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The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.
The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.
A computer program was developed to account approximately for the effects of finite wing thickness in transonic potential flow over an oscillation wing of finite span. The program is based on the original sonic box computer program for planar wing which was extended to account for the effect of wing thickness. Computational efficiency and accuracy were improved and swept trailing edges were accounted for. Account for the nonuniform flow caused by finite thickness was made by application of the local linearization concept with appropriate coordinate transformation. A brief description of each computer routine and the applications of cubic spline and spline surface data fitting techniques used in the program are given, and the method of input was shown in detail. Sample calculations as well as a complete listing of the computer program listing are presented.
A computer program was developed to account approximately for the effects of finite wing thickness in the transonic potential flow over an oscillating wing of finite span. The program is based on the original sonic-box program for planar wing which was previously extended to include the effects of the swept trailing edge and the thickness of the wing. Account for the nonuniform flow caused by finite thickness is made by application of the local linearization concept. The thickness effect, expressed in terms of the local Mach number, is included in the basic solution to replace the coordinate transformation method used in the earlier work. Calculations were made for a delta wing and a rectangular wing performing plunge and pitch oscillations, and the results were compared with those obtained from other methods. An input quide and a complete listing of the computer code are presented.
It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.
Coast down tests were performed on a box shaped ground vehicle used to simulate the aerodynamic drag of high volume transports such as delivery vans, motor homes and trucks. The results of these tests define the reduction in aerodynamic drag that can be obtained by the addition of either a boattail or a truncated boattail to an otherwise blunt based vehicle. Test velocities ranged up to 96.6 km/h (60 mph) with Reynolds numbers to 1.3 x 10 the 7th power. The full boattail provided an average 32 percent reduction in drag at highway speeds whereas the truncated boattail provided an average 31 percent reduction in drag as compared to the configuration having the blunt base. These results are compared with one tenth scale wind tunnel model data.
The black box multigrid (BOXMG) code, which only needs specification of the matrix problem for application in the multigrid method was investigated. It is contended that a major problem with the multigrid method is that each new grid configuration requires a major programming effort to develop a code that specifically handles that grid configuration. The SOR and ICCG methods only specify the matrix problem, no matter what the grid configuration. It is concluded that the BOXMG does everything else necessary to set up the auxiliary coarser problems to achieve a multigrid solution.
The development and applications of a box truss design for large space antennas are discussed. A kinematic model with a mesh reflector was constructed. A prototype cube is described. Details of fabrication are given.
A study of display configurations and their effect on pilot-aircraft system response was undertaken. An examination of conventional displays was done to provide a set of data that can be used for comparison with advanced displays. An examination of an advanced display design that includes the use of a digital computer and a cathode ray tube to provide a drawing of a three dimensional box is done. The results show the improvement in system performance that can be obtained with the advanced display. Studies were conducted using the General Aviation Simulator, but verification of the results with the advanced display was also obtained from flight tests.
A fast computer code COSAL for transition prediction in three dimensional boundary layers using compressible stability analysis is described. The compressible stability eigenvalue problem is solved using a finite difference method, and the code is a black box in the sense that no guess of the eigenvalue is required from the user. Several optimization procedures were incorporated into COSAL to calculate integrated growth rates (N factor) for transition correlation for swept and tapered laminar flow control wings using the well known e to the Nth power method. A user's guide to the program is provided.
Simple photoelastic models were used to identify a cross-section geometry that would eliminate the severe stress concentrations at the bond line between box stiffeners diffusion bonded to a panel skin. Experimental fatigue-test data from titanium test specimens quantified the allowable stress in terms of cycle life for various joint geometries. It is shown that the effect of stress concentration is reduced and an acceptable fatigue life is achieved.
A study of electron propagation using the leaky box model is discussed. It is shown that a truncated pathlength distribution due to a lack of nearby sources is responsible for the steepening of the electron spectrum. The electron spectrum is broken into three regions: a low-energy region where electron storage is dominated by escape, a medium energy region in which the electron energy loss lifetime is sufficiently short to dominate propagation, but not so short as to prevent electrons from propagating throughout the storage region, and a third energy region in which the energy loss lifetime is shorter than the time it takes for cosmic rays to diffuse to earth from the nearest source. The asymptotic slope of the electron spectrum is shown to be steeper than that of the injection spectrum by more than one power of energy.
A parametric analysis was performed in order to define the slewing capability of the Earth Observation Spacecraft (EOS) box-truss antenna. The input data for the analysis consisted of the slew rate, settling time, damping, maneuver frequencies, and attitude hold times of the antenna. The dynamic transient response of the antenna was evaluated, and the results are compared with NASA operational requirements. The results of the parametric analysis are summarized in a series of tables.
Mass and strength analyses and system requirements identified titanium-box-stiffened-skin wall candidate for lightweight fuselage of pressurized vehicle. Photoelastic models of stiffener-to-skin joint used to identify quickly modifications to joint that lowers severity of stress concentration. Results with various photoelastic models cut from polyurethane sheet led to novel diffusion-bond joint with reduced stress concentration.
A new equilvalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.
A wind-tunnel investigation has been conducted at Mach numbers of 1.50, 2.16, and 2.86 to obtain axial-force data on a metric rectangular-box cavity with various length-to-depth ratios. The model was tested at angles of attack from -4 deg to -2 deg. The results are summarized to show variations in cavity axial-force coefficient for deep- and shallow-cavity configurations with detached and attached cavity flow fields, respectively. The results of the investigation indicate that for a wide range of cavity lengths and depths, good correlations of the cavity axial-force coefficients (based on cavity rear-face area) are obtained when these coefficients are plotted as a function of cavity length-to-depth ratio. Abrupt increases in the cavity axial-force coefficients at an angle of attack of 0 deg. reflect the transition from an open (detached) cavity flow field to a closed (attached) cavity flow field. Cavity length-to-depth ratio is the dominant factor affecting the switching of the cavity flow field from one type to the other. The type of cavity flow field (open or closed) is not dependent on the test angles of attack except near the critical value of length-to-depth ratio.
The intent of the present experiment is to define a near optimum value of drag coefficient for a high volume type of vehicle through the use of a boattail, on a vehicle already having rounded front corners and an underbody seal, or fairing. The results of these tests will constitute a baseline for later follow-on studies to evaluate candidate methods of obtaining afterbody drag coefficients approaching the boattail values, but without resorting to such impractical afterbody extensions. The current modifications to the box-shaped vehicle consisted of a full and truncated boattail in conjunction with the faired and sealed underbody. Drag results from these configurations are compared with corresponding wind tunnel results of a 1/10 scale model. Test velocities ranged up to 96.6 km/h (60 mph) and the corresponding Reynolds numbers ranged up to 1.3 x 10 to the 7th power based on the vehicles length which includes the boattail. A simple coast-down technique was used to define drag.
A new equivalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.