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Results for “Closed form solution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Performance of end-face seals with diametral tilt and coning - Hydrodynamic effects

Hydrodynamic effects in end-face seals with diametral tilt and coning are analyzed. A closed-form solution for the axial separating force and the restoring and transverse moments is presented that covers the whole range from zero to full angular misalignment at various degrees of coning. Both low-pressure seals with cavitating flow and high-pressure seals with full fluid film are considered. The effect of coning is to reduce the axial force and the restoring and transverse moments compared to their magnitude in flat-face seals. Strong coupling between diametral tilt and transverse moment is demonstrated. This transverse moment which is entirely due to hydrodynamic effects can be the source of dynamic instability in the form of seal wobble.

Sharoni, A.↗
NASA NTRS1979

Thermographic measurement of fatigue damage

The paper presents a thermographic technique developed to measure the extent of fatigue damage in composite materials during fatigue loading. It is noted that heat generated by cyclic loading of fatigue damaged material raises the surface temperature. These temperatures were measured with an infrared camera and were used as boundary conditions in a finite element heat transfer program, which has been developed especially to calculate the extent of the heat generation zone, and thereby to define the fatigue damage zone. It is reported that the finite element program was verified by comparing calculated heat generation with the actual heat generation for a simple heat transfer problem that had a closed form solution. Damage zones are calculated for several boron/epoxy fatigue specimens from thermograms of specimens. The calculated damage zones were compared with damage detected by C-scan, X-ray, and scanning electron microscope (SEM) examinations. It is concluded that the analysis was effective in locating the boundaries of the fatigue damage zones.

Whitcomb, J. D.↗
NASA NTRS1980

Dual-spin spacecraft nutation control using articulated payloads

A technique is presented for achieving active control of nutation on a dual-spin spacecraft with an articulated payload through use of the payload's control system. Using the Orbiting Solar Observatory (OSO)-8 as an illustration, the closed-form solution to the nutation/control system dynamic interaction is presented. Control system design criteria are developed which establish the basic stability of the interaction. Design procedures are described to achieve the most effective nutation damping. Limitations on the amount of damping which can be achieved are characterized as functions of spacecraft and payload mass properties and servo-design parameters. The design techniques presented are verified through a series of on-orbit tests recently conducted on the OSO-8 spacecraft.

Slafer, L. I.↗
NASA NTRS1980

Higher order mode propagation in nonuniform circular ducts

This paper presents an analytical investigation of higher order mode propagation in a nonuniform circular duct without mean flow. An approximate wave equation is derived on the assumptions that the duct cross section varies slowly and that mode conversion is negligible. Exact closed form solutions are obtained for a particular class of converging-diverging circular duct which is here referred to as 'circular cosh duct'. Numerical results are presentd in terms of the transmission loss for the various duct shapes and frequencies. The results are applicable to studies of multimodal propagation as well as single mode propagation. The results are also applicable to studies of sound radiation from certain types of contoured inlet ducts, or of sound propagation in a converging-diverging duct of somewhat different shape from a cosh duct.

Cho, Y. C.↗
NASA NTRS1980

Local distributed estimation

Based on partial differential equations of motion the closed form solution for the optimal estimation of a spatially continuous state vector is derived, using a continuously distributed sensor. Local control is shown to be the feedback that minimizes a quadratic performance index of sensor and process disturbances. A detailed example of the control of a string in tension is presented.

Schaechter, D. B.↗
NASA NTRS1980

Multipulse precession of spinning spacecraft with flexible appendages

A multipulse precession scheme for spinners with large flexible appendages is described. By choosing the prescribed time delay between pulses as integer (or half integer) multiples of the several incommensurate modal periods it is possible to leave both central spinner and appendages in a final state of negligible nutation. Computer simulations illustrate the several schemes. The results indicate that the proposed method is relatively insensitive to parameter variations such as thruster and inertia uncertainties. Complete equations are presented, including a closed form solution for an important special case: the appendage plane contains the central body mass center.

Vogel, E.↗
NASA NTRS1979

Theoretical performance of multi-layer grid patterns for solar cells

Multilayer grid patterns consist of fine closely spaced grid lines overlaid by coarser patterns of wider and thicker grid lines to collect the current from the finer grids with low series voltage drop and low active-layer sheet losses. An analytical approach leads to closed form solutions with simple relationships between the power losses in the active layer, in the grid and shadowing losses for optimum design proportions. The results show that multilayer grids, with line thickness equal to line width, greatly reduce losses in cell efficiency under concentration conditions of high current collection. (AlGa)As-pn GaAs cells of areas 1-25 sq cm and sheet resistance 40 ohms/square are considered. Also the performance of a n/p GaAs cell of dimensions 10 x 10 cm is studied. With optimized grid patterns high efficiencies are predicted for large area cells.

Flat, A.↗
NASA NTRS1981

A potential-flow/boundary-layer method for calculating subsonic and transonic airfoil flow with trailing-edge separation

The development of a potential-flow/boundary-layer method for calculating subsonic and transonic turbulent flow past airfoils with trailing-edge separation is reported. A moment-of-momentum integral boundary-layer method is used which employs the law-of-the-wall/law-of-the-wake velocity profile and a two-layer eddy-viscosity model and ignores the laminar sublayer. All integrals across the boundary layer are obtained in closed form. Separation is assumed to occur when the shearing-stress velocity vanishes. A closed-form solution is derived for separated-flow regions where the shearing stress is negligible. In the potential-flow method, the exact form of the airfoil boundary condition is used, but it is applied at the chord line rather than the airfoil surface. This allows the accurate computation of flow about airfoils at large angles of attack but permits the use of body-oriented Cartesian computational grids. The governing equation for the perturbation velocity potential contains several terms in addition to the classical small-disturbance terms.

Barnwell, R. W.↗
NASA NTRS1980

Radiative transfer theory for passive microwave remote sensing of a two-layer random medium with cylindrical structures

A model of the vegetation layer as a two-layer random medium with a small correlation length l sub rho in the horizontal direction, and a large correlation length l sub z in the vertical direction, is presented for fields with cylindrical structures. As l sub z approaches infinity, closed form solutions are derived for the brightness temperatures; the kernels in the scattering terms of the radiative transfer equations result in delta functions showing that forward scattering is dominant over all other directions. The results are compared with the Gaussian quadrature method data for numerical solution of the radiative transfer equations.

Chuang, S. L.↗
NASA NTRS1981

Stability of flow over plates with porous suction strips

This paper addresses the stability of two-dimensional, incompressible boundary-layer flow over plates with suction through porous strips. The mean flow is calculated using linearized triple-deck, closed-form solutions. The stability results of the triple-deck theory are shown to be in good agreement with those of the interacting boundary layers. Then different configurations of number, spacing, and mass flow rate through such porous strips are analyzed and compared with nonsimilar uniform-suction stability results from the point of view of applicability to laminar flow control.

Reed, H. L.↗
NASA NTRS1981

Radiative transfer theory for active remote sensing of a homogeneous layer containing spherical scatterers

The radiative transfer theory with a Rayleigh scattering model is used to study the effect of volume scattering for active microwave remote sensing of low-loss and scattering dominant areas by obtaining backscattering cross sections through iterative and numerical approaches. The iterative approach gives closed form solutions which are valid when the effect of scattering is small. The depolarization of the backscattered power is shown to be a second-order effect. For the general cases, a numerical approach is used to solve the radiative transfer equations. The theoretical results are compared and illustrated for the various cases.

Shin, R. T.↗
NASA NTRS1981

Influence of sideslip on the kinematics of the helicopter in steady coordinated turns

A steep coordinated helical turn at extreme angles of attack with inherent sideslip is of primary interest in this study. Unlike fixed-wing aircraft, the helicopter in a steady coordinated turn will inherently sideslip. A set of exact kinematic equations describing this motion in steady helical turns has been developed, and a rational definition for the load factor that best characterizes a coordinated turn for a helicopter has been proposed. An analysis has also been completed on the effects of sideslip on the kinematic relationships in a coordinated turn which is based on new closed-form solutions which relate the aircraft angular rates and pitch and roll attitudes to the turn parameters, angle of attack, and sideslip. The results show that the bank angle of the aircraft can differ markedly from the tilt angle of the normal load factor and that the normal load factor can also differ substantially from the accelerometer reading along the vertical body axis of the aircraft. Generally, sideslip has a strong influence on the pitch attitude and roll rate of the helicopter. The study also indicates that pitch rate is independent of angle of attack in a coordinated turn and that in the absence of sideslip, angular rates about the stability axes are independent of the aerodynamic characteristics of the aircraft.

Chen, R. T. N.↗
NASA NTRS1982

Mode Propagation in Nonuniform Circular Ducts with Potential Flow

A previously reported closed form solution is expanded to determine effects of isentropic mean flow on mode propagation in a slowly converging-diverging duct, a circular cosh duct. On the assumption of uniform steady fluid density, the mean flow increases the power transmission coefficient. The increase is directly related to the increase of the cutoff ratio at the duct throat. With the negligible transverse gradients of the steady fluid variables, the conversion from one mode to another is negligible, and the power transmission coefficient remains unchanged with the mean flow direction reversed. With a proper choice of frequency parameter, many different modes can be made subject to a single value of the power transmission loss. A systematic method to include the effects of the gradients of the steady fluid variables is also described.

Cho, Y. C.↗
NASA NTRS1982

Stability of boundary layers with porous suction strips: Experiment and theory

Low turbulence tunnel experiments on the stability and transition of 2 D boundary layers on flat plates with and without suction are described. A number of general suction cases are discussed. Test results showed that the maximum stabilization occurred when the suction was moved toward the Branch I neutral point. An analytical study of the stability of two dimensional, incompressible boundary layer flows over plates with suction through porous strips was performed. The mean flow was calculated using linearized triple deck, closed form solutions. The stability results of the triple deck theory are shown to be in good agreement with those of the interacting boundary layers. An analytical optimization scheme for the suction configuration was developd. Numerical calculations were performed corresponding to the experimental configurations. In each case, the theory correctly predicts the experimental results.

Reynolds, G. A.↗
NASA NTRS1982

Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle

The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion.

Vinh, N. X.↗
NASA NTRS1982

Extensional collapse modes of structural members

Attenuation of the load transmitted to a vehicle occupant by the structure, either by modifying structural assembly, changing geometry of its elements, or adding specific load limiting devices to help dissipate kinetic energy was studied. General aviation aircraft have fuselage subfloors of a built up structure which are generally very stiff perpendicular to the floor of the cabin. The subfloor structure, designed to crush at an appropriate force level, can be used to advantage in a crash by dissipating energy through plastic buckling of the floor beams and frames. Simple closed form solutions to predict the mean crushing force levels of subfloor designs is useful in engineering practice. The crushing process of thin walled, plate formed, open structures with particular emphasis on L and cruciform shapes was analyzed. Lower and upper bound solutions for the mean crushing strength of cruciforms are obtained by considering modes of deformation which account for both bending and extensional deformation. It is the importance of extensional deformation to the energy absorption process, representing at least one third of the dissipated energy is shown.

Hayduk, R. J.↗
NASA NTRS1981

A new look at Fresnel field computation using the Jacobi-Bessel series

Computational procedures that would be useful in finding the Fresnel field from a knowledge of the Jacobi-Bessel expansion of the far field are considered. The range of validity of the Fresnel approximation is carefully examined by comparing it with the exact closed form solution for the uniform circular aperture. Also investigated numerically, and in great detail, is the range of validity (over theta) of the Fresnel small angle (FSA) approximation. For moderate sized apertures as small as 10 wavelengths, it is found that the FSA approximation is very accurate to angles as wide as four or more sidelobes (as seen in the far zone). A very efficient computational method is shown to exist for the radiation integral in the form of a single series expansion that is analytically continuous and convergent for a wide range of observation points in three-dimensional space.

Galindo-Israel, V.↗