conclude that local blood pressure gradients can be measured by noninvasive studies of FAP.
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
The development of high-speed volumetric laser-induced fluorescence measurements of formaldehyde (CH 2 O-LIF) using a pulse-burst laser operated at a repetition rate of 100 kHz is presented here. A novel laser scanning system employing an acousto-optic deflector (AOD) enables quasi-4D CH 2 O-LIF imaging at a scan frequency of 10 kHz. The diagnostic capability of time-resolved volumetric imaging is demonstrated in a partially premixed DME/air lifted turbulent jet flame near the flame base. Simultaneous imaging of laser beam profiles is performed to account for the laser pulse energy fluctuation and laser sheet inhomogeneity. With the accurate registration of laser sheet positions, the volumetric reconstruction of CH 2 O-LIF signals is performed within a detection volume of 17.3 × 11.9 × 2.3 mm 3 with an average out-of-plane spatial resolution of 250μm. A surface detection algorithm with adaptive thresholding is used to determine the global maximum intensity gradient by calculating gradient percentiles. The flame topology characteristics are investigated by evaluating the 3D curvatures of CH 2 O surfaces. Curvatures calculated using 2D data systematically underestimate the full 3D curvature due to the lack of out-of-plane information. The inner surfaces near the turbulent fuel jet exhibit higher probabilities of large mean curvature than the outer surfaces. The saddle and cylindrical structures are dominant on both the inner and outer surfaces and the elliptic structures occur with lower probability. The results suggest that the damping of turbulent fluctuations by the temperature increase through the CH 2 O region reduces the curvature, but the local structure topology remains self-similar.
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient technique for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is introduced. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of $O(N)$ , where $N$ is the number of parameters used to describe the outer flux surface or coil shapes.
The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Here, two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w = (0.298, 0.284, 0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β = (0.5, 0.7, 0.99), somewhat higher than the w = 0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w = 1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w = 0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.
This paper develops a method for updating the gradient vector of the limit state function in reliability analysis using Broyden's rank one updating technique. In problems that use commercial code as a black box, the gradient calculations are usually done using a finite difference approach, which becomes very expensive for large system models. The proposed method replaces the finite difference gradient calculations in a standard first order reliability method (FORM) with Broyden's Quasi-Newton technique. The resulting algorithm of Broyden updates within a FORM framework (BFORM) is used to run several example problems, and the results compared to standard FORM results. It is found that BFORM typically requires fewer functional evaluations that FORM to converge to the same answer.
The public release of WRF has two options for calculating horizontal gradients in the horizontal diffusion scheme. When the default option (diff_opt = 1) is used, horizontal gradients are calculated along coordinate surfaces, which roughly follow the terrain surface due to WRF’s terrain-conforming grid (i.e. along a sloping line in Fig. 1). Over steeply sloping terrain, horizontal gradients calculated in this way become inaccurate because they do not capture horizontal variation correctly. Therefore, another option exists (diff_opt = 2), for which Taylor series are used to approximate the derivative along a truly horizontal line. During WFIP2, HRRR forecasts switched from using diff_opt = 1 to diff_opt =2, and this was shown to improve velocity predictions, especially within observed cold pools (Olson et al., 2019).
Yamaguchi and Feingold (2012) note that the cloud fields in their Weather Research and Forecasting (WRF) large-eddy simulations (LESs) of marine stratocumulus exhibit a strong sensitivity to time stepping choices. In this study, we reproduce and analyze this sensitivity issue using two stratocumulus cases, one marine and one continental. Results show that (1) the sensitivity is associated with spurious motions near the moisture jump between the boundary layer and the free atmosphere, and (2) these spurious motions appear to arise from neglecting small variations in water vapor mixing ratio (qv) in the pressure gradient calculation in the acoustic substepping portion of the integration procedure. We show that this issue is remedied in the WRF dynamical core by replacing the prognostic equation for the potential temperature θ with one for the moist potential temperature θm=θ(1+1.61qv), which allows consistent treatment of moisture in the calculation of pressure during the acoustic substeps. With this modification, the spurious motions and the sensitivity to the time stepping settings (i.e., the dynamic time step length and number of acoustic substeps) are eliminated in both of the example stratocumulus cases. This modification improves the applicability of WRF for LES applications, and possibly other models using similar dynamical core formulations, and also permits the use of longer time steps than in the original code.
Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.
Horizontal mixing coefficients K(yy) and K(yz) were computed using potential vorticity and gradients calculated from NMC data for geopotential heights and temperatures. It was found that the mid-latitude to polar mixing coefficients depend on the use of nongeostrophic winds, which yield K(yy) values which are mostly positive, whereas geostophic winds yield K(yy) values which were largely negative near the polar region. A comparison of the K(yy) values calculated from the potential vorticity fluxes and gradients with the K(yy) values calculated using the momentum balance between the flux of potential vorticity and the residual circulation has shown that the residual-circulation-balanced K(yy) values in the upper stratosphere were much larger than the values calculated by the present method. It is suggested that this difference is the result of breaking gravity waves in the upper stratosphere and lower mesosphere.
Error analysis for respiratory index and oxygen gradient calculations
The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.
This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered-reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.