WAHA Code - development of single phase code (original) (raw)
Numerical scheme of the WAHA code
This paper describes the numerical scheme used in the WAHA code that was developed within the WAHALoads project for simulations of fast transients in 1D piping systems. Two-fluid model equations described in a companion paper entitled "Two-Fluid Model of the WAHA Code for Simulations of Water Hammer Transients," are solved with an operator splitting procedure: the non-conservative characteristic upwind scheme is used to solve the hyperbolic part of the equations with the non-relaxation source terms, while the relaxation source terms are treated in the second step of the operator splitting procedure. Water properties are calculated with a newly developed set of subroutines that use pretabulated water properties. Special models that were developed for treatment of the abrupt area changes and branches in the piping systems are described. Various test cases, which were used to test the accuracy of the basic numerical scheme and the accompanying numerical models, are described and discussed together with the typical results of simulations.
Two-Phase Flow Water Hammer Transients : Towards the WAHA Code
In view of developing and validating a new code aimed at predicting fast transient two-phase flows in NPPs, extensive experimental data sets are being collected by means of three test facilities in the WAHALoads project. The paper reports on the benchmark exercises which show the need for a specific code using advanced numerical methods, on the experiments which have been carried out, and on the main characteristics of the code itself.
WAHA Code - numerical method of WAHA code
The document gives an overview of the numerical method, which is used in the current version of the WAHA code and is planned to be used in the final version of the WAHA code. The described numerical scheme can be used with conservative, primitive, or with some other sets of basic variables. The final choice of the basic variables depends on the simulations of the smooth-area change flows that are currently tested. Another undetermined choice is a number of the basic equations, which depends on the chosen physical model. The most likely choice is the 6-eq. two-fluid model, however, if the assumption of the thermal equilibrium of the vapor phase is adopted, the 5-eq. two-fluid model will be used. Some minor details that are not clarified in the present version of the document (for example: treatment of very small vapor or liquid volume fractions) will be addressed in the next versions of the document.
Depressurization of Vertical Pipe with Temperature Gradient Modeled with WAHA Code
Science and Technology of Nuclear Installations, 2012
The subcooled decompression under temperature gradient experiment performed by Takeda and Toda in 1979 has been reproduced using the in-house code WAHA version 3. The sudden blowdown of a pressurized water pipe under temperature gradient generates a travelling pressure wave that changes from decompression to compression, and vice versa, every time it reaches the two-phase region near the orifice break. The pressure wave amplitude and frequency are obtained at different locations of the pipe's length. The value of the wave period during the first 20 ms of the experiment seems to be correct but the pressure amplitude is overpredicted. The main three parameters that contribute to the pressure wave behavior are: the break orifice (critical flow model), the ambient pressure at the outlet, and the number of volumes used for the calculation. Recent studies using RELAP5 code have reproduced the early pressure wave (transient) of the same experiment reducing the discharge coefficient and the bubble diameter. In the present paper, the long-term pipe pressure, that is, 2 seconds after rupture, is used to estimate the break orifice that originates the pressure wave. The numerical stability of the WAHA code is clearly proven with the results using different Courant numbers.
Flow models and numerical schemes for single/two-phase transient flow in one dimension
Applied Mathematical Modelling
In the two-phase flow field, a traditional mathematical model for simulating the transition of severe slugging flow presents a challenge when liquid slugs completely block pipelines. Accordingly, an advanced and practical slug model that is derived from a mixture model associated with a slip closure is essential to solving the problem in cooperation with the two-fluid model. The model can offset numerical instability that arises from the discontinuous function of the friction factor across the transition from one flow pattern to the other. Two numerical schemes, the non-iterative and the iterative, are developed, and the proposed schemes can stably predict the transient problems under the Courant-Friedrichs-Lewy (CFL) condition for semi-implicit/implicit schemes. In the present work, pressure transients produced by a complex phenomenon, named water hammer effect, are captured using the single-phase flow model in one-dimension to verify the applicability of the numerical schemes and the friction factor model. At last, the analysis of the two-phase transient flow in a pipeline-riser system indicates that the significant advantage of the present schemes is the robustness that the numerical prediction of the severe slugging behaviour is accurate and stable.
Transient simulation of two-phase flows in pipes
International Journal of Multiphase Flow, 1998
Transient simulation of two-phase gas-liquid flow in pipes requires considerable computational efforts. Until recently, most available commercial codes are based on the two-fluid model which includes one momentum conservation equation for each phase. However, in normal pipe flow operation, especially in oil and gas transport, the transient response of the system proves to be relatively slow. Thus it is reasonable
In this report, three reduced two phase flow models are presented. The first one is a totally conservative model implanted in EUROPLEXUS as SG2P. It generates strong pressure oscillations at the contact discontinuities, and it blows up numerically in some difficult cases. Then, two quasiconservative five-equation models are implanted as SGMP in EUROPLEXUS. The "Topology Transport Equation" in SGMP-Model 1 has no additional term. The mixture sound speed is calculated as "Frozen Sound Speed". The "Topology Transport Equation" in SGMP-Model 2 has an additional term to describe the interaction between the phases, which represents the compressibility of the phases. The associated mixture sound speed corresponds to the Wallis formula. All of these two models are successfully extended to multiphase case. Several tests are carried out. Both of these models can treat the interface between the fluids correctly. The SGMP-Model 1 is numerically more robust. However, when there are two coexisting phases, it cannot treat the mixture in a physically correct way. Thus, the SGMP-Model 2 should be chosen to simulate the fluids mixture. RESUME / CONCLUSIONS de niveau DO en cas de niveau confidentialité supérieur du document SO
Testing the numerical method for one-dimensional shock treatment
In the early 80's the SMUP computer code was developed at the "Jozef Stefan" Institute for simulation of two-phase flow in steam generators. It was suitable only for steady-state problems and was unable to simulate transient behaviour. In this paper, efforts are presented to find a suitable numerical method to renew the old SMUP computer code. The obsolete numerical code has to be replaced with a more efficient one that would be able to treat time-dependent problems. It also has to ensure accurate solution during shock propagations. One-dimensional shock propagations in a tube were studied at zero viscosity. To simplify the equation of state the ideal gas was chosen as a working fluid. Stability margins in the form of transport matrix eigenvalues were calculated. Results were found to be close to those already published.
International Journal of Multiphase Flow, 2008
The paper deals with the problem of the wall shear stress during rapid transient 1D flows in a piping system caused by water hammers in two-phase flow induced by a fast valve closure. The evolution of the transient wall shear stress is interpreted in terms of two steps. The first step is a sudden and dramatic change of the wall shear stress due to the passage of the pressure wave. The second step is a relaxation process of the shear stress which is modeled from the Extended Irreversible Thermodynamics theory. The friction relaxation model (FRM) presented in the first part of this paper describes both steps of the evolution of the wall shear stress during water hammers. The second part of the paper deals with the application of the FRM model as a closure law in the WAHA code. The main purpose of the WAHA code is to predict various situations relative to single-and two-phase water hammer transients in piping systems. The last part of the paper deals with the simulation of several cases from the UMSICHT databank using the adapted WAHA computer code with the FRM model. The results of these simulations are systematically compared with the experimental data. It is concluded that the new FRM model has a clear effect on water hammer pressure wave damping and on the pressure wave propagation velocity.
Energies
Subchannel codes have been widely used for thermal-hydraulics analyses in nuclear reactors. This paper details the development of a novel subchannel code within the Idaho National Laboratory’s (INL) Multi-physics Object Oriented Simulation Environment (MOOSE). MOOSE is a parallel computational framework targeted at the solution of systems of coupled, nonlinear partial differential equations, that often arise in the simulation of nuclear processes. As such, it includes codes/modules able to solve the multiple linear and nonlinear physics that describe a nuclear reactor, under normal operation conditions or accidents. This includes thermal-hydraulics, fuel performance, and neutronics codes, between others. A MOOSE-based subchannel code is a new addition to the fleet of INL-developed codes, based on the MOOSE framework. In this work, we present the derivation of the subchannel equations for a single-phase fluid, we proceed with the description of the algorithm that is used to solve the...
Simplified Transient Two-Phase Model for Pipe Flow
2017
Two-phase flow analyses are critical to successful design and operations of two-phase and multiphase pipe flow applications found in major industrial fields, such as petroleum, nuclear, chemical, geothermal and space industries. Due to difficulties in obtaining analytical transient solutions, approximate solutions have been applied to two-phase pipe flow. However, these approximate solutions neglect convective terms in two-phase Navier-Stokes equations. The aim of this current study was to develop transient tools to predict transient two-phase pipe flow. The objectives of this study were to develop a simplified transient model and to validate the proposed model with published experimental data. A simplified transient two-phase pipe flow model was obtained in this study by simplifying the two-phase Navier-Stokes equations. The simplified equations include: (i) a transient continuity equation of combined two-phase flow that includes two new dimensionless terms; (ii) transient two-phas...
Simulation of hydraulic transients in hydropower systems using the 1-D-3-D coupling approach
Journal of Hydrodynamics, Ser. B, 2012
Although the hydraulic transients in pipe systems are usually simulated by using a one-dimensional (1-D) approach, local three-dimensional (3-D) simulations are necessary because of obvious 3-D flow features in some local regions of the hydropower systems. This paper combines the 1-D method with a 3-D fluid flow model to simulate the Multi-Dimensional (MD) hydraulic transients in hydropower systems and proposes two methods for modeling the compressible water with the correct wave speed, and two strategies for efficiently coupling the 1-D and 3-D computational domains. The methods are validated by simulating the water hammer waves and the oscillations of the water level in a surge tank, and comparing the results with the 1-D solution data. An MD study is conducted for the transient flows in a realistic water conveying system that consists of a draft tube, a tailrace surge tank and a tailrace tunnel. It is shown that the 1-D-3-D coupling approach is an efficient and promising way to simulate the hydraulic transients in the hydropower systems in which the interactions between 1-D hydraulic fluctuations of the pipeline systems and the local 3-D flow patterns should be considered.
Modelling and transient simulation of water flow in pipelines using WANDA Transient software
Ain Shams Engineering Journal, 2015
Pressure transients in conduits such as pipelines are unsteady flow conditions caused by a sudden change in the flow velocity. These conditions might cause damage to the pipelines and its fittings if the extreme pressure (high or low) is experienced within the pipeline. In order to avoid this occurrence, engineers usually carry out pressure transient analysis in the hydraulic design phase of pipeline network systems. Modelling and simulation of transients in pipelines is an acceptable and cost effective method of assessing this problem and finding technical solutions. This research predicts the pressure surge for different flow conditions in two different pipeline systems using WANDA Transient simulation software. Computer models were setup in WANDA Transient for two different systems namely; the Graze experiment (miniature system) and a simple main water riser system based on some initial laboratory data and system parameters. The initial laboratory data and system parameters were used for all the simulations. Results obtained from the computer model simulations compared favourably with the experimental results at Polytropic index of 1.2.
Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers
Journal of Biomechanics, 1989
The accuracy of nonlinear and linear one-dimensional models in describing pulse wave propagation in a uniform cylindrical viscoelastic tube, with Womersley's parameter a equal to 7.6 at 1 Hz, was evaluated. To this end calculations of wave propagation using these models were compared with the experimentally determined propagation of the pressure wave in the tube. The experimentally generated pressure pulse had an amplitude of 9.0 kPa and caused a relative radius change of about 17%. The static pressure vs cross-sectional area relation was found to be nonlinear for these pressure changes. Maximum fluid velocity was about 2.9 ms-', while the phase velocity was about 5.4 m s-I. The radius change and the ratio of fluid and phase velocities violated the linear model assumptions. The nonlinear model with viscous fluid friction modelled on the basis of Poiseuille's law and treating the tube wall as purely elastic, underestimated the damping of the pulse wave and predicted the formation of shock waves, which were not found experimentally. In the linear models, the viscous friction of the blood was modelled according to either Poiseuille's law or Womersley's theory and the tube wall was treated as either linearly elastic or linearly viscoelastic. A description of the viscous friction of the blood based on Poiseuille's law underestimated damping. Disregarding the viscoelasticity of the tube wall resulted in an underestimation of both phase velocity and damping. In spite of the nonlinearity of the system, the linear viscoelastic Womersley model described the pulse wave propagation satisfactorily. NOMENCLATURE damping coefficient, real part of y viscoelastic constants internal cross-sectional area of tube reference cross-sectional area of tube dAldp phase constant, imaginary part of y viscoelastic constants phase velocity static compliance complex frequency dependent compliance inner tube diameter viscous fluid friction term linearized viscous fluid friction term Bessel functions of order zero and one, respectively Reynolds number: N, = 2Rup/q transmural pressure reference transmural pressure radial coordinate inner tube radius time axial component of fluid velocity axial fluid velocity averaged over tube crosssection axial coordinate Womersley's dimensionless parameter: r=R(pwlr~)"" complex propagation coefficient fluid viscosity fluid density wall shear stress angular frequency
Comparison between the two-component pressure approach and current transient flow solvers
Journal of Hydraulic Research, 2008
Some hydraulic applications are characterized by systems originally flowing in free-surface conditions that subsequently undergo flow regime transition into pressurized flow during rapid filling events. Currently, models simulating these flow regime transitions are classified by approaches that either track the location of the pressurized front or use the Preissmann slot concept. While Preissmann slot models are popular for their overall simplicity, they have some limitations, such as the inability to simulate full-pipe flows with piezometric heads below the pipe crown. Recently, a new model named Two-Component Pressure Approach overcame some limitations of current flow regime transition models. However, the performance of this new method has not been tested against existing models. Also, similarly to Preissmann slot models, when shock-capturing methods are used in the computations, postshock numerical oscillations appear in the results. This article presents a comparison between TPA model and three transient flow models. The models are based on the Interface-Tracking approach, the Preissmann slot concept and a standard closed pipe Method of Characteristics code. A procedure to reduce the post-shock oscillation problem is presented. TPA results show good agreement with the results from the models considered in this study.
Comparison of two-fluid models on steam-water transients
ESAIM: Mathematical Modelling and Numerical Analysis, 2016
This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, models are compared with each other and with experimental data in two different cases of steamwater transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment.
International Journal of Engineering and Technology
The subject of multiphase flow encompasses a vast field hosting different technological contexts, wide spectrum of different scales and broad range of engineering disciplines along with multitude of different analytical approaches. A persistent theme throughout the study of multiphase flow is the need to model and predict the detailed behavior of such flow and the phenomenon it manifests. In general, there are three ways to explore the models of multiphase flow: (1) Develop laboratory-sized models through conducting lab experiments with good data acquisition systems; (2) Advance theoretical simulations by using mathematical equations and models for the flow; and (3) Build computer models through utilization of power and size of modern computers to address the complexity of the flow. While full-scale laboratory models are essential to mimic multiphase flow to better understand its boundaries, the predictive capability and physical understanding must depend on theoretical and computational models. Such a combination has always been a major impediment in the industry and academia. Different numerical methods and models with dissimilar concepts are being conveniently used to simulate multiphase flow systems depending on different concepts. Some of these methods do not respect the balance while others damp down strong gradients. The degree of complexity of these models makes the solution practically not reachable by numerical computations despite the fact that many rigorous and systematic studies have been undertaken so far. The essential difficulty is to describe the turbulent interfacial geometry between the multiple phases and take into account steep gradients of the variables across the interface in order to determine the mass, momentum and energy transfers. NASA-VOF 3D is a transient free surface fluid dynamics code developed to calculate confined flows in a low gravity environment using the Volume of Fluid (VOF) algorithm. In this study, theoretical investigation has been carried out to better understand the impact of a horizontal bend on incompressible two-phase flow phenomenon. NASA-VOF 3D has been considered as the CFD platform for major modifications carried out to the main two governing equations; namely the Continuity (Mass Conservation) and the Momentum (Navier-Stokes) equations using the Volume of Fluid (VOF) algorithm. The modifications consisted of deriving and developing the governing equations needed to reflect the impact of the bend on the transition. Numerical operators have also been developed to gain better convergence during calculations. This paper presents the details of this theoretical and numerical study and the derivations of the modified governing equations.
Fluids, 2021
This paper presents a low-pressure experimental validation of a two-phase transient pipeline flow model. Measured pressure and flow rate data are collected for slug and froth flow patterns at the low pressure of 6 bar at the National University of Singapore Multiphase Flow Loop facility. The analyzed low-dimensional model proposed in comprises a steady-state multiphase flow model in series with a linear dynamic model capturing the flow transients. The model is based on a dissipative distributed parameter model for transient flow in transmission lines employing equivalent fluid properties. These parameters are based solely on the flowing conditions, fluid properties and pipeline geometry. OLGA simulations are employed as an independent method to validate the low-dimension model. Both low-dimensional and OLGA models are evaluated based on the estimated two-phase pressure transients for varying gas volume fraction (GVF). Both models estimated the two-phase flow transient pressure withi...