Analytical and numerical modeling of the transient elasto-dynamic response of a cylindrical tube to internal gaseous detonation

This paper reports the analytical and numerical modeling of the transient elasto-dynamic structural response of a cylindrical tube with finite length to internal detonation loading. The formulation of the proposed analytical model considers the effects of transverse shear and rotary inertia and also describes the effects of reflected waves. In the numerical part of this study, several transient-dynamic linear-elastic finite element analyses are carried out to obtain the structural response of the tube to pressure loads moving at different speeds. The results of the analytical and numerical simulations are compared with experimental results reported in the literature. It is shown that these models are capable of predicting the dynamic structural response of detonation tubes with a high degree of accuracy.     

Elasto/visco-plastic dynamic response of thin shells of revolution subjected to mechanical or thermal loads or both

An analytical method for the elasto/visco-plastic dynamic problems of axisymmetrical thin shells subjected to mechanical or thermal loads or both is developed. The equations of motion and the relations between the strains and displacements are derived by extending Sanders' elastic-shell theory. For the constitutive relations, Perzyna's elasto/visco-plastic equations, including the temperature effect, are employed. The derived fundamental equations are numerically solved by the finite-difference method. As numerical examples, simply supported cylindrical shells made of mild steel are treated, and the following two cases are analyzed: a non-uniformly heated cylindrical shell subjected to impulsive internal pressure, and an internally pressurized cylindrical shell subjected to impulsive thermal load. In both cases, the variations of displacements and internal forces with time are discussed.     

Experimental and analytical investigation of the cylindrical part of a metallic vessel reinforced by filament winding while submitted to internal pressure

In this work, we present an experimental and analytical investigation of a hydrogen storage vessel. This vessel is made of a carbon/epoxy envelope coated on a metal liner. In the theoretical part, an analytical model is proposed in which the laminate composite is assumed to be an anisotropic purely elastic material, whereas the liner is considered as an elasto-plastic material. The suggested analytical model provides an exact solution for stresses and strains on the cylindrical section of the vessel solution submitted to mechanical static loading. The aim of the experimental part is to validate the results of the theoretical model by manufacturing and testing some prototype vessels. Some analytical results are compared with the finite element solutions, a good correlation is observed.     

Self-organized generation of transverse waves in diverging cylindrical detonations

Self-organized generation of transverse waves associated with the transverse wave instabilities at a diverging cylindrical detonation front was numerically studied by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. After solution validation, four mechanisms of the transverse wave generation were identified from numerical simulations, and referred to as the concave front focusing, the kinked front evolution, the wrinkled front evolution and the transverse wave merging, respectively. The propagation of the cylindrical detonation is maintained by the growth of the transverse waves that match the rate of increase in surface area of the detonation front to asymptotically approach a constant average number of transverse waves per unit length along the circumference of the detonation front. This cell bifurcation phenomenon of cellular detonations is discussed in detail to gain better understanding on detonation physics.     

Predictive model of onset of pipe failure due to a detonation of hydrogen–air and hydrocarbon–air mixtures

A fuel specific detonation wave in a pipe propagates with a predictable wave velocity. This internal detonation wave speed determines the level of flexural wave excitation of pipes and the possibility of resonance response leading to a serious structural damage. In this paper, we study the elastic response of metallic tubes and establish the resonance conditions of pipe breakage for internally loaded pipe structures. The analytical results are compared to the high strain rate calculation of a multi-material blast wave analysis using a hydrocode. Various power industries using hydrogen and hydrocarbon fuels exposed to such potential hazards may benefit from the findings of this paper.     

Analytical solution of transverse shear strain vibration of gas detonation loaded tube near second critical speed (shear group velocity)

Analytical solution of transverse shear strain vibration of a tube caused by internal gaseous detonation near the second critical speed (shear group velocity) is not reported in the literature. It is performed based on a steady state model and first order shear deformation theories (model I and II) in this paper, and the results are verified through comparison with the finite element results reported in the literature. There are no known experimental ways of directly measuring dynamic transverse shear strain and only theoretical results and numerical data are available. The finite element method is very time consuming compared with the analytical solution. It is shown in this paper that the resonance phenomenon of the transverse shear strain vibration near the second critical speed can be predicted by steady state model and first order shear deformation theories. The first order shear deformation theory (model II) has a good agreement with finite element results in prediction of dynamic amplification factors and critical speeds.     

Propagation and quenching of detonation waves in particle laden mixtures

Propagation and quenching of curved detonation waves in particle laden mixtures were investigated analytically and numerically using the square wave model and quasi-steady state assumption, respectively. An analytical expression describing the combined effects of heat and momentum losses because of the interaction between the particle and gas phases, as well as the effect of wave curvature on detonation velocity, was obtained. Detonation quenching and multiple detonation regimes were examined. Numerical simulation of the detonation wave structure was also made. The results showed that particle heat loss, momentum loss and wave curvature considerably reduce the detonation speed and cause detonation quenching. It is also shown that, for fixed particle volume fractions, smaller particles cause a larger heat loss from the gas phase and result in a lower detonation velocity and narrow detonation limit.     

Effect of obstacles on the detonation diffraction and subsequent re-initiation

The DCRFoam solver (density-based compressible solver) built on the OpenFOAM platform is used to simulate the reflection and diffraction processes that occur when detonation waves collide with various objects. Static stoichiometric hydrogen–oxygen mixtures diluted with 70% Ar are used to form stable detonation waves with large cells, with initial conditions of 6.67 kPa pressure and 298 K temperature. The diameters of the cylindrical obstacle range from 6 mm to 22 mm, with x = 230 mm, x = 244 mm, and x = 257 mm being the chosen position. Cylindrical, square, triangular, and inverted triangular obstacles are used, and the quenched detonation re-initiation processes behind them are investigated. In the detonation diffraction process, four triple points exist at the same time due to the effect of cylindrical obstacles of smaller diameters. The re-initiation distance of the detonation wave increases with the increase of cylindrical obstacle diameter. Both the Mach reflection angle and the decoupled angle decrease as the diameter increases. When the location of the cylindrical obstacles is changed, the detonation wave dashes into the obstacles with its different front structures, it is easier to realize the detonation re-initiation when the weak incident shock at the front of a detonation wave strikes the obstacles, and the re-initiation distance decreases by 17.1% when compared with the longest re-initiation distance. The detonation re-initiation distance is shortest under the action of cylindrical obstacles, however the quenched detonation cannot be re-initiated when the inverted triangle and square obstacles are used. The suppression effects of inverted triangle and square obstacles on detonation waves are more evident.     

Lean hydrogen-air premixed flame with heat loss

In this paper results of large-scale experiments and numerical simulations of premixed lean hydrogen-air spherical flame propagation with and without high heat losses are presented. Experiments were carried out in a cylindrical volume of 4.5 m³ covered with thin polyethylene film. The heat loss surface is a 50 mm layer of steel wool. Analysis of heat loss effect on combustion products expansion and flame surface density is done. The combination of these parameters governs the manner in which the flame accelerates. It is shown that the loss of heat released at the combustion can significantly reduce the speed of flame propagation and suppress the acceleration of the flame front. Comparison of experimental results and numerical simulations are presented. The subject and results of the study are of critical importance for the industrial explosion safety and may be applied in the areas of internal combustion engines and detonation suppression devices.     

开孔和补强对圆柱壳轴压屈曲的影响分析

  [目的]  早期的圆柱壳轴压屈曲试验结果与理论偏差较大,导致差异的因素较多,其中初始几何缺陷是产生差异的主要因素。  [方法]  文章采用一种专用的轴压屈曲试验平台,可以利用激光位移传感器扫描壳体三维实际形貌。屈曲试验轴压采用液压装置,轴压数据通过称重传感器读取。  [结果]  试验结果表明:开孔降低了圆柱壳轴压屈曲临界载荷,在开孔处插入圆管补强件,提高了圆柱壳轴压屈曲临界载荷。基于壳体形貌实测数据建立了有限元模型,利用Abaqus对圆柱壳、开孔圆柱壳和补强圆柱壳进行非线性屈曲有限元分析。  [结论]  模拟得到的规律与试验规律一致,壳体轴向载荷均是先呈线性增大后减小,开孔圆柱壳轴压屈曲临界载荷最小,含补强件圆柱壳轴压屈曲临界载荷次之,未开过孔的圆柱壳轴压屈曲临界载荷最大。对不同壳体的临界载荷模拟值与试验值进行了比较,其中最小的相对误差只有13.8%。说明运用此方法可以预测壳体轴压屈曲临界载荷,对壳体屈曲设计具有参考价值。     

Fatigue behaviour of oblique nozzles on cylindrical shells submitted to internal pressure and axial forces

In detailed analytical checks against fatigue failure, the local notch stress approach can be considered as one of the most advanced methods for predicting the fatigue behaviour of a mechanical structure. However, it is based on a detailed strength analysis, including macroscopic notch effects, of the real structure, e.g., at weld seams. In this paper, the fatigue behaviour of oblique nozzles on cylindrical shells submitted to internal pressure, axial force and combined loading is analysed according to these principles. Detailed three-dimensional, parametric, finite element models based on brick elements are applied to describe the mechanical behaviour of the structure for a wide range of relevant geometrical parameters. The results of the serial finite element analyses are approximated analytically and thus can be offered to potential users to determine the stresses at arbitrary points of the nozzle-to-vessel junction and to predict the most probable location of fatigue failure.     

Effects of Thermal Loading on the Buckling and Vibration of Ring-Stiffened Functionally Graded Shell

A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia. Heat conduction equation across the shell thickness is used to determine the temperature distribution. Material properties are assumed to be graded across the shell wall thickness of according to a power-law, in terms of the volume fractions of the constituents. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied. The obtained results have been compared with the analytical results of other researchers, which showed good agreement. The new features of thermal vibration and buckling of ring-stiffened functionally graded cylindrical shells and some meaningful and interesting results obtained in this article are helpful for the application and the design of functionally graded structures under thermal and mechanical loads.     

Dynamic response and crack propagation of pre-flawed square tube under internal hydrogen-oxygen detonation

With a validated fluid-structure-fracture coupling approach, this paper studied the dynamic response and crack propagation of pre-flawed square tube under internal hydrogen-oxygen detonation. Fracture of tube was judged by a bivariate failure criterion derived from the underlying failure mechanism at high strain rate conditions. A programed burn approach based on the CJ theory was applied to simulate gaseous detonation. The coupling between detonation wave and tube was realized by penalty contact algorithm with an improved contact stiffness calculation formula. It was demonstrated that the peak pressure at tube edge is 29% higher than that at the middle of tube face. The dominant crack driving force comes from the specific vibration and deformation modes of square tube, where the deformed round section of tube corresponds to the maximum stress wave that travels behind the flexural waves on the tube. Above mechanism makes the backward cracks branch or turn before the forward cracks and the speeds of front and back branch cracks comparable to each other, which is opposite or different from the cases of round tubes. The crack behaviors with different initial flaw locations and detonation pressures were summarized and identified in detail. The forward crack speed can be up to 900 m/s, while the backward crack speeds are generally 65%–85% of above and the branch cracks run at about 100 m/s. In addition, the crack speed has a certain increase immediately after crack branching or turning. Among the three initial flaw location cases, the tube with initial flaw at the middle of face is most resistant to crack propagation under internal detonations.     

Detonation propagation characteristic of H2–O2–N2 mixture in tube and effect of various initial conditions on it

As for the premixed H₂–O₂–N₂ gas ignited and induced by flame in tube, this paper represents systemic researches on its detonative formation process and flow field changes under different initial conditions (pressure, temperature, component concentration). The conservational Euler equation set with chemical reaction is taken as the basic gas phase equation model and the reduced elementary chemical reaction and shock wave problem are considered available so as to establish a theoretical model of premixed H₂–O₂–N₂ combustible gas detonation process. A unity coupling TVD format with second-order accuracy is adopted to solve the gas phase equation and deduce the two-dimension Riemann invariant, and the TVD format for solution of the polycomponent convection equation with elementary chemical reaction is proposed. Meanwhile, a time splitting format is adopted to perfectly treat with the rigid problem resulted from the higher time difference value between gas phase flow characteristic time and chemical reaction characteristic time. It is shown by the calculation results that the detonation waves form certain angle with relation to the tube wall surface at the initial stage of ignition, so as to incur reflections and form reflection waves; during the propagation of the detonation waves, the reflection wave structures are propagated backwards the back of waves constantly, so the whole flow field is characterized of obvious two-dimension. Besides, the excessive pressure detonation occurs at first before formation of the stable detonation propagation process, then a stable detonation propagation process forms finally. Mixed gas detonation characteristics resulted from different calculated-initially parameters are different. The higher the initial temperature and pressure of flame is, the shorter the induction time for detonation formed due to combustion acceleration of the mixed gas is, but which nearly brings no great influence on the later propagation process of the detonation waves. The initial mixed gas component can influence the detonation characteristic of the mixed gas observably, when the quantity relative ratio is close to 1 and the mixed gas with larger reaction activity, its detonation propagation speed is rapider and the pressure after detonation waves is higher. The simulation result keeps accordant with the calculated result of the typical C–J detonation theory model.     

On the mechanical and thermal transient analysis of cylinder-to-cylinder vessels by a finite plate method

A problem common to the pressure vessel analyst is the evaluation of stresses in nozzle-to-cylinder structures subjected to internal pressure, nozzle axial force and nozzle moments. In this paper, the finite plate method—discussed by Brown³¹ in a paper on nozzle-to-cylinder structures subjected to internal pressure—is extended to include axial force and moments at the nozzle terminus. The purpose is to provide an economical alternative to 3-D geometric analytical and experimental stress analysis of such structures.The finite plate concept explored by Rodabaugh²⁵ as a geometric approximation of a finite region of the cylinder about the nozzle is used as the axisymmetric attachment to the nozzle. The variable plate parameters are the outer radius dimension and the harmonic loading at the outer radius of the plate. The parameters are determined for the pressure problem by utilising the shell solution of stresses about a circular hole in a cylinder as data for matching in the flat plate with a hole solution. The parameters for the axial force and moment loading of the nozzle problem are determined by utilising the cylindrical shell series solution of Bijlaard³² for radial force and moment loading and the series solution for asymmetrically loaded axisymmetric plates. Once the parameters are determined, the structural stresses may be calculated by means of an interfacing numerical axisymmetric geometry, asymmetric loading shell or finite element program.In this paper the theoretical development of the geometric and pressure load parameters is briefly reviewed. The analytical development of the parameters for axial force, inplane moment and out of plane moment is presented in detail. The range of applicability is reviewed for the various types of loading.Examples are presented for nozzle-to-cylinder structures loaded by pressure, axial nozzle force, inplane moment at the nozzle and out of plane loading at the nozzle. Finite plane results are compared with the ORNL model No. 3 data obtained by strain gauge and 3-D finite element methods and loaded by nozzle loads. The finite plate results versus the experimental data obtained by Van Campen²⁷ and 3-D finite element data for internal pressure are briefly discussed. In all instances the data compare favourably at the critically stressed location which is at the nozzle-to-cylinder juncture.A comparison of 3-D finite element, 2-D finite element with the finite plate assumptions and some 2-D finite element nozzle-to-hemisphere data from thermal loading is presented.Finally, some observations were made with respect to the assessment of nozzle loads not analytically treated.     

Fracture response of pipelines subject to large plastic deformation under bending

Demand for long-distance offshore pipelines is steadily increasing. High internal pressure combined with bending/tension, accompanied by large plastic strains, along with the potential flaws in girth welds make the structural integrity of pipelines a formidable challenge. The existing procedures for the fracture assessment of pipelines are based on simplified analytical methods, and these are derived for a load-based approach. Hence, application to surface cracked pipes under large deformation is doubtful. The aim of this paper is to understand and identify various parameters that influence the fracture response of cracks in pipelines under more realistic loading conditions. The evolution of CTOD of a pipeline segment with an external circumferential surface crack is investigated under pure bend loading as well as bending with internal pressure. Detailed 3D elastic–plastic finite element simulations are performed. The effects of crack depth, crack length, radius-to-thickness ratio and material hardening on fracture response are examined. The results show that at moderate levels of CTOD, the allowable moment capacity of the pipe decreases significantly with increase in internal pressure. Further, the variation of CTOD with strain can be well approximated by a simple linear relationship.     

Thermoelastic Deformations of Cylindrical Multi-Layered Shells Using a Direct Approach

In this article we study the deformation of thermo-elastic multi-layered shells, using a Cosserat model. By this direct approach, the shell-like bodies are modeled as deformable surfaces with a triad of rigidly rotating directors assigned to every point. The thermal effects are described with the help of two independent temperature fields. Concerning cylindrical orthotropic layered shells, we establish a general solution procedure for a class of thermal stresses problems. These analytical solutions are compared in some special cases with the corresponding three-dimensional solutions and thus, the thermo-elastic coupling coefficients for shells are identified in terms of the material/geometrical parameters of the layers. Finally, we present a comparison between our theoretical results and the numerical solutions obtained by a finite element analysis of a 3-layered cylindrical shell.     

Experimental and numerical study on multi-wave modes of H2/O2 rotating detonation combustor

H₂/O₂ are desirable propellants for rocket-based rotating detonation engines but are rarely reported. This report presents an experimental study on rotating detonations powered by H₂/O₂. A non-premixed three-dimensional numerical simulation was conducted via OpenFOAM-based code. The experimental results revealed more than five co-rotating detonation waves at various flow rates with a propagation speed below 2000 m/s. Furthermore, an adjustment stage was observed prior to the stabilization of the detonation in the N-wave mode. The wavenumber in the adjustment stage varied between N and N+1 when the flow rate was 153 g/s and between N-1 and N+1 at 186 g/s. The simulation results revealed that multiple waves and low filling heights characterized the flow field of the H₂/O₂ rotating detonation. The severe deflagration of the contact surface led to new detonation waves at excessive filling heights. This supports further exploration of the potential application of H₂/O₂ propellants in rotating detonation rocket engines.     

管道截面突缩对爆轰波起爆特性的影响

为研究管道截面突缩对爆轰波起爆特性的影响,在突缩比为5:3的截面突缩管道及直管内对不同初始压力下甲烷氧气预混气体的起爆特性进行了实验研究,利用离子探针获得管道内火焰传播速度,并通过二维数值模拟探究了3种不同突缩比的截面突缩管道内火焰及压力的传播特性.实验结果表明,截面突缩管道内爆轰波起爆距离随着初始压力的降低而逐渐增加...