High Pressure Gradient Research Articles

Development of depth-averaged nonlinear flow model for fractures considering heterogeneity and significant inertial effects

Fluid flow through fractures is central to many engineering applications and geophysical processes. Although the intertwined effects of aperture heterogeneity and inertial forces on fluid flow have been interrogated in last few decades, it remains challenging to accurately predict fracture flow field at high pressure gradient conditions when inertial effects are significant. To address this challenge, we rigorously derived a depth-averaged nonlinear flow model by introducing a quadratic velocity term into the linear flow model (i.e., Local Cubic Law that describes a linear relationship between pressure gradient and fluid flux) at the mechanistic level. The supporting laboratory experiments and direct numerical simulations through six rough-walled fractures with varying roughness further confirmed the robustness of the proposed model. We found that the predictive model outperforms existing alternatives with acceptable relative errors in mean velocity (<7%) considering a broad range of Reynolds number (0.01–167), suggesting its superior performance of handling pronounced inertial effects. Lastly, we parameterized the new model by establishing an empirical function that related parameter (ω) in the model to measurable fracture properties (i.e., aperture); this makes the predictive model viable and straightforward for predicting local velocity fields in pressurized engineered environments.

Viscoplastic effects of Newtonian fluids in nanopores: a molecular dynamics study

Understanding the influence of fluid–solid interactions on low-velocity non-Darcy flow in ultra-low permeability reservoirs is essential for enhanced oil recovery. The Poiseuille flows of C12H26 and argon under different pressure gradients in a nanopore are simulated using the molecular dynamics method. The results demonstrate that the confined fluids behave as elastic solids under lower pressure gradient but as viscous fluids under higher pressure gradient in the simulation. With increase of the external pressure gradient, the generated shear stress exceeds the yield stress related to the fluid-solid interaction and leads to a transition. This phenomenon indicates that the confined fluids in the nanopore exhibit apparent viscoplasticity. According to the viscoplastic hypothesis, the confined fluid can be divided into elastic and viscous layers, depending on the competition between the shear and yield stresses. The simulation results also indicate the yield stress increases near the wall. Assuming that the yield stress is inversely proportional to the distance from the wall, a non-Darcy flow model is proposed to calculate the flow rate by pressure gradient. The predictions of the model are consistent with the simulations for both C12H26 and argon, indicating the similarity of viscoplastic effects on the seepage of both fluid-nanopore systems.

Experimental Investigation of Flow Control on a High-Lift Wing Using Modulated Pulse Jet Vortex Generator

In this paper, the potential of a novel active flow control strategy by means of a modulated pulse jet vortex generator to enhance high-lift performance is demonstrated on a two-dimensional supercritical National Aeronautics and Space Administration (NASA) SC(2)-0714 airfoil with a single slotted trailing-edge flap at a high deflection angle. Fast-switching solenoid valves and compressed air were used as actuators to excite the flow. The vortex generator slot pairs were incorporated into the shoulder of the trailing-edge flap, where the flow separation occurs due to the high flow deflection and severe adverse pressure gradient. In these experiments, in addition to the simple square-wave excitation signal, a burst-modulated excitation signal as a novel pulse jet sequence was implemented to produce the unsteady blowing. The burst-modulation signal was used for the first time for a fast-switching solenoid valve actuator. The experiments were performed at a freestream velocity of 25 m/s with a corresponding Reynolds number of about 1×106 for a range of angles of attack from 0° to 20° at flap deflection angles from 0° to 35°. The results indicated that the ejection from vortex generator slot pairs was able to prevent flow separation completely in most conditions. These measurements revealed that the burst-modulated excitation was accompanied by more aerodynamic improvements and less air consumption relative to the simple pulsed jet excitation. In the best flow control mode, the results showed about a 12.6% increase in the lift coefficient and a 19.8% decrease in the drag coefficient.

Characteristics of thermal plume from an array of rectangular straight fins with openings on the base in natural convection

Straight rectangular fins with openings in the base surface in natural convection exhibit greater heat transfer than rectangular fins without openings in the base. In this paper, thermal plume arising from such fin configuration used as a heat sink for natural convection cooling of light-emitting diode (LED) grow lights is investigated using three-dimensional conjugate laminar flow simulations. Understanding of plume characteristics is crucial in optimizing the cooling performance as well as optimal placement of grow lights from ceilings and walls in proximity. A prototype LED grow light was designed and experimentally measured to assess the cooling performance, and numerical simulations were conducted to investigate the plume structure. The results showed that openings in the base enhanced vertical draft of air, mixing, and overall heat transfer rate. It was found that local pressure gradient is proportional to the degree of mixing of ambient air into the plume. Low pressure regions around the fins and channels showed upward convection of plume mass and a high pressure region below the fins indicated higher concentration of denser air mass. High pressure gradients were observed in the openings, which further justifies the significance of openings in improving mixing of ambient air with the plume to enhance heat transfer.

Hybrid RANS/LES study of tip leakage vortex instability and turbulence characteristics of a transonic turbine cascade

To conduct detailed investigations about vortex instability and turbulence characteristics near a transonic turbine tip region, a highly accuracy hybrid Reynolds averaged Navier Stokes (RANS) / large eddy simulation (LES) method, namely detached eddy simulation (DES)-type method, is adopted at the exit isentropic Mach number of 0.95. Validation results show that this hybrid method can provide an accurate prediction against experiments. In contrast with the RANS method, this method can exhibit superiority in capturing detailed small-scale flow structures and more realistic turbulence distribution. Based on various identification methods, two predominant instability patterns of tip leakage vortex (TLV), namely, vortex wandering and breakdown have been recognized successfully in its downstream progression. Due to the supplement of tip leakage flow (TLF), the TLV maintains a concentrated vortex morphology with a monotonically increasing transverse wandering magnitude inside the blade passage. Subsequently, the TLV breakdown phenomenon, which is mainly due to the high adverse pressure gradient aggravated by shock waves, can be observed downstream the trailing edge. Meanwhile, a “spiral-type” vortex breakdown is distinguished firstly in a transonic turbine environment, which cannot be found in the previous RANS literature. To investigate the nature of the vortex instability, we perform an analysis based on the vorticity transport equation, it's found that the convection term due to the velocity gradient dominated the leakage vorticity damping. Combined the triple decomposition with the proper orthogonal decomposition (POD) method, the mechanisms of vortex wandering have been further revealed, which exhibits non-zero perturbations in transverse modes and a helical mode in the streamwise direction. Furthermore, detailed analysis of the turbulence characteristics has been also conducted, which contains distributions of Reynolds stress terms and the turbulent kinetic energy (k) along the TLV core trajectory. It can be recognized that the high adverse pressure gradient by shock waves can result in a sharp increase of Reynolds normal stresses (τii), which can stretch the TLV in different directions and exerts detrimental effects on the vortex breakdown. As a complementary, the turbulent anisotropy is also evaluated by the Lumley triangle method, which exhibits a variation from the one-component anisotropy to a two-component morphology as the TLV migrating downstream, while a isotropic turbulence field may be formed downstream the trailing edge due to the intense mixing. Predicted turbulence characteristics, vortical instabilities, and their flow mechanism can provide guide towards lower loss design and flow control of the turbine blade.

Enhancing solute transport by pressure-wave driven flow in unsaturated porous media

Solutes and their limited mobilization in heterogeneous porous media may lead to subsurface salinization and contamination evident in various environmental settings. Previous studies showed that flow and transport driven by pressure waves in porous media under saturated conditions significantly enhance solute displacement compared to drag-dominant (Darcy) flow and transport, resulting in more thorough remediation. However, experimental evidence lacks demonstration of such transport under unsaturated conditions. We investigate solute leaching in a flow cell, experimentally modeling solute displacement from an unsaturated, saline, fine-textured soil region to the surrounding coarse-textured soil. The extent of mobilization efficiency is evaluated by comparing solute breakthrough measurements between two leaching treatments, with drag-dominant continuous flux (CF) and pressure-wave pulse flux (PPF). The results indicate that the PPF treatment provided an additional 75% solute mass that leached from the fine-textured region per unit volume of water compared to the CF. The effect is partly due to the impact of the pressure waves on water imbibition into the medium. The PPF induced relatively high pressure gradients at the wetting front compared to percolation during the CF, thus wetting the media in a more spatially uniform pattern. Consequently, the PPF treatment led to higher water content at and behind the front, which increased the continuity of the water phase across the fine-textured and coarse-textured soils and enhanced transport. The study is a proof of concept for pressure-wave driven flow to enhance local wetting and solute transport in unsaturated soil.

Impact of Transcatheter Aortic Valve Implantation on Severe Gastrointestinal Bleeding in Patients With Aortic Stenosis

To investigate the effectiveness of transcatheter aortic valve implantation (TAVI) for resolving gastrointestinal bleeding (GIB) in patients with severe GIB and severe aortic stenosis. This was an observational study of consecutive TAVI procedures from 2011 to 2018, identified through a prospectively maintained institutional database. Patients with severe GIB defined as abnormal hemoglobin/hematocrit and overt bleeding or positive fecal occult blood test. Groups were compared for differences in baseline clinical and procedural characteristics and post-TAVI outcomes. A total of 1,192 patients who underwent TAVI were identified, of which 164 patients (13.8%) were found to have had severe GIB. Society of Thoracic Surgeons-Predicted Risk of Mortality scores were higher in the severe GIB group than in the non-GIB group (8.8 ± 5.3 vs 7.6 ± 4.5, p=0.002). The 30-day mortality was similar across each group (p >0.05), with overall 30-day mortality being 3.2% (38 of 1,192) for the entire cohort. Of the 164 TAVIs with severe GIB, 130 (79.3%) had resolution of their GIB after their TAVI. Patients without resolution of their GIB had higher aortic valve mean pressure gradients after their TAVI (15.0 ± 5.3 vs 9.0 ± 4.3). In conclusion, TAVI was associated with substantial reductions in severe GIB. Despite higher baseline risk, patients with severe GIB achieved similar outcomes, including 30-day mortality, compared with patients without GIB. TAVI may be a safe and effective treatment for patients with severe aortic stenosis and severe GIB, whereas persistently high transvalvular pressure gradients after TAVI may be related to the likelihood of recurrent GIB.

CO2-responsive gel particles and wormlike micelles coupling system for controlling CO2 breakthrough in ultra-low permeability reservoirs

CO2 flooding in ultra-low permeability reservoirs is an effective means to boost oil production, while the complex fractures formed by fracturing in the initial development stage induce severe CO2 channeling. Therefore, a CO2-responsive coupling system, which coupled CO2-responsive gel particles (CRPGP) with CO2-responsive wormlike micelles (CTWM) was prepared to restrain CO2 breakthrough. To testify the EOR capacity during CO2 flooding of the responsive coupling system, the interaction between CRPGP and CTWM, and responsiveness of coupling system was investigated, followed by core flooding and rock slab flooding experiments. Experiment results showed that after the coupling system was exposed with CO2, the particle size of CRPGP increased, spherical micelles of CTWM transformed to wormlike micelles, CRPGP and CTWM were integrated through hydrophobic association among wormlike micelles and hydrophobic chains in CRPGP, and the coupling system’s apparent viscosity increased from 10.4 mPa·s to 2339 mPa·s. Moreover, 0.5 pore volume (PV) CO2-responsive coupling system injection and further CO2 flooding could dramatically boost oil production in fractured cores and rock slabs, which was primarily ascribed to the aggrandizement of sweeping volume resulting from the plugging effect of CRPGP and mobility ratio improvement of the coupling system. Compared with single slug plugging of fractures, multi-stage regulation of fractures could establish a higher-pressure gradient, and more crude oil in the matrix was activated with enhanced oil recovery (EOR) of 22.8%. All the experimental results demonstrated that the CO2-responsive coupling system has great EOR capacity during CO2 flooding, which provided novel insights for ultra-low permeability reservoirs EOR technology that incorporated with CO2 resource utilization and storage.

Thermo-economic analysis of an oxygen production plant powered by an innovative energy recovery system

Oxy-fuel combustion is considered an attractive alternative to reduce pollutant emissions, which uses high-purity oxygen mixed instead of air for combustion processes. However, purchasing large amounts of high-purity oxygen may be unprofitable for certain industrial sectors, discouraging its implementation. Considering this, the potential of an oxygen production cycle for factories using oxy-fuel combustion is studied by performing a thermo-economic analysis where high-purity oxygen, electricity, and natural gas prices are considered. Oxygen is produced by membrane means, where mixed ionic-electronic conducting membranes are used, which require high temperatures and pressure gradients to work properly. A set of turbochargers is implemented, chosen by scaling an off-the-shelf model, what introduces an innovative way of waste energy recovering for improving the performance of the cycle. The whole cycle is powered by waste heat from high temperature flue gases, and it is sized for a ceramic manufacturing factory. In this work, two cases are analysed, differentiated by considering additional heating and the vacuum generation method in the oxygen line. The first case exhibits smaller production levels, although better profitability (31 €t−1), whereas the second case displays higher production levels and production costs (33 €t−1). Both cases are competitive concerning the average price of high-purity oxygen, supposing an average of 50 €t−1 in wholesale markets, proving the potential of the proposed alternative for oxygen production.

Structural analysis of compact heat exchanger samples fabricated by additive manufacturing

Compact heat exchangers are extensively employed in the industry due to their flexibility, geometric configuration characteristics, and the low ratio between heat transfer area by volume. Usually, these heat exchangers are exposed to high thermal and pressure gradients, which can cause structural failures during the operation. A new fabrication method employing additive manufacturing was evaluated to produce that equipment in this context. Twelve samples of 316L stainless steel that simulated a heat exchanger geometry were fabricated in two machines. A test rig was constructed for hydrostatic tests to evaluate their structural integrity through strain gauges. Some samples were submitted to pressures up to 700 bar without any leakage. The results show that printing orientation is crucial to the process, which influences material properties and, consequently, the von Mises stress observed. Properties on vertical orientation present lower stress levels. The influence of heat treatment was also verified, showing that machining processes locally alter mechanical properties. In parallel, a numerical study was developed for structural evaluation. It was observed that the pressurization of the distribution chamber strongly influences the stress of prototype channels. The high-stress region does not surpass the material yield strength for the test pressure. Furthermore, any deformation on the experimental prototype was not observed, indicating that the geometric characteristics guarantee a structural integer of the heat exchanger core. It is highlighted that the numerical results proved a good adherence to experimental results.

On the statistical properties of fluid flows with transitional power-law rheology in heterogeneous porous media

In this work, we study non-Newtonian fluid flow in heterogeneous porous media. We are interested in fluids presenting a specific change in rheology: Newtonian below a certain shear rate and power law above. Since porous media generally exhibit strong spatial heterogeneity at large geological scales, we study the interaction between such inhomogeneity and the nonlinear rheology of the fluid. The coupling between permeability heterogeneity and nonlinear rheology significantly affects the flow. We are particularly in the statistical properties of the velocity field (mean, variance, correlation, etc). Depending on the imposed mean pressure gradient, three macroscopic flow regimes are identified. For a low or high average pressure gradient, the average flow rate increases linearly or according to a power law, respectively. In the latter regime, we observe that the velocity field is more heterogeneous for shear-thinning fluids than for shear-thickening fluids. This is corresponding to a channeling effect of shear-thinning fluids. The intermediate regime corresponds to a progressive and inhomogeneous change of the local rheology. This transient regime is then characterized in terms of pressure gradient range. The flow field is also analyzed statistically. The spatial distribution of the regions above the rheology threshold shows interesting statistical properties. For instance, they exhibit multiscale characteristics (fractal), similar to other critical systems (percolation, avalanches, etc.). If the distribution of their area follows a power-law, the exponent is independent of the disorder. This suggests a kind of “universality” in this problem. More surprisingly, even though some statistical properties are independent of the parameters, an interesting abrupt rotation of the correlations is found for a particular set of parameters. This is explained by using some symmetries of the problem. • The flow of a non-Newtonian fluid in heterogeneous macroscopic porous media is studied. • If the rheology shows a change in behavior, a strong coupling between nonlinear rheology and heterogeneity is observed. • Three macroscopic flow regimes are observed. • The transient flow regime shows multiscale (fractal) properties that are independent of the parameters and the magnitude of the heterogeneity. • An abrupt change in the direction of correlation is also observed for a certain set of parameters.

Quantitative Characterization of Excess Pressure Gradient in the Upper Interval of Es4 Member of Dongying Depression and Its Indicative Significance for Oil Migration and Accumulation

Excess pressure is the main driving force of oil migration in the source-reservoir system of overpressured petroliferous basins. It can reflect the change in driving force for oil migration and its influence on oil accumulation in overpressure transport layers. The drilling stem test (DST) data, well logging data, and seismic velocity data are used to describe the plane distribution of the excess pressures in the Es4s member of the Dongying Depression. Then, the values and directions of the excess pressure gradient, which can indicate oil migration and accumulation, are calculated based on the plane distribution of the excess pressure in the Es4s member of the Dongying Depression. The results suggest that overpressure is widely developed in the Es4s member of the Dongying Depression, and the excess pressure gradually decreases from the center to the edge of each sag, while the variation in the excess pressure gradient is characterized by “low-high-low” in a circular band around the sags. The excess pressure in the sag areas exceeds 15 MPa, but the excess pressure gradient is mainly between 0 and 1 MPa/km. The excess pressure in the northern steep slope zone of the Lijin sag and the northern steep slope zone of the Minfeng sag are less than 15 MPa, while the excess pressure gradient ranges from 1 to 7 MPa/km. The excess pressure in the central anticline belt and the gentle slope belt in the south of the Niuzhuang sag are between 0 and 15 MPa, and the excess pressure gradient is from 0 MPa/km to 2 MPa/km. From geochemical evidence, local oil migration directions indicated by the excess pressure gradient are consistent with those indicated by the ratio parameters of carbazole compounds in crude oil samples, indicating that the direction of the excess pressure gradient can indicate the dominant direction of oil migration driven by excess pressure, and the oil from the Es4s source rock is mainly distributed in the areas with a high excess pressure gradient or the areas with a low excess pressure gradient and low excess pressure (area II).

Study on the Flow and Acoustic Field of an Electronic Expansion Valve under Refrigeration Condition with Phase Change

A combined numerical-experiment investigation on the flow and acoustic field of an electronic expansion valve (EEV) is conducted in this paper. In an electronic expansion valve (EEV) under refrigeration condition, it is usually complex about internal flow. There are high pressure gradient and velocity gradient in the flow field, and it also involves the process of flashing phase change, physical property change, and heat transfer, which is difficult to simulate directly. After many explorations in this paper, the flow field of EEV under refrigeration condition is simulated by a four-step computational fluid dynamics (CFD). On this basis, the noise of EEV which is induced by the internal turbulent flow and propagates outward through the shell of EEV is simulated by a Hybrid Method. Numerical simulations of the mass flow rate (MFR) and sound pressure level (SPL) are verified by experimental data. Then, the characteristics of the internal flow field causing the external acoustic radiation are analyzed and used to create an improved design that can reduce the SPL while the MFR hardly changes.

K-kL TÜRBÜLANS MODELİNİN UYGULAMASI, DOĞRULAMASI VE GiRDAP YAKALAMA YETENEKLERİNİN DEĞERLENDİRİLMESİ

This study presents the first results of a new turbulence model implementation in our compressible finite volume CFD solver. The k - kL turbulence model is one of the newest two-equation models, and it is based on the ideas of Rotta’s two-equation model. Various research groups progressively develop the model, and it is maturing rapidly. Reports suggest that the k - kL turbulence model provides superior results compared to the other two-equation turbulence models in specific problems. The improved solutions are observed mainly for the flows with high adverse pressure gradients, the blunt-body wakes and jet interactions. We have implemented the k - kL model (with the standard designation of k-kL-MEAH2015) in our solver, and we are testing it rigorously. This paper presents our results on standard turbulence test cases: subsonic flat plate and subsonic wall-mounted bump. The results compare well with the reference study previously presented and published by model developers. The design of the k - kL model prevents excessive production of turbulence and dissipation; hence it preserves vortices significantly better than the other two-equation models. The implemented model is also tested with a transonic fin trailing vortex case to support this statement. Results show that the k-kL model yields considerably better results than the SST turbulence model in cases including vortices.

Analysis of transient flow field characteristics during the closing process of water distributor valve core

The integrated water distributor (IWD) is the adjustment terminal during the interval injection process. Its quality and performance are directly related to the effect of layered water injection. The IWD’s flow field is considered the research object, and the transient simulation is developed with Fluent dynamic grid and Fluid-Structure Interaction technology. The internal flow of the IWD during closing is simulated, and the mechanical behavior of the valve core is analyzed. The results show that: as the valve opening decreases, the high-speed areas appear at the throat of the valve core and the upper wall of the valve outlet; the throat of the valve presents a higher pressure gradient; the most serious deformation point appears on the lower side of the valve core, and the deformation increases as the valve core move down; the maximum equivalent strain occurs at the root of the valve core and increases as the valve core moves down.

Numerical and Thermal Investigation of Magneto-Hydrodynamic Hybrid Nanoparticles (SWCNT-Ag) under Rosseland Radiation: A Prescribed Wall Temperature Case.

Thermal heat generation and enhancement have been examined extensively over the past two decades, and nanofluid technology has been explored to address this issue. In the present study, we discuss the thermal heat coefficient under the influence of a rotating magneto-hydrodynamic hybrid nanofluid over an axially spinning cone for a prescribed wall temperature (PWT) case. The governing equations of the formulated problem are derived by utilizing the Rivlin–Ericksen tensor and boundary layer approximation (BLA). We introduce our suppositions to transform the highly non-linear partial differential equations into ordinary differential equations. The numerical outcomes of the problem are drafted in MATLAB with the of help the boundary value problem algorithm. The influences of several study parameters are obtained to demonstrate and analyze the magneto-hydrodynamic flow characteristics. The heat and mass transfer coefficients increase and high Nusselt and Sherwood numbers are obtained with reduced skin coefficients for the analyzed composite nanoparticles. The analyzed hybrid nanofluid (SWCNT-Ag–kerosene oil) produces reduced drag and lift coefficients and high thermal heat rates when compared with a recent study for SWCNT-MWCNT–kerosene oil hybrid nanofluid. Maximum Nusselt (Nu) and Sherwood (Sh) numbers are observed under a high rotational flow ratio and pressure gradient. Based on the results of this study, we recommend more frequent use of the examined hybrid nanofluid.

Edge plasma relaxations due to diamagnetic stabilization

A new mechanism for pressure profile relaxations in an edge tokamak plasma is derived from simulations within the two-fluid three-dimensional turbulence code EMEDGE3D. The relaxation is due to diamagnetic coupling in the resistive ballooning/drift wave dynamics: Unstable modes experience explosive growth at high pressure gradients after a phase in which they are stabilized by the diamagnetic coupling leading to the onset of a transport barrier. The sheared E × B flow does not play any significant role. After relaxation, the transport barrier forms again and it sets the conditions for a new relaxation event, resulting in an oscillatory behavior. We find that energy flux into the scrape-off layer decreases with the increasing oscillation frequency and that the oscillations are tamed by increasing plasma temperature. This behavior is reminiscent of the so-called type-III edge localized modes. A one-dimensional model reproducing the relaxations is also derived.

Patterned Interference Radiation Force for Transcranial Neuromodulation.

Compared with the conventional method of transcranial focused ultrasound stimulation using a single transducer or a focused beam, the compression and tensile forces are generated from the high-pressure gradient of a standing wave that can generate increased stimulation. We experimentally verified a neuromodulation system using patterned interference radiation force (PIRF) and propose a method for obtaining the magnitude of the radiation force, which is considered the main factor influencing ultrasound neuromodulation. The radiation forces generated using a single focused transducer and a standing wave created via two focused transducers were compared using simulations. Radiation force was calculated based on the relationship between the acoustic pressure, radiation force and time-averaged second-order pressure obtained using an acoustic streaming simulation. The presence of the radiation force was verified by measuring the time-averaged second-order pressure generated due to the radiation force, by using a glass tube.

Numerical study of blowdown period of double-end break loss of coolant accident in PWR based on RELAP5

Loss of coolant accident (LOCA) is one of the most severe accidents of nuclear power plants (NPP). During the early blowdown period, the system is in a high-pressure gradient and high-velocity gradient state. Therefore, the hydrodynamic forces and safety analysis are highly related to calculating thermal-hydraulic parameters in the flow field. This paper studied the factors and modeling methods that affect the calculation of thermal-hydraulic characteristics under large break LOCA conditions. Firstly, the reactor core and primary system of a typical two-loop pressurized water reactor (PWR) NPP is modeled using the system analysis code RELAP5 Mod4.0. The normal operation state is obtained after the steady calculation. Then, transient calculation of double-end break LOCA is implemented considering the effects of break opening time and the pressurizer. The influence of the results on the calculation of hydrodynamic force has also been analyzed. Finally, the modeling method of reactor pressurized vessel (RPV) downcomer is presented. It is found that the flow field can be better simulated when the downcomer is modeled with parallel channels and several transverse junctions. Thus, this paper provides meaningful suggestions for modeling and simulation in the early blowdown period under LOCA conditions and contributes to further hydrodynamic load calculation and reactor safety analysis.

Pressure-Tight and Non-stiff Volume Penalization for Compressible Flows

Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous media, and approximates a solid object in the limit of vanishing porosity. In its simplest form, the momentum equations are augmented by a term penalizing the fluid velocity, yielding good results in many applications. However, it induces numerical stiffness, especially if high-pressure gradients need to be balanced. Here, we focus on the effect of the reduced effective volume (commonly called porosity) of the porous medium. An approach is derived, which allows reducing the flux through objects to practically zero with little increase of numerical stiffness. Also, non-slip boundary conditions and adiabatic boundary conditions are easily constructed. The porosity terms allow keeping the skew symmetry of the underlying numerical scheme, by which the numerical stability is improved. Furthermore, very good conservation of mass and energy in the non-penalized domain can be achieved, for which the boundary smoothing introduces a small ambiguity in its definition. The scheme is tested for acoustic scenarios, for near incompressible and strongly compressible flows.