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NASA NTRS1995

A test of a vortex method for the computation of flap side edge noise

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

Martin, James E.↗
NASA NTRS1995

Standard Methods for Bolt-Bearing Testing of Textile Composites

The response of three 2-D braided materials to bolt bearing loading was evaluated using data generated by Boeing Defense and Space Group in Philadelphia, PA. Three test methods, stabilized single shear, unstabilized single shear, and double shear, were compared. In general, these textile composites were found to be sensitive to bolt bearing test methods. The stabilized single shear method yielded higher strengths than the unstabilized single shear method in all cases. The double shear test method always produced the highest strengths but these results may be somewhat misleading. It is therefore recommended that standard material comparisons be made using the stabilized single shear test method. The effects of two geometric parameters, W/D and e/D, were also studied. An evaluation of the effect of the specimen width (W) to hole diameter (D) ratio concluded that bolt bearing responses were consistent with open hole tension results. A W/D ratio of 6 or greater should be maintained. The proximity of the hole to the specimen edge significantly affected strength. In all cases, strength was improved by increasing the ratio of the distance from the hole center to the specimen edge (e) to the hole diameter (D) above 2. An e/D ratio of 3 or greater is recommended.

Portanova, M. A.↗
NASA NTRS1996

Artificial Boundary Conditions Based on the Difference Potentials Method

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Tsynkov, Semyon V.↗
NASA NTRS1996

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

Ku, Hwar-Ching↗
NASA NTRS1996

Krylov Subspace and Multigrid Methods Applied to the Incompressible Navier-Stokes Equations

We consider numerical solution methods for the incompressible Navier-Stokes equations discretized by a finite volume method on staggered grids in general coordinates. We use Krylov subspace and multigrid methods as well as their combinations. Numerical experiments are carried out on a scalar and a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of GCR and multigrid methods.

Vuik, C.↗
NASA NTRS1997

Estimation of Slow Crack Growth Parameters for Constant Stress-Rate Test Data of Advanced Ceramics and Glass by the Individual Data and Arithmetic Mean Methods

The two estimation methods, individual data and arithmetic mean methods, were used to determine the slow crack growth (SCG) parameters (n and D) of advanced ceramics and glass from a large number of room- and elevated-temperature constant stress-rate ('dynamic fatigue') test data. For ceramic materials with Weibull modulus greater than 10, the difference in the SCG parameters between the two estimation methods was negligible; whereas, for glass specimens exhibiting Weibull modulus of about 3, the difference was amplified, resulting in a maximum difference of 16 and 13 %, respectively, in n and D. Of the two SCG parameters, the parameter n was more sensitive to the estimation method than the other. The coefficient of variation in n was found to be somewhat greater in the individual data method than in the arithmetic mean method.

Choi, Sung R.↗
NASA NTRS1996

A General Interface Method for Aeroelastic Analysis of Aircraft

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Tzong, T.↗
NASA NTRS1998

Interfacing with Legacy using Remote Method Invocation

The assignment described was enough to make a neophyte Java developer bolt for the door: provide a remote method for use by an applet which invokes a native method that wraps a function in an existing legacy library. The purpose of the remote method is to return an instance of a class object whose contents reflect the data structure returned by the legacy function. While embroiled in implementation, I would have spent the time wading through their JNI use group archive as well, but I couldn't seem to locate one. Subsequently, I made the decision to try to document my findings in order to assist others. Before we start on the class design, let's look at what the existing legacy code does. The C function to be called, Get-Legacy-Data, consists of two steps: an ASII file is read from the local disk and its contents are parsed into a Legacy_Type structure whose address is passed as an argument by the caller. The legacy code was compiled into a shared object library, legacy. so, using the IRIX 6.2 compiler and then loaded onto the Web server, a Silicon Graphics Indy station loaded with the IRIX 6.4 operating system. As far as the class design is concerned, the first thing required is a class to act as a template for the data structure returned by the legacy function. This class, JLegacy, declares a series of public instance variables which correspond to the members of Legacy_Type and provides a parameterless constructor. This constructor is never called, not even by the native method which allocates the object for return to the remote method. Next, the remote interface declaration for the remote object must be defined. In order for JLegacyRO to implement getJLegacy, JLegacyRO must interface with the existing legacy code through a native method, getn. getn is declared in the JLegacyRO class but implemented in C, just like the legacy code. getn returns a JLegacy instance and is declared static since its implementation is the same for all instances of the JLegacyRO class.

Howard, Scott M.↗
NASA NTRS1997

A Modified Linear-Mixing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures

The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit. When multiple scattering is significant, the method reproduces the atmospheric path radiance of the mixture with less than 3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter epsilon = (Sigma)f(sub i) absolute value of bar omega(sub i) - bar omega(sub mix)/bar omega(sub i), is larger than approx. 0.1, where bar omega(sub i) and f(sub i) are the single-scattering albedo and the fractional abundance of the i th component, and bar omega(sub i) is the effective single-scattering albedo of the mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when epsilon = 0.0 and give similar results when epsilon less than or equal to 0.05. For optical depths larger than approx. 0.5, or when epsilon greater than 0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998.

Abdou, W. A.↗
NASA NTRS1997

A Modified Linear-Mixing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures

The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit. When multiple scattering is significant, the method reproduces the atmospheric path radiance of the mixture with less than 3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter e = the sum of f(sub i)[(bar)omega(sub i) - (bar)omega(sub mix)]/(bar)omega(sub i) is larger than approximately 0.1, where (bar)omega(sub i)and f(sub i) are the single-scattering albedo and the fractional abundance of the ith component, and (bar)omega(sub mix) is the effective single-scattering albedo of the Mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when epsilon = 0.0 and give similar results when epsilon is less than or equal to 0.05. For optical depths larger than approximately 0.5, or when epsilon is greater than 0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998.

Abdou, W. A.↗
NASA NTRS1999

Structural Embeddings: Mechanization with Method

The most powerful tools for analysis of formal specifications are general-purpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a well-developed method generally have less powerful automation. It is natural, therefore, to try to combine the better-developed methods with the more powerful general-purpose tools. An obstacle is that the methods and the tools often employ very different logics. We argue that methods are separable from their logics and are largely concerned with the structure and organization of specifications. We, propose a technique called structural embedding that allows the structural elements of a method to be supported by a general-purpose tool, while substituting the logic of the tool for that of the method. We have found this technique quite effective and we provide some examples of its application. We also suggest how general-purpose systems could be restructured to support this activity better.

Munoz, Cesar↗
NASA NTRS1996

The Newton Modified Barrier Method for QP Problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.

Melman, A.↗
NASA NTRS2000

A Bridge Health Monitoring Method Using the Hilbert-Huang Transform: A Case Study

We have developed a new method for nondestructive instrument method to monitor the health of a bridge. This new method is based on a transient test load and simple data collection. The nuclear of the method is the new invented nonstationary and nonlinear time series analysis method, the Empirical Mode Decomposition and Hilbert Spectral Analysis. The final decision on the health of the bridge structure is based on the nonlinear characteristic of the data, and on the comparison between the free and the forced vibration frequencies. Thus this alternative method enjoys many advantages: (1) no a priori data required, (2) simple data collection, and (3) minimum traffic disruption. Results from a case study of the Shing-Nan Bridge in Hou-Wei will be reported.

Huang, Norden E.↗
NASA NTRS2000

Microencapsulation and Electrostatic Processing Method

Methods are provided for forming spherical multilamellar microcapsules having alternating hydrophilic and hydrophobic liquid layers, surrounded by flexible, semi-permeable hydrophobic or hydrophilic outer membranes which can be tailored specifically to control the diffusion rate. The methods of the invention rely on low shear mixing and liquid-liquid diffusion process and are particularly well suited for forming microcapsules containing both hydrophilic and hydrophobic drugs. These methods can be carried out in the absence of gravity and do not rely on density-driven phase separation, mechanical mixing or solvent evaporation phases. The methods include the process of forming, washing and filtering microcapsules. In addition, the methods contemplate coating microcapsules with ancillary coatings using an electrostatic field and free fluid electrophoresis of the microcapsules. The microcapsules produced by such methods are particularly useful in the delivery of pharmaceutical compositions.

Morrison, Dennis R.↗
NASA NTRS2000

Alternative Methods of the Thermospheric Atomic Oxygen Density Determination

Atomic oxygen density in the upper thermosphere (approximately 300 km) can be calculated using ground based incoherent scatter radar and Fabry-Perot interferometer measurements. Burnside et al. [1991] was the first to try this method, but Buonsanto et al. provided an extensive treatment of the method in 1997. This paper further examines the method using 46 nights of data collected over six years and the latest information on the oxygen collision frequency. The method is compared with the MSIS-86 atomic oxygen prediction values, which are based upon in situ rocket born and satellite measurements from the 70's to the mid-80's In general, the method supports the MSIS-86 model, but indicates several areas of discrepancy. Furthermore, no direct correlation is found between the geomagnetic conditions and the difference between the method and MSIS-86 predictions.

Bennett. Adam C.↗
NASA NTRS2000

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗
NASA NTRS2001

Alternative Method for the Thermospheric Atomic Oxygen Density Determination

Atomic oxygen density in the upper thermosphere (approximately 300 km) can be calculated using ground based incoherent scatter radar and Fabry-Perot interferometer measurements. Burnside et al. was the first to try this method, but Buonsanto et al. provided an extensive treatment of the method in 1997. This paper further examines the method using 46 nights of data collected over six years and the latest information on the oxygen collision frequency. The method is compared with the MSIS (Mass Spectrometer Incoherent Scatter)-86 atomic oxygen prediction values, which are based upon in situ rocket born and satellite measurements from the 70s to the mid-80s. In general, the method supports the MSIS-86 model, but indicates several areas of discrepancy. Furthermore, no direct correlation is found between the geomagnetic conditions and the difference between the method and MSIS-86 predictions.

Bennett, A. C.↗
NASA NTRS2001

A New Method to Cross Calibrate and Validate TOMS, SBUV/2, and SCIAMACHY Measurements

A unique method to validate back scattered ultraviolet (buv) type satellite data that complements the measurements from existing ground networks is proposed. The method involves comparing the zenith sky radiance measurements from the ground to the nadir radiance measurements taken from space. Since the measurements are compared directly, the proposed method is superior to any other method that involves comparing derived products (for example, ozone), because comparison of derived products involve inversion algorithms which are susceptible to several type of errors. Forward radiative transfer (RT) calculations show that for an aerosol free atmosphere, the ground-based zenith sky radiance measurement and the satellite nadir radiance measurements can be predicted with an accuracy of better than 1 percent. The RT computations also show that for certain values of the solar zenith angles, the radiance comparisons could be better than half a percent. This accuracy is practically independent of ozone amount and aerosols in the atmosphere. Experiences with the Shuttle Solar Backscatter Ultraviolet (SSBUV) program show that the accuracy of the ground-based zenith sky radiance measuring instrument can be maintained at a level of a few tenth of a percent. This implies that the zenith sky radiance measurements can be used to validate Total Ozone Mapping Spectrometer (TOMS), Solar Backscatter Ultraviolet (SBUV/2), and The SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) radiance data. Also, this method will help improve the long term precision of the measurements for better trend detection and the accuracy of other BUV products such as tropospheric ozone and aerosols. Finally, in the long term, this method is a good candidate to inter-calibrate and validate long term observations of upcoming operational instruments such as Global Ozone Monitoring Experiment (GOME-2), Ozone Mapping Instrument (OMI), Ozone Dynamics Ultraviolet Spectrometer (ODUS), and Ozone Mapping and Profiler Suite (OMPS).

Ahmad, Ziauddin↗