Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “deflection equations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Full-scale study of the cooling system aerodynamics of an operating piston engine installed in a light aircraft wing panel

Measurements of the drag and of the nacelle internal pressures on a wing and nacelle that housed a horizontally opposed piston engine were made in the 40- by 80-Foot Wind Tunnel at Ames Research Center. These tests are follow-ons to earlier tests made with the same wing and nacelle but in which the engine was replaced with an electric motor and an adjustable orifice plate. In the initial tests the orifice plate was used to control the rate of cooling-air flow through the nacelle and thereby to simulate a range of gasoline engine types. Good agreement was found between the results of those tests and of the test reported here. Also, the upper and lower plenum pressure and cooling-air flow rate were found to be related by conventional equations used to represent the flow through orifices. Tests were run with three cooling air inlet sizes over a free-stream velocity range from 50 to 150 knots, an angle of attack range from 0 deg to 10 deg, and a cowl-flap deflection range from 0 deg to 30 deg. The data were analyzed by computing a flow coefficient similar to that used in the analysis of orifices. It was found that all of the flow coefficient values fell within a band that varied linearly with inlet area. The linear mean line through this band provides an estimate of the relationship between cooling-air flow rate and upper plenum pressure over a wide range of test conditions.

Corsiglia, V. R.↗
NASA NTRS1948

A general small-deflection theory for flat sandwich plates

A small-deflection theory is developed for the elastic behavior of orthotropic flat plates in which deflections due to shear are taken into account. In this theory, which covers all types of flat sandwich construction, a plate is characterized by seven physical constants (five stiffnesses and two Poisson ratios) of which six are independent. Both the energy expression and the differential equations are developed. Boundary conditions corresponding to simply supported, clamped, and elastically restrained edges are considered.

Libove, Charles↗
NASA NTRS1982

A model for unsteady transonic indicial responses

A method of characterizing the indicial curve for the response frequencies of flutter in the transonic regime by means of a time scale parameter is illustrated. Time linearization of the unsteady potential equation is assumed adequate and the perturbed potential about a steady flow is defined with appropriate boundary conditions. An indicial motion can then be obtained for a given mode, with the lift and drag coefficients which result from a step change in incidence or control surface deflection available to describe any kind of motion. The lift and drag coefficients are shown to result analytically by addition of the multiplicand involving the time scale parameter. If the coefficients are maximized, then at reduced frequencies only two parameters are necessary to form the indicial response curve.

Fung, K.-Y.↗
NASA NTRS1928

Determination of the air forces and moments produced by the ailerons of an airplane

As a rule, the actual lift distribution at the wing tips shows deviations from the theoretical distribution, so that an approximate evaluation of the distribution may be regarded as satisfactory. After a few brief remarks on the fundamentals of the exact computation, the method will be so presented that the lift distribution for deflected ailerons may be determined for other values of the parameter p from the results already obtained. Coefficients will then be given in the form of diagrams and numerical tables, from which the desired forces and moments can be easily obtained by substitution in the given equations.

ROLLING & YAWING MOMENTS - WINGS↗
NASA NTRS1940

A theoretical study of lateral stability with an automatic pilot

The influence of automatic operation of the aileron and rudder controls on the lateral stability of an airplane is discussed. The control deflections are assumed to be proportional to the deviations and to the rates of deviation of the airplane from steady-flight conditions. The effects of changes in the types of deviation governing control application are considered. For one simple method of control in which the aileron deflection is proportional to the angle of bank and the rudder deflection is proportional to the angle of yaw, the effect of lag in control application is studied and regions of stability with and without lag are given. For the simple control with lag, curves are included that show the variations in the roots of the stability equation with changes in the amount of control applied. It is concluded that, although the simple control provides a satisfactory means of varying most of the lateral stability characteristics, the stability in azimuth will always be poor for such a control.

Imlay, Frederick H↗
NASA NTRS1999

A Study of the December 1992 Westerly Wind Burst Event during TOGA COARE

Using the Penn State/NCAR MM5 mesoscale model, a westerly wind burst (WWB) that occurred during the period from 19 to 30 December 1992 over the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) has been simulated and compared with observation. This event is characterized by the presence of super cloud clusters and the occurrence of a major WWB that extended over the western and central Pacific Ocean. Although several of the observed convective systems were not precisely simulated by MM5, the model did capture many other observed characteristics, such as the explosive development of convection, the cyclonic circulation and the WWB. The WWB resulted from the coalescence of three types of tropical disturbances. The first type was a low-level westerly jet (LWJ) that developed at the equator and may be associated with the eastward propagation of an ISO (Intraseasonal Oscillation). The second type featured an easterly wave-like disturbance that originated in the south central Pacific Ocean and propagated westward. Finally, the third type involved a cross-equatorial flow that deflected Northern Hemispheric easterlies into the Southern Hemisphere and may be caused by inertial instability. These disturbances worked in concert, resulting in intense convection over the TOGA COARE region. Once intense convection developed, a large-scale circulation was produced over the western Pacific warm pool, propagated eastward, and initiated a WWB.

Chen, Chaing↗
NASA NTRS2018

Curvilinear Displacement Transfer Functions for Deformed Shape Predictions of Curved Structures Using Distributed Surface Strains

Curvilinear Displacement Transfer Functions were formulated for deformed shape predictions of different curved structures using surface strains. The embedded curved beam (depth-wise cross section of a curved structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. The discrete approach enabled piecewise integrations of a curvature-strain differential equation for the embedded curved beam to yield closed-form Curvilinear Displacement Transfer Functions, which are written in terms of embedded curved-beam geometrical parameters and surface strains. By inputting the surface strain data, the Curvilinear Displacement Transfer Functions can transform surface strains into deflections along each embedded curved beam for mapping out the overall structural deformed shapes. The finite-element method was used to analytically generate the surface strains of the curved beams. The deformed shape prediction accuracies were then determined by comparing the theoretical deflections with the finite-element-generated deflections, which were used as yardsticks. By introducing the correction factors in simple mathematical forms, the Curvilinear Displacement Transfer Functions can be quite accurate for shape predictions of different curved-beam structures ranging from limit case of straight beam up to semicircular curved beam.

Ko, William L.↗
NASA NTRS1984

Turbulent heat transfer in a channel with two right-angled bends

A numerical study is reported on the flow and heat transfer in a channel with two right-angled bends. The k-epsilon turbulence model with a refined near-wall model is adopted for the computation of the flow field for step ratios ranging H/W = 1-4 and for Reynolds numbers Re = 3,000-10,000. The solution method of the governing transport equations is based on the modified hybrid scheme which produces very small truncation error. As a result of extensive computations, the complex flow patterns in the channel with two bends are clarified and the mechanisms of heat transfer are explained relating to the flow behaviors of separation, deflection, recirculation, and reattachment.

Amano, R. S.↗
NASA NTRS2014

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗
NASA NTRS1973

Large amplitude flutter of a low aspect ratio panel at low supersonic speeds comparison of theory and experiment

Flutter boundaries, as well as flutter limit cycle amplitudes, frequencies and stresses were computed for a panel of length-width ratio 4.48 exposed to applied in-plane and transverse loads. The Mach number range was 1.1 to 1.4. The method used involved direct numerical integration of modal equations of motion derived from the nonlinear plate equations of von Karman, coupled with linearized potential flow aerodynamic theory. The flutter boundaries agreed reasonably well with experiment, except when the in-plane loading approached the buckling load. Structural damping had to be introduced, to produce frequencies comparable to the experimental values. Attempts to compute panel deflections or stress at a given point met with limited success. There is some evidence, however, that deflection and stress maxima can be estimated with somewhat greater accuracy.

Ventres, C. S.↗
NASA NTRS1990

Plasma fluctuations in the magnetosheath downstream from Uranus

The Voyager plasma experiment observed large-amplitude plasma fluctuations in the Uranian magnetosheat downstream from the planet. This is a region that has not been well sampled in the earth's magnetosphere. These waves have periods of tens of minutes, are characterized by an anticorrelation between the plasma density and temperature, and are associated with deflections in the flow angle of the plasma. These fluctuations are observed only in regions where the magnetic field is rapidly varying. These waves have time and distance scales placing them in the MHD regime, but their characteristics are not compatible with any known solution of the MHD equations. It is suggested that these fluctuations are produced by the solar wind interaction with the magnetosphere at the bow shock, but the physics governing the production and propagation of these fluctuations is not understood.

Richardson, John D.↗
NASA NTRS1991

Numerical prediction of the unsteady flowfield around the F-18 aircraft at large incidence

This paper describes a numerical method capable of solving the steady and unsteady viscous flow around complete aircraft configurations at high angles of attack. This method is used to simulate the external flow around the F-18 aircraft, including deflected control surfaces. The current technique employs a generalized overset zonal grid scheme to decompose the computational space around the aircraft. The grid around various components of the aircraft are created numerically using a three-dimensional hyperbolic grid generation procedure. The Reynolds-averaged Navier-Stokes equations are integrated using a time-accurate, implicit procedure. Results for the turbulent flow around the F-18 aircraft at 30 degrees angle of attack show the details of the flowfield structure, including the unsteadiness created by the vortex burst and the resulting fluctuating airloads exerted on the vertical tail. The computed results agree fairly well with flight data for surface pressure, surface flow pattern, vortex burst location, and the dominant frequency for tail load fluctuations.

Rizk, Yehia M.↗
NASA NTRS1991

Navier-Stokes solutions about the F/A-18 wing-LEX-fuselage configuration with multi-block structured grids

Three-dimensional thin-layer Navier-Stokes computations are presented for the F/A-18 configuration. The modeled configuration includes an accurate surface representation of the fuselage, leading-edge-extension, as well as the wing with and without leading-edge-flap deflection. A multi-block structured volume grid with various topologies is generated using transfinite interpolation technique. The flowfield domain is divided into twenty blocks, each representing a particular geometrical complexity of the configuration. The results are obtained from an algorithm for solving the compressible Navier-Stokes equations that incorporates an upwind-biased, flux-difference-splitting approach. In addition, a newly developed capability that allows for generalized surface patching among blocks is employed. Turbulent results are presented for flow conditions that correspond to recent NASA F/A-18 High Alpha Research Vehicle flight experiments. Good correlations between the computations and the flight test results are disclosed for both surface flow patterns as well as surface pressure distributions.

Ghaffari, Farhad↗
NASA NTRS1993

Hypervelocity impact on shielded plates

A ballistic limit equation for hypervelocity impact on thin plates is derived analytically. This equation applies to cases of impulsive impact on a plate that is protected by a multi-shock shield, and it is valid in the range of velocity above 6 km/s. Experimental tests were conducted at the NASA Johnson Space Center on square aluminum plates. Comparing the center deflections of these plates with the theoretical deflections of a rigid-plastic plate subjected to a blast load, one determines the dynamic yield strength of the plate material. The analysis is based on a theory for the expansion of the fragmented projectile and on a simple failure criterion. Curves are presented for the critical projectile radius versus the projectile velocity, and for the critical plate thickness versus the velocity. These curves are in good agreement with curves that have been generated empirically.

Smith, James P.↗
NASA NTRS1981

Temperature-dependent creep buckling of plates

Time-dependent lateral deflection of flat rectangular plates is predicted by the Norton-Bailey (Norton 1929, Bailey 1935) power law for material creep. The plates have a through-thickness steady-state temperature distribution, and the effects are considered by using Maxwell's law to modify the power creep law. Equations are derived for creep exponents of 3 and 5, using the sandwich plate element to predict creep buckling of plates. Predictions of creep buckling with a temperature variation between the inner and outer plate surfaces are found to be somewhat dependent on the creep buckling relationship assumed. When significant scatter justifies a variation in the creep constants up to an order of magnitude, discrepancies in predictions using the two exponents are reasonable, and for one engineering material, the predictions have the same degree of agreement with experimental data as have the respective creep laws.

Ross, D. A.↗
NASA NTRS1982

Coupled flap-lag-torsional dynamics of hingeless rotor blades in forward flight

The aeroelastic stability and response problem of the coupled flap-lag-torsional dynamics of an isolated hingeless rotor blade in forward flight is considered. Linear, quasi-steady aerodynamics below stall is included. The spatial dependence of the partial differential nonliner equations of motion is discretized using a multimodal Galerkin method. The nonlinear time dependent equilibrium position (steady state response) about which the equations are linearized is obtained by solving a sequence of linear periodic response problems (quasilinearization). Results illustrating blade behavior in forward flight for both soft-in-plane and stiff-in-plane designs are presented. Quasilinearization provides a clear indication of the cases when nonlinear terms due to moderate deflections are important. The results indicate that nonlinearities affect system stability much more than system response. This implies that for obtaining blade vibrations and loads, approximate analytical models based on linearized formulations could be employed, whereas for determining blade stability a more accurate nonlinear analysis would be required.

Friedmann, P. P.↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
NASA NTRS1972

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

Stricklin, J. A.↗