Multi-dimensional modelling of multiphase flow physics: high-speed nozzle and jet flows — a case study

Multi-dimensional modelling of multiphase flows has become more prevalent as computer capabilities have significantly expanded. Such analyses are necessary if the flow physics demonstrates behavior that is fundamentally different from the estimates of one-dimensional analyses. Multiphase multi-dimensional behavior may involve physical mechanisms that interact with the flow field transverse to the main fluid direction and feedback into downstream processes. Consider the physics of high-speed internal nozzle flow, downstream external jet flow and the dynamics of jet breakup. This is a prime example of a coupled problem where multi-dimensional aspects may need to be considered. This paper examines multiphase physics as an illustration of the conditions under which multi-dimensional modelling would be required. Internal nozzle flow can involve cavitation phenomena, and as the geometry becomes more abrupt or asymmetric, multi-dimensional modelling is required. High-speed simulations using our internal flow model, CAVALRY, indicate that cavitation behavior can become oscillatory as the nozzle shape is altered. This exiting internal flow emerges as a multi-dimensional external jet flow, whose downstream breakup can be noticeably influenced by the inlet conditions as well as the jet breakup mechanisms. Jet breakup models first developed for the TEXASV model are utilized in the multi-dimensional KIVA code simulations for gas–liquid flows. The simulation results suggest that similar jet breakup mechanisms are operative for a multi-fluid system. Our comparisons to particular sets of data for high-speed nozzle flow and jet breakup in a gas suggest that the approach can be extended to multiphase systems using similar concepts; i.e. TEXAS-3d.     

Turbulent heat mixing of a heavy liquid metal flow in the MEGAPIE target geometry—The heated jet experiment

The MEGAPIE target installed at the Paul–Scherrer Institute is an example of a spallation target using eutectic liquid lead–bismuth (Pb⁴⁵Bi⁵⁵) both as coolant and neutron source. An adequate cooling of the target requires a conditioning of the flow, which is realized by a main flow transported in an annular gap downwards, u-turned at a hemispherical shell into a cylindrical riser tube. In order to avoid a stagnation point close to the lowest part of the shell a jet flow is superimposed to the main flow, which is directed towards to the stagnation point and flows tangentially along the shell.The heated jet experiment conducted in the THEADES loop of the KALLA laboratory is nearly 1:1 representation of the lower part of the MEGAPIE target. It is aimed to study the cooling capability of this specific geometry in dependence on the flow rate ratio (Q_main/Q_jet) of the main flow (Q_main) to the jet flow (Q_jet). Here, a heated jet is injected into a cold main flow at MEGAPIE relevant flow rate ratios. The liquid metal experiment is accompanied by a water experiment in almost the same geometry to study the momentum field as well as a three-dimensional turbulent numerical fluid dynamic simulation (CFD). Besides a detailed study of the envisaged nominal operation of the MEGAPIE target with Q_main/Q_jet = 15 deviations from this mode are investigated in the range from 7.5 ≤ Q_main/Q_jet ≤ 20 in order to give an estimate on the safe operational threshold of the target.The experiment shows that, the flow pattern establishing in this specific design and the turbulence intensity distribution essentially depends on the flow rate ratio (Q_main/Q_jet). All Q_main/Q_jet-ratios investigated exhibit an unstable time dependent behavior. The MEGAPIE design is highly sensitive against changes of this ratio.Mainly three completely different flow patterns were identified. A sufficient cooling of the lower target shell, however, is only ensured if Q_main/Q_jet ≤ 12.5. In this case the jet flow covers the whole lower shell. Although for Q_main/Q_jet ≤ 12.5 the flow is more unstable compared to the other patterns most of the fluctuations close to the centerline are in the high frequency range (>1 Hz), so that they will not lead to severe temperature fluctuations in the lower shell material. In this case the thermal mixing occurs on large scales and is excellent.For flow rate ratios Q_main/Q_jet > 12.5 complex flow patterns consisting of several fluid streaks and vortices were identified. Since in these cases the jet flow does not fully cover the lower shell an adequate cooling of the MEGAPIE target cannot be guaranteed and thus temperatures may appear exceeding material acceptable limits.All conducted experiments show a high sensitivity to asymmetries even far upstream. A comparison of the numerical simulation, which assumed a symmetric flow, with the experimental data was due to the experimentally found asymmetry only partially possible.     

FIPMIGR — A computer program for studying migration of fission products in a temperature gradient

FIPMIGR is a computer program for studying migration of fission products in a fuel pin. Migration in a temperature gradient and in a concentration gradient is considered. The geometry is cylindrical with migration only in the radial direction.As an example the diffusion of Ba is calculated and compared with experimental results. The migration of Ba is well described using the diffusion constant for Ba in BaO and a heat of transport of −100 kJ mol⁻¹. The great sensitivity of the theoretical prediction to temperature is clearly demonstrated. Both theory and experiments show that there is a temperature or power above which migration becomes clearly visible. The critical temperature is about 1700 K and the power level in the S176 experiments [2] was then about 40 kW m⁻¹.     

Overview of the 10 MW high temperature gas cooled reactor—test module project

This paper discusses the historical development of the high temperature gas cooled reactor (HTGR) in China. China's development strategy of the HTGR will be explained in this text. The aim, design, construction and commissioning of the 10 MW HTGR—test module (HTR-10) will be explained herein. The engineering experiments, which were developed for the HTR-10, will also be introduced. The experience leading to an accumulation of knowledge during the development of China's HTGR will be summarized in this article.     

Modelling of ballistic low energy ion solid interaction — conventional analytic theories versus computer simulations

The “philosophy” behind, and the “psychology” of the development from analytic theory to computer simulations in the field of atomic collisions in solids is discussed and a few examples of achievements and perspectives are given.     

Equations of state and spinodal lines — a review

Modern thermal processes in the power industry involve ever increasing heat fluxes and rapid transients. Simulating such processes requires accurate thermodynamic properties and correlations that encompass stable as well as metastable states. Here we review the development of cubic equations of state that can be made to yield very accurate thermodynamic properties of liquids in saturation and metastable (superheated) states. These cubic equations enable us to develop predictions and correlations for a number of other quantities which are either useful in themselves or for application to boiling and two-phase flow. Examples of such results include predictions of the saturation pressure, the limiting liquid superheat, the destructive energy available to a superheated liquid, the surface tension of a saturated fluid and the approach of the specific heat at constant pressure to infinity at the spinodal point. These topics are described and discussed, and it emerges that these seemingly separate topics can be unified by the use of cubic equations of state. We pay particular attention to the issue of a possible connection between the limit of liquid superheat and the liquid spinodal line.     

Fatigue — determination of a more realistic usage factor

The ability to use a suitable counting method for determining the stress range spectrum in elastic and simplified elastic-plastic fatigue analyses is of crucial importance for enabling determination of a realistic usage factor. Determination of elastic-plastic strain range using the K_e factor from fictitious elastically calculated loads is also important in the event of elastic behaviour being exceeded. This paper thus examines both points in detail. A fatigue module with additional options, which functions on this basis is presented. The much more realistic determination of usage factor presented here offers various economic benefits depending on the application.     

Thermodynamic properties of nonstoichiometric urania-gadolinia solid solutions in the temperature range 700–1100° C

Partial molar thermodynamic quantities for urania-gadolinia solid solutions of compositions U_1−yGd_yO_2+x, with y values of 0.04 to 0.27, have been obtained using a solid electrolyte galvanic cell technique. The measurements were made for O/M ratios ranging from near stoichiometry to 2.20, and for temperatures ranging from 700 to 1100°C. The results for pure UO_2+x are in accordance with data reported earlier. The oxygen potentials for U_1−yGd_yO_2+x are higher than for pure UO_2+x and increase positively with increasing Gd content or excess oxygen. They can be represented as a function of the mean U valence, except at the stoichiometric composition. Both the partial molar entropy and enthalpy increase negatively with increasing Gd content or excess oxygen.     

Soil-structure interaction analyses by finite elements — State of the art

In this paper the authors have attempted to summarize the current capability for evaluating soil-structure interaction effects during earthquakes using finite element procedures. A concise summary of methods available, together with their capabilities and relative costs is presented. It is suggested that finite element procedures provide a powerful tool for use in the design of nuclear plants, especially for embedded structures, and their applicability in this respect is illustrated by comparing computed results with those recorded in a nuclear plant during a strong motion earthquake. It is concluded that when the methods are used in conjunction with good engineering judgment and with full recognition of their limitations, they provide evaluations of response with a level of accuracy entirely adequate for engineering design.     

Use of the α → β quartz transition to monitor the temperature increase produced by a proton microbeam

Ion microbeams induce in certain cases local heating of a sample under investigation, especially in insulators. To obtain experimental values of this temperature increase, we used a quartz sample which presents its own internal thermometer with the α → β transition observed at 573°C. At this temperature, the transition is easily observed from the rapid variation of the bubble size contained in a melted inclusion trapped in the quartz. We measured the temperature increase produced by a 3 MeV proton microbeam. For this purpose, the nuclear microprobe chamber was equipped with a sample heating stage. The decrease of the power injected by the heater element (beam on) required to observe the transition has been interpreted as a local increase of the temperature under microbeam exposure.     

Sintering studies of urania powder compacts — Analysis of a flow model

An attempt has been made to analyse the sintering data of urania powder compacts prepared form its precursor ammonium diuranate calcined and sintered in hydrogen atmosphere for various soaking times and temperatures. Better sintering behaviour was observed in compacts prepared from powders calcined below 800 ° C, which were non-crystalline under X-ray diffraction study. Frenkel's sintering mechanism as applicable for the non-crystalline powders was applied to understand the densification behaviour in which the viscosity term was linearly related to shear stress and strain rate as also its relationship with time was assumed to be either linear or exponential in nature. A plot between shear stress (to induce densification) and time indicated that (i) a critical time (T_crit) is necessary to induce any observable sintering stress in these powders and T_crit, values increased with decrease in calcination temperature and (ii) the amount of shear stress increased with higher sintering temperatures and was related to time, exponentially.     

Laser joining of silicon carbide—a new technology for ultra-high temperature resistant joints

High performance ceramics, e.g., silicon carbide (SiC), can widely be used in the nuclear sector because of their excellent thermo chemical and radiological properties. However, it has not been possible to utilise this great potential since the technologies for high temperature resistant joining of these ceramic materials are not yet satisfying.This paper describes an innovative laser joining technology that allows the firm vacuum gas tight binding between any shaped bodies made of these ceramic materials. The joints obtained are temperature resistant at 1600 °C and above. The method is based on a solder that is specially made from Al₂O₃, Y₂O₃ and SiO₂ and melted locally in the joining zone by use of laser radiation. The paper discusses the influence of the laser beam wave length, the seam geometry and the solder composition on the quality of the braze joint. The advantages of this new method are illustrated by means of laser brazed SiC capsules and other parts and compared with conventional joining methods.     

Aging material evaluation and studies by non-destructive techniques (AMES-NDT) — a European network project

This paper presents results obtained in a round-robin action organized in a concerted action of ten partners in the EURATOM program of the European Community. The objective of the research was to document the state of the art of available non-destructive testing (NDT) techniques in order to characterize material aging phenomena based on a reduction of Charpy-V energy and a shift in the fracture appearance transition temperature. Therefore, samples from the Japanese nuclear reactor pressure vessel JRQ-steel (ASMT Standard A533-B Class 1) have been thermally treated at 700°C for 18 h with a subsequent water quenching. Besides micromagnetic and electromagnetic NDT, the positron annihilation technique, ultrasonic reverberation by using Laser ultrasonics and the thermo-electrical power have been applied to characterize the aged material states.     

Is there an effect of the proximity of a “free-surface” on the formation of End-Of-Range defects?

We have studied the effect of the proximity of the wafer surface on the formation of End-Of-Range defects. These experiments are aimed at elucidating the behavior, upon annealing, of the Si self-interstitial supersaturation responsible for transient enhanced diffusion of boron in pre-amorphized silicon wafers. By implanting with Ge at constant energy while carefully etching away increasing thicknesses of the amorphous layer the nucleation and growth of End-Of-Range defects have been studied by transmission electron microscopy. Clearly, no influence in the loop population can be shown even when using state-of-the-art “quantitative” electron microscopy. These results are explained by considering that the c/a interface is a diffusion barrier for the Si self-interstitial atoms during the nucleation stage, i.e., when the supersaturation is high. Only after the solid phase epitaxial regrowth, i.e., during the coalescence of the loops when the supersaturation is already low, the surface can interact with the loops. However, this interaction is not measurable through the observation of extended defects and this leads to simplifying assumptions for the simulation of Transient Enhanced or Retarded Diffusion in pre-amorphized Si wafers.     

Random cyclic stress–strain responses of a stainless steel pipe-weld metal II — a modeling

This paper pays special attention to an issue that there is a significant scatter of the stress–strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Efforts are made to reveal the random fatigue damage character by fracture surface observations and to model the random responses by introducing probability-based stress–strain curves of Ramberg–Osgood relation and its modified form. Results reveal that the fatigue damage is subjected to, 3-D interacting and involved microcracks. The three stages, namely microstructural short cracks (MSC), physical short cracks (PSC) and long cracks (LC) subdivided by Miller and de los Rios, can give a good characterization of the damage process. Both micro- and macro-behaviour of the material have the character of three stages. The 3-D effects are strong in the MSC stage, tend to a gradual decrease in the PSC stage, and then show saturation after going to the LC stage. Intrinsic causes of the random behaviour are the difference and evolution of the microstructural conditions ahead of the dominant crack tips. The ‘effectively short fatigue crack criterion’ introduced by Zhao et al. in observing the material surface short crack behaviour could facilitate an understanding of the mechanism of interaction and evolution. Based on the previous obtained appropriate assumed distribution, normal model, for the cyclic stress amplitude, the probability-based curves are approximated by the mean value and standard deviation cyclic stress–strain curves. Then, fatigue analysis at arbitrarily given reliability can be conveniently made according to the normal distribution function. To estimate these curves, a maximum likelihood method is developed. The analysis reveals that the curves could give a good modeling of the random responses of material.     

Comments on: “Studies on diversion cross-flow between two parallel channels communicating by a parallel slot — Part I” by A. Tapucu

Unique design techniques are needed for low activity ceramic materials in first wall/blanket regions of fusion reactors. A Weibull probabilistic design approach is used to characterize the scatter in the fracture strength and the size effect. Results indicate that ceramic first wall/blanket structures should be modular and each module should be proof tested. The ceramic materials should have high fracture strength, high Weibull modulus, and minimal strength degradation due to subcritical crack growth. The Weibull statistical analysis is coupled with finite element thermal and stress analysis and the probability of failure of ceramic first wall/blanket design concepts is predicted. The usefulness of the approach is demonstrated by optimizing the geometry of the structure to produce minimum probability of failure.     

Random cyclic stress-strain responses of a stainless steel pipe-weld metal I — a statistical investigation

This paper pays a special attention to the issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Statistical investigation is made to the cyclic stress amplitudes of this material. Three considerations are given. They consist of the total fit, the consistency with fatigue physics and the safety in practice of the seven commonly used statistical distributions, namely Weibull (two- and three-parameter), normal, lognormal, extreme minimum value, extreme maximum value and exponential. Results reveal that the data follow meanwhile the seven distributions but the local effects of the distributions yield a significant difference. Any of the normal, lognormal, extreme minimum value and extreme maximum value distributions might be an appropriate assumed distribution for characterizing the data. The normal and extreme minimum models are excellent. Other distributions do not fit the data as they violate two or three of the mentioned considerations.     

Irradiation creep by dislocation glide enabled by preferred absorption of point defects — theory and experiment

Creep by climb-enabled glide of dislocations may be calculated by mathematically specifying both the origin of the net point defect flux producing the climb and the mode of glide deformation. In general, the net flux contains components arising from (1) differences in point defect capture efficiencies among dislocations and other types of sinks such as cavities, and (2) from differences in capture efficiencies among dislocations whose Burgers vectors are at different orientations with respect to the stress direction. Proposed models based on the first component and employing several modes of glide deformation are reviewed. The characteristics of creep based on the second component, stress induced preferred absorption of point defects on dislocations and subsequent glide, PAG-creep, are described for one mode of glide deformation. Effects of point defect trapping at impurities on creep by this mechanism and on the corresponding climb component of creep are evaluated. Comparison is made with experimental data from light-ion irradiations. The sensitivity of predicted creep rates to the detailed microstructure is emphasized.     

Reply to: “Comments on studies on diversion cross-Flow between two parallel communicating channels by a lateral slot — Part I” by J. Weisman

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.