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Hypersonic and supersonic angle of attack flow about asymmetric and axisymmetric blunt bodies based on time dependent finite difference theory and method of characteristics
A variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. The VAM yields the best fit to the data by minimizing an objective function S which is a measure of the lack of fit. The SASS data are described and the function S and the analysis procedure are defined. Analyses of a single ship report which are analogous to Green's functions are presented. The analysis procedure is tuned and its sensitivity is described using the QE II storm. The procedure is then applied to a case study of September 6, 1978, south of Japan.
A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.
A program for calculating a C-type mesh around airfoil like shapes is described. The Jameson/Caughey approach is used: a parabolic transformation coupled with a shearing transformation. The algebraic algorithm is capable of efficiently generating nearly orthogonal grids. A high degree of grid control is possible. The user may specify grid boundaries, number of grid lines, and location of (and spacing in) trailing edge and leading edge fine mesh areas. The capability of embedding fine mesh regions, for use with new adaptive grid techniques, is being developed. Grids generated by the program were used in Euler flow flow calculatons by W. Usab. Results superior to results calculated on previous O-type grids were obtained. Specifically, calculations converged faster using C-grids rather than 0-grids, total pressure loss spikes at the trailing edge of the airfoil were eliminated, and the Ni method converged with zero artificial smoothing for a subcritical case (resulting overall total pressure loss was then nearly zero). These improvements were attributed to higher grid orthogonality, especially at the trailing edge. The program itself is fairly straightforward. Roughly half of the 800 code lines are comment lines.
The backscattering coefficient from a slab of thin randomly oriented dielectric disks over a flat lossy ground is used to reconstruct the inclination angle and area distributions of the disks. The disks are employed to model a leafy agricultural crop, such as soybeans, in the L-band microwave region of the spectrum. The distorted Born approximation, along with a thin disk approximation, is used to obtain a relationship between the horizontal-like polarized backscattering coefficient and the joint probability density of disk inclination angle and disk radius. Assuming large skin depth reduces the relationship to a linear Fredholm integral equation of the first kind. Due to the ill-posed nature of this equation, a Phillips-Twomey regularization method with a second difference smoothing condition is used to find the inversion. Results are obtained in the presence of 1 and 10 percent noise for both leaf inclination angle and leaf radius densities.
A computer code for solving the Reynolds averaged full Navier-Stokes equations has been developed and applied using sheared H-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady state calculations. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications in less than 100 multigrid cycles on the finest mesh.
A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.
A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.
Measurements were taken of the roughness characteristics of ice accreted on NACA 0012 airfoils in the NASA Glenn Icing Research Tunnel (IRT). Tests were conducted with size scaled, using models with chords of 26.7, 53.3, and 80.0 cm, and with liquid-water content scaled, both according to previously-tested scaling methods. The width of the smooth zone which forms on either side of the leading edge of the airfoil and the diameter of the roughness elements are presented in non-dimensional form as functions of the accumulation parameter. The smooth-zone width was found to decrease with increasing accumulation parameter. The roughness-element diameter increased with accumulation parameter until a plateau was reached. This maximum diameter was about 0.06 times twice the model leading-edge radius. Neither smooth-zone width nor element diameter were affected by a change in freezing fraction from 0.2 to 0.4. Both roughness characteristics appeared to scale with model size and with liquid-water content.
The friction and wear performance of a Cu-4Al top foil coating has been investigated in Generation I foil air bearings. The copper alloy was applied by a novel deposition technique (ion diffusion) and the journal was coated with PS304, a plasma spray deposited high temperature composite solid lubricant coating. The ion diffusion coating process deposits a desirable smooth layer compared to other methods like cathodic arc deposition. The tribological performance of bearings with and without Cu-4Al foil coatings were evaluated through start-stop tests on an air bearing test rig at 25 and 650 C. The results indicate that the Cu-4Al assists during the initial break-in period, gives more stable friction performance with respect to temperature, and appears to prevent top foil wear at high temperature. The measured load capacity coefficient was 0.5, which was comparable to earlier testing of more advanced design Generation III bearings coated with standard cathodic arc deposited Cu-4Al. However, further studies are needed to determine if deeper penetration of the copper alloy into the foil would help make the transition in friction behavior from contact with the Cu-4Al coated foil to contact with the base foil material more gradual. Also, future work is recommended to assess the performance of ion diffusion coatings with different Cu-based alloy compositions and to investigate the effect the coating has on the elastic modulus of the foil material.
Multi-Mission Earth Entry Vehicles (MMEEVs) are blunt-body vehicles designed with the purpose of transporting payloads from outer space to the surface of the Earth. To achieve high-reliability and minimum weight, MMEEVs avoid use of limited-reliability systems, such as parachutes and retro-rockets, instead using built-in impact attenuators to absorb energy remaining at impact to meet landing loads requirements. The Multi-Mission Systems Analysis for Planetary Entry (M-SAPE) parametric design tool is used to facilitate the design of MMEEVs and develop the trade space. Testing was conducted to characterize the material properties of several candidate impact foam attenuators to enhance M-SAPE analysis. In the current effort, four different Rohacell foams are tested at three different, uniform, strain rates (approximately 0.17, approximately 100, approximately 13,600%/s). The primary data analysis method uses a global data smoothing technique in the frequency domain to remove noise and system natural frequencies. The results from the data indicate that the filter and smoothing technique are successful in identifying the foam crush event and removing aberrations. The effect of strain rate increases with increasing foam density. The 71-WF-HT foam may support Mars Sample Return requirements. Several recommendations to improve the drop tower test technique are identified.
A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.
Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.
Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.
A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.
Tractions that cells exert on their substrates are essential in cell spreading, migration, and contraction. These tractions can be determined by plating the cells on a flexible gel and measuring the deformation of the gel by using fluorescent beads embedded just below the surface of the gel. In this article we describe the image correlation method (ICM) optimized for determining the displacement field of the gel under a contracting cell. For the calculation of the traction field from the displacement field we use the recently developed method of Fourier transform traction cytometry (FTTC). The ICM and FTTC methods are applied to human airway smooth muscle cells during stimulation with the contractile agonist histamine or the relaxing agonist isoproterenol. The overall intensity of the cell contraction (the median traction magnitude, the energy transferred from the cell to the gel, and the net contractile moment) increased after activation with histamine, and decreased after treatment with isoproterenol. Cells exhibited regional differences in the time course of traction during the treatment. Both temporal evolution and magnitude of traction increase induced by histamine varied markedly among different cell protrusions, whereas the nuclear region showed the smallest response. These results suggest that intracellular mediators of cell adhesion and contraction respond to contractile stimuli with different rates and intensities in different regions of the cell.