On the analytical solution of transient friction in channel flows

The transient friction in channel mean flows is the sum of two contributions,i.e.,the underlying laminar flow(ULF)and the purely turbulent component(PTC),and the contributions are analyzed separately by theoretical experiments.It is found that,the transient friction may be higher or remarkably lower than that in equal-Reynolds number steady-state flows.The universal time constant for plane-parallel laminar flows is reported,and the role of the time constant in a turbulent mean flow is examined.It is shown that the time constant is related to the turbulence's frozen time.Finally,a study of the logarithmic layer during the transient flow is accomplished,which shows that the logarithmic layer is destroyed.

A transient production prediction method for tight condensate gas wells with multiphase flow

Considering the phase behaviors in condensate gas reservoirs and the oil-gas two-phase linear flow and boundary-dominated flow in the reservoir,a method for predicting the relationship between oil saturation and pressure in the full-path of tight condensate gas well is proposed,and a model for predicting the transient production from tight condensate gas wells with multiphase flow is established.The research indicates that the relationship curve between condensate oil saturation and pressure is crucial for calculating the pseudo-pressure.In the early stage of production or in areas far from the wellbore with high reservoir pressure,the condensate oil saturation can be calculated using early-stage production dynamic data through material balance models.In the late stage of production or in areas close to the wellbore with low reservoir pressure,the condensate oil saturation can be calculated using the data of constant composition expansion test.In the middle stages of production or when reservoir pressure is at an intermediate level,the data obtained from the previous two stages can be interpolated to form a complete full-path relationship curve between oil saturation and pressure.Through simulation and field application,the new method is verified to be reliable and practical.It can be applied for prediction of middle-stage and late-stage production of tight condensate gas wells and assessment of single-well recoverable reserves.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Equivalent Method of Integrated Power Generation System of Wind, Photovoltaic and Energy Storage in Power Flow Calculation and Transient Simulation

针对工程实际开展风光储联合发电系统在潮流计算和机电暂态仿真中的等值方法研究，旨在为大容量风光储联合发电系统的并网仿真分析奠定基础。将潮流计算的等值分为单元机组和集电系统2部分来研究。单元机组等值采用根据不同控制模式选取不同节点类型的方法，针对集电系统等值提出基于损耗不变原则的方法。等值模型和详细模型的算例结果表明，潮流计算等值方法具有较好的精度。在机电暂态仿真动态等值中，基于实际工程计算的最严重工况分析原则，提出运行在满出力点的单机“倍乘”等值模型，为工程计算中的风光储联合发电系统动态等值提供了一种解决方案。

THEORETICAL ANALYSIS ON HYDRAULIC TRANSIENT RESULTED BY SUDDEN INCREASE OF INLET PRESSURE FOR LAMINAR PIPELINE FLOW

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.

Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

Impact of Typical Steady-state Conditions and Transient Conditions on Flow Ripple and Its Test Accuracy for Axial Piston Pump

The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated working conditions. However, the pump usually has to work in large-scale and time-variant working conditions. Therefore, the flow ripple characteristics of pump and analysis for its test accuracy with respect to variant steady-state conditions and transient conditions in a wide range of operating parameters are focused in this paper. First, a simulation model has been constructed, which takes the kinematics of oil film within friction pairs into account for higher accuracy. Afterwards, a test bed which adopts Secondary Source Method is built to verify the model. The simulation and tests results show that the angular position of the piston, corresponding to the position where the peak flow ripple is produced, varies with the different pressure. The pulsating amplitude and pulsation rate of flow ripple increase with the rise of pressure and the variation rate of pressure. For the pump working at a constant speed, the flow pulsation rate decreases dramatically with the increasing speed when the speed is less than 27.78% of the maximum speed, subsequently presents a small decrease tendency with the speed further increasing. With the rise of the variation rate of speed, the pulsating amplitude and pulsation rate of flow ripple increase. As the swash plate angle augments, the pulsating amplitude of flow ripple increases, nevertheless the flow pulsation rate decreases. In contrast with the effect of the variation of pressure, the test accuracy of flow ripple is more sensitive to the variation of speed. It makes the test accuracy above 96.20% available for the pulsating amplitude of pressure deviating within a range of ~6% from the mean pressure. However, with a variation of speed deviating within a range of ±2% from the mean speed, the attainable test accuracy of flow ripple is above 93.07%. The model constructed in this research proposes a method to determine the flow ripple characteristics of pump and its attainable test accuracy under the large-scale and time-variant working conditions. Meanwhile, a discussion about the variation of flow ripple and its obtainable test accuracy with the conditions of the pump working in wide operating ranges is given as well.

Influence of Blade Thickness on Transient Flow Characteristics of Centrifugal Slurry Pump with Semi-open Impeller

As the critical component, the impellers of the slurry pumps usually have blades of a large thickness. The increasing excretion coefficient of the blades affects the flow in the impeller resulting in a relatively higher hydraulic loss, which is rarely reported. In order to investigate the influence of blade thickness on the transient flow characteristics of a centrifugal slurry pump with a semi-open impeller, transient numerical simulations were carried out on six impellers, of which the meridional blade thickness from the leading edge to trailing edge varied from 5-10 mm, 5-15 mm, 5-20 mm, 10-10 mm, 10-15 mm, and 10-20 mm, respectively. Then, two of the six impellers, namely cases 4 and 6, were manufactured and experimentally tested for hydraulic performance to verify the simulation results. Results of these tests agreed reasonably well with those of the numerical simulation. The results demonstrate that when blade thickness increases, pressure fluctuations at the outlet of the impeller become severe. Moreover, the standard deviation of the relative velocity in the middle portion of the suction sides of the blades decreases and that at the outlet of the impeller increases. Thus, the amplitude of the impeller head pulsation for each case increases. Meanwhile, the distribution of the time-averaged relative flow angle becomes less uniform and decreases at the outlet of the impeller. Hence, as the impeUer blade thickness increases, the pump head drops rapidly and the maximum efficiency point is offset to a lower flow rate condition. As the thickness of blade trailing edge increases by 10 mm, the head of the pump drops by approximately 5 m, which is approximately 10 % of the original pump head. Futhermore, it is for the first time that the time-averaged relative flow angle is being considered for the analysis of transient flow in centrifugal pump. The presented work could be a useful guideline in engineering practice when designing a centrifugal slurry pump with thick impeller blades.

A semi-analytical rate-transient analysis model for light oil reservoirs exhibiting reservoir heterogeneity and multiphase flow

Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously.This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,and improve the evaluation of reservoir/fracture properties.A new,general,semi-analytical model is proposed that explicitly accounts for multiphase flow,fractalbased reservoir heterogeneity,anomalous diffusion,and pressure-dependent fluid properties.This is achieved by introducing a new Boltzmann-type transformation,the exponent of which includes reservoir heterogeneity and anomalous diffusion.In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,the modified Boltzmann variable allows the conversion of three partial differential equations(PDE's)(i.e.,oil,gas and water diffusion equations)into ordinary differential equations(ODE's)that are easily solved using the Runge-Kutta(RK)method.A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties,recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously.Using the slope of the straight line on the modified time-power-law plot,the linear flow parameter can be estimated with more confidence.Moreover,because of the new Boltzmann-type transformation,reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.Using the new semi-analytical model,the effects of multiphase flow,reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated.For the case of approximately constant flowing pressure,multiphase flow impacts initial oil rate,which is a function of oil relative permeability and well flowing pressure.However,multiphase flow has a minor effect on the oil production decline exponent.Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent.The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios,leading to more accurate production forecasting and better-informed capital planning.

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger- Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

An Experimental Study of the Flowrate Transients in Slug Flow

An investigation of the characteristics of flowrate transientswithin slug flow was conducted in a large- scale outdoor testingfacility. The test section consisted of a 378 m long, 7.62 cmdiameter stainless steel pipe. Air and water were used as the testfluids. The response to a change of flowrate of either phase or twophases Was measured using a series of pressure transducers anddifferential pressure transducers. An increase or decrease In gasflowrate caused a pressure overshoot above the value at new steadystate or led to a pressure undershoot To form a temporary stratifiedflow.

Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by com- bining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-w shear stress trans- port （SST） turbulence model, coupled with a two-equation F-Reo transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re = 7.5 × 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages： quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pres- sure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrody- namic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.

Transient fluid flow in the Binbei district of the Songliao Basin, China Evidence from apatite fission track thermochronology

The Songliao Basin is famous for the Daqing Oilfield, the biggest in China. However, no economic hydrocarbon reservoir has been found in the northeastern Binbei district. Its thermal history, which is of great importance for hydrocarbon generation and migration, is studied with apatite fission track （AFT） thermochronology. Samples with depositional ages of the late Cretaceous （-108-73 Ma） are analyzed. The AFT ages of the samples from reservoir rock （depositional age 〉 76.1 Ma） fall between the late Cretaceous （724-5 Ma） and the early Eocene （414-3 Ma） period, indicating their total annealing after deposition. In contrast, two samples from the main seals of the Qingshankou （depositional age 〉 89.3 Ma） and the Nenjiang Formation （depositional age 〉 73.0 Ma） are not annealed or partially annealed （AFT ages of 974-9 Ma and 704-4 Ma, respectively）. Because the maximum burial temperature （〈90 ℃） evidenced by low vitrinite reflectance （Ro〈0.7） is not high enough to account for the AFT total annealing （110-120 ℃）, the transient thermal effect arising from the syntectonic fluid flow between the late Cretaceous and the early Eocene is proposed. Transient thermal effects from fluid flow explains the indicated temperature discrepancies between the AFT thermometer and the Ro thermometer because the transient thermal effect from the fluid flow with a temperature high enough （110-120 ℃） to anneal the AFT thermometer does not last long enough （104-105 yrs.） for an enhancement of the Ro （minimum 106- 107 yrs. under the same temperature）. This indicates that dating thermal effect from fluid flow might be a new means to reconstruct the tectonic history. It also answers why the samples from the main seals are not annealed because the seals will prohibit fluid flow and supply good thermal insulation. The large-scale fluid flow in the Binbei district calls for a new idea to direct the hydrocarbon exploration.

NUMERICAL ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW

We present the numerical analysis of a coupled method for the numerical simulation of transient viscoelastic flow obeying a differential constitutive equation with a Newtonian viscosity. The scheme used is based on Euler implicit method in time and maintains at each time step a couple of the velocity u and the viscoelastic part of the stress σ. Approximation in space is made by finite element method. The approximate stress, velocity and pressure are, respectively, P1-continuous, p2-continuous, and p1continuous. Upwinding needed for convection of σ is made by a 'Streamline Upwind Petrov Galerkin' method (SUPG).

THEORETICAL ANALYSIS ON HYDRAULIC TRANSIENT RESULTED BY SUDDEN INCREASE OF INLET PRESSURE FOR LAMINAR PIPELINE FLOW

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.

DOUBLE METHOD OF CHARACTERISTICS TO ANALYZE HYDRAULIC-THERMAL TRANSIENTS OF PIPELINE FLOW

The hydraulic and thermal transients in pipeline flow were studied. The method of characteristics for hydraulic transient analysis of batch transport of pipeline flow had been improved. The thermal transient equation, in which the term with v 3 was involved, had been inferred, while the corresponding method of characteristics was constructed. The double method of characteristics, which can be used to study the coherent hydraulic-thermal transients of batch transport of pipeline flow, was developed.

Attenuation analysis of hydraulic transients with laminar-turbulent flow alternations

An improved compound mathematical model is established to simulate the attenuation of hydraulic transients with laminar-turbulent alternations,which usually occur when the pipeline flow velocity fluctuates near the critical velocity.The laminar friction resistance and the turbulent friction resistance are considered respectively in this model by applying different resistance schemes to the characteristics method of fluid transient analysis.The hydraulic transients of the valve closing process are simulated using the model.A more reasonable attenuation of hydraulic transients is obtained.The accurate attenuation is more distinct than that obtained from the traditional mathematical model.The research shows that the hydraulic transient is a type of energy waves,and its attenuation is caused by the friction resistance.The laminar friction resistance is more important than the turbulent friction resistance if the flow velocity is smaller than the critical velocity.Otherwise the turbulent friction resistance is more important.The laminar friction resistance is important in the attenuation of hydraulic transients for the closing process.Thus,it is significant to consider the different resistances separately to obtain more accurate attenuation of hydraulic transients.

CALCULATION ON TWO-PHASE FLOW TRANSIENTS AND THEIR EXPERIMENTAL RESEARCH

From basic equations of gas-liquid, solid-liquid, solid-gas two-phase flow,the calculating method on flow transients of two-phase flow is developed by means of characteristicmethod. As one example, a gas-liquid flow transient is calculated and it agrees well with theexperimental result. It is shown that the method is satisfactory for engineering demand.

Numerical simulation of transient flow performance during different periods in centrifugal pumpNumerical simulation of transient flow performance during different periods in centrifugal pump

The instantaneous variations of the hydraulic characteristics take place in centrifugal pumps during their start-up,shutdown and other variable speed operations.In this paper,the variable speed method was proposed to simulate the transient internal flow field and the external performance of the pump during starting and stopping periods.The terms of accelerations due to variable speeds in the flow governing equations were analyzed in a multiple reference of frame(MRF).A transient CFD simulation was performed for a typical centrifugal pump by using ANSYS-CFX with the standard k-εturbulence model.The entire simulation process was composed of four stages:start-up,normal run,shutdown and post-shutdown.The function of rotating speed with regard to time was set by CEL language directly into the impeller domain in the pre-processor of the software to conduct variable speed simulation.The variations of the flow field in the centrifugal pump were obtained from the transient simulation.The changing laws of flow rate,head and other performance parameters over time were also analyzed and summarized.

Algorithm for transient growth of perturbations in channel Poiseuille flow

This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.