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NASA NTRS2005

Conservative Patch Algorithm and Mesh Sequencing for PAB3D

A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.

Pao, S. P.↗

NASA NTRS1990

Low-gravity fluid physics: A program overview

An overview is presented of the microgravity fluid physics program at Lewis Research Center. One of the main reasons for conducting low gravity research in fluid physics is to study phenomena such as surface tension, interfacial contact angles, and diffusion independent of such gravitationally induced effects as buoyant convection. Fluid physics is at the heart of many space-based technologies including power systems, thermal control systems, and life support systems. Fundamental understanding of fluid physics is a key ingredient to successful space systems design. In addition to describing ground-based and space-based low-gravity facilities, selected experiments are presented which highlight Lewis work in fluid physics. These experiments can be categorized into five theme areas which summarize the work being conducted at Lewis for OSSA: (1) isothermal/iso-solutal capillary phenomena; (2) capillary phenomena with thermal/solutal gradients; (3) thermal-solutal convection; (4) first- and second-order phase transitions in a static fluid; and (5) multiphase flow.

Source record↗

NASA NTRS1994

Two-layer viscous instability in a rotating couette device

A novel experiment to study the interfacial shear instability between two liquids is described. Density-matched immiscible liquids are confined between concentric cylinders such that the interface is parallel to the cylinder walls. Interfacial waves that develop because of viscosity differences between the shearing fluids are studied as a function of rotation rate and depth ratio using optical techniques. Conditions neutral stability and the most unstable wavenumber agree reasonably well with predictions from linear stability analysis of the Navier-Stokes equations. Illumination using laser sheets allows precise measurement of the interface shape. Future experiments will verify the correctness of weakly nonlinear theories that describe energy transfer and saturation of wave growth by nonlinear effects. Measurements of solitary wave shapes, that occur far above neutral stability, will be compared to similar measurements for systems that have gravity as an important force to determine how gravity effects large disturbances. These results will be used to interpret slug and annular flow data that have been obtained in other mu g studies.

Gallagher, Christopher↗

NASA NTRS1993

Development of an Atomization Methodology for Spray Combustion

In liquid rocket propulsion, the knowledge and the understanding of liquid-gas interfacial phenomena are very important. This is important for predicting the onset of cavitation occurring in swirl injection elements used in STME, as well as atomization processes in shear-induced injectors (co-axial) and impinging injector elements. From the fact that all the physical processes including droplet size distribution, droplet dispersion, mixing and combustion are controlled by atomization processes, it is expected that the successful incorporation of the volume of fraction (VOF) will greatly enhance the analytical capability of predicting spray combustion processes in liquid-fueled engines. In this paper, a methodology is developed to define and track interfaces between two fluids in non-orthogonal, body-fitted grids using a single fractional volume of fluid (VOF) variable to describe the distribution of the liquid phase in a gas-liquid flow field. This method was implemented in a mature CFD code MAST (Multiphase All-Speed Transient) utilizing the general PISO-C algorithm. For the preliminary study on the analysis of spray combustion and tracking of the interface between two phases, we will report on the progress of the simulation of the instability on the liquid column; the surface wave instability and the droplet breakup from the liquid surface.

Seung, S. P.↗

NASA NTRS1999

Unusual Contact-Line Dynamics of Thick Films and Drops

We report several novel phenomena In contact-line and fingering dynamics of macroscopic spinning drops and gravity-driven films with dimensions larger than the capillary length. It is shown through experimental and theoretical analysis that such macroscopic films can exhibit various interfacial shapes, including multi valued ones, near the contact line due to a balance between the external body forces with capillarity. This rich variety of front shapes couples with the usual capillary, viscous, and intermolecular forces at the contact line to produce a rich and unexpected spectrum of contact-line dynamics. A single finger develops when part of the front becomes multivalued on a partially wetting macroscopic spinning drop in contrast to a different mechanism for microscopic drops of completely wetting fluids. Contrary to general expectation, we observe that, at high viscosity and low frequencies of rotation, the speed of a glycerine finger increases with increasing viscosity. Completely wetting Dow Corning 200 Fluid spreads faster over a dry inclined plane than a prewetted one. The presence of a thin prewetted film suppresses fingering both for gravity-driven flow and for spin coating. We analyze some of these unique phenomena in detail and offer qualitative physical explanations for the others.

Veretennikov, Igor↗

NASA NTRS1993

Wave effects on ocean-ice interaction in the marginal ice zone

The effects of wave train on ice-ocean interaction in the marginal ice zone are studied through numerical modeling. A coupled two-dimensional ice-ocean model has been developed to include wave effects and wind stress for the predictions of ice edge dynamics. The sea ice model is coupled to the reduced-gravity ocean model through interfacial stresses. The main dynamic balance in the ice momentum is between water-ice stress, wind stress, and wave radiation stresses. By considering the exchange of momentum between waves and ice pack through radiation stress for decaying waves, a parametric study of the effects of wave stress and wind stress on ice edge dynamics has been performed. The numerical results show significant effects from wave action. The ice edge is sharper, and ice edge meanders form in the marginal ice zone owing to forcing by wave action and refraction of swell system after a couple of days. Upwelling at the ice edge and eddy formation can be enhanced by the nonlinear effects of wave action; wave action sharpens the ice edge and can produce ice meandering, which enhances local Ekman pumping and pycnocline anomalies. The resulting ice concentration, pycnocline changes, and flow velocity field are shown to be consistent with previous observations.

Liu, Antony K.↗

NASA NTRS2014

Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.

Yang, H. Q.↗

NASA NTRSDate not supplied

Validation of a Two-Phase CFD Model for Predicting Tank Self-Pressurization in the Ground-Based K-Site Experiment

A two-phase CFD model for self-pressurization of a cryogenic storage tank partially filled with liquid hydrogen is presented using the Volume-Of-Fluid approach for representing the phase boundary and the associated interfacial heat, mass and momentum transfer between the liquid and the vapor regions. The CFD model is validated against self-pressurization experiment performed in the K-site flightweight hydrogen storage tank at NASA Glenn Research Center. Laminar and turbulent simulations together with conjugated heat transfer analysis are performed. Effects of turbulence, as well as tank wall conduction are presented and discussed. Predicted tank pressures and fluid temperatures are compared with the experimental data at two different heat loads for validating the CFD model.

phase change↗

NASA NTRS1995

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small round-off errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out.

Baker, Gregory↗

NASA NTRS2001

Flame Synthesis of Single- and Multi-Walled Carbon Nanotubes and Nanofibers

Metal-catalyzed carbon nanotubes are highly sought for a diverse range of applications that include nanoelectronics, battery electrode material, catalysis, hydrogen storage media and reinforcing agents in polymer composites. These latter applications will require vast quantities of nanotubes at competitive prices to be economically feasible. Moreover, reinforcing applications may not require ultrahigh purity nanotubes. Indeed, functionalization of nanotubes to facilitate interfacial bonding within composites will naturally introduce defects into the tube walls, lessening their tensile strength. Current methods of aerosol synthesis of carbon nanotubes include laser ablation of composite targets of carbon and catalyst metal within high temperature furnaces and decomposition of a organometallics in hydrocarbons mixtures within a tube furnace. Common to each approach is the generation of particles in the presence of the reactive hydrocarbon species at elevated temperatures. In the laser-ablation approach, the situation is even more dynamic in that particles and nanotubes are borne during the transient cooling phase of the laser-induced plasma for which the temperature far exceeds that of the surrounding hot gases within the furnace process tube. A shared limitation is that more efficient methods of nanoparticle synthesis are not readily incorporated into these approaches. In contrast, combustion can quite naturally create nanomaterials such as carbon black. Flame synthesis is well known for its commercial scalability and energy efficiency. However, flames do present a complex chemical environment with steep gradients in temperature and species concentrations. Moreover, reaction times are limited within buoyant driven flows to tens of milliseconds. Therein microgravity can greatly lessen temperature and spatial gradients while allowing independent control of flame residence times. In preparation for defining the microgravity experiments, the work presented here focuses on the effect of catalyst particle size and reactant gas in 1g.

VanderWal, R. L.↗

NASA NTRS2009

Computer Code for Nanostructure Simulation

Due to their small size, nanostructures can have stress and thermal gradients that are larger than any macroscopic analogue. These gradients can lead to specific regions that are susceptible to failure via processes such as plastic deformation by dislocation emission, chemical debonding, and interfacial alloying. A program has been developed that rigorously simulates and predicts optoelectronic properties of nanostructures of virtually any geometrical complexity and material composition. It can be used in simulations of energy level structure, wave functions, density of states of spatially configured phonon-coupled electrons, excitons in quantum dots, quantum rings, quantum ring complexes, and more. The code can be used to calculate stress distributions and thermal transport properties for a variety of nanostructures and interfaces, transport and scattering at nanoscale interfaces and surfaces under various stress states, and alloy compositional gradients. The code allows users to perform modeling of charge transport processes through quantum-dot (QD) arrays as functions of inter-dot distance, array order versus disorder, QD orientation, shape, size, and chemical composition for applications in photovoltaics and physical properties of QD-based biochemical sensors. The code can be used to study the hot exciton formation/relation dynamics in arrays of QDs of different shapes and sizes at different temperatures. It also can be used to understand the relation among the deposition parameters and inherent stresses, strain deformation, heat flow, and failure of nanostructures.

Filikhin, Igor↗

NASA NTRS1999

Numerical Modeling of Crystal of ZnSe by Physical Vapor Transport - Towards a more Comprehensive Formulations

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.

Ramachandran, N.↗

NASA NTRS1998

Crystal Growth of ZnSe by Physical Vapor Transport: A Modeling Study

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of Physical Vapor Transport (PVT) growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe arc reported in this paper. The PVI process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The preliminary results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided.

Ramachandran, Narayanan↗

NASA NTRSDate not supplied

CFD Modeling of Tank Pressurization and Axial Jet Mixing Experiments with and without Non-Condensable Gas in the Ullage

A two-phase CFD model for tank pressurization and following jet mixing of a cryogenic storage tank is presented using VOF approach for representing the phase boundary and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. The CFD model was validated against pressurization and liquid jet mixing data for a 110-inch diameter tank provided by Bullard1. Cases with like-gas and non-condensable gas pressurization are studied. The results of the cases with like-gas pressurization and following mixing are presented first, focusing on the effects of turbulence at the vapor-liquid interface on the tank pressure and phase change rates predictions. The second part of this paper is devoted to testing and validating the CFD model against non-condensable gas pressurization and following mixing. Tank pressures predicted in both cases are compared with each other and with the experimental data.

Computational Fluid Dynamics↗

NASA NTRSDate not supplied

CFD Modeling of Tank Pressurization and Axial Jet Mixing Experiments with and without Non-Condensable Gas in the Ullage

A two-phase CFD model for tank pressurization and following jet mixing of a cryogenic storage tank is presented using VOF approach for representing the phase boundary and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. The CFD model was validated against pressurization and liquid jet mixing data for a 110-inch diameter tank provided by Bullard. Cases with like-gas and non-condensable gas pressurization are studied. The results of the cases with like-gas pressurization and following mixing are presented first, focusing on the effects of turbulence at the vapor-liquid interface on the tank pressure and phase change rates predictions. The second part of this paper is devoted to testing and validating the CFD model against non-condensable gas pressurization and following mixing. Tank pressures predicted in both cases are compared with each other and with the experimental data.

Computational Fluid Dynamics↗

NASA NTRS2008

Bonding by Hydroxide-Catalyzed Hydration and Dehydration

A simple, inexpensive method for bonding solid objects exploits hydroxide-catalyzed hydration and dehydration to form silicate-like networks in thin surface and interfacial layers between the objects. The method can be practiced at room temperature or over a wide range of temperatures. The method was developed especially to enable the formation of precise, reliable bonds between precise optical components. The bonds thus formed exhibit the precision and transparency of bonds formed by the conventional optical-contact method and the strength and reliability of high-temperature frit bonds. The method also lends itself to numerous non-optical applications in which there are requirements for precise bonds and/or requirements for bonds, whether precise or imprecise, that can reliably withstand severe environmental conditions. Categories of such non-optical applications include forming composite materials, coating substrates, forming laminate structures, and preparing objects of defined geometry and composition. The method is applicable to materials that either (1) can form silicate-like networks in the sense that they have silicate-like molecular structures that are extensible into silicate-like networks or (2) can be chemically linked to silicate-like networks by means of hydroxide-catalyzed hydration and dehydration. When hydrated, a material of either type features surface hydroxyl (-OH) groups. In this method, a silicate-like network that bonds two substrates can be formed either by a bonding material alone or by the bonding material together with material from either or both of the substrates. Typically, an aqueous hydroxide bonding solution is dispensed and allowed to flow between the mating surfaces by capillary action. If the surface figures of the substrates do not match precisely, bonding could be improved by including a filling material in the bonding solution. Preferably, the filling material should include at least one ingredient that can be hydrated to have exposed hydroxyl groups and that can be chemically linked, by hydroxide catalysis, to a silicate-like network. The silicate-like network could be generated in situ from the filling material and/or substrate material, or could be originally present in the bonding material.

Gwo, Dz-Hung↗

NASA NTRS2012

NASA Tech Briefs, May 2012

Topics covered include: An "Inefficient Fin" Non-Dimensional Parameter to Measure Gas Temperatures Efficiently; On-Wafer Measurement of a Multi-Stage MMIC Amplifier with 10 dB of Gain at 475 GHz; Software to Control and Monitor Gas Streams; Miniaturized Laser Heterodyne Radiometer (LHR) for Measurements of Greenhouse Gases in the Atmospheric Column; Anomaly Detection in Test Equipment via Sliding Mode Observers; Absolute Position of Targets Measured Through a Chamber Window Using Lidar Metrology Systems; Goldstone Solar System Radar Waveform Generator; Fast and Adaptive Lossless Onboard Hyperspectral Data Compression System; Iridium Interfacial Stack - IrIS; Downsampling Photodetector Array with Windowing; Optical Phase Recovery and Locking in a PPM Laser Communication Link; High-Speed Edge-Detecting Line Scan Smart Camera; Optical Communications Channel Combiner; Development of Thermal Infrared Sensor to Supplement Operational Land Imager; Amplitude-Stabilized Oscillator for a Capacitance-Probe Electrometer; Automated Performance Characterization of DSN System Frequency Stability Using Spacecraft Tracking Data; Histogrammatic Method for Determining Relative Abundance of Input Gas Pulse; Predictive Sea State Estimation for Automated Ride Control and Handling - PSSEARCH; LEGION: Lightweight Expandable Group of Independently Operating Nodes; Real-Time Projection to Verify Plan Success During Execution; Automated Performance Characterization of DSN System Frequency Stability Using Spacecraft Tracking Data; Web-Based Customizable Viewer for Mars Network Overflight Opportunities; Fabrication of a Cryogenic Terahertz Emitter for Bolometer Focal Plane Calibrations; Fabrication of an Absorber-Coupled MKID Detector; Graphene Transparent Conductive Electrodes for Next- Generation Microshutter Arrays; Method of Bonding Optical Elements with Near-Zero Displacement; Free-Mass and Interface Configurations of Hammering Mechanisms; Wavefront Compensation Segmented Mirror Sensing and Control; Long-Life, Lightweight, Multi-Roller Traction Drives for Planetary Vehicle Surface Exploration; Reliable Optical Pump Architecture for Highly Coherent Lasers Used in Space Metrology Applications; Electrochemical Ultracapacitors Using Graphitic Nanostacks; Improved Whole-Blood-Staining Device; Monitoring Location and Angular Orientation of a Pill; Molecular Technique to Reduce PCR Bias for Deeper Understanding of Microbial Diversity; Laser Ablation Electrodynamic Ion Funnel for In Situ Mass Spectrometry on Mars; High-Altitude MMIC Sounding Radiometer for the Global Hawk Unmanned Aerial Vehicle; PRTs and Their Bonding for Long-Duration, Extreme-Temperature Environments; Mid- and Long-IR Broadband Quantum Well Photodetector; 3D Display Using Conjugated Multiband Bandpass Filters; Real-Time, Non-Intrusive Detection of Liquid Nitrogen in Liquid Oxygen at High Pressure and High Flow; Method to Enhance the Operation of an Optical Inspection Instrument Using Spatial Light Modulators; Dual-Compartment Inflatable Suitlock; Large-Strain Transparent Magnetoactive Polymer Nanocomposites; Thermodynamic Vent System for an On-Orbit Cryogenic Reaction Control Engine; Time Distribution Using SpaceWire in the SCaN Testbed on ISS; and Techniques for Solution- Assisted Optical Contacting.

Source record↗

NASA NTRSDate not supplied

Modeling Autogenous Pressurization and Draining of a Cryogenic Storage Tank in Normal Gravity

A two-phase CFD model for autogenous pressurization and draining of a cryogenic storage tank is presented using both the Sharp Interface and Volume-Of-Fluid (VOF) approaches for capturing the front and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. Both models are validated against data provided by the Cryogenic Propellant Storage and Transfer (CPST) Engineering Development Unit (EDU) experiment. The results of the autogenous pressurization are presented first, focusing on the phase change and turbulence effects on the tank pressure and temperature predictions. Both the Sharp Interface (SI-CFD) and VOF (VOF-CFD) multiphase models predict tank pressure during pressurization within 3% of the measured values. The sensitivity of key physical and numerical parameters of the problem are tested using the Sharp Interface model. Effects of the accommodation coefficient (AC), and the computational grid structure are studied. The second part of this paper is devoted to validating the SI-VOF model, with an enhanced capability of moving the liquid-vapor interface, against the draining segment of the EDU experiment. The VOF-CFD model was also used to simulate tank draining and its results were compared with the results of the Sharp Interface model with the moving interface. Both models predict tank pressure during draining within 3.5% of the measured values. Pressure decrease rate is underpredicted by both models during the first 100 seconds of draining but matches the experimental rate for the rest of the simulation.

Computational Fluid Dynamics↗