Dynamic behaviour of direct spring loaded pressure relief valves in gas service: II reduced order modelling

A previous study of gas-service direct-spring pressure relief valves connected to a tank via a straight pipe is continued by deriving a reduced-order model for predicting oscillatory instabilities such as valve flutter and chatter. The reduction process uses collocation to take into account a finite number N of acoustic pressure waves within the pipe, resulting in a set of 2N+3 ordinary differential equations. Following a novel non-dimensionalization, it is shown analytically that the model can exhibit, at experimentally realistic parameter values, instabilities associated with coupling between the valve and acoustic waves in the pipe. The thresholds for each instability are such that for a given flow rate, the first mode to go unstable as the inlet pipe length increases is the quarter-wave mode, then a three-quarter wave, a 5/4-wave etc. Thus the primary mode of instability should always be due to the quarter wave. In the limit of low flow rates, a simple approximate expression is found for the quarter-wave instability threshold in the form of inlet pipe length against mass flow rate. This threshold curve is found to agree well with simulation of the full model. For higher flow rates there is a need to include fluid convection, inlet pressure loss and pipe friction in order to get good agreement. The reduced model enables the dependence of the stability curve on key dimensionless physical parameters to be readily computed.     

Dynamic behavior of direct spring loaded pressure relief valves in gas service: Model development,measurements and instability mechanisms

A synthesis of previous literature is used to derive a model of an in-service direct-spring pressure relief valve. The model couples low-order rigid body mechanics for the valve to one-dimensional gas dynamics within the pipe. Detailed laboratory experiments are also presented for three different commercially available values, for varying mass flow rates and length of inlet pipe. In each case, violent oscillation is found to occur beyond a critical pipe length, which may be triggered either on valve opening or closing. The test results compare favorably to the simulations using the model. In particular, the model reveals that the mechanism of instability is a Hopf bifurcation (flutter instability) involving the fundamental, quarter-wave pipe mode. Furthermore, the concept of the effective area of the valve as a function of valve lift is shown to be useful in explaining sudden jumps observed in the test data. It is argued that these instabilities are not alleviated by the 3% inlet line loss criterion that has recently been proposed as an industry standard.     

管道结构对氢/空预混气体爆炸特性影响研究

为研究管道结构对氢-空预混气体爆炸特性影响,采用实验与数值模拟相结合的方法,分析不同管道结构内氢-空预混气体燃爆时火焰传播进程、爆炸压力、湍流动能变化及流场分布.结果表明:90°弯管对氢-空预混气体爆炸强度增强作用明显高于T型分岔管和直管.火焰阵面在结构突变处褶皱变形较明显,并出现大尺度强湍流和涡团,气团脉动速度与湍流...     

ORDER CLASSIFICATION OF URBAN CATCHMENTS1

ABSTRACT: Stream order systems provide useful classification methods according to the number of tributaries collected. In urban catchments, sewer line order is a concepot concept providing for the same type of classification. Horton's stream order system is used to classify sewers beginning with the smallest lines as first order to the largest main sewer which is sixth order for two catchments studied. Average tributary area, average length and number of lines are shown as functions of order. The bifurcation ratios are also presented. They can be used for finding the number of sewer lines in the next order. The number of first order lines depend on lot size and the bifurcation ratios vary widely.     

近期长江口南北槽分流口河段悬沙输运机制研究

针对近期长江口南北槽分流口地区出现新的河床冲淤演变情况,对分流口河道尤其北槽入口河段多次实测水文结果进行分析,探讨了分流口河道悬沙输运机制。〖JP2〗通过引入输沙机制影响强度尺度参数,得到悬沙输运机制的数学表达形式,并进一步探讨了北槽入口河道产生淤积的原因。结果表明：(1)北槽分流口存在三级输沙机制,且不同输沙机制项在近口段、口中段和口内段各段中影响程度也不相同;(2)分流口泥沙来源于南港河段,在向“南港-北槽”输运过程中,一部分泥沙受到分流潜堤拦截,落淤在潜堤北侧造成九段沙沙头持续淤长;(3)悬沙在口中段受两项输沙机制的共同控制下,跨跃航槽,横向输运。并在输移过程中落淤,最终形成北槽入口局部区域的持续淤积     

高等动物捕食对赤潮藻类模型非线性动力学行为的影响

针对多种群赤潮藻类的生态系统,运用非线性动力学理论,研究了高等动物捕食行为对该系统所产生的复杂动力学行为的影响。结果发现：藻类生态系统对高等动物的捕食有很强的敏感性,后者加剧了前者的复杂动力学行为的变化,在考虑生态系统模型的建立时,高等动物的捕食及其转化率是两个非常重要的因素。     

障碍物在分岔附近对瓦斯爆炸压力影响的实验研究*

为研究置障条件下不同分岔角度管道中瓦斯爆炸压力变化规律,采用长15 m、截面为160 mm×100 mm的矩形和直径160 mm的半圆形组成的拱形模拟巷道,通过改变分岔角附近障碍物的形状与阻塞比,研究瓦斯爆炸在30~45°与30~60°双分岔管道分岔角附近的压力变化规律。结果表明:瓦斯爆炸在30~45°和30~60°双分岔管道中,分岔角后2支管压力均有所增大,且45°和60°支管中压力变化较30°支管更加明显;障碍物位于30°分岔角后,当阻塞比为0.4时,障碍物形状对2~4测点爆炸压力的影响均表现为矩形最大,拱形次之,圆形最小;管道中矩形障碍物对2,3测点爆炸压力的影响随阻塞比增加而增大,对测点4爆炸压力的影响则随阻塞比的增加而减小;设置矩形障碍物时,30~45°双分岔管道中2,3测点的压力增幅大于30~60°双分岔管道,且压力增幅随阻塞比增加而增大,而测点4的表现则相反,30~60°双分岔管道大于30~45°双分岔管道,且压力增幅随阻塞比增加而减小。     

长江河口中央沙位移变化与南北港分流口稳定性研究

中央沙位于长江口南北港分流口河段，这一河段集中了宝钢等一批重要码头，下游有长兴岛造船基地和长江口深水航道等重点工程，因此分流口保持稳定至关重要。以1870年中央沙出现雏形以来的海图为基础资料，利用ArcGIS等GIS软件，研究了中央沙发育演变的位移变化及其典型剖面特征，发现中央沙的变化特点是在长期径流作用下后退和承接上游底沙下泄发生上提的“下移-上提-再下移……”的周期性演变规律。再进一步对南北港分流口各个沙洲近10年来面积和体积进行计算，结合实测水文资料对通道演变进行了分析，认为现阶段长江口南北港分流口处于不稳定时期，应尽早实施分流口整治工程，稳定河势、滩势和减小底沙下泄对下游的威胁.     

Y型合流分岔隧道临界风速计算模型

临界风速是Y型合流分岔隧道能否有效抑制烟气侵入分岔支路的重要参数。为确定Y型合流分岔隧道临界风速计算公式,对影响Y型合流分岔隧道临界风速的相关因素进行量纲分析,推导出临界风速与火源热释放率、主分隧道高度比、连拱长度及隧道分岔夹角这4个因素的无量纲函数关系式。通过数值模拟得到临界风速最大的火源位置,并对上述4个影响因素进行了量化分析。结果表明:火源距分岔段隧道洞口15～25 m时临界风速最大;当无量纲火源热释放速率小于0. 3时,隧道临界风速与火源热释放率呈现1/3次方关系,当无量纲火源热释放速率大于0. 3时,隧道临界风速不再随火源热释放速率增加而增加;临界风速与分岔隧道高度比近似成-3/10次方关系,与分岔夹角成-3/40次方关系,而与连拱长度无关。进而得到分岔隧道临界风速的无量纲计算模型,且与数值模拟结果吻合良好。     

Pattern formation of a predator-prey system with Ivlev-type functional response

In this paper, we investigate the spatial pattern formation of a predator-prey system with prey-dependent functional response Ivlev-type and reaction-diffusion. The Hopf bifurcation of the model is discussed, and the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained. Based on this, we perform the spiral and the chaotic spiral patterns via numerical simulation, i.e., the evolution process of the system with the initial conditions which was small amplitude random perturbation around the steady state. For the sake of learning the pattern formation of the model further, we perform three categories of unsymmetric initial condition, and find that with these special initial conditions the system can emerge not only spiral pattern but also target pattern and so on, and the effect of these special conditions on the formation of spatial patterns is less and less with more and more iterations but the effect does not decay forever. This indicates that for prey-dependent type predator-prey system, pattern formations do depend on the initial conditions, while for predator-dependent type they do not.