Leakage effects in laminar duct flow: a numerical study

The influence of transverse leakage into a pressure-driven laminar flow in an infinitely long square duct is investigated. By a simple decomposition of the resulting three-dimensional pressure field, the leakage-induced secondary flow problem decouples from the primary flow problem. The numerical study reveals that two qualitatively different secondary flow patterns may occur, depending on the leakage flow rate. For a given streamwise pressure gradient it is observed that the axial mass flow rate may reduce by about 30 percent under certain leakage conditions, accompanied by a corresponding 50 percent increase in the Darcy-Weisbach friction factor.Nomenclature D duct height and width - D _h hydraulic diameter - D _i,j cell divergence - F dimensionless pressure force - h dimensionless slit height,H/D - H slit height - i,j indices - K streamwise kinematic pressure gradient - n summation index, time level - p dimensionless pressure - p pressure increment - P pressure - cross-sectional pressure variation - q dimensionless volumetric axial flow rate - Q leakage flow rate in m²/s - Re leakage Reynolds number,U ₀ D/ - Re _q primary flow Reynolds number - t time increment - x, y dimensionless cross-sectional coordinates - x, y cell widths - X, Y cross-sectional coordinates - z dimensionless axial coordinate - Z axial coordinate - u, v, w dimensionless velocity components - U, V, W velocity components - U ₀ leakage velocity,Q/H - V cross-sectional average velocity - W ₀ dummy velocity scale Greek letters density - kinematic viscosity - overrelaxation factor     

Exact quasi-steady solution of the problem of hydraulic fracturing of a permeable formation

An exact solution of the problem of hydraulic fracturing in a permeable medium with continuous fluid injection in a partially penetrated formation is constructed using the Perkins-Kern fracture model. The amount of fluid leakage from the fracture is determined using the pressure field of the fluid filtrate defined by the Shchelkachev equation (of the piezoconductivity type). Universal profiles of the fluid pressure in the fracture and the rate of fluid flow from it are obtained. It is shown that at the Perkins-Kern fracture tip, there is a dramatic increase in the leakage from the fracture.     

摆动液压缸圆环螺旋流的流动及内泄漏研究

考虑液压油的黏度随温度与压强的变化, 以连续性方程、N-S方程、能量方程为基础, 推导出螺旋摆动液压缸内部圆环螺旋流的速度方程及泄漏量方程. 运用大型通用CFD仿真软 件fluent对螺旋摆动液压缸内部的圆环螺旋流流场及泄漏规律进行数值仿真. 对螺旋摆 动液压缸内螺旋流动的理论计算与仿真结果进行对比分析, 结果表明理论推导正确, 从而为螺旋摆动 缸内泄漏及容积耗损提供理论依据.     

Hydrodynamics of viscous fluid through porous slit with linear absorption

The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.     

螺旋槽端面微间隙高速气流润滑密封特性

考虑入口气流压力损失和出口阻塞效应,建立了微间隙端面高速气体润滑密封分析数学模型,对螺旋槽端面微间隙高速气流润滑密封特性进行研究.重点分析了不同密封间隙、密封压力和转速等工况条件下,入口压力损失和出口阻塞效应对开启力、泄漏率及气膜刚度等密封特性参数的影响规律.结果表明:高速气体阻塞效应使出口压力高于环境压力,压力损失使入口气膜压力下降,导致泄漏率和气膜刚度明显下降,并使开启力增加.随着密封压力和密封间隙的增加,阻塞效应增强,导致泄漏率和气膜刚度显著降低.密封压力10 MPa时,泄漏率降低可达20%,气膜刚度的下降可达30%以上.     

A Semi-Analytical Solution for Large-Scale Injection-Induced Pressure Perturbation and Leakage in a Laterally Bounded Aquifer–Aquitard System

A number of (semi-)analytical solutions are available to drawdown analysis and leakage estimation of shallow aquifer–aquitard systems. These solutions assume that the systems are laterally infinite. When a large-scale pumping from (or injection into) an aquifer–aquitard system of lower specific storativity occurs, induced pressure perturbation (or hydraulic head drawdown/rise) may reach the lateral boundary of the aquifer. We developed semi-analytical solutions to address the induced pressure perturbation and vertical leakage in a “laterally bounded” system consisting of an aquifer and an overlying/underlying aquitard. A one-dimensional radial flow equation for the aquifer was coupled with a one-dimensional vertical flow equation for the aquitard, with a no-flow condition imposed on the outer radial boundary. Analytical solutions were obtained for (1) the Laplace-transform hydraulic head drawdown/rise in the aquifer and in the aquitard, (2) the Laplace-transform rate and volume of leakage through the aquifer–aquitard interface integrated up to an arbitrary radial distance, (3) the transformed total leakage rate and volume for the entire interface, and (4) the transformed horizontal flux at any radius. The total leakage rate and volume depend only on the hydrogeologic properties and thicknesses of the aquifer and aquitard, as well as the duration of pumping or injection. It was proven that the total leakage rate and volume are independent of the aquifer’s radial extent and wellbore radius. The derived analytical solutions for bounded systems are the generalized solutions of infinite systems. Laplace-transform solutions were numerically inverted to obtain the hydraulic head drawdown/rise, leakage rate, leakage volume, and horizontal flux for given hydrogeologic and geometric conditions of the aquifer–aquitard system, as well as injection/pumping scenarios. Application to a large-scale injection-and-storage problem in a bounded system was demonstrated.     

Effect of multiple DBD plasma actuators on the tip leakage flow structure and loss of a turbine cascade

In this paper, the effects of multiple dielectric barrier discharge (DBD) plasma actuators on the leakage flow structures and loss conditions have been numerically studied in an axial turbine cascade. Kriging surrogate model is adopted to obtain the optimal cases. The physical mechanism of flow structures inside the gap that control leakage flow is presented, which is obtained by analyzing the flow topology, the evolution of the flow structures and its influence on the secondary velocity and loss conditions in the passage as well. The results show that the induced vortex caused by DBD actuators can change the leakage flow direction inside the tip gap and make the separation bubble break earlier, leading to a new type of the flow pattern. When the actuators are applied, the speed of leakage flow is significantly reduced and the angle between leakage flow and main flow has an obviously diminution, causing the reduction of mixing losses in the passage compared with the Baseline case. Furthermore, the comparison of secondary velocity shows that the tip leakage vortex (TLV) approaches the suction surface, resulting in reduced affected area and weakened loss strength. Plasma actuators can diminish the loss coefficient in both TLV and passage vortex near the casing (PVC) zones. The actuators arranged near the trailing edge mainly affect the strength of TLV, while the actuators in the leading edge area contribute to the loss reduction in the zone of PVC.     

长输管道泄漏故障诊断方法的研究

将序贯概率比检测法（SPRT）应用到管道泄漏的在线故障诊断中，基于SPRT检测法提出了泄漏识别因子，该因子的提出大大提高了泄漏监测系统的识别精度。同时对于非稳定流体，引入了相对稳定过程的概念，通过对均衡流量的检验可以进行泄漏监测。最后，利用参数识别等方法对泄漏进行定位，实验结果证明了方法的有效性。     

中低速下干气密封型槽仿生改进研究

为解决干式气体端面密封在中低速或启动停车阶段密封性能不稳定的问题,在现有螺旋槽端面型槽结构的基础上借鉴仿生学设计方法提出了仿生多流通道螺旋槽干气密封端面结构.基于气体润滑理论模型,采用数值分析方法计算了气体端面气膜压力控制方程-雷诺方程,研究对比了普通螺旋槽和多流通道槽的端面压力分布.在改变操作参数和端面气膜厚度的条件下分析对比了普通螺旋槽和多流通道槽两种干气密封的开启力,泄漏率,刚度和刚漏比的变化规律,并研究了槽的通道数对密封性能的影响规律.结果表明:中低速下多流通道细长螺旋槽具有高的稳定性和好的密封性,汇流槽在增加密封稳定性的同时可降低泄漏率.     

Simplified modeling of blast waves from metalized heterogeneous explosives

The detonation of a metalized explosive generates a complex multiphase flow field. Modeling the subsequent propagation of the blast front requires a detailed knowledge of the metal particle dynamics and reaction rate. Given the uncertainties in modeling these phenomena, a much simpler, 1D compressible flow model is used to illustrate the general effects of secondary energy release due to particle reaction on the blast front properties. If the total energy release is held constant, the blast pressure and impulse are primarily dependent on the following parameters: the proportion of secondary energy released due to afterburning, the rate of energy release, the location the secondary energy release begins, and the range over which it occurs. Releasing the total energy over a longer time period in general reduces the peak blast overpressure at a given distance. However, secondary energy release reduces the rate of decay of the shock pressure, increases the local gas temperature and hence increases the velocity of the secondary shock front. As a result, for certain values of the above parameters, the peak blast impulse may be increased by a factor of about two in a region near the charge. The largest augmentation to the near-field peak impulse results when the secondary energy is released immediately behind the shock front rather than uniformly within the combustion products.     

A Thickened-Hole Model for Large Eddy Simulations over Multiperforated Liners

Flow instabilities such as Rotating Stall and Surge limit the operating range of centrifugal compressors at low mass-flow rates. Employing compressible Large Eddy Simulations (LES), their generation mechanisms are exposed. Toward low mass-flow rate operating conditions, flow reversal over the blade tips (generated by the back pressure) causes an inflection point of the inlet flow profile. There, a shear-layer induces vortical structures circulating at the compressor inlet. Traces of these flow structures are observed until far downstream in the radial diffuser. The tip leakage flow exhibits angular momentum imparted by the impeller, which deteriorates the incidence angles at the blade tips through an over imposed swirling component to the incoming flow. We show that the impeller is incapable to maintain constant efficiency at surge operating conditions due to the extreme alteration of the incidence angle. This induces unsteady flow momentum transfer downstream, which is reflected as compression wave at the compressor outlet traveling toward the impeller. There, the pressure oscillations govern the tip leakage flow and hence, the incidence angles at the impeller. When these individual self-exited processes occurs in-phase, a surge limit-cycle establishes.     

On pulsating flow of polymeric fluids

The flow problem of an elastico-viscous fluid in a straight circular pipe under the influence of a fluctuating pressure gradient is considered. Adopting a simple, generalized Maxwell model, it is shown that the percentage increase in the mean flow rate rises with increasing frequency of fluctuation. The value of the mean pressure gradient at which the flow rate enhancement attains its maximum value is determined entirely by inelastic calculations.     

Pressure transients during injection: Constant rate and convolution solutions

Pressure transient testing during water injection is undertaken to evaluate the injection potential of a well. If properly interpreted, it can yield information such as effective mobilities of fluids, wellbore damage, and residual oil saturation. This is best done by the simultaneous use of downhole flow-rate and pressure measurements. Analytical solutions obtained under various assumptions for pressure response of an injection well are investigated. For a constant downhole flow rate, it is demonstrated that exact solutions may be obtained for an infinite reservoir during both the injection and the falloff periods. Due to the inherent nonlinearity of the problem, the constant rate solutions are not readily extended for the general case of varying flow rates. Therefore, we have employed an approximate technique. This technique can be used with an altered form of convolution and permits calculation of the pressure response for arbitrary rate data. The range of parameters under which this method may be used are also identified. Computational methods related to convolution are presented. The numerical techniques developed in this paper are sufficiently general that they may be applied to similar well-testing problems involving single-phase flow.     

零重力条件下低温射流抑制大尺寸液氢储罐热分层的数值研究

液氢是一种常用的沸点低、易蒸发的空间低温推进剂.空间微重力环境中浮力对流被极大减弱,当推进剂储罐壁面存在局部漏热时,储罐内部气液两相流体系会出现环绕漏热源的热分层现象,引起局部过热沸腾,导致储罐内部压力急剧增大,危害系统结构安全.利用低温射流抑制储罐热分层现象是一种有效手段.低温流体通过设置在储罐内部的射流喷嘴与储罐内...     

蜿蜒边界下平面流的线性流动稳定性

为便于数值分析,蜿蜒河流水动力和演变模型中一般隐性假设二次时均流-二次涡的关系与明渠流时均流-明渠湍流的关系相同,但由于高雷诺数下的DNS算力限制和实验尺度限制,这种隐含假设是否成立目前尚无相关湍流研究来支撑.文章试图通过分析明渠湍流和二次湍流发展初期的研究,侧面揭示其湍流结构的异同.通过对曲线正交坐标系下的平面二维NS方程使用双参数摄动的方法,建立了一种求解蜿蜒边界弱非线性层流的摄动解法,并推导得出一个适用于蜿蜒边界的EOS方程以及其特征值问题的解法.蜿蜒边界下弱非线性层流解为一系列蜿蜒谐波分量的叠加,其中线性部分使得两壁产生流速差,非线性部分随着雷诺数增大呈指数增长.水流的扰动增长率特征谱的第一模态与直道流相似,由3条曲线、4个波段合成,但其长波段和短波段的扰动流场与直道流不同,所有短波段的扰动流速近似于KH涡.蜿蜒边界对内部水流扰动有一定的选择性.偏角幅值越大扰动增长越快;蜿蜒波数的影响则为先增后减,有一个使扰动增长最快的蜿蜒波数.扰动流场由一个典型的TS波和一对波包形式的二次涡叠加而成,波包只有纵向流速分量,包络线由蜿蜒波数控制,波包内是与直道扰动波参数相同的TS波.     

A representation of the solution of the Gromeko problem for viscous and elastico-viscous fluids

The solution of the Gromeko problem [1] on unsteady flow of a viscous fluid in a long circular pipe is among the few exact solutions of the Navier-Stokes equations. Its effective solution is obtained only when the longitudinal pressure gradient is given as an arbitrary time function. However, in practice we encounter cases when the flow rate is a known time function. This sort of problem arises, in particular, in rheological experiments using viscometers with a given flow rate. In this case the determination of the pressure gradient from the given flow rate leads in the general case to a very unwieldy expression. Below we present an effective solution of this problem for viscous and elasticoviscous media using the method of solving the inlet flow problem for a steady flow of a viscous fluid in a semi-infinite pipe. It is shown that for the case of a viscous fluid these two problems are actually equivalent.     

Flow driven by a stamped metal cooling fan – Numerical model and validation

This paper presents a numerical fluid flow model for the stamped metal cooling fans popularly employed in electric motors. An experimental system is constructed to measure the performance of the cooling fan. The agreements between model prediction and experimental data are reasonably good. Parametric studies with the numerical model indicate that the viscous heating in the fluid and the variation of the air density have negligible effects on the fan performance. The blade edge thickness affects the flow driving capability of the fan. With various pressure differentials, three flow regimes are recognized. The first is the axial component dominated flow. In the second regime, the flow has a forward axial flow and a backward leakage flow. The third one is the leakage flow dominated regime, when the pressure differential across the fan is large.     

An indirect pressure-gradient technique for measuring instantaneous flow rates in unsteady duct flows

A new technique is presented for making measurements of the instantaneous flow rate in unsteady laminar pipe flows. It utilizes a relationship between flow rate and pressure-gradient history that is an exact solution to the Navier–Stokes equations for parallel, developed flow of constant-property Newtonian fluids undergoing arbitrary unsteadiness from an initially steady or stationary state. The method does not rely on any assumption about velocity profiles, and applies instantaneously in momentarily reversing flow. Experimental comparisons between direct measurements of the cumulative flow and the results of this technique indicate that it is capable of providing measurements of cumulative flow and flow rate which are accurate to within a few percent at any instant during a flow transient, provided the instantaneous pressure gradient can be measured with this accuracy.     

气藏压裂水平井非稳态流动分析

应用Green函数和Newman积原理,建立了压裂水平井与气藏耦合的非稳态流动模型,并给出求解方法。所建立的模型可应用多种约束条件,考虑了井筒压降和加速度的影响,并适用于各向异性气藏。实例计算表明：水平井在早期非稳态阶段的流量比拟稳态阶段大得多。早期非稳态流动阶段,各条裂缝之间未发生干扰,流量的大小与裂缝条数成正比例关...     

Simulation in primitive variables of incompressible flow with pressure Neumann condition

A velocity–pressure algorithm, in primitive variables and finite differences, is developed for incompressible viscous flow with a Neumann pressure boundary condition. The pressure field is initialized by least‐squares and updated from the Poisson equation in a direct weighted manner. Simulations with the cavity problem were made for several Reynolds numbers. The expected displacement of the central vortex was obtained, as well as the development of secondary and tertiary eddies. Copyright © 1999 John Wiley & Sons, Ltd.