Winfred A. Foster

Three-dimensional finite element analysis of soil interaction with a rigid wheel

1. IntroductionFiniteelementanalysis(FEM)hasbeenutilizedformanyapplicationsinengineering. Early applications of FEM were primarily focused on linearelasticmaterials.However,FEMhasincreasinglybeenutilizedtoanalyzenon-linear,non-elasticmaterialssuchassoil[1].Theseapplicationshavetendedtofocusonstaticsolutionssuchasearthendamsandotherstationarythree-dimensionalsoil-basedstructures.MorerecentlyFEMhasbeenusedinnon-linear,soildynamicapplications[2].Unlikemetals,soilshaveverylittletensilestrength.Whencompressed,theyyieldandbecomepermanentlydeformed.Thesetendenciesmakeanymodelingeffortincludingsoilinteractionnon-linear[3–6].Non-linearproblemstypicallyrequiretheuseoflargenumbersoffiniteelementswhichproduceverylongcomputationaltimes.Specifically,severalagricultural,constructionandmilitaryapplicationsmayrequireFEMtosimulatethethree-dimensional,non-linearinteractionsbe-tween a vehicle and the soil it traverses. These applications presently relyheavilyonbuildandtestdesignmethods.Successfulsimulationwouldprovidetheopportunityforsignificantcostreductioninthedesignprocess.Thispaperfocusesonthecontactandinteractionbetweenawheelandthesoilitismovingover.Uptothispoint,stablesolutionsweretypicallyobtained

A Review of Analytical Methods for Solid Rocket Motor Grain Analysis

Analytical methods for solid rocket motor grain design are proving to be tremendously beneficial to some recent efforts to optimize solid-rocket propelled missiles. The analytical approach has fallen out of favor in recent decades; however, for some classes of grains, the analytical methods are much more efficient than grid-based techniques. This paper provides a review of analytical methods for calculating burn area and port area for a variety of cylindrically perforated solid rocket motor grains. The equations for the star, long spoke wagon wheel, and dendrite grains are summarized and the development of the burn-back equations for the short spoke wagon wheel and the truncated star configurations are included. This set of geometries and combinations of these geometries represent a very wide range of possibilities for two-dimensional grain design. Introduction In many practical solid rocket motor design efforts, final geometric designs for grains are arrived at using numerical layering techniques. This process is geometrically versatile and imminently practical for cases in which small numbers of final geometries are to be considered. However, for a grain design optimization process in which large numbers of grain configurations are to be considered, generating grids for each candidate design is often prohibitive. For such optimization processes, analytical developments of burn perimeter and port area for two-dimensional grains are critically important. Most modern texts on solid rocket propulsion do not provide geometric details for grain design. This paper will offer a review of analytical methods for determining burn area and port area as a function of burn distance for a selection of common grain designs. Analytical developments for solid rocket motor grains were much more prevalent in the decades before widespread use of microcomputers. A summary of one version of the burn back equations for the star grain and for part of one type of wagon wheel can be found in Barrere. Analytical methods have also been developed for the truncated star and for the dendrite. Other potential grain configurations are described in NASA publications but very few geometric details are given in such publications. 1 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 20-23 July 2003, Huntsville, Alabama AIAA 2003-4506 Copyright

Numerical analysis of ignition transients in solid rocket motors

A model to analyze the unstready multidimensional turbulent flow in the head-end, star slot section of a solid rocket motor during the ignition transient is developed. The present paper examines the fluid dynamic aspects of the starting transient. A finite-difference solution of the unsteady, compressible, full Navier-Stokes equations, together with a two-equation k-epsilon turbulence model, is obtained utilizing the MacCormack explicit, predictor-corrector technique. Computed results for the flow in the slot are compared with experimental data obtained in cold flow tests of a scaled model of the Space Shuttle SRM head-end, star grain section. The agreement between the calculated flowfield and existing experimental data is very good.

Results of an experimental investigation of the flow field in the head-end star slot section of a Solid Rocket Motor

Cold flow tests of a one-tenth scale model based on the geometry of the Space Shuttle Solid Rocket Motor, SRM, head-end section and its single-port igniter, along with two models of a four port igniter, have been conducted. The tests were done to establish quantitative as well as qualitative data on the behavior of the flow inside the star slot during the early part of the ignition transient. This paper presents the data obtained from these tests and discusses the implications of the data with respect to ignition transients of solid rocket motors which have head-end star grains.

Analysis of ignition and flame spreading in the Space Shuttle head-end star grain

A model to analyze the unsteady, multidimensional, turbulent flow in the head-end, star slot section of a solid rocket motor (SRM) during ignition transients is presented. This paper examines the complex interactions between the expanding igniter plume, the flow field within the star slot, the heat transfer to the solid propellant, ignition of the propellant, and subsequent flame spreading across the surface of the grain in the slot. The analysis provides a description of the ignition transient sequence from the onset of igniter flow to complete ignition of the head-end star slot region of the SRM.

Numerical analysis of an unsteady confined supersonic jet

Abstract A numerical calculation technique to analyze the time-dependent flow field induced by a supersonic jet expanding into a confined volume is presented. The expanding, developing jet flow and the complex flow pattern within the confining volume are described by the unsteady, compressible, Navier-Stokes equations. The equations are solved using a MacCormack explicit predictor-corrector type of numerical technique. The analysis is applicable to a family of problems including flows within certain solid rocket motor configurations and thermo-electric energy conversion systems.

Numerical analysis of unsteady multiple jet plume interactions

Abstract The prediction of the transient behavior of multiple jet plume systems is important in engineering problems such as those encountered in solid rocket motor (SRM) design. Many SRMs employ a pyrogen-type ignition system, which consists of one or more hot exhaust plumes that induce burning in the motor propellant grain through impingement and subsequent heat transfer. Experimental cold-flow studies have indicated that aerodynamic plume-on-plume interactions, as well as plume-on-wall interactions, can significantly modify the heat transfer to the propellant grain. Such interactions are studied here with a computational model previously utilized in the study of unsteady confined supersonic jets. The model uses a MacCormack explicit, predictor-corrector finite-difference solution of the unsteady, compressible, full Navier-Stokes equations, coupled with a two-equation k − e turbulence model. A parametric study of the transient behavior of multiple plume systems is performed and the degree of interaction between the plumes is investigated.

Direct Measurement of Internal Flow Velocities In A Star-Slot Model

This paper presents the results of a cold flow experiment to make direct measurements of the velocity distribution in a model of a solid rocket motor star grain propellant slot. The experimental procedure utilizes a multi-component laser Doppler velocimeter (LDV) and an apparatus for seeding the flow with aluminum particles to determine the velocity components at various discrete locations within the star slot. The test article used in this investigation was a one-tenth scale, cold flow model based on the geometry of the Space Shuttle solid rocket motor head-end section. The results obtained for the direct measurements of velocity are compared to velocities calculated from measured pressure distributions, to data obtained from oil smear experiments and flow visualization videos, and to heat transfer calorimeter data.

Experimental investigation of the flow field in the head-end star slot section of a solid rocket motor

A test program has been developed to investigate the complex flowfield in the head-end, star grain section of a solid rocket motor. Documentation of the flowfield pattern is to be obtained using both flow visualization techniques and quantitative methods, including static pressure measurements, heat transfer coefficient measurements, and hot-wire anemometry. A cold-flow, one-tenth-scale model based on the geometry of the Space Shuttle SRM head-end section and its single-port igniter, along with two models of a four-port igniter, have been constructed. The scale factor is derived from a scaling analysis which matches Reynolds number between the model and the full-scale flowfield in the star grain section. The NASA Marshall Space Flight Center 14 x 14 inch trisonic wind tunnel will be utilized for the cold flow tests. Since the work is still in progress, no results are included.

Analysis of thermal performance of penetrated multi-layer insulation

Results of research performed for the purpose of studying the sensitivity of multi-layer insulation blanket performance caused by penetrations through the blanket are presented. The work described in this paper presents the experimental data obtained from thermal vacuum tests of various penetration geometries similar to those present on the Hubble Space Telescope. The data obtained from these tests is presented in terms of electrical power required sensitivity factors referenced to a multi-layer blanket without a penetration. The results of these experiments indicate that a significant increase in electrical power is required to overcome the radiation heat losses in the vicinity of the penetrations.