Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve

In this paper, the effect of a partially closed in-line valve, viscoelasticity, and unsteady friction on the transient behavior of a pressurized pipe is examined. Such an analysis is executed by considering global energy quantities evaluated by means of a one-dimensional numerical model calibrated on the basis of a huge amount of laboratory tests. In the numerical experiments, the effect of the initial conditions and in-line valve characteristics has been analyzed by considering different values of the initial Reynolds number, N₀, in-line valve head loss coefficient, χ, and location, δ. By introducing dimensionless quantities, exponential laws are shown to interpolate the time-history of maxima of both pressure and global energy quantities reliably with the related coefficients being a function of N₀, χ, and δ. Thus, the links between the decay of pressure peaks at single sections and the dissipation of the global kinetic and internal energy are established. Moreover, it is shown that a given decay of pressure peaks may derive from very different transients. This result has crucial implications to inverse transient analysis based on the evaluation of the pressure decay at a given section with particular attention to the uniqueness of the solution.     

The solution of the variational problem of the construction of the contour of a two-regime pipe

This paper is devoted to the problem of the optimal shaping of the supersonic part of a pipe in those cases when the engine is designed to operate in two essentially distinct regimes. The different regimes may be determined, for example, by a difference in fuel consumption, in the configuration of the pipe, which may be a consequence of some adjustment in the conditions of the external medium, etc. We consider two cases. In one of these the pipe may be controlled by a central body moved into it, and in this case only two regimes are possible for such a pipe, i.e., when there is a central body and when the central body is absent. In the second, the flow parameters at the inlet of the pipe, which has no subsonic part, vary for some reason while the configuration of the pipe is fixed (for example, due to a change in fuel consumption or in the parameters at the entrance to the air intake, etc.). We obtain the necessary conditions determining the shape of the optimal contour, and to construct it we develop a numerical algorithm. We give examples of optimal pipes, the contours of which are constructed by the abovementioned algorithm and compare them with pipes chosen in accordance with other considerations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 96–103, July–August, 1973.The author wishes to thank A. N. Kraiko for drawing his attention to the problem.     

Experimental study of air–water flow in downward sloping pipes

This paper presents results from seven experimental facilities on the co-current flow of air and water in downward sloping pipes. As a function of the air flow rate, pipe diameter and pipe slope, the required water discharge to prevent air accumulation was determined. In case the water discharge was less than the required water discharge, the air accumulation and additional gas pocket head loss were measured. Results show that volumetric air discharge as small as 0.1% of the water discharge accumulate in a downward sloping section. The experimental data cover all four flow regimes of water-driven air transport: stratified, blow-back, plug and dispersed bubble flow. The analysis of the experimental results shows that different dimensionless numbers characterise certain flow regimes. The pipe Froude number determines the transition from blow-back to plug flow. The gas pocket head loss in the blow-back flow regime follows a pipe Weber number scaling. A numerical model for the prediction of the air discharge as a function of the relevant system parameters is proposed. The novelty of this paper is the presentation of experimental data and a numerical model that cover all flow regimes on air transport by flowing water in downward inclined pipes.     

Numerical study on effects of check valve closure flow conditions on pressure surges in pumping station with air entrainment

This paper proposes a numerical procedure to better compute the characteristics of pressure surges when check valves close under different flow conditions in a pumping station. Studies have shown that the effects of check valve closure on the pressure transients are predominantly dependent on the magnitude and gradient of the flow velocities immediately downstream of the check valve at the instant of valve closure. Through the present study, it was noted that the transient flow velocities near the check valve of a fluid system are also dependent on the characteristics of the air entrained into the fluid system. An improved numerical computational procedure for the fluid system with air entrainment under different transient conditions downstream of the check valve is also proposed in this paper. With a fluid system operating within the critical range of air entrainment values, the present analysis showed that there is a possibility of ‘high pressure surges’ when the check valves were closed at flow rates other than the positive flow conditions. This phenomenon was confirmed through field observations. This study thus concludes that a detailed numerical transient analysis of the fluid system, with various assumed amounts of entrained air, is necessary whenever there is the possibility of air entrainment into the fluid system, and that the flow conditions at the instant of check valve closure need to be modelled. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimal numerical flux of power-law fluids in some partially full pipes

Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models.

This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge.

Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.     

Effect of viscosity on the autoignition of a reacting moving mixture

Ya. B. Zel'dovich has established [1] that in a continuous-flow reactor two ignition regimes are possible: forced ignition and autoignition.It is important to consider the special properties of the autoignition regime associated with the hydromechanics of laminar flow and heat transfer through the pipe wall. In [2, 3] it was shown that the effect of heat of friction on heat transfer in long pipes is qualitative in character. Moreover, according to Schlichting [4], in certain cases the temperature gradient for such flows due to the heat of friction may reach 10–30°, which is comparable with the preexplosion temperature rise in the stationary theory of thermal explosion [5]. In this connection it is clear that under certain conditions the heat of friction may considerably reduce the explosion limit.This paper is devoted to a study of the effect of heat of friction on the explosion limit of a reacting fluid in a long cylindrical pipe. The dynamic autoignition regime due to heat of friction is examined. In particular, it is established that, other things being equal, by increasing the pressure drop it is possible to obtain explosion of the reacting system.     

Direct numerical simulation of the flow in the intake pipe of an internal combustion engine

The incompressible flow in the intake pipe of a laboratory-scale internal combustion engine at Reynolds numbers corresponding to realistic operating conditions was studied with the help of direct numerical simulations. The mass flow through the curved pipe remained constant and the valve was held fixed at its halfway-open position, as is typically done in steady flow engine test bench experiments for the optimization of the intake manifold. The flow features were identified as the flow evolves in the curved intake pipe and interacts with the cylindrical valve stem. The sensitivity of the flow development on the velocity profile imposed at the inflow boundary was assessed. It was found that the flow can become turbulent very quickly depending on the inflow profile imposed at the pipe inlet, even though no additional noise was added to mimic turbulent velocity fluctuations. The transition to turbulence results from competing and interacting instability mechanisms both at the inner curved part of the intake pipe and at the valve stem wake. Azimuthal variations in the local mass flow exiting the intake pipe were identified, in agreement with previously reported measurement results, which are known to play an important role in the charging motion inside the cylinder of an internal combustion engine.     

管系内一维可压缩流动数值建模与特性分析

针对复杂管系内可压缩流体,基于有限体积法,采用HLLC(Harten-Lax-vanLeerContact)格式和黎曼求解器构建了有限控制体数值离散方法,引入虚拟节点用于连接有限控制体,借助虚拟节点给出控制体之间数值通量的计算格式,发展了一种管道内一维流动数值建模方法。针对含有分支管路的管系,在管道连接部位构建了分支管路拟一维流动数值计算模型。基于所发展的一维流动数值方法,建立了变径管道和含60°分支管道内流动计算模型,验证了该方法的收敛性和有效性;基于虚拟节点的数值格式处理变径管激波问题具有一定精度优势。研究了变径管和分支管模型中可压缩流体激波、稀疏波等的传播机理,分析了管径对相邻支管压力的影响,为工程管路设计提供了参考。     

Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

In the present study, Runge–Kutta schemes are used to simulate unsteady flow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central difference scheme. Second‐order dissipative terms are added in regions of high gradients while they are switched off in smooth flow regions using a total variation diminishing (TVD) switch. The method is applied to both one‐ and two‐dimensional water hammer formulations. Both laminar and turbulent flow cases are simulated. Different turbulence models are tested including the Baldwin–Lomax and Cebeci–Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two‐dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non‐dimensional parameter is identified that controls the damping of pressure transients in elastic pipes. Copyright © 2006 John Wiley & Sons, Ltd.     

DYNAMICS OF A SUBMERGED AND INCLINED CONCENTRIC PIPE SYSTEM WITH INTERNAL AND EXTERNAL FLOWS

In this paper, we formulate a mathematical model to study the dynamics of submerged and inclined concentric pipes with different lengths. The governing equations of motion for the inner pipe are derived under small deformation assumptions and with the consideration of gravitational forces, turbulent boundary layer thickness of external flow, fluid frictional forces, and inertia effects. We obtain discretized dynamical equations using spatial finite-difference schemes and calculate the resonant frequencies of a particular pipe system design. In addition, by varying the operating conditions, we identify a few critical parameters pertaining to the proper design of such pipe systems.     

LOCAL AND GLOBAL INSTABILITY OF FLUID-CONVEYING PIPES ON ELASTIC FOUNDATIONS

We investigate the relationship between the local and global bending motions of fluid-conveying pipes on an elastic foundation. The local approach refers to an infinite pipe without taking into account its finite ends, while in the global approach we consider a pipe of finite length with a given set of boundary conditions. Several kinds of propagating disturbances are identified from the dispersion relation, namely evanescent, neutral and unstable waves. As the length of the pipe is increased, the global criterion for instability is found to coincide with local neutrality, whereby a local harmonic forcing only generates neutral waves. For sets of boundary conditions that give rise only to static instabilities, the criterion for global instability of the long pipe is that static neutral waves exist. Conversely, for sets of boundary conditions that allow dynamic instabilities, the criterion for global instability of the long pipe corresponds to that for the existence of neutral waves of finite nonzero frequency. These results are discussed in relation with the work of Kulikovskii and other similar approaches in hydrodynamic stability theory.     

Transient solution for flow of evaporating fluid in parallel pipes using analysis based on flow patterns

Flow with evaporation in parallel lines with common inlet and outlet headers may result in an uneven flow distribution among the parallel pipes. The prediction of the flow rate distribution in steady state as well as under transient conditions was based on simplified models. In this paper a more accurate time dependent model based on the temporal-local flow pattern in the pipe is presented. The pipe is subdivided into numerical sections and the calculation of the pressure drop in each cell is based on mechanistic models that are specific for the flow pattern in the cell.     

Poroelasticity-III: Conditions on the Interfaces

In this, the third part of our paper, we continue consideration of the major elements of the poroelastic theory which we started in Parts I and II (in Lopatnikov and Gillespie, Transp Porous Media, 84:471?C492, 2010; Transp Porous Media, 89:475?C486, 2011). This third part is devoted to considering the general interfacial conditions, consistent with the governing differential equations of the theory. Specifically, we will consider associated mass and momentum conservation laws. Because we developed the theory by construction, general boundary conditions obtained can be applied to the arbitrary interfaces: boundaries between different materials or, for example, moving interfaces of the shock fronts. We do not consider here the last group of conservation laws: the energy conservation laws, which we are going to introduce and investigate in the special part, devoted to the shock wave propagation. In the meantime, special attention is devoted to discussing the problem of ??partial permeability?? of the interfaces reflected in the literature. Particularly we show, that in the stationary case, the general theory allows only two conditions: either the interface is completely penetrable, or the interface is completely impenetrable. Thus, ??partial permeability?? solution always appears as only an approximation of an exact dynamic problem, which includes either thin low-permeable interfacial layer (with permeable boundaries), or a non-homogeneous boundary containing permeable and non-permeable patterns.     

Modelling of the moisture concentration field due to cyclical hygrothermal conditions in thick laminated pipes

The paper presents a new method to calculate the moisture concentration field induced by cyclical environmental conditions in thick laminated pipes. The solution which is obtained is composed of a transient solution over the interior of the pipe wall and a fluctuating solution within two thin regions, close to the inner and outer lateral surfaces of the pipe wall. The thickness of these two regions is depending on both materials and frequency conditions. The transient solution is determined by using an analytical method based on the solving in average of the field equation. The fluctuating solution is derived from a finite difference scheme. It is shown that after some period of time the transient solution tends towards a permanent time independent solution. In that case, the fluctuating solution becomes a periodic solution which is conditioned by the cyclical boundary conditions. Finally, the effect of particular cyclical conditions on the moisture concentration in thick wall pipes will be tackled.     

噪声对管道超声纵向导波损伤检测的影响

在管道超声导波检测技术的基础上,对不同程度纵向缺陷的损伤检测进行了数值模拟.利用缺陷反射信号对损伤的定位,通过改变管壁局部刚度,研究了缺陷反射信号强度变化的相关规律以及超声导波对缺陷的敏感度,分析了噪声信号对损伤识别的影响,并利用小波的分解和重构算法将信噪分离.结果表明不同程度的信噪比会对超声导波检测法造成一定的影响,通过低通滤噪的方法对信号进行信噪分离,可实现高噪条件下的损伤检测.     

Experimental investigation on the slip between oil and water in horizontal pipes

This work is devoted to study of the slip phenomenon between phases in water–oil two-phase flow in horizontal pipes. The emphasis is placed on the effects of input fluids flow rates, pipe diameter and viscosities of oil phase on the slip. Experiments were conducted to measure the holdup in two horizontal pipes with 0.05 m diameter and 0.025 m diameter, respectively, using two different viscosities of white oil and tap water as liquid phases. Results showed that the ratios of in situ oil to water velocity at the pipe of small diameter are higher than those at the pipe of big diameter when having same input flow rates. At low input water flow rate, there is a large deviation on the holdup between two flow systems with different oil viscosities and the deviation becomes gradually smaller with further increased input water flow rate.     

气固两相分支管流动及流量分配特性的研究

在水平T型分支管道中,用压缩空气对平均粒径为0．5mm砂石进行气固两相流试验。试验结果表明,当压缩空气的流速大于33m／s时,T型分支接头处没有固相沉积,两个分支管路分配的流量几乎相同。当压缩空气的流速小于33m／s时,分支接头处出现沉积,并且沉积量和分支管路的流量分配与分支管路上阀门开度有关:开度相同时,分支接头两侧的固相沉积量和流量分配相同;开度不同时,阀门开度小的一侧分支接头处的沉积量少,其分配的流量也少。     

ABSOLUTE AND CONVECTIVE BENDING INSTABILITIES IN FLUID-CONVEYING PIPES

The effect of internal plug flow on the lateral stability of fluid conveying pipes is investigated by determining the absolute or convective nature of the instability from the analytically derived linear dispersion relation. The fluid–structure interaction is modelled by following the work of Gregory & Paı̈doussis. The formulation of the fluid-conveying pipe problem is shown to be related to previous studies of a flat plate in the presence of uniform flow by Brazier-Smith & Scott and Crigthon & Oswell. The different domains of stability, convective instability, and absolute instability are explicitly derived in control parameter space. The effects of flow velocity, fluid–structure mass ratio, stiffness of the elastic foundation, bending rigidity and axial tension are considered. Absolute instability in flexural pipes prevails over a wide range of parameters. Convective instability is mostly found in tensioned pipes, which are modelled by a generalized linear Klein–Gordon equation. The impulse response is given in closed form or as an integral approximation and its behaviour confirms the results found directly from the dispersion equation.     

扭管混合实验研究

本文通过实验研究扭管中的混沌现象,用烟气显示扭管截面上的混沌对流图像并和数值结果比较,分析其中的马蹄形映及其对流体混合的作用。结果表明,在实际的扭管流动中,由于在管截面上出现马蹄形映射（混沌）,使得其中的流体受到剧烈的拉伸的折叠,实现高效的混合操作。     

Network Model of Flow,Transport and Biofilm Effects in Porous Media

In this paper, we develop a network model to determine porosity and permeability changes in a porous medium as a result of changes in the amount of biomass. The biomass is in the form of biofilms. Biofilms form when certain types of bacteria reproduce, bond to surfaces, and produce extracellular polymer (EPS) filaments that link together the bacteria. The pore spaces are modeled as a system of interconnected pipes in two and three dimensions. The radii of the pipes are given by a lognormal probability distribution. Volumetric flow rates through each of the pipes, and through the medium, are determined by solving a linear system of equations, with a symmetric and positive definite matrix. Transport through the medium is modeled by upwind, explicit finite difference approximations in the individual pipes. Methods for handling the boundary conditions between pipes and for visualizing the results of numerical simulations are developed. Increases in biomass, as a result of transport and reaction, decrease the pipe radii, which decreases the permeability of the medium. Relationships between biomass accumulation and permeability and porosity reduction are presented.