A Stable Pressure-Correction Scheme for Time-Accurate Non-Premixed Combustion Simulations

Partial depletion of the primary circuit during a hypothetical small break loss of coolant accident can lead to the interruption of one-phase flow natural circulation. In this case, the decay heat is removed from the core in the reflux-condenser mode. For the scenario of a hot leg side leak and hot leg safety injection thermal hydraulics analyses using the system code ATHLET showed, that weakly borated condensate can accumulate in particular in the pump loop seal of those two loops, which do not receive safety injection. According to these ATHLET-calculations, one-phase flow is maintained in the remaining two loops at high residual heat conditions because of the entrainment of safety injection coolant into the steam generators. After refilling of the primary circuit, natural circulation in the two stagnant loops simultaneously re-establishes and the de-borated slugs are shifted towards the reactor pressure vessel (RPV). Mixing in the downcomer and the lower plenum is an important phenomenon mitigating the reactivity insertion into the core in this postulated scenario. Therefore, mixing of the de-borated slugs with the ambient coolant in the RPV was investigated at the four loop 1:5 scaled ROCOM mixing test facility. Based on the ATHLET-calculations, a volume flow rate of 5% of the nominal rate was set in the loops running in one-phase flow. The volume flow rate in the two restarting loops increases from zero to 6%. In these two loops, de-borated slugs of 7.2 m3 were assumed corresponding to the volume of the whole loop seal. An experimental parameter study was carried out with different duration of the flow ramp and variation of the density difference between de-borated slug and ambient coolant due to differences in boron concentration and temperature. The variation of the density difference significantly changes the mixing behavior. With no density difference, the weakly borated coolant almost perpendicularly flows down in the downcomer and a maximum of 64% of the initial perturbation is detected in the core entry section below the loops where the slugs were formed. Increasing the density difference, a stratification is observed in the downcomer. The less dense slugs flow around the core barrel at the top of the downcomer. At the opposite side the lower borated coolant is entrained by the colder safety injection water and transported to the core. This entrainment effect leads to the admixture of boron from the safety injection to the under-borated slugs. Consequently, the maximum under-boration at the core entry is lower. For the maximum investigated density difference of 2%, a value of 31% only of the initial under-boration was measured at the core entrance.

Cations were precipitated with potassium antimonate in the cochlea of the guinea pig and electron microscopy was used to analyze the distribution of the formed reaction products. Differences in precipitate density between neighboring cells in Reissner's membrane, in the stria vascularis and in the limbus are described. Electron spectroscopic imaging was performed to obtain information about the spatial distribution of the precipitates and their elemental composition.

Mixing of miscible shear-thinning fluids in a lid-driven cavity

The lower combination of oil and gas in the southern margin of Xinjiang is deeply buried, with high formation pressure, high downhole temperature, complex formation, complex completion process and long construction period, which requires the completion fluid to have good settlement stability under the conditions of high density and high temperature. The laboratory method was used to evaluate the oil-based completion fluid with resistance temperature of 135 ℃ and 165 ℃. The results show that XZ oil-based completion fluid has good rheological properties and little change in electrical stability after aging at 135 ℃ for 16 h. The density of 2.5 g/cm3 XZ oil-based completion fluid is kept at 135 ℃ for 15 days. The glass rod can fall to the bottom freely with a small amount of soft sedimentation and no hard sedimentation. It can be easily poured out without stirring. The sedimentation factor is less than 0.52. After aging at 165 ℃ for 16 h, the rheological properties and demulsification voltage of oil-based completion fluid change little. When the density of oil-based completion fluid is 2.5 g/cm3, the glass rod can fall to the bottom freely after standing at 165 ℃, with a small amount of soft sedimentation and no hard sedimentation. It can be easily poured out without stirring, and the sedimentation factor is less than 0.52. XZ oil-based completion fluid has good rheological properties and electrical stability after high temperature aging for 16 h. After the XZ oil-based completion fluid is still at high temperature, the density difference between the upper and lower layers increases gradually with the increase of temperature; after 15 days of constant temperature at 220 ℃, the glass rod can fall to the bottom freely, with a small amount of soft sedimentation, no hard sedimentation, and can be easily poured out without stirring, and the sedimentation factor is less than 0.52, which indicates that the temperature resistance of the completion fluid formula reaches 220 ℃, and can meet the requirement of sedimentation stability for 15 days. The field test results show that in well Gaotan-1, the oil-based completion fluid enters the wellbore and remains for 10.5 days continuously to maintain good high temperature settlement stability. In well Hutan-1, the oil-based completion fluid entered the wellbore and remained for 7.25 days continuously, which maintained good high temperature settlement stability and ensured the smooth completion, killing and well testing operation.KeywordsHigh temperatureHigh densityOil basedCompletion fluidSettlement stability

Recently, the Cartesian grid method was used on simulations of fluid flow around the complex geometry problems. In this paper, the Cartesian grid method with cut cells are used to simulate incompressible viscous flows around moving objects. In this study, the small cut cells are merged with neighboring cells. The code was developed based on Fractional Step Method on Finite Volume Method. In time integrate, the second order explicit Adams-Bashforth method was used for the convective terms and second order implicit Crank-Nicholson method was used for the diffusive terms. Some moving boundary problem are simulated using the presented code and compared with other previous numerical and experimental results.

The transport element method is described and implemented in the simulation of the non-premixed reacting shear layer. The method, a natural extention of the vortex element method, resolves the low Mach number variable density flow and the exothermic reacting field. The effect of combustion on the flow is accommodated by incorporating a volumetric expansion velocity component and by modifying the integration of the vorticity equation to include expansion-related and baroclinic terms. The reacting field equations describing a single step, irreversible, chemical reaction, are simplified by the introduction of Schvab-Zeldovich (SZ) conserved scalars whose transport is sufficient to compute the evolution of combustion in the case of infinite reaction rate. In the case of finite rate chemistry the evolution of one primitive scalar, the product mass-fraction, is also computed. The vorticity, conserved scalar gradient and product mass fraction are discretized amongst fields of transport elements. Their time evolution is implemented by advecting the elements at the local velocity while simultaneously integrating their transport equations along particle trajectories. The integration of the vorticity and the conserved scalar gradient equations is simplified using ideas from kinematics. A novel core expansion scheme that avoids the problems associated with the conventional implementation is used to simulate diffusion. Field quantities are obtained using convolutions over the elements. Results indicate that the method is able to accurately reproduce the essential features of the flow. Convergence of the solution in time is approximately linear. Moreover, the finite reaction rate solution at low Karlovitz number bear strong similarities to that of the infinite reaction rate model. This similarity is exploited in validating the part of the numerical methodology related to the integration of the product mass-fraction equation.

The flow of an oil layer around an advancing skimming vessel was investigated theoretically on the following assumptions: (1) the oil layer is so thin that the velocity distribution is uniform over the depth; (2) there is no shear and tension at the oil-water interface; and (3) the density difference between oil and water is so small that the elevation of the air-oil interface is negligible. The investigation showed that the oil layer flow is replaced by a supercritical flow in a shallow open water channel which is characterized by the densimetric Froude number in the ideal case of inviscid fluids with no interfacial tension. Tank tests have been carried out to verify the theoretical model and its simulation of an oil layer flow, using scale models of a mono-hull vessel. Similar models with different entrance angles have been tested, at varying ship speeds and oil layer thicknesses. The test results show that the theoretical model and the similitude are valid at lower densimetric Froude numbers, and the effect of the Froude number appears at higher densimetric Froude numbers.

Two-dimensional multiphase flows with material interface due to density difference are numerically simulated on unstructured grid system by an in-house solution code (PowerCFD). This code employs an unstructured cell-centered method based on a conservative pressure-based finite volume method and adopts a high resolution method (CICSAM) in a volume of fluid (VOF) scheme for the accurate phase interface capturing. The test cases are the Rayleigh-Taylor instability (density ratio of 2), the oil bubble rising in a partially filled container (density ratio of 2), the air bubble rising in a fully filled container with bubble shedding (density ratio of 100) and the droplet splash (density ratio of about 1000), which are typical benchmark problems among multiphase flows with material interface due to density difference. The present results are compared with other numerical solutions found in the literature. It is found that the present method simulates efficiently and accurately complex interface flow such as multiphase flows with material interface due to both density difference and instability.

This paper presents an efficient heuristic algorithm for the channel assignment problem in cellular radio networks. The task is to find channel assignment with minimum frequency bandwidth necessary to satisfy given demands from different nodes in a cellular network. At the same time the interference among calls within the same cell and from different neighboring cells are to be avoided, where interference is specified as the minimum frequency distance to be maintained between channels assigned to a pair of nodes. The simplest version of this problem, where only cochannel interferences are considered, is NP-complete. The proposed algorithm could generate a population of random valid solutions of the problem very fast. The best among them is the optimum or very near to optimum solution. For all problems with known optimal solutions, the algorithm could find them. A statistical estimation of the performance of the proposed algorithm is done. Comparison with other methods show that our algorithm works better than the algorithms that we have investigated.

A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d3f, a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Hassanizadeh and Leijnse (1995) (Adv Water Resour 18(4):203–215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.

Stabilizing nodal integration in dynamic smoothed particle finite element method: A simple and efficient algorithm

Simulation of dam-break flow with grid adaptation

Managing recharge of freshwater into saline aquifers requires accurate estimation of the heterogeneous permeability field for maximizing injection and recovery efficiency. Here we present a methodology for subsurface characterization in saline aquifers that takes advantage of the density difference between the injected freshwater and the ambient saline groundwater. We combine high‐resolution forward modeling of density‐driven flow with an efficient Bayesian geostatistical inversion algorithm. In the presence of a density difference between the injected and ambient fluids due to differences in salinity, the pressure field is coupled to the spatial distribution of salinity. This coupling renders the pressure field transient: the time evolution of the salinity distribution controls the density distribution which then leads to a time‐evolving pressure distribution. We exploit this coupling between pressure and salinity to obtain an improved characterization of the permeability field without multiple pumping tests or additional salinity measurements. We show that the inversion performance improves with an increase in the mixed convection ratio—the relative importance between viscous forces from injection and buoyancy forces from density difference. Our work shows that measuring transient pressure data at multiple sampling points during freshwater injection into saline aquifers can be an effective strategy for aquifer characterization, key to the successful management of aquifer recharge.

A numerical modeling approach was used to investigate the relevancy of the feedback mechanisms between geochemical reactions and variable density flow during free convection. The problem was studied by reformulating the classic Elder problem as a reactive multicomponent transport problem. It was found that for the studied system, the importance of this feedback decreased with increasing density contrast between intruding salinized water and the ambient fresh water body. For the smaller density contrasts, the flow patterns that develop during intrusion in the reactive simulations are characterized by different convection cells, higher rates of plume descent, and an increase in the total mass of solutes by up to 22% at the end of the simulation compared to the nonreactive simulations. For field situations, the results suggest that it may be necessary to consider the feedback between reactions and variable density flow where subtle density variations drive flow such as in contaminant plumes. For seawater intrusion problems, however, the feedback mechanism appears to be negligible for most cases.

The rotating movement of three immiscible fluids—a benchmark problem