Photothermoelastic analysis of bonded propellant grains

A two-dimensional model of the transversal cross section of a bonded rocket propellant grain was subjected to uniform and steady thermal loading and, alternatively, to mechanically applied uniform radial displacements on the outer boundary. The optimization of perforation contours (attained in previous research programs by applying uniform pressure on the outer boundary of the grain model) was confirmed for both types of thermal loading. The concentration factor at the fillets of the inner contour was determined. An attempt was made to predict the maximum strain in the actual propellant subjected to the same thermal conditions. The material used for the model was a urethane rubber. The thermoelastic properties of the model material were determined.     

Instability and failure of internally pressurized ductile metal cylinders

Forlong, ductile, thick-walled tubes under internal pressure instabilities and final failure modes are studied experimentally and theoretically. The test specimens are closed-end cylinders made of an aluminum alloy and of pure copper and the experiments have been carried out for a number of different initial external radius to internal radius ratios. The experiments show necking on one side of the tubes at a stage somewhat beyond the maximum internal pressure. All tubes, except for one aluminum alloy tube, failed by shear fracture under decreasing pressure. The aluminum alloy tubes exhibited localized shear deformations in the neck region prior to fracture and also occasionally surface wave instabilities. The numerical investigation is based on an elastic-plastic material model for a solid that develops a vertex on the yield surface, using representations of the uniaxial stress-strain curves found experimentally. In contrast to the simplest flow theory of plasticity this material model predicts shear band instabilities at a realistic level of strain. A rather sharp vertex is used in the material model for the aluminum alloy, while a more blunt vertex is used to characterize copper. The theoretically predicted bifurcation into a necking mode, the cross-sectional shape of the neck, and finally the initiation and growth of shear bands from the highly strained internal surface in the neck region are in good agreement with the experimental observations.     

Continuum modeling of a porous solid with pressure-sensitive dilatant matrix

The pressure-sensitive plastic response of a material has been studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an upper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker–Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.     

Uniqueness and stability of rigid-plastic cylinders under internal pressure and axial tension

Uniqueness of deformation and stability of the equilibrium configuration of a long closed-ended cylinder of rigid-plastic material, obeying the von Mises yield criterion, are examined under internal pressure and axial tensile load. Sufficient conditions are derived for uniqueness of the current state of the finitely deformed cylinder. By considering a material model of the Ramberg-Osgood type, it is shown that uniqueness is guaranteed up to a stage when either of the loads (or both) attains a maximum. For such a material model, “pressure-tension interaction curves” are obtained for some values of the wall-ratio and the strain-hardening index. Under internal pressure and small tension, however, the possibility of a bifurcation preceding a stability loss is shown to exist for certain cylinder geometry and material hardening properties.     

Supercritical nitrogen free jet investigated by spontaneous Raman scattering

The injection of fuel and oxidizer in high pressure rocket combustion chambers is simulated in a model experiment dedicated to investigate the phenomenology of coaxial injection at supercritical pressures. Cryogenic nitrogen is injected in a pressurized reservoir of N₂ at ambient temperature at 4 Mpa and 6 Mpa, above the critical pressure for nitrogen of 3.4 Mpa. The radial density distribution of the N₂ is determined by spontaneous Raman-scattering, from the measured densities temperature distributions are derived. The radial density and temperature pro les are analyzed as a function of the distance from the injector for x/D = 1 to 30. The influence of density gradients, internal field effects and interference effects on the performance of the Raman technique when applied to turbulent high density flows is discussed. Received: 5 August 1998/Accepted: 10 January 1999     

A pseudo two-dimensional photoelastic method of testing axisymmetric geometries

Problems involving three-dimensional bodies which possess axial symmetry reduce to two-dimensional analytical problems. If a wedge-shaped portion of an axisymmetric body is tested subjected to the proper boundary condition, then a pseudo two-dimensional photoelastic method of testing may be used. This results in tremendous simplification in testing procedures, particularly when slight changes in model geometry are to be made during the course of testing. This method has been applied to axisymmetric solidpropellant rocket grains to conduct a parametric study of various conicyl geometries. Both pressure and thermal loads were considered for a case-bonded grain. Six parameters were required to define the geometry. The effects of these parameters and of the material properties of the grain were investigated, and parametric curves showing the variation of the maximum stress with those parameters are presented. The experimental results are compared with results obtained from a finite-element computer solution. Good agreement is obtained.     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

Effect of elastomer slight compressibility

This paper is concerned with the constitutive equation for slightly compressible elastic material under finite deformations. We show that material slight compressibility can be effectively taken into account in the case of high hydrostatic pressure or highly confined material. In all other situations the application of the incompressible and nearly incompressible material theories gives practically the same results. Therefore it is of interest to consider the problem in which allowing for material slight compressibility leads to results essentially different from those obtained with help of the incompressible material model. In the present paper this difference has been demonstrated for the problem of high hydrostatic pressure causing an increase of the ‘bulk’ and ‘shear’ material moduli. The behavior of a long hollow cylinder of real material under finite deformations is analyzed. The cylinder is subjected to internal pressure and axial and circular displacements at the outer surface. This problem has been solved analytically using the small parameter method. The solution obtained predicts a decrease of the axial and circular displacements of the outer surface under fixed shear (axial and circular) forces when the internal pressure is applied.     

Experimental research on the rotating detonation in gaseous fuels�Coxygen mixtures

An experimental study on rotating detonation is presented in this paper. The study was focused on the possibility of using rotating detonation in a rocket engine. The research was divided into two parts: the first part was devoted to obtaining the initiation of rotating detonation in fuel–oxygen mixture; the second was aimed at determination of the range of propagation stability as a function of chamber pressure, composition, and geometry. Additionally, thrust and specific impulse were determined in the latter stage. In the paper, only rich mixture is described, because using such a composition in rocket combustion chambers maximizes the specific impulse and thrust. In the experiments, two kinds of geometry were examined: cylindrical and cylindrical-conic, the latter can be simulated by a simple aerospike nozzle. Methane, ethane, and propane were used as fuel. The pressure–time courses in the manifolds and in the chamber are presented. The thrust–time profile and detonation velocity calculated from measured pressure peaks are shown. To confirm the performance of a rocket engine with rotating detonation as a high energy gas generator, a model of a simple engine was designed, built, and tested. In the tests, the model of the engine was connected to the dump tank. This solution enables different environmental conditions from a range of flight from 16 km altitude to sea level to be simulated. The obtained specific impulse for pressure in the chamber of max. 1.2 bar and a small nozzle expansion ratio of about 3.5 was close to 1,500 m/s.     

黏弹性准饱和土中球空腔动力特性

在频率域内研究了内水压力作用下分数导数型黏弹性准饱和土中球空腔的稳态动力响应. 通 过引入与孔隙率有关的应力系数合理地确定了介质和孔隙水共同承担的内水压力值. 将土骨 架和衬砌分别视为具有分数导数本构模型的黏弹性体和多孔柔性材料, 基于Biot两相介质模 型, 通过引入位移势函数解耦得到了内水压力作用下分数导数型黏弹性准饱和土中半封闭球 形空腔的位移、应力和孔隙水压力解析表达式. 考察了物性和几何各参数对球形空腔动力响 应的影响, 结果表明: 分数导数本构模型更合理地描述了土体的动力学行为; 饱和度对应力 和孔隙水压力影响较大, 而对位移影响较小.     

Analysis of deformation of nozzleless rocket propellent

Based on the Total Lagrangian approach and the integral constitutive relation, the viscoelastic large deformation incremental variational equation is derived, and the finite element program of axisymmetric problems is written. By using this program the bore change of propellent of nozzleless rocket under the action of both the internal pressure and burning is dealt with in detail.     

Surrogate model‐based strategy for cryogenic cavitation model validation and sensitivity evaluation

The study of cavitation dynamics in cryogenic environment has critical implications for the performance and safety of liquid rocket engines, but there is no established method to estimate cavitation‐induced loads. To help develop such a computational capability, we employ a multiple‐surrogate model‐based approach to aid in the model validation and calibration process of a transport‐based, homogeneous cryogenic cavitation model. We assess the role of empirical parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogates including polynomial response surface, radial basis neural network, kriging, and a predicted residual sum of squares‐based weighted average surrogate model. The global sensitivity analysis results indicate that the performance of cavitation model is more sensitive to the changes in model parameters than to uncertainties in material properties. Although the impact of uncertainty in temperature‐dependent vapor pressure on the predictions seems significant, uncertainty in latent heat influences only temperature field. The influence of wall heat transfer on pressure load is insignificant. We find that slower onset of vapor condensation leads to deviation of the predictions from the experiments. The recalibrated model parameters rectify the importance of evaporation source terms, resulting in significant improvements in pressure predictions. The model parameters need to be adjusted for different fluids, but for a given fluid, they help capture the essential fluid physics with different geometry and operating conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

软化材料厚壁筒的解析解及其稳定性分析

将弹塑性材料的应力应变全过程曲线简化为三线性模型(弹性-线性软化-残余理想塑性),并假设材料服从Tresca屈服准则和关联流动法则,推导出受内压厚壁筒的解析解.在这个解析解的基础上,讨论了厚壁筒的平衡稳定性问题,内压达到临界载荷时,厚壁筒丧失稳定性,其临界载荷就是软化塑性材料厚壁筒的承载能力.     

Calculating the Time to Creep Failure of Thin-Walled Pipes under Internal Pressure

The time to failure is calculated for thin-walled pipes subjected to internal pressure, to internal pressure and tension, and to internal pressure and bending. The problems are solved using the concept of equivalent stresses. The equivalent stresses are found from a mixed delayed-failure criterion relating the maximum normal stress and the intensity of tangent stresses. The criterion includes an additional material constant, which is determined experimentally. The calculated results and experimental data are compared and found to be in satisfactory agreement     

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth.A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.     

不同材料参数和内压的轮胎对单腹板轮毂变形的影响

将轮胎材料简化为各向同性超弹性材料特性，考虑轮胎与轮毂和地面之间的三维接触以及轮胎中钢丝圈的影响，建立飞机单腹板机轮整体结构有限元模型。主要分析不同轮胎材料参数和内压下，单腹板轮毂轮缘处的径向变形，结果表明；轮毂剖面上测点的应变值与实验结果基本一致。轮胎下沉量与轮毂测点的径向变形和轮毂所受的载荷基本呈线性关系；凸出一侧的轮缘变形最大；轮胎下沉量较大时。轮胎材料参数对轮毂的径向变形影响明显；轮毂测点径向变形在1-2.5mm时，相同的径向变形，轮毂受到的总载荷受轮胎材料参数变化而变化，而在变形较大或较小时，影响不明显。对于同一种轮胎材料，不同的内压，轮毂的变形减轻比较大，气压越高，对于相同的轮胎下沉量，轮毂受到总体荷载也越高。     

Multi‐material closure model for high‐order finite element Lagrangian hydrodynamics

We present a new closure model for single fluid, multi‐material Lagrangian hydrodynamics and its application to high‐order finite element discretizations of these equations 1 . The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high‐order variational generalization of the method of Tipton 2 . This computation is defined by the notion of partial non‐instantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one‐dimensional two‐material problems, followed by two‐dimensional and three‐dimensional multi‐material high‐velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.     

固体火箭发动机柔性接头摆动密封可靠性研究

柔性接头由弹性件与增强件交替粘接而成,是固体火箭发动机进行推力矢量控制的重要装置,因而柔性接头的摆动密封性能对固体火箭发动机而言至关重要.为研究固体火箭发动机柔性接头摆动过程中的密封可靠性,以内聚力模型作为粘接界面的本构模型,通过计算柔性接头各界面的损伤情况及界面间的接触应力,并定义界面节点单元间、界面间以及柔性接头的...     

A model of debonding instability for solid propellant rocket motor: Part I - Uniform longitudinal and transverse stress rate

The interface between a soft and a hard material is vulnerable to debonding because of the prevailing high stress gradient that could be further aggravated under dynamic transient conditions. Such a situation is common in a solid-fuel rocket motor where unstable debonding could be triggered from the initiation of a macrocrack near the interface. The transition from a survival state to a failure state requires knowledge of how the nonlinear, dissipative and nonhomogeneous effects of the dissimilar material interface would interact with load.The solid-fuel rocket motor problem is modeled by a three-layered composite system made of steel, adhesive and rubber under plane extension. Assessed are the time dependent nonhomogeneous deformation and possible failure modes. Only initial properties of the materials were used to determine the evolution of nonequilibrium response. This is made possible by application of the isoenergy density theory that accounts for internal heat generation and energy dissipation effects. Results are presented in two parts. In Part 1, the applied stress rates are assumed to be 0.75 ksi/s in both the longitudinal and transverse direction while Part II assumes different stress rates in these two directions. At approximately one second after loading, a slanted but straight macrocrack of about 5 × 10⁻³ in. is predicted to occur in the rubber next to the interface. This initial crack was found to become unstable at eight seconds and was estimated to be close to the adhesive/rubber interface over a length of 1.88 in. The onset of fracture depended directly on the load transient behavior.     

Numerical simulation of transpiration cooling through porous material

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite‐element solver for the corresponding porous medium flow is presented and coupled with a finite‐volume solver for the compressible Reynolds‐averaged Navier–Stokes equations. The two‐dimensional and three‐dimensional results at Mach number Ma = 0.5 and hot gas temperature T_HG=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.