Two-dimensional, parabolic boundary value problems as the limiting case of one- dimensional boundary value problems
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Rothe, E.↗
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INPUTB: A thermal/structural data interface program for 2-dimensional and 3-dimensional interpolation
A computer program (INPUTB) for interpolation in both space and time, and based on a linear interpolation scheme using simplex spatial regions is described. The program was developed to provide data interfacing between the output from thermal analyzers and the input to the BOPACE 3-D program. The INPUTB interpolator is of a general nature and could be used for other tasks. The INPUTB program utilizes temperature values which are given at some sequence of time for a list of strategically located thermal nodes. It operates on these values by performing a double interpolation to provide temperature values at another desired sequence of times for a list of structural nodes.
Vos, R. G.↗
Experiments on the stability and transition of two-dimensional and three-dimensional boundary layers with suction
The preliminary experimental development work directed towards the understanding of transition in boundary layers with suction is presented. The basic stability experiment was established and the facility was certified.
Saric, W. S.↗
Interaction of a two-dimensional strip boundary layer with a three-dimensional transonic swept-wing code
A 3D inviscid transonic analysis code was combined with a 2D strip integral boundary layer technique to form an approximate interaction procedure for analyzing the flow over a high aspect ratio wing near cruise conditions. Converged results obtained using the procedure for an aspect ratio 10.3 supercritical wing are discussed. Angle of attack adjustments were made during the iterative procedure in order to compensate for the viscous lift loss. A comparison of the calculations with experimental data is presented.
Newman, P. A.↗
Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation
In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.
Ito, Kazufumi↗
Computation of three-dimensional effects on two dimensional wings
A 2-D numerical investigation was performed to determine the effect of a Gurney flap on a NACA 4412 airfoil. A Gurney flap is a flat plate on the order of 1 to 3 percent of the airfoil chord length, oriented perpendicular to the airfoil chord line and located at the trailing edge of the airfoil. An incompressible Navier Stokes code, INS2D, was used to calculate the flow field about the airfoil. The fully turbulent results were obtained using the Baldwin-Barth one-equation turbulence model. Gurney flap sizes of 0.5, 1, 1.25, 1.5, 2, and 3 percent of the airfoil chord were studied. Computational results were compared with experimental results where possible. The numerical solutions show that the Gurney flap increases airfoil lift coefficient with only a slight increase in drag coefficient. Use of a 1.5 percent chord Gurney flap increases the maximum lift coefficient by approximately 0.3 and decreases the angle of attack for a given lift coefficient by more than 3 degrees. The numerical solutions exhibit detailed flow structures at the trailing edge and provide a possible explanation for the increased aerodynamic performance.
Cummings, Russell M.↗
Comparison of two-dimensional and three-dimensional droplet trajectory calculations in the vicinity of finite wings
Computational predictions of ice accretion on flying aircraft most commonly rely on modeling in 2D. These 2D methods treat an aircraft geometry either as wing-like with infinite span, or as an axisymmetric body. Recently, fully 3D methods have been introduced that model an aircraft's true 3D shape. Because 3D methods are more computationally expensive than 2D methods, 2D methods continue to be widely used. However, a 3D method allows investigation of whether it is valid to continue applying 2D methods to a finite wing. The extent of disagreement between LEWICE, a 2D method, and LEWICE3D, a 3D method, in calculating local collection efficiencies at the leading edge of finite wings is investigated.
Mohler, Stanley R., Jr.↗
Investigation of three-dimensional flow field in a turbine including rotor/stator interaction. II - Three-dimensional flow field at the exit of the nozzle
The nozzle exit flowfield was measured at two axial locations with a miniature five-hole probe. Measurements were taken from hub-to-tip, blade-to-blade at 21 radial locations and at two axial locations downstream of the nozzle trailing edge to resolve the flowfield accurately including the nozzle wake, secondary flow region, horseshoe vortex and losses. All three components of the velocity, stagnation pressure, static pressure, and pitch and yaw angles have been resolved very accurately. The wake data seems to indicate that the decay of the wake is faster than the wake of an isolated nozzle row. The cause of this is attributed to the presence of the rotor downstream. A distinct vortex core has been observed near the tip. The indications are that the horseshoe vortex and the passage vortex have merged to produce a single loss core region. Roughly a third of the blade height passage near the tip and a third of the blade height near the hub is dominated by secondary flow, passage vortex and the horseshoe vortex phenomena. Only the middle third of the nozzle behaves as per design. These and other data are presented, interpreted and synthesized to understand the nozzle flowfield.
Zaccaria, M.↗
Implications of three-dimensional tracer studies for two-dimensional assessments of the impact of supersonic aircraft on stratospheric ozone
A 2D model which uses residual circulation and diffusion and a 3D model which uses winds from a stratospheric data assimilation system are used to estimate transport and dispersion of supersonic aircraft exhaust in the lower stratosphere. The seasonal behavior of the exhaust fields in the two models are is similar, but there is a significant difference in the placement of stratosphere/troposphere exchange in the two models. In the 2D model, exhaust transport to the troposphere occurs mostly at high latitudes, while in the 3D model it occurs at middle latitudes and is clearly associated with synoptic scale events. This may be particularly important to assessment calculations, as the pollutant source is mostly in middle latitudes. The 3D model is also used to examine the transport and dispersion of exhaust in three typical flight corridors: North Atlantic, North Pacific, and tropical. There are no systematic differences that suggest that one corridor is inherently more or less polluting than another.
Douglass, Anne R.↗
The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems
A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.
Chang, Sin-Chung↗
Three-dimensional structural damage localization system and method using layered two-dimensional array of capacitance sensors
A system and method for detecting damage to a structure is provided. The system includes a voltage source and at least one capacitor formed as a layer within the structure and responsive to the voltage source. The system also includes at least one sensor responsive to the capacitor to sense a voltage of the capacitor. A controller responsive to the sensor determines if damage to the structure has occurred based on the variance of the voltage of the capacitor from a known reference value. A method for sensing damage to a structure involves providing a plurality of capacitors and a controller, and coupling the capacitors to at least one surface of the structure. A voltage of the capacitors is sensed using the controller, and the controller calculates a change in the voltage of the capacitors. The method can include signaling a display system if a change in the voltage occurs.
Curry, Mark A↗
Three-Dimensional Porous Particles Composed of Curved, Two-Dimensional, Nano-Sized Layers for Li-Ion Batteries
Thin Si films coated on porous 3D particles composed of curved 2D graphene sheets have been synthesized utilizing techniques that allow for tunable properties. Since graphene exhibits specific surface area up to 100 times higher than carbon black or graphite, the deposition of the same mass of Si on graphene is much faster in comparison -- a factor which is important for practical applications. In addition, the distance between graphene layers is tunable and variation in the thickness of the deposited Si film is feasible. Both of these characteristics allow for optimization of the energy and power characteristics. Thicker films will allow higher capacity, but slower rate capabilities. Thinner films will allow more rapid charging, or higher power performance. In this innovation, uniform deposition of Si and C layers on high-surface area graphene produced granules with specific surface area (SSA) of 5 sq. m/g.
Yushin, Gleb↗
Numerical investigations in three-dimensional internal flows
The present study is a preliminary investigation into the behavior of the flow within a 28 degree total geometric turning angle hypothetical Mach 10 inlet as calculated with the full three-dimensional Navier-Stokes equations. Comparison between the two-dimensional and three-dimensional solutions have been made. The overall compression is not significantly different between the two-dimensional and center plane three dimensional solutions. Approximately one-half to two-thirds of the inlet flow at the exit of the inlet behave nominally two-dimensionally. On the other hand, flow field non-uniformities in the three-dimensional solution indicate the potential significance of the sidewall boundary layer flows ingested into the inlet. The tailoring of the geometry at the inlet shoulder and on the cowl obtained in the two-dimensional parametric design study have also proved to be effective at controlling the boundary layer behavior in the three-dimensional code. The three-dimensional inlet solution remained started indicating that the two-dimensional design had a sufficient margin to allow for three-dimensional flow field effects. Although confidence is being gained in the use of SCRAM3D (three-dimensional full Navier-Stokes code) as applied to similar flow fields, the actual effects of the three-dimensional flow fields associated with sidewalls and wind tunnel installations can require verification with ground-based experiments.
Rose, William C.↗
Quasi-three-dimensional turbomachinery flow calculations on multiple hub-to-shroud stream surfaces
Results are presented from a quasi-three-dimensional calculation of steady (relative), inviscid, adiabatic, subsonic/shock-free transonic flow on multiple hub-to-shroud stream surfaces through turbomachinery blade rows. The quasi-three-dimensional technique incorporates some three-dimensional effects while retaining much of the simplicity of two-dimensional computational methods. Three typical turbomachinery flowfield calculations are presented including an axial-flow compressor rotor, a turbine stator vane cascade, and a radial-inflow turbine rotor. The calculations were performed using quasi-three-dimensional extensions of existing two-dimensional methods. The current results represent an intermediate step in the complete quasi-three-dimensional solution process. However, the results demonstrate the usefulness of the quasi-three-dimensional technique in complementing and extending the applicability of the two-dimensional methods of turbomachinery flow analysis.
Thompson, H. D.↗
Three-dimensional co-culture process
The present invention relates to a 3-dimensional co-culture process, more particularly to methods or co-culturing at least two types of cells in a culture environment, either in space or in unit gravity, with minimum shear stress, freedom for 3-dimensional spatial orientation of the suspended particles and localization of particles with differing or similar sedimentation properties in a similar spatial region to form 3-dimensional tissue-like structures. Several examples of multicellular 3-dimensional experiences are included. The protocol and procedure are also set forth. The process allows simultaneous culture of multiple cell types and supporting substrates in a manner which does not disrupt the 3-dimensional spatial orientation of these components. The co-cultured cells cause a mutual induction effect which mimics the natural hormonal signals and cell interactions found in the intact organism. This causes the tissues to differentiate and form higher 3-dimensional structures such as glands, junctional complexes polypoid geometries, and microvilli which represent the corresponding in-vitro structures to a greater degree than when the cell types are cultured individually or by conventional processes. This process was clearly demonstrated for the case of two epithelial derived colon cancer lines, each co-cultured with normal human fibroblasts and with microcarrier bead substrates. The results clearly demonstrate increased 3-dimensional tissue-like structure and biochemical evidence of an increased differentiation state. With the present invention a variety of cells may be co-cultured to produce tissue which has 3-dimensionality and has some of the characteristics of in-vitro tissue. The process provides enhanced 3-dimensional tissue which create a multicellular organoid differentiation model.
Wolf, David A.↗
Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis
An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully implicit (Newton) methods for the CFD analyses; (2) adopting a Bezier-Bernstein polynomial parameterization of two- and three-dimensional surfaces; and (3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use. The new aerodynamic shape optimization procedure is demonstrated in the design of both two- and three-dimensional inviscid aerodynamic problems including a two-dimensional supersonic internal/external nozzle, two-dimensional transonic airfoils (resulting in supercritical shapes), three-dimensional transport wings, and three-dimensional supersonic delta wings. Each design application results in realistic and useful optimized shapes.
Burgreen, Gregory W.↗
Direct Simulation of Evolution and Control of Three-Dimensional Instabilities in Attachment-Line Boundary Layers
The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic- source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in at-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.
Joslin, Ronald D.↗
Secondary instability in three-dimensional magnetic reconnection
We consider the transition to turbulence in three-dimensional reconnection of a magnetic neutral sheet. We find that the transition can occur via a three-step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two-dimensional quasi-steady state. Third, this secondary equilibrium is itself unstable when it is perturbed by three-dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three-dimensional linear stability properties of the two-dimensional saturated tearing layer. The numerical simulations are performed with a semi-implicit, pseudospectral-Fourier collocation algorithm. We identify a three-dimensional secondary linear stability which grows on the ideal timescale. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three-dimensional field, with the two-dimensional field acting as a catalyst.
Dahlburg, R. B.↗