Two-phase two-fluid model solver based on a high-resolution total variation diminishing scheme

A new numerical method and a solver for the two-phase two-fluid model are developed using an innovative high-resolution, Total Variation Diminishing (TVD) scheme. The new scheme is derived first for scalar hyperbolic problems using the method of flux limiters, then extended to the two-phase two-fluid model. A hybridization of the monotone 1st-order upwind scheme and the Quadratic Upstream Interpolation scheme (QUICK) is implemented using a new flux limiter function. The new function is derived in a systematic manner by imposing conditions necessary to ensure the TVD properties of the resulting scheme. For temporal discretization, the theta method is used, and values for the parameter theta are chosen such that the scheme is unconditionally stable (1/2≤theta≤1). Finite volume techniques with staggered mesh are then used to develop a solver for the one-dimensional two-phase two-fluid model based on different numerical schemes including the new scheme developed here. Linearized equations of state are used as closure relations for the model, with linearization derivatives calculated numerically using water properties based on the IAPWS IF-97 standard. Numerical convergence studies were conducted to verify, first, the new numerical scheme and then, the two-phase two-fluid solver. Numerical scheme results are presented for one-dimensional pure advection problem with smooth and discontinuous initial conditions and compared to those of other classical and high-resolution numerical schemes. Convergence rates for the new scheme are examined and shown to be higher compared to those of other schemes. For smooth solutions, the new scheme was found to exhibit a convergence rate of 1.3 and a convergence rate of 0.82 for discontinuous solutions. The two-phase two-fluid model solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The new solver based on the new TVD scheme is shown to exhibit higher-order accuracy compared to other numerical schemes with convergence rate of 0.8. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in common nuclear thermal-hydraulics codes like TRACE and RELAP5. The solver is shown to exhibit numerical stability when implemented to problems with discontinuous solutions and results of the new solver were free of spurious oscillations

The Sixth Annual Thermal and Fluids Analysis Workshop

The Sixth Annual Thermal and Fluids Analysis Workshop consisted of classes, vendor demonstrations, and paper sessions. The classes and vendor demonstrations provided participants with the information on widely used tools for thermal and fluids analysis. The paper sessions provided a forum for the exchange of information and ideas among thermal and fluids analysis. Paper topics included advances an uses of established thermal and fluids computer codes (such as SINDA and TRASYS) as well as unique modeling techniques and applications

Elliptical instability in the planetary fluid cores

x, 111 leaves ; 29 cmElliptical instability may be excited in any rotating flow with elliptically deformed streamlines. Investigating this instability in containers with spheroidal or ellipsoidal boundaries is of geophysical and astrophysical interest as many stars and planets are either rotating ellipsoidal fluid bodies or have substantial fluid cores which are either ellipsoidal, in the absence of a solid inner core, or ellipsoidal shells such as the Earth’s fluid core; elliptical instability may be excited in these bodies as a result of the gravitational pull of a secondary body such as a moon or a large asteroid orbiting these bodies. In this thesis, the nonlinear evolution of elliptical instability in an inviscid incompressible rotating triaxial ellipsoid is numerically studied using the least-square finite element method. After validating the method by reproducing some known results, it is applied to other configurations in order to investigate some open questions on this subject, namely, the effects of the oblateness of the ellipsoid and the frequency ratio of the orbital speed of the secondary body on the evolution of the elliptical instability. We have found that if the parameters of the system, i.e. the flattening ratio and the frequency ratio of the background rotation, are in the range of the spin-over instability, a repetitive three-dimensional rigorous motion is maintained indefinitely; otherwise, instability may be excited initially, once the streamlines become elliptical, for certain ranges of the system parameters; however, as time elapses the motion becomes two dimensional with small displacement amplitudes in x- and y- directions

Development of an integrated BEM approach for hot fluid structure interaction: BEST-FSI: Boundary Element Solution Technique for Fluid Structure Interaction

As part of the continuing effort at NASA LeRC to improve both the durability and reliability of hot section Earth-to-orbit engine components, significant enhancements must be made in existing finite element and finite difference methods, and advanced techniques, such as the boundary element method (BEM), must be explored. The BEM was chosen as the basic analysis tool because the critical variables (temperature, flux, displacement, and traction) can be very precisely determined with a boundary-based discretization scheme. Additionally, model preparation is considerably simplified compared to the more familiar domain-based methods. Furthermore, the hyperbolic character of high speed flow is captured through the use of an analytical fundamental solution, eliminating the dependence of the solution on the discretization pattern. The price that must be paid in order to realize these advantages is that any BEM formulation requires a considerable amount of analytical work, which is typically absent in the other numerical methods. All of the research accomplishments of a multi-year program aimed toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-orbit engine hot section components are detailed. Most of the effort was directed toward the examination of fluid flow, since BEM's for fluids are at a much less developed state. However, significant strides were made, not only in the analysis of thermoviscous fluids, but also in the solution of the fluid-structure interaction problem

Flood Routing on Small Streams: A Review of Muskingum-Cunge, Cascading Reservoirs, and Full Dynamic Solutions

Flood wave routing methods are adapted for small, naturally meandering streams. A simplified derivation of the Muskingum-Cunge equation is presented, based on Perumal and Kalinin-Milyukov's "characteristic reach length" concept. The derivation was extended to meandering streams, using the "parallel channels" analogy. "Cascading reservoirs", a second approximate method, is shown to be a special case of Muskingum-Cunge when properly formulated. Both approximate methods were evaluated against two "fully dynamic" solutions: the UNET-based solver in HEC-RAS and the National Weather Service's FLDWAV program. The four models were tested on four natural streams in northeastern Kansas. Detailed procedures for creating "equivalent reaches" were developed. The sensitivity of model stability was tested against variations in distance step size and other controls. HEC-RAS and FLDWAV gave nearly identical results for all the test reaches. The two approximate methods also performed well, but with deviations which are discussed. Recommendations were given for setting distance steps in fully dynamic solutions

Desarrollo de una herramienta computacional para la comprobación estructural de presas

Nowadays, dam safety is becoming more relevant in our society due to the importance of its functions (power generation, water supply, flood control) and the severity of the consequences in case of a serious breakdown. The "safety of hydraulic infrastructures" is one of the priorities according to the R&D Spanish State Program which is oriented to social challenges. Thanks to recent improvements in the modelling of dams as well as the evolution of computational resources, it is possible to perform more detailed analysis. However, most of commercial software is devoted to more common problems (e.g. buildings, bridges) without considering specific aspects of dams: concrete ageing process, joints during the construction process, contact with the ground or uplift pressure. The development of a specific application for dam engineering, both for construction phase and operating period, is the main objective of this project. The thesis presents the computational tool, which is based on finite element formulations and solves thermomechanical problem using weak coupling, designed for analysing the operating period. The proposed software is validated with a real case: La Baells dam. The computational results have shown excellent agreement with the obtained data during monitoring process

Development of BEM for ceramic composites

BEST-CMS (boundary element solution technology - composite modeling system) is an advanced engineering system for the micro-analysis of fiber composite structures. BEST-CMS is based upon the boundary element program BEST3D which was developed for NASA by Pratt and Whitney Aircraft and the State University of New York at Buffalo under contract NAS3-23697. BEST-CMS presently has the capabilities for elastostatic analysis, steady-state and transient heat transfer analysis, steady-state and transient concurrent thermoelastic analysis, and elastoplastic and creep analysis. The fibers are assumed to be perfectly bonded to the composite matrix, or in the case of static or steady-state analysis, the fibers may be assumed to have spring connections, thermal resistance, and/or frictional sliding between the fibers and the composite matrix. The primary objective of this user's manual is to provide an overview of all BEST-CMS capabilities, along with detailed descriptions of the input data requirements. In the next chapter, a brief review of the theoretical background is presented for each analysis category. Then, chapter three discusses the key aspects of the numerical implementation, while chapter four provides a tutorial for the beginning BEST-CMS user. The heart of the manual, however, is in chapter five, where a complete description of all data input items is provided. Within this chapter, the individual entries are grouped on a functional basis for a more coherent presentation. Chapter six includes sample problems and should be of considerable assistance to the novice. Chapter seven includes capsules of a number of fiber-composite analysis problems that have been solved using BEST-CMS. This chapter is primarily descriptive in nature and is intended merely to illustrate the level of analysis that is possible within the present BEST-CMS system. Chapter eight contains a detail description of the BEST-CMS Neutral File which is helpful in writing an interface between BEST-CMS and any graphic post-processor program. Finally, all pertinent references are listed in chapter nine

Topics in Magnetohydrodynamics

To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc

3D-modeling of swing check valve with connection to dynamic behavior used in system studies

This Master’s Thesis is the result of the collaboration between The Technical Faculty of Lund University and TÜV NORD Sweden AB. Focus has been directed towards the nuclear industry where this thesis is one of several other Master’s Theses regarding the dynamic modeling of a swing check valve. It is necessary for the nuclear industry to be able to model flow transients which involve the dynamic behaviour of the swing check valve. The modeling is commonly executed by one-dimensional codes such as RELAP5, DRAKO and DYVRO. This work has applied the swing check valve theory by (Li and Liou, 2003) in order to retrieve results from three-dimensional modeling using computational fluid dynamics (CFD) to derive useful correlations for one-dimensional code implementation. The accuracy of the CFD-model has been investigated by comparing results of interest after changing the modeling set-up in the CFD-software ANSYS FLUENT. The impact of cell density, solver dependence and choice of turbulence model are a couple of interesting preferences which have been investigated in a sensitivity analysis. The simulations are constructed to yield results for useful parameters for the swing check valve theory. Results from CFD-simulations give resembling results compared to the experiments by (Li and Liou, 2003). One particular correlation was found regarding the coupling of the coefficients in the theory of (Li and Liou, 2003) and was implemented in RELAP5. Through this work conclusions has been made that the implementation of a general one-dimensional model based on the theory of (Li and Liou, 2003) will be complex due to coefficient dependence.The importance of swing check valve modeling The nuclear industry is putting a great deal of effort to master the modeling of pipe systems. The swing check valve is a common system component and the closing procedure of the valve can cause dangerous magnitudes in pressure rise. The Swing Check Valve It is of great importance in the nuclear industry to be able to model flow transients to determine hydraulic loads within various pipe systems. The hydraulic loads will result in stresses which can cause severe damages on pipe systems or on single components. To ensure the highest possible safety, flow transients within pipe systems are modeled to ensure that the system can withstand and cope with these loads. The hydraulic loads initially starts to propagate due to change in pressure within the system. Pressure changes can occur due to pump stops or valve operation. The figure below presents a closing scenario where water hammer is induced due to closing of a regular valve. Back flow can be prevented or greatly reduced by a check valve. Check valves are often used in nuclear power plant applications, mainly due to design features, size variation, and economy. Check valves are one of few valves models that can operate without external control. A swing check valve commonly consists of a disc connected to a hinge pin inside the valve housing. The most basic function of a check valve is to allow throughflow in one direction and prevent in the opposite. This property is valuable when reversed flow is undesirable and must be minimized. The modeling is commonly executed by one-dimensional codes such as RELAP5 and DRAKO. This work has used the swing check valve theory by G.Li and J.C.P. Liou in order to retrieve results from three-dimensional modeling using computational fluid dynamics (CFD) to derive useful correlations for one-dimensional code implementation It is not suitable to simulate large pipe systems with CFD since it would most likely be too time consuming and inconvenient. That is why single components can be CFD-modeled and implemented as one-dimensional components in a larger system which can be modeled many times faster and still give accurate results, useful for constructing large systems. CFD-simulations The simulations in ANSYS FLUENT included both stationary cases with a fixed valve disc and transient cases where the valve disc was implemented as a dynamic zone which was allowed to move with the flow. The need of both stationary and transient simulations is due to the swing check valve theory of Li and Liou which states that the hydraulic can be divided into two components, one stationary and one rotational. T_H = T_HS + T_HR CFD-simulations in ANSYS FLUENT was necessary since it was not possible to set up and construct physical experiments like the authors behind the theory did. The results from CFD was compiled in order to visualize how the valve acts according to changes of flow which was set up to simulate real system pump stops, which is a common cause for back flow ion the industry. Useable results? Simulations in CFD gave all important parameters used in the theory of Li and Liou. Hence, it can be stated that CFD is a useful and powerful simulation tool for valve simulation. However, the implementation of a general and useful one-dimensional valve model was a difficult task, especially due to important coefficient correlations in the theory. The comparison between the closing time of the valve from CFD and one-dimensional implementation in RELAP5 showed differences for all investigated pump stops. It is troublesome to give an exact explanation for this inconsequent behavior. The CFD-model can be used for further simulations where more correlations can be investigated, especially for transient cases which probably holds the keys for a successful crossing between the three-dimensional- and one dimensional world. References Li. G and J.C.P Liou. Swing Check Valve Characteristics and Modeling During Transients. Journal of Fluids Engineering,125(10):1043-1050, 200