Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Moment 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 757 records · Page 42

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Lin, Ray-Quing↗

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Peters, D. A.↗

Use of an optimized controller and a finite-state stall model to find trimmed helicopter flight controls

An auto-pilot is applied to helicopter rotor flap-lag-torsion equations in order to obtain the control settings for a trimmed flight condition. The rotor aerodynamic description includes a state-space dynamic stall model for lift and for pitching moments. Thus, an attempt is made to trim the rotor for flight conditions in which significant stall and torsional deformations are present. The auto-pilot is extended to Q-bladed rotors by a series of time-delay terms. As a result, the optimum gains and time constants depend upon the number of blades as well as upon the torsional stiffness.

Peters, David A.↗

Radiation transport around axisymmetric blunt body vehicles using a modified differential approximation

A moment method for computing 3D radiative transport in axisymmetric thermochemical nonequilibrium flows is developed. The method uses the P-1 approximation to reduce the governing system of integro-differential equations to a coupled set of partial differential equations. The numerical solution of these equations for realistic variations of the radiation properties is discussed. Representative results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Hartung, Lin C.↗

Modeling near wall effects in second moment closures by elliptic relaxation

The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.

Laurence, D.↗

Deformation and Flexibility Equations for ARIS Umbilicals Idealized as Planar Elastica

The International Space Station relies on the active rack isolation system (ARIS) as the central component of an integrated, stationwide strategy to isolate microgravity space-science experiments. ARIS uses electromechanical actuators to isolate an international standard payload rack from disturbances due to the motion of the Space Station. Disturbances to microgravity experiments on ARIS isolated racks are transmitted primarily via the ARIS power and vacuum umbilicals. Experimental tests indicate that these umbilicals resonate at frequencies outside the ARIS controller s bandwidth at levels of potential concern for certain microgravity experiments. Reduction in the umbilical resonant frequencies could help to address this issue. This work documents the development and verification of equations for the in-plane deflections and flexibilities of an idealized umbilical (thin, flexible, inextensible, cantilever beam) under end-point, in-plane loading (inclined-force and moment). The effect of gravity is neglected due to the on-orbit application. The analysis assumes an initially curved (not necessarily circular), cantilevered umbilical with uniform cross-section, which undergoes large deflections with no plastic deformation, such that the umbilical slope changes monotonically. The treatment is applicable to the ARIS power and vacuum umbilicals under the indicated assumptions.

Hampton, R. David↗

Pressures in Tumuli: A Study of Tumuli Formation

Tumuli form via localized inflation in surface lava flows. These domed features have widths of 10-20 m, lengths of 10-150 m, and heights of 1-9 m. The axial fracture exposes a brittle crust overlying a ductilely deformed layer. The total crustal thickness is typically less than lm. Tumuli are observed on both terrestrial and martian lava flow surfaces, and provide insight on the flow formation processes and rates. Past studies have estimated the inflation pressure using a bending model for a circular, thin elastic plate, assuming small deflection (Rossi and Gudmundson, 1996). This formulation results in unrealistic pressures for some tumuli. We thus examine alternative models, including those with different shapes, bending of the ductile crust, large deflection, plastic deformation, and thick plate bending. Using the thickness of the ductile crust in the equations for thin, circular plates reduces most pressures to reasonable values. Alternative plate shapes do not cause a significant reduction in inflation pressure. Although the large deflection equations should be applicable based on the plate thickness to tumuli height ratios, they give even less realistic pressures. Tumuli with unrealistic pressures appear to have exceeded the critical bending moment, and have relatively thick crusts, requiring thick plate bending models.

Hansen, James E.↗

Modeling Attitude Dynamics in Simulink: A Study of the Rotational and Translational Motion of a Spacecraft Given Torques and Impulses Generated by RMS Hand Controllers

In order to study and control the attitude of a spacecraft, it is necessary to understand the natural motion of a body in orbit. Assuming a spacecraft to be a rigid body, dynamics describes the complete motion of the vehicle by the translational and rotational motion of the body. The Simulink Attitude Analysis Model applies the equations of rigid body motion to the study of a spacecraft?s attitude in orbit. Using a TCP/IP connection, Matlab reads the values of the Remote Manipulator System (RMS) hand controllers and passes them to Simulink as specified torque and impulse profiles. Simulink then uses the governing kinematic and dynamic equations of a rigid body in low earth orbit (LE0) to plot the attitude response of a spacecraft for five seconds given known applied torques and impulses, and constant principal moments of inertia.

Mauldin, Rebecca H.↗

Toward a Unified Parameterization of the Boundary Layer and Moist Convection: A New Type of Mass-Flux Model - Part 1

Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.

Lappen, Cara-Lyn↗

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗

Dataset for manuscript "Rotational Memory Function of SPC/E water"

Memory effect are essential for dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function entering the memory equation. Memory functions of dipole rotations for polar liquids have never been calculated. We present here calculations of memory functions and single-dipole rotations and of the overall system dipole moment for SPC/E water measured by dielectric spectroscopy. The memory functions for single-particle and collective dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation function and the connection between the collective and single-particle relaxation times in terms of the Kirkwood factor. The dataset includes single particle and system dipole moments, including their time-dependence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Finite Element Analysis of a Deployable Space Structure

The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Weeks, G. E.↗

Helicopter rotor wake geometry and its influence in forward flight. Volume 1: Generalized wake geometry and wake effect on rotor airloads and performance

An analytic investigation to generalize wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deformation in the prediction of rotor airloads and performance is described. Volume 1 presents a first level generalized wake model based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. Use of distorted wake models results in the occurrence of numerous blade-vortex interactions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging.

Egolf, T. A.↗

Supersonic full-potential method applied to missile bodies

The NCOREL full-potential method with an entropy correction is presently applied to supersonic missile flowfield problems. After defining the salient characteristics of the method, a combination of linear theory with NCOREL and experimental data is used to isolate the nonlinear features of the supersonic flow so that the influence of geometry and flow conditions on the development of such flow nonlinearities can be appreciated. Comparisons of experimental longitudinal force and moment data with NCOREL and various linear theory predictions are presented for several generic missile airframe configurations of circular and elliptic cross section. The NCOREL code solves the nonconservative full potential equation in a spherical coordinate system; exact boundary conditions are defined on the missile surface.

Pittman, J. L.↗

Computational study of the aerodynamics and control by blowing of asymmetric vortical flows over delta wings

Some of the work is described which was done in a study of the flow field produced by tangential leading edge blowing on a 60 deg. delta wing. The flow is studied computationally by solving the Thin Layer Navier-Stokes equations. Steady state flow fields are calculated for various angles of attack and yaw, with and without the presence of tangential leading edge blowing. The effectiveness of blowing as a rolling moment control mechanism to extend the envelope of controllability is illustrated at pre- and post-stall angles of attack. The numerical grid is generated using algebraic grid generation and various interpolation and blending techniques. The jet emanates from a slot with linearly varying thickness and is introduced into the flow field using the concept of an actuator plane, thereby not requiring resolution of the jet slot geometry. The Baldwin-Lomax algebraic turbulence model is used to provide turbulent closure. The computational results are compared with those of experiments.

Craig, Ken↗

A kinetic theory treatment of heat transfer in plane Poiseuille flow with uniform pressure

Plane compressible Poiseuille flow with uniform pressure (Couette flow with stationary boundaries) is revisited where the Lees two-steam method with the Enskog equation of change is applied. Single particle velocity distribution functions are chosen, which preserve the essential physical features of this flow with arbitrary but uniform plate temperatures and gas pressure. Lower moments are shown to lead to expressions for the parameter functions, molecular number densities, and temperatures which are entirely in agreement with those obtained in the analysis of Lees for compressible plane Couette flow in the limit of low Mach number and vanishing mean gas velocity. Important simplifications result, which are helpful in gaining insight into the power of kinetic theory in fluid mechanics. The temperature distribution, heat flux, as well as density, are completely determined for the whole range of Knudson numbers from free molecular flow to the continuum regime, when the pressure level is specified.

Bahrami, Parviz A.↗