Turbulent flow around single concentric long capsule in a pipe

A numerical solution was developed for the equations governing the turbulent flow around single concentric long capsule in a pipe. First, a turbulence model was established for the concentric annulus between the capsule and the pipe to simulate the flow as axi-symmetric, two dimensional, steady flow without edge effect. Second, the same case was considered taking into account the edge effect. Finally, turbulence modelling was established to simulate the case as a three dimensional steady flow, with a view of investigating the validity of axi-symmetric flow assumption. Three different turbulence models were used: an algebraic model (Baldwin–Lomax model) and two types of two-equation models (k–ε and k–ω). Obtained results of pressure gradient along the capsule were compared with available experimental data to verify the used models. In addition, experimental data of the velocity profiles of other investigators were also used in this concern. The results predicted by the three different turbulence models were shown to agree well with the experimental data, though precision differed from one to another.     

重物落水后运动过程的数学模型

为了迅速有效地封堵在汛期河道堤防出现的溃口,建立了重物落水后运动过程的微分方程模型,并采用单因子分析法进行误差分析.分析了不同水流速度、不同投放高度和不同投放方式对模型的影响.然后通过小型试验验证了所建模型的合理性及正确性.结果表明,该模型能够较准确地模拟重物落水后的运动过程,有利于辅助防灾减灾工作的顺利进行.     

Transient Modeling and Simulation of Gas Pipe Networks with Characteristic Diagram Models for Compressors

One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1–3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential-algebraic system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrostatic Ash and Water Flow Mixture Modeling

Slurry flow consisting of 63% electrostatic filter ash and 37% water is subject of investigation reported in this contribution which tries to determine the most appropriate rheological model. The authors have modeled experimental data obtained from actual experimental setup, i.e. pipe viscometer and derived model parameters for Power Law as well as for Sisko model. Based on this analysis a numerical simulation of experiment has been attempted using well known Power Law model and taking the advantage of CFX 4.3 numerical code. This was mainly attempted in order to verify use of the same numerical package later for purpose of building a library of friction coefficients to be used in pipe flow analysis with lumped parameters computer code.     

Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data

Several nonlinear constitutive equations have been proposed to overcome the limitations of the linear eddy-viscosity models to describe complex turbulent flows. These nonlinear equations have often been compared to experimental data through the outputs of numerical models. Here we perform a priori analysis of nonlinear eddy-viscosity models using direct numerical simulation (DNS) of simple shear flows. In this paper, the constitutive equation is directly checked using a tensor projection which involves several invariants of the flow. This provides a 3 terms development which is exact for 2D flows, and a best approximation for 3D flows. We provide the quadratic nonlinear constitutive equation for the near-wall region of simple shear flows using DNS data, and estimate their coefficients. We show that these coefficients have several common properties for the different simple shear flow databases considered. We also show that in the central region of pipe flows, where the shear rate is very small, the coefficients of the constitutive equation diverge, indicating the failure of this representation for vanishing shears.     

Modeling water hammer in viscoelastic pipes using the wave characteristic method

For the first time, the wave characteristic method (WCM) is used to simulate transient flow in viscoelastic pipes. The WCM is based on Newton's second law equating the change in momentum and net pressure forces applied on the liquid, which leads to the Joukowsky equation. The friction head loss within a pipe segment is replaced by an imaginary friction orifice with the same head loss. Here the Joukowsky equation is rederived for elastic pipes on the basis of the conservation of energy principle. Then the same method is used to derive a quadratic equation for the conservation of energy in viscoelastic pipes. Under a relaxation assumption, the square root of the energy equation yields a linear equation that is applicable with the superposition principle. The method developed is studied numerically and verified with experimental data from the literature. The water hammer in a simple pipe system consisting of a reservoir, a pipe, and a valve is demonstrated. Parameters calibrated with the method of characteristics are taken from the literature and used as essential input data for the proposed WCM. A constant friction coefficient of the pipe is considered. Even if a small number of friction orifices are selected, good agreement is found between the experimental data and the simulation results especially for the first pressure head cycles. Finally, the numerical results obtained with both the WCM and the method of characteristics are compared to investigate the effectiveness of the WCM. The WCM shows superior computational efficiency in determining the maximum pressure.     

Finite element analysis of flood discharge atomization based on water–air two-phase flow

Flood discharge atomization is a phenomenon of water fog diffusion caused by the discharge of water from a spillway structure, which brings strong wind and heavy rainfall. These unnatural winds and rainfall are harmful for the safe operation of hydropower stations with high water heads. Compared to the method of prototype observations, physical models and mathematical models, which are semi-theoretical and semi-empirical, numerical simulation methods have the advantage of being not limited by a similar scale and are more economical. A finite element model is presented to simulate flood discharge atomization based on water–air two-phase flow in this paper. Equations governing flood discharge atomization are composed of partial differential equations of mass and momentum conservation laws with unknowns for pressure, velocity and the water concentration. The finite element method is used to solve the governing equations by adopting appropriate solution strategies to increase the convergence and numerical stability. Then, the finite element model is applied to a practical project, the Shuibuya hydropower station, which experienced a flood discharge in 2016. Simulation results show that the proposed model can simulate flood discharge atomization with efficient convergence and numerical stability in three dimensions, and good agreement was observed between numerical simulations and prototype observational data. Based on the simulation results, the mechanism of flood discharge atomization was analyzed.     

The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions

This article examines the magnetohydrodynamic (MHD) flow of non-Newtonian nanofluid in a pipe. The temperature of the pipe is assumed to be higher than the temperature of the fluid. In particular two temperature dependent viscosity models, have been considered. The nonlinear partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by homotopy analysis method (HAM). Explicit analytical expressions for the velocity field, the temperature distribution and nano concentration have been derived analytically. The effects of various physical parameters on velocity, temperature and nano concentration are discussed by using graphical approach.     

A comparison of one-dimensional and three-dimensional models for the simulation of gas–solids transport systems

This paper compares the use of one-dimensional (1-D) and a three-dimensional (3-D) models to simulate the flow of a gas–solids mixture through a pipeline. Both models solve steady flow conservation equations for mass, momentum and energy. The implementation of each model is presented in terms of the changes made to the generic model in order to describe this type of flow. Performance data was obtained for a pneumatic conveying system used to convey pulverised fuel ash (PFA) in a power station. Each model was used to simulate the behaviour of this ash transfer line.     

Damping of water hammer oscillations – comparison of 3D CFD and 1D calculations using two selected models for pipe friction

Water hammer calculations are important for power plants, drinking water systems and procedural facilities. In most cases, the piping systems are very big and the probability of a resonance between a part of the piping system and a hydraulic oscillation resulting from water hammer is very high. The limiting factors for the amplitudes of the structural stresses and strains are the structural and hydraulic damping. In general, one-dimensional codes based on the method of characteristics with quasi-steady friction models are used to calculate the hydraulic system. This results in too small damping of the pressure oscillation and thus in an overestimation of the structural loads. Two models from the literature for a more physical reproduction of the fluid damping using one-dimensional codes are presented and compared with a quasi-steady pipe friction model. Additionally, a three-dimensional computational fluid dynamics simulation of a water hammer oscillation in a small pipe section including a 90°-bend was carried out. A comparison of the results of the three-dimensional simulation and the one-dimensional calculations with regard to the pressure and friction velocity distributions was performed, the performance of the models was evaluated and the limits of validity were identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Study on Hypersonic Flow and Aerodynamic Heating北大核心CSCD

基于有限差分法开发了高超声速流动与换热问题气热耦合仿真求解器,运用该求解器对三种典型高超声速流动与换热问题开展了仿真研究,得到了相应的气动参数、热流密度分布。高超声速后台阶的存在使表面气动参数、热流分布不再连续;随着缝深的提高,缝隙局部流速迅速降低,对流换热效应减弱;高超声速无限长圆管绕流中,边界层外部区域气动参数随时间变化不大,边界层内存在较大的温度梯度,壁面温度随时间升高。三个算例的仿真结果均与试验测量值进行了对比,验证了所开发的求解器的计算能力。     

The instability of the flow in a suddenly blocked pipe

This paper considers the decay of Poiseuille flow within a suddenlyblocked pipe. For small to moderate times the flow is shownto consist of an inviscid core flow coupled with a boundarylayer at the pipe wall. A small-time asymptotic solution isdeveloped and it is shown that this solution is valid for timesup to the point at which the boundary layer fills the wholepipe. A small-time composite solution is used to initiate anumerical marching procedure which overcomes the small-timesingularity that arises in the flow and so allows us to describethe ultimate decay of the flow within a blocked pipe. The stabilityof this flow is then considered using both a quasi-steady approximationand a transient-growth analysis based upon marching solutionsof the linearized Navier–Stokes equations. Our transientstability analysis predicts a critical Reynolds number, fortransition to turbulence, in the range 970 < Re < 1370.     

Modeling and simulation of a gas distribution pipeline network

This research study focuses on the modeling and simulation of a gas distribution pipeline network with a special emphasis on gas ducts. Gas ducts are the most important components of such kind of systems since they define the major dynamic characteristics. Isothermal, unidirectional flow is usually assumed when modeling the gas flow through a gas duct. This paper presents two simplified models derived from the set of partial differential equations governing the dynamics of the process. These models include the inclination term, neglected in most related papers. Moreover, two numerical schemes are presented for the integration of such models. Also, it is shown how the pressure drop along the pipe has a strong dependency with the inclination term. To solve the system dynamics through the proposed numerical schemes a based MATLAB-Simulink library was built. With this library it is possible to simulate the behavior of a gas distribution network from the individual simulation of each component. Finally, the library is tested through three application examples, and results are compared with the existing ones in the literature.     

A statistical model of the controller functions of the human temperature- regulating system in water

In a previous paper, a least-squares approach was used to develop a model of the control system's response to temperature stresses in an air environment. This procedure has now been applied to the case of temperature stresses during water immersion. The model presented here includes equations for predicting metabolic heat production and surface blood flow. In addition, upper and lower limits have been determined for each controller response. Validity of the model has been tested via simulation. The control system model developed in this study was incorporated in an existing complete temperature-regulation system simulation model. Thus modified, the complete model was used to simulate a number of published experiments. Graphical and statistical analysis indicates that the model is valid over a wide range of temperatures.     

Generating Boundary Conditions for the Calculation of Tsunami Propagation on Nested Grids

Some boundary conditions used to numerically simulate tsunami generation and propagation are studied. Special attention is given to generating boundary conditions thatmake it possible to simulate tsunami waves with desired characteristics (amplitude, time period and, in general, waveform). Since the water flow velocity in a propagating tsunami wave is uniquely defined by its height and ocean depth, one can simulate a wave propagating from the boundary into the simulation area. This can be done by specifying the wave height and water flow velocity on the boundary. This method is used to numerically simulate the propagation of a tsunami from the source to the coast on a sequence of refined grids. In this numerical experiment the wave parameters are transferred from the larger area to the subarea via boundary conditions. This method can also generate a wave that has certain characteristics on a specified line.     

Management strategies for the control of eutrophication processes in Fogliano lagoon (Italy): a long-term analysis using a mathematical model

Models are developed and used to analyse and test different management strategies aimed at limiting eutrophication processes in Fogliano Lagoon: modification of lagoon hydrodynamics by tidal flow regulation, harvest of algae biomass, reclaim of sediments. Mathematical models, which have been constructed and proposed, simulate, on a multiyear time scale, the main ecological processes responsible for the most important effects of eutrophication: vegetal blooms, summer anoxia. For different management strategies, hydrodynamic fields produced by wind and tide, and three-dimensional concentration fields of significant species in the ecological phenomena, in water and into sediments, are quantified and compared. The species simulated are: in the water column dissolved oxygen, phytoplanktonic biomass, macrophytic biomass, orthophosphate, dissolved organic carbon, particulate organic carbon and hydrogen sulphide; in sediments dissolved oxygen, dissolved organic carbon, particulate organic carbon, orthophosphate, adsorbed phosphorous and hydrogen sulphide. On the basis of the results of the simulations carried out, the best management strategy limiting eutrophication processes in Fogliano lagoon has been pointed out.     

Capturing coalescence and break-up processes in vertical gas–liquid flows: Assessment of population balance methods

Gas–liquid flows are commonly encountered in industrial flow systems. Numerical studies have been performed to assess the performances of different population balance approaches – direct quadrature method of moments (DQMOMs), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) model – in tracking the changes of gas void fraction and bubble size distribution under complex flow conditions and to validate the model predictions against experimental measurements from medium- and large-sized vertical pipes. Subject to different gas injection method and flow conditions, bubble size evolution exhibited a coalescence dominant trend in the medium-sized pipe; while bubble break-up was found to be dominant in large-sized pipe. The two experiments were therefore strategically selected for carrying out a thorough examination of existing population balance models in capturing the complicated behaviour of bubble coalescence and break-up. In general, predictions of all the different population balance approaches were in reasonable agreement with experimental data. More importantly, encouraging results have been obtained in adequately capturing the dynamical changes of bubbles size due to bubble interactions and transition from wall peak to core peak gas void fraction profiles. As a compromise between numerical accuracy and computational time, DQMOM has performed rather well in capturing the essential two-phase flow structures within the medium- and large-sized vertical pipes when compared to those of ABND and homogeneous MUSIG models. From a practical perspective, the ABND model may still be considered as a more viable approach for industrial applications of gas–liquid flow systems.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Transient flow in natural gas pipeline – The effect of pipeline thermal model

One-dimensional, nonisothermal gas flow model was solved to simulate the slow and fast fluid transients, such as those typically found in high-pressure gas transmission pipelines. The results of the simulation were used to understand the effect of different pipeline thermal models on the flow rate, pressure and temperature in the pipeline. It was found that simplified flow model with steady-state heat transfer term overestimates the amplitude of the temperature fluctuations in the pipeline. This result indicated that unsteady heat transfer model with the effect of heat accumulation in the surroundings of the pipeline should be used to calculate the gas parameters at locations of interest within high-pressure gas transmission pipelines.