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.

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.

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.

Simulations of the Transient Flow Generated from a Started Flat Plate

Transient operations are commonly founded in fluid machineries such as the starting, stopping, and variations of rotor speeds, etc. Flow generated from a started fiat plate is of fundamental importance. Experiments have been done to observe the flow evolution in current researches. And in order to explore the flow in more detailed scale, some vortex methods with high resolution and other numerical methods were developed to solve various related problems by some researchers. But the promotion of vortex method to engineering application is rare due to its complexity and difficulty in specifying the boundary conditions. In order to build up a method of numerical study for such problems, a simplified model is built up with a flat plate. The development of two-dimensional viscous incompressible flow generated from an impulsively started and uniformly accelerated infinitesimally thin flat plate is simulated numerically. A dynamic mesh（DM） method based on the spring analogue and local remeshing is applied to realize the mesh motion caused by the started plate. Researches show that the mesh quality will decline under large grid shear force during the updating process. To conquer this problem, a region near the plate is separated to guarantee the mesh quality at location of interest which is the innovation of the present paper. All computations at least cover a period during which the plate translates 6 times its length. The simulated instantaneous velocity profiles, flow structures and drag coefficients under several Reynolds numbers （20 ≤ Re ≤ 126） and accelerations （20 m/s2≤ a ≤ 152 m/s2） are presented and compared with existing results in literatures. Comparisons are found to be satisfactory, confirming the validity of the current proposed method（region separated DM）. The proposed DM method is firstly used to study the transient flow generated from a started flat plate and can be used in further study of transient characteristics during transient operations of turbo machineries.

Calculation of the Water Distribution Networks Based on the Theory of Slow Transient Flow

Urban water supply network is a modern urban survival and development of the infrastructure of a city,and its normal running conditions have important significance. The actual hydraulic process in the variableload water distribution networks can be treated as the slow transient flow which belongs to the unsteady flow. This paper analyzes the multi-loops network slow transient model based on graph theory,and the link flow matrix is treated as the variables of the discrete solution model to simulate the process of the slow transient flow in the network. With the simulation of hydraulic regime in an actual pipe network,the changing laws of the flow in the pipes,nodal hydraulic heads and other hydraulic factors with the passage of time are obtained. Since the transient processes offer much more information than a steady process,the slow transient theory is not only practical on analyzing the hydraulic condition of the network,but also on identifying hydraulic resistance coefficients of pipes and detecting the leakage in networks.

An analysis method of injection and production dynamic transient flow in a gas field storage facility

A dynamic transient flow analysis method considering complex factors such as the cyclic injection and production history in a gas field storage facility was established in view of the limitations of the existing methods for transient flow analysis and the characteristics of the injection-production operation of strongly heterogeneous gas reservoirs, and the corresponding theoretical charts were drawn. In addition, an injection-production dynamic transient flow analysis model named "three points and two stages" suitable for an underground gas storage(UGS) well with alternate working conditions was proposed. The "three points" refer to three time points during cyclic injection and production, namely, the starting point of gas injection for UGS construction, the beginning and ending points of the injection-production analysis stage;and the "two stages" refer to historical flow stage and injection-production analysis stage. The study shows that the dimensionless pseudo-pressure and dimensionless pseudo-pressure integral curves of UGS well flex downward in the early stage of the injection and production process, and the dimensionless pseudo-pressure integral derivative curve is convex during the gas production period and concave during the gas injection period, and the curves under different flow histories have atypical features. The new method present in this paper can analyze transient flow of UGS accurately. The application of this method to typical wells in Hutubi gas storage shows that the new method can fit the pressure history accurately, and obtain reliable parameters and results.

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.

Numerical Calculation of Transient Flow of Polymer Foam in Porous Media

Based on the mathematical model of one dimension transient flow of the polymer foam in porous media, the numerical calculation method of the flow mentioned above by using the finite difference method is given. Through the experiments of one dimension transient flow of HPAM (Hydrolytic Polyacrylamide) foam in the artificial sandstone core, the HPAM foam generation and coalescence coefficient of the mathematical model mentioned above are determined. The profiles of the liquid phase saturation, the pressure drop and the number density of one dimension transient flow of HPAM foam with the dimensionless time in artificial sandstone core are numerically calculated and analyzed by using the numerical calculation method.

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.

Godunov-type solutions for gas-liquid two-phase transient flows with gas release effects

The gas-liquid two-phase homogenous flow has been extensively investigated without the effect of gas release.However,the dissolved gas will release when internal water pressure drops below saturation pressure during hydraulic transients.This results in inaccuracy or even invalidity of the existing model for homogenous flows,especially for the reproduction of two-phase mass transfer processes.To address this problem,this paper couples the gas release model with conservation equations of homogenous flows,which are numerically solved by the second-order Godunov-type scheme(GTS).Specifically,a virtual-cell method is adopted at system boundaries to achieve the same second-order accuracy as interior cells,which is realized by the monotonic upwind scheme for conservation laws(MUSCL-Hancock scheme).Simulated pressure curves by the proposed model are compared with a series of analytical,numerical and experimental results.It indicates that the proposed model with gas release effects reproduces actual pressure responses most accurately,with minimum relative error and root mean squared error compared with experimental data.Moreover,the gas release leads to dynamic synchronous fluctuations of void fraction,wave speed and pressure head,including the opposite trends of void fraction and pressure,and higher void fraction leading to greater wave speed depression.Furthermore,sensitivity analysis is concluded with recommended Courant number,and different gas release effects in different initial void fractions.Present research increases the basic understanding of two-phase mass transfer processes and their implications for hydraulic transients.

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.

NUMERICAL SIMULATION OF TRANSIENT FLOW AROUND A SHIP IN UNSTEADY BERTHING MOTION

Ship berthing is a specific maneuver operation. The flow around a berthing ship and the forces acting on the hull are quite different from those for a ship in normal navigation. By solving the unsteady Reynolds-Averaged Navier-Stokes （RANS） equations, the transient flow field around a ship undergoing unsteady lateral motion is simulated and the varying lateral hydrodynamic force acting on the hull is evaluated in this article. The numerical results obtained with different turbulence models are analyzed and compared with experimental results and other numerical results published in literature, and a turbulence model more suitable for simulation of the viscous flow around a ship undergoing unsteady berthing is determined.

Transient Flow in Rapidly Filling Air-Entrapped Pipelines with Moving Boundaries

A mathematical model is presented for transient flow in a rapidly filling pipeline with an entrapped air pocket. The influence of transient shear stress between the pipe wall and the flowing fluid is taken into account. A coordinate transformation technique is employed to generate adaptive moving meshes for the multiphase flow system as images of the time-independent computational meshes in auxiliary domains. The method of characteristics is used to reduce the coupled nonlinear hyperbolic partial differential equations governing the motion of the filling fluid, entrapped air, and blocking fluid to ordinary differential equations. Numerical solution of resulting equations shows that the transient shear stresses have only a small damping effect on the pressure fluctuations. The peak pressure in the entrapped air pocket decreases significantly with increasing initial entrapped air volume, but decreases slightly with increasing initial entrapped air pressure.

Transient flow model and pressure dynamic features of tree-shaped fractal reservoirs

A transient flow model of tree-shaped fractal reservoirs is built by embedding a fracture network simulated by a tree-shaped fractal network into a matrix system. The model can be solved using the Laplace conversion method. The dimensionless bottom hole pressure can be obtained using the Stehfest numerical inversion method. The bi-logarithmic type curves for the trce-shaped fractal reservoirs are thus obtained. The pressure transient responses under different fractal factors are discussed. The factors with a primary effect on the inter-porosity flow regime include the initial branch number N, the length ratio α, and the branch angle θ. The diameter ratio β has a significant effect on the fracture radial flow, the inter-porosity and the total system radial flow regimes. The total branch level M of the network mainly influences the total system radial flow regime. The model presented in this paper provides a new methodology for analyzing and predicting the pressure dynamic characteristics of naturally fractured reservoirs.

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。

THEORETIC SOLUTION OF TRANSIENT FLOW OF LIQUID IN THE PIPE WITH FLUID MACHINERY

The transient flow of liquid in the pipe with fluid machinery is analysed in this pa- per.The theoretic solution of the transient flow produced due to the regulation of fluid machin- ery is found by use of the method of the Laplace transformation.

Computational fluid dynamic(CFD)modelling of transient flow in the intermittent gas lift

A computational fluid dynamics model(CFD)is developed for intermittent gas lift techniques.The simulation is conducted for a test section of 18 m vertical tube with 0.076 m in diameter using air as injection gas and oil as a formation fluid.The results obtained from the CFD model are validated with the experiment results from the literature.The current study shows that computational modeling is a proven simulation program for predicting intermittent gas lift characteristics and the transient flow parameters that are changing with time and position in the coordinate system.The model can predict the slug velocity behavior for different injection pressure.The slug velocity profile shows three regions;the first region is the rapid acceleration at the initial time of injection,the second region shows the nearly constant velocity until the slug reaches the surface and the third region is again the rapid acceleration when the liquid starts to produce.Also,the results obtained from this model show that as the gas injection pressure increases,the liquid slug velocity increase,and the region of the constant velocity decrease.The effect of the injection time on the liquid production rate has been studied for two different gas injection pressures of 40 psig and 50 psig.The developed model shows that more than 50%of the liquid production is coming from after flow period.

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

Transient Hydromagnetic Stagnation-Point Flow across a Vertical Surface with Partial Slip in a Chemically Reactive Medium

A numerical study of partial slip boundary condition is investigated. The stagnation-point flow problem involving some physio-chemical parameters has been elucidated. The process involves developing a multivariate mathematical model for the flow and transforming it into a coupled univariate equation. Key parameters of interest in the study are the buoyancy force, the surface stretching, the unsteadiness, the radiation, the dissipation effects, the slip effects, the species reaction and the magnetic field parameters. It is concluded that the impact of physio-chemical factors significantly alters the kinematics of the flow in order to optimally achieve desired product characteristics.