Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “CALCULATION METHODS”

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 199 records · Page 11

A method for calculating the lift and center of pressure of wing-body-tail combinations at subsonic, transonic, and supersonic speeds

A method is presented for calculating the lift and pitching-moment characteristics of circular cylindrical bodies in combination with triangular, rectangular, or trapezoidal wings or tails through the subsonic, transonic, and supersonic speed ranges. The method covers unbanked wings, sweptback leading edges or sweptforward trailing edges, low angles of attack, and the effects of wing and tail incidence. The wing-body interference is handled by the method presented in NACA RM's A51J04 and A52B06, and the wing-tail interference is treated by assuming one completely rolled-up vortex per wing panel and evaluating the tail load by strip theory. A computing table and set of design charts are presented which reduce the calculations to routine operations. Comparison is made between the estimated and experimental characteristics for a large number of wing-body and wing-body-tail combinations. Generally speaking, the lifts were estimated to within plus-or-minus 10 percent and the centers of pressure were estimated to within plus-or-minus 0.02 of the body length. The effect of wing deflection on wing-tail interference at supersonic speeds was not correctly predicted for triangular wings with supersonic leading edges.

Nielsen, Jack N↗

A general method for calculating three-dimensional compressible laminar and turbulent boundary layers on arbitrary wings

The method described utilizes a nonorthogonal coordinate system for boundary-layer calculations. It includes a geometry program that represents the wing analytically, and a velocity program that computes the external velocity components from a given experimental pressure distribution when the external velocity distribution is not computed theoretically. The boundary layer method is general, however, and can also be used for an external velocity distribution computed theoretically. Several test cases were computed by this method and the results were checked with other numerical calculations and with experiments when available. A typical computation time (CPU) on an IBM 370/165 computer for one surface of a wing which roughly consist of 30 spanwise stations and 25 streamwise stations, with 30 points across the boundary layer is less than 30 seconds for an incompressible flow and a little more for a compressible flow.

Cebeci, T.↗

Methods for calculation of engineering parameters for gas separation

A group additivity method is generated which allows estimation, from the structural formulas alone, of the energy of vaporization and the molar volume at 25 C of many nonpolar organic liquids. Using these two parameters and appropriate thermodynamic relations, the vapor pressure of the liquid phase and the solubility of various gases in nonpolar organic liquids are predicted. It is also possible to use the data to evaluate organic and some inorganic liquids for use in gas separation stages or liquids as heat exchange fluids in prospective thermochemical cycles for hydrogen production.

Lawson, D. D.↗

Development of advanced modal methods for calculating transient thermal and structural response

Higher-order modal methods for predicting thermal and structural response are evaluated. More accurate methods or ones which can significantly reduce the size of complex, transient thermal and structural problems are desirable for analysis and are required for synthesis of real structures subjected to thermal and mechanical loading. A unified method is presented for deriving successively higher-order modal solutions related to previously-developed, lower-order methods such as the mode displacement and mode-acceleration methods. A new method, called the force-derivative method, is used to obtain higher-order modal solutions for both uncoupled (proportionally-damped) structural problems as well as thermal problems and coupled (non-proportionally damped) structural problems. The new method is called the force-derivative method because, analogous to the mode-acceleration method, it produces a term that depends on the forcing function and additional terms that depend on the time derivatives of the forcing function.

Camarda, Charles J.↗

Improved Woodward's panel method for calculating edge suction forces

A new technique to improve Woodward's (1968) unified subsonic and supersonic panel method is described. The pressure prediction is improved based on a new two-dimensional theory. The method used by Lan (1977) is then used to calculate the leading-edge and side-edge suction forces by direct use of the predicted pressure distribution. The method is applicable to both subsonic and supersonic flow. It is shown that the improved Woodward panel method is capable of accurately predicting leading-edge and side-edge suction forces in subsonic and supersonic flow. Therefore, the method can be used not only to predict the vortex lift of complex planforms through the method of suction analogy, but also to calculate some lateral-directional stability derivatives.

Lan, C. E.↗

Improved method for calculating transonic velocities on blade-to-blade stream surfaces of a turbomachine

A method was developed to improve the accuracy of an existing computer program used to calculate transonic velocities on a blade-to-blade surface of a turbomachine. The method eliminates problems encountered in obtaining solutions with the velocity gradient equation when large gradients in velocity occur through the blade row. With the improved method, results indicate that the transonic solution can be obtained by scaling the velocities obtained at the reduced mass flow rate where all velocities are subsonic thereby eliminating the need for a solution of the velocity gradient equation. Solutions obtained with the scaling method on a two dimensional compressor cascade and an axial turbine stator show good agreement with experimental data. The results obtained for the stationary blade rows and comparison of analytical results obtained with and without the present method suggest that the method will yield an improved solution for centrifugal compressor impellers.

Wood, J. R.↗

Reliability of the finite element method for calculating free edge stresses in composite laminates

The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.

Whitcomb, J. D.↗

Summary of Methods for Calculating Dynamic Lateral Stability and Response and for Estimating Lateral Stability Derivatives

A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Reference is also made to reports presenting experimental data that should be useful in making estimates of the derivatives. Detailed estimating methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic- and supersonic-speed conditions.

Campbell, John P↗

Summary of methods for calculating dynamic lateral stability and response and for estimating aerodynamic stability derivatives

A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Detailed estimation methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic and supersonic speed conditions.

Campbell, John P↗

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Korkan, K. D.↗

On a new method for calculating the potential flow past a body of revolution

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Kaplan, Carl↗

Probing phase stability in CrMoNbV using cluster expansion method, CALPHAD calculations and experiments

High entropy alloys (HEA), a novel class of materials with multiple principal elements, allow us to tune the properties within a wide composition range where the solid-solution phase is stable. However, it is difficult to experimentally determine the boundaries of the single-phase region. In this paper, we calculate the phase diagram of the CrMoNbV quaternary system, as well as its constituent binary and ternary subsystems, using a combination of the cluster expansion method and CALPHAD calculations. We further verify these results by carrying out experiments at two different compositions of the full quaternary system. Furthermore, our work shows how these computational tools can enable efficient discovery and development of new HEAs.

36 MATERIALS SCIENCE↗

A new blade element method for calculating the performance of high and intermediate solidity axial flow fans

A method is presented to design and predict the performance of axial flow rotors operating in a duct. The same method is suitable for the design of ducted fans and open propellers. The unified method is based on the blade element approach and the vortex theory for determining the three dimensional effects, so that two dimensional airfoil data can be used for determining the resultant force on each blade element. Resolution of this force in the thrust and torque planes and integration allows the total performance of the rotor, fan or propeller to be predicted. Three different methods of analysis, one based on a momentum flow theory; another on the vortex theory of propellers; and a third based on the theory of ducted fans, agree and reduce cascade airfoil data to single line as a function of the loading and induced angle of attack at values of constant inflow angle. The theory applies for any solidity from .01 to over 1 and any blade section camber. The effects of the duct and blade number can be determined so that the procedure applies over the entire range from two blade open propellers, to ducted helicopter tail rotors, to axial flow compressors with or without guide vanes, and to wind tunnel drive fans.

Borst, H. V.↗

Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft

A simple unified numerical method applicable to non-planar subsonic aircraft has been developed for calculating either the induced drag for an arbitrary loading or the optimum aircraft loading which results in minimum induced drag. The method utilizes a vortex lattice representation of the aircraft lifting surfaces coupled with the classic equations and theorems for computing and minimizing induced drag. Correlation of results from the numerical method with non-planar solutions obtained from other more complex theories indicates very good agreement. Comparison of the induced-drag computations using the numerical method with experimental data for planar and non-planar configurations was also very good.

Blackwell, J. A., Jr.↗

Method for calculating lift distributions for unswept wings with flaps or ailerons by use of nonlinear section lift data

A method is presented which allows the use of nonlinear section lift data in the calculation of the spanwise lift distribution of unswept wings with flaps or ailerons. This method is based upon lifting line theory and is an extension to the method described in NACA rep. 865. The mathematical treatment of the discontinuity in absolute angle of attack at the end of the flap or aileron involves the use of a correction factor which accounts for the inability of a limited trigonometric series to represent adequately the spanwise lift distribution. A treatment of the apparent discontinuity in maximum section lift coefficient is also described. Simplified computing forms containing detailed examples are given for both symmetrical and asymmetrical lift distributions. A few comparisons of calculated characteristics with those obtained experimentally are also presented.

Sivells, James C↗

An Impulse-Momentum Method for Calculating Landing-Gear Contact Conditions in Eccentric Landings

An impulse-momentum method for determining impact conditions for landing gears in eccentric landings is presented. The analysis is primarily concerned with the determination of contact velocities for impacts subsequent to initial touchdown in eccentric landings and with the determination of the effective mass acting on each landing gear. These parameters determine the energy-absorption requirements for the landing gear and, in conjunction with the particular characteristics of the landing gear, govern the magnitude of the ground loads. Changes in airplane angular and linear velocities and the magnitude of landing-gear vertical, drag, and side impulses resulting from a landing impact are determined by means of impulse-momentum relationships without the necessity for considering detailed force-time variations. The effective mass acting on each gear is also determined from the calculated landing-gear impulses. General equations applicable to any type of eccentric landing are written and solutions are obtained for the particular cases of an impact on one gear, a simultaneous impact on any two gears, and a symmetrical impact. In addition a solution is presented for a simplified two-degree-of-freedom system which allows rapid qualitative evaluation of the effects of certain principal parameters. The general analysis permits evaluation of the importance of such initial conditions at ground contact as vertical, horizontal, and side drift velocities, wing lift, roll and pitch angles, and rolling and pitching velocities, as well as the effects of such factors as landing gear location, airplane inertia, landing-gear length, energy-absorption efficiency, and wheel angular inertia on the severity of landing impacts. -A brief supplementary study which permits a limited evaluation of variable aerodynamic effects neglected in the analysis is presented in the appendix. Application of the analysis indicates that landing-gear impacts in eccentric landings can be appreciably more severe than impacts in symmetrical landings with the same sinking speed. The results also indicate the effects of landing-gear location, airplane inertia, initial wing lift, side drift velocity, attitude, and initial rolling velocity on the severity of both initial and subsequent landing-gear impacts. A comparison of the severity of impacts on auxiliary gears for tricycle and quadricycle configurations is also presented.

Yntema, Robert T↗

DeepMC: a deep learning method for efficient Monte Carlo beamlet dose calculation by predictive denoising in magnetic resonance-guided radiotherapy

Abstract Emerging magnetic resonance (MR) guided radiotherapy affords significantly improved anatomy visualization and, subsequently, more effective personalized treatment. The new therapy paradigm imposes significant demands on radiation dose calculation quality and speed, creating an unmet need for the acceleration of Monte Carlo (MC) dose calculation. Existing deep learning approaches to denoise the final plan MC dose fail to achieve the accuracy and speed requirements of large-scale beamlet dose calculation in the presence of a strong magnetic field for online adaptive radiotherapy planning. Our deep learning dose calculation method, DeepMC, addresses these needs by predicting low-noise dose from extremely noisy (but fast) MC-simulated dose and anatomical inputs, thus enabling significant acceleration. DeepMC simultaneously reduces MC sampling noise and predicts corrupted dose buildup at tissue-air material interfaces resulting from MR-field induced electron return effects. Here we demonstrate our model’s ability to accelerate dose calculation for daily treatment planning by a factor of 38 over traditional low-noise MC simulation with clinically meaningful accuracy in deliverable dose and treatment delivery parameters. As a post-processing approach, DeepMC provides compounded acceleration of large-scale dose calculation when used alongside established MC acceleration techniques in variance reduction and graphics processing unit-based MC simulation.

Engineering↗