Results for “level sets” — Page 9

NASA NTRSDate not supplied

CDC Bioreactor Configuration Method for Volume Level Control with Controlled Inlet and Outlet Flow

Environmental Control Life Support Systems and other microbiological biofilm studies often utilize small scale bioreactors. Among these options are the popular BioSurface CDC bioreactors, currently being utilized by Marshall Space Flight Center groups researching the impact of biofilms on life support systems. After a recent experimental regime, it was determined additional equipment could be added to augment the capabilities of the bioreactors. Previous research configurations such as ASTM E3161-21 relied on an outlet stream gravity draining from a side drain port located above sampling coupons. This limited applications to experimental conditions with a controlled inlet and uncontrolled outlet flow. With the introduction of a small single pole single throw (SPST) reed float switch and a peristaltic pump connected to the outlet drain and a chassis controller, the bioreactor is able to maintain a set level. The modification allows additional variables to be tested, including highly adjustable fill and flush cycles, bioreactor volume, draining and filling control. Once the configuration modifications were implemented through the installation of the new equipment, data was collected to ensure the stability of the level measurements. As the level control switch is a float switch, consideration was taken into account for effects of internal stirring speed, along with effects of inlet and outlet flow rate. Data presented in this study will illustrate the stability and effectiveness of the configuration changes in equipment made to the bioreactor. These configuration changes have demonstrated control method to conduct biofilm mitigation techniques for ECLSS hardware research. The controlled level capabilities allow for a constant drip feed flow rate into the bioreactors, a key aspect of the biofilm mitigation testing.

CDC Bioreactor↗

NASA NTRSDate not supplied

CDC Bioreactor Configuration Method for Volume Level Control with Controlled Inlet and Outlet Flow

Environmental Control Life Support Systems and other microbiological biofilm studies often utilize small scale bioreactors. Among these options are the popular BioSurface CDC bioreactors, currently being utilized by Marshall Space Flight Center groups researching the impact of biofilms on life support systems. After a recent experimental regime, it was determined additional equipment could be added to augment the capabilities of the bioreactors. Previous research configurations such as ASTM E3161-21 relied on an outlet stream gravity draining from a side drain port located above sampling coupons. This limited applications to experimental conditions with a controlled inlet and uncontrolled outlet flow. With the introduction of a small single pole single throw (SPST) reed float switch and a peristaltic pump connected to the outlet drain and a chassis controller, the bioreactor is able to maintain a set level. The modification allows additional variables to be tested, including highly adjustable fill and flush cycles, bioreactor volume, draining and filling control. Once the configuration modifications were implemented through the installation of the new equipment, data was collected to ensure the stability of the level measurements. As the level control switch is a float switch, consideration was taken into account for effects of internal stirring speed, along with effects of inlet and outlet flow rate. Data presented in this study will illustrate the stability and effectiveness of the configuration changes in equipment made to the bioreactor. These configuration changes have demonstrated control method to conduct biofilm mitigation techniques for ECLSS hardware research. The controlled level capabilities allow for a constant drip feed flow rate into the bioreactors, a key aspect of the biofilm mitigation testing.

CDC Bioreactor↗

NASA NTRSDate not supplied

CDC Bioreactor Configuration Method for Volume Level Control with Controlled Inlet and Outlet Flow

Environmental Control Life Support Systems and other microbiological biofilm studies often utilize small scale bioreactors. Among these options are the popular BioSurface CDC bioreactors, currently being utilized by Marshall Space Flight Center groups researching the impact of biofilms on life support systems. After a recent experimental regime, it was determined additional equipment could be added to augment the capabilities of the bioreactors. Previous research configurations such as ASTM E3161-21 relied on an outlet stream gravity draining from a side drain port located above sampling coupons. This limited applications to experimental conditions with a controlled inlet and uncontrolled outlet flow. With the introduction of a small single pole single throw (SPST) reed float switch and a peristaltic pump connected to the outlet drain and a chassis controller, the bioreactor is able to maintain a set level. The modification allows additional variables to be tested, including highly adjustable fill and flush cycles, bioreactor volume, draining and filling control. Once the configuration modifications were implemented through the installation of the new equipment, data was collected to ensure the stability of the level measurements. As the level control switch is a float switch, consideration was taken into account for effects of internal stirring speed, along with effects of inlet and outlet flow rate. Data presented in this study will illustrate the stability and effectiveness of the configuration changes in equipment made to the bioreactor. These configuration changes have demonstrated control method to conduct biofilm mitigation techniques for ECLSS hardware research. The controlled level capabilities allow for a constant drip feed flow rate into the bioreactors, a key aspect of the biofilm mitigation testing.

CDC Bioreactor↗

DOE OSTI2017

Interface tracking simulations of bubbly flows in PWR relevant geometries

[en] Highlights: • Simulations were performed for turbulent bubbly flows in PWR subchannel geometry. • Liquid turbulence is fully resolved by direct numerical simulation approach. • Bubble behavior is captured using level-set interface tracking method. • Time-averaged single- and two-phase turbulent flow statistical quantities are obtained. - Abstract: The advances in high performance computing (HPC) have allowed direct numerical simulation (DNS) approach coupled with interface tracking methods (ITM) to perform high fidelity simulations of turbulent bubbly flows in various complex geometries. In this work, we have chosen the geometry of the pressurized water reactor (PWR) core subchannel to perform a set of interface tracking simulations (ITS) with fully resolved liquid turbulence. The presented research utilizes a massively parallel finite-element based code, PHASTA, for the subchannel geometry simulations of bubbly flow turbulence. The main objective for this research is to demonstrate the ITS capabilities in gaining new insight into bubble/turbulence interactions and assisting the development of improved closure laws for multiphase computational fluid dynamics (M-CFD). Both single- and two-phase turbulent flows were studied within a single PWR subchannel. The analysis of numerical results includes the mean gas and liquid velocity profiles, void fraction distribution and turbulent kinetic energy profiles. Two sets of flow rates and bubble sizes were used in the simulations. The chosen flow rates corresponded to the Reynolds numbers of 29,079 and 80,775 based on channel hydraulic diameter (D_h) and mean velocity. The finite element unstructured grids utilized for these simulations include 53.8 million and 1.11 billion elements, respectively. This has allowed to fully resolve all the turbulence scales and the deformable interfaces of individual bubbles. For the two-phase flow simulations, a 1% bubble volume fraction was used which resulted in 17 bubbles in the smaller case and 262 bubbles in the larger case. In the larger simulation case the size of the resolved bubbles is 0.65 mm in diameter, and the bulk mesh cell size is about 30 microns. Those large-scale simulations provide new level of details previously unavailable and were enabled by the excellent scaling performance of our two-phase flow solver and access to the state-of-the-art supercomputing resources. The presented simulations used up to 256 thousand processing threads on the IBM BG/Q supercomputer “Mira” (Argonne National Laboratory).

Nuclear Science & Technology↗

DOE OSTI2017

A finite element/level set model of polyurethane foam expansion and polymerization

Polyurethane foams are used widely for encapsulation and structural purposes because they are inexpensive, straightforward to process, amenable to a wide range of density variations (1 lb/ft3 - 50 lb/ft3), and able to fill complex molds quickly and effectively. Computational model of the filling and curing process are needed to reduce defects such as voids, out-of-specification density, density gradients, foam decomposition from high temperatures due to exotherms, and incomplete filling. This paper details the development of a computational fluid dynamics model of a moderate density PMDI structural foam, PMDI-10. PMDI is an isocyanate-based polyurethane foam, which is chemically blown with water. The polyol reacts with isocyanate to produces the polymer. PMDI- 10 is catalyzed giving it a short pot life: it foams and polymerizes to a solid within 5 minutes during normal processing. To achieve a higher density, the foam is over-packed to twice or more of its free rise density of 10 lb/ft3. The goal for modeling is to represent the expansion, filling of molds, and the polymerization of the foam. This will be used to reduce defects, optimize the mold design, troubleshoot the processed, and predict the final foam properties. A homogenized continuum model foaming and curing was developed based on reaction kinetics, documented in a recent paper; it uses a simplified mathematical formalism that decouples these two reactions. The chemo-rheology of PMDI is measured experimentally and fit to a generalized- Newtonian viscosity model that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. The equations are combined with a level set method to determine the location of the foam-gas interface as it evolves to fill the mold. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics, viscosity, and other material properties are all sensitive to temperature. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including two configurations of a mock structural part and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed for future work.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Calculated Ionization Potentials of MO 3 and MO 2 for M = U, Mo, W, and Nd

Here, ionization potentials (IPs) for MO 3 and MO 2 for M = U, Mo, W, and Nd have been predicted using the Feller–Peterson–Dixon (FPD) approach at the coupled cluster CCSD(T)/complete basis set level including additional corrections. The additional corrections are mostly small, with spin-orbit effects contributing less than 0.05 eV, except for NdO 2 where the correction lowers the IP by 0.26 eV. The IPs for UO 3 and UO 2 are calculated to be 9.59 and 6.09 eV, respectively. The calculated IPs for MoO 3 and WO 3 are very similar, 11.13 and 11.11 eV, respectively, and MoO 2 and WO 2 are 8.51 and 8.79 eV, respectively. MoO 2 has a triplet ground state, whereas WO 2 has a singlet ground state. The calculated IP for NdO 2 is 7.90 eV. NdO 3 does not achieve a high +VI formal oxidation state on the lanthanide and has an IP of 7.80 eV. These calculated IPs are expected to have error bars of ±0.04 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗

DOE OSTI2021

A coupled fluid-mechanical workflow to simulate the directed energy deposition additive manufacturing process

Simulation of additive manufacturing processes can provide essential insight into material behavior, residual stress, and ultimately, the performance of additively manufactured parts. In this work, we describe a new simulation based workflow utilizing both solid mechanics and fluid mechanics based formulations within the finite element software package SIERRA (Sierra Solid Mechanics Team in Sierra/Solid Mechanics 4.52 User’s Guide SAND2019-2715. Technical report, Sandia National Laboratories, 2011) to enable integrated simulations of directed energy deposition (DED) additive manufacturing processes. In this methodology, a high-fidelity fluid mechanics based model of additive manufacturing is employed as the first step in a simulation workflow. This fluid model uses a level set field to track the location of the boundary between the solid material and background gas and precisely predicts temperatures and material deposition shapes from additive manufacturing process parameters. Next, the resulting deposition shape and temperature field from the fluid model are then mapped into a solid mechanics formulation to provide a more accurate surface topology for radiation and convection boundary conditions and a prescribed temperature field. Solid mechanics simulations are then conducted to predict the evolution of material stresses and microstructure within a part. By combining thermal history and deposition shape from fluid mechanics with residual stress and material property evolutions from solid mechanics, additional fidelity and precision are incorporated into additive manufacturing process simulations providing new insight into complex DED builds.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Spread of Values of a Cantor-Type Fractal Continuous Nonmonotone Function

By using the Q{sub 5}{sup ∗}-representation of numbers[0,1]∋x=β{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(β{sub α{sub k(x)k}}∏{sub j=1}{sup k−1}q{sub α{sub j(x)j}})=Δ{sub α{sub 1(x)α{sub 2(x)…α{sub k(x)…}{sup Q{sub 5}{sup ∗}}}}} determined by the quinary alphabet A{sub 5} ≡ {0, 1, 2, 3, 4} and an infinite stochastic matrix ‖q{sub ik}‖, i ∈ A{sub 5}, k ∈ N, with positive elements (q{sub 0k} + q{sub 1k} + q{sub 2k} + q{sub 3k} + q{sub 4k} = 1) such that ∏{sub k=1}{sup ∞}max{sub i}{q_i_k}=0 and β{sub 0k} = 0, β{sub i + 1, k} = β{sub ik} + q{sub ik}, i= (0,4)-bar , we define a continuous Cantor-type function by the equalityf(Δ{sub α{sub 1…α{sub k…}{sup Q{sub 5}{sup ∗}}}})=δ{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(δ{sub α{sub k(x)k}}∑{sub j=1}{sup k−1}g{sub α{sub j(x)j}})≡Δ{sub α{sub 1(x)…α{sub k(x)…}{sup G}}}, where δ{sub 0n} = 0, δ{sub 1n}=((2+ε{sub n})/4), δ{sub 2n}=(2/4)=δ{sub 3n}, and δ{sub 4n}=((2−ε{sub n})/4), i.e., δ{sub i + 1, n} = δ{sub in} + g{sub in}, n ∈ N, and (ε{sub n}) is a given sequence of real numbers such that 0 ≤ ε{sub n} ≤ 1. We prove that this function is well defined and continuous. Moreover, it does not have intervals of monotonicity, except the intervals where it is constant. A criterion of bounded variation of the function is also established. We are especially interested in the problem of level sets of the function and in the topological and metric properties of the images of Cantor-type sets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

The Importance of Viscous and Interfacial Forces in the Hydrodynamics of the Top-Submerged-Lance Furnace

The purpose of this work is to focus on the hydrodynamics of a Top-Submerged-Lance (TSL) smelting furnace, understanding how liquid properties and operational parameters act on key factors of a TSL process, such as splashing, mixing, mass transfer area, and bubble development. A deep knowledge of all those aspects is needed since they all influence the smelting reaction rates; hence the efficiency of the reactor. The characterization and scaling of the TSL gas injection are commonly based on the modified Froude number, the ratio of dynamic and gravitational forces. Detailed literature research reveals a potential weakness of this approach, since it does not consider the effects of viscosity and surface tension. To investigate this question an extensive parametric study was performed applying computational fluid dynamics to cold and non-reactive flows, which provided a broad overview of the physics of the flow. The analysis was performed on fluid dynamic properties (liquid density, liquid viscosity, surface tension) and operational variables (gas volume flow, lance immersion depth). The coupled Level Set—Volume of Fluid model, available in the commercial solver ANSYS Fluent{sup ®}, was used to resolve the gas–liquid interface in the multiphase flow. The results of the work underscore the significance of the viscous and interfacial forces for gas injection in smelting slags, confirming the incompleteness of applying only the Froude number to describe such flows.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Numerical comparison of bubbling in a waste glass melter

Radioactive tank waste is scheduled for vitrification at the Hanford Tank Waste Treatment and Immobilization Plant, also known as the Vit Plant, being constructed at the Hanford Site. Testing of the pilot-scale, joule-heated DuraMelter 1200 at the Vitreous State Laboratory has shown that bubbling increases the melt rate, and as a result, melter throughput. Computational fluid dynamics (CFD) models of this pilot-scale waste glass melter were developed to improve our understanding of the processes that occur within the melter to aid in process optimization and troubleshooting of the Vit Plant melters. Unfortunately, model validation is complicated by the difficulty of obtaining suitable experimental data for operational melters attributed to the large-scale, radioactivity and high temperatures at which these melters are operated. This study focuses on confirming the fidelity of the CFD models to accurately reproduce the bubbling behavior. Because of the paucity of experimental data at the resolution required for CFD validation, a code-to-code comparison was used to evaluate two common approaches for simulating flows of immiscible fluids on numerical grids and resolving multiphase interfaces. Here, the volume of fluid and level set methods are used to track the dynamically evolving interfaces between the molten glass and the air bubbles. To aid in the verification of the results of these codes, a comparison of the bubble behavior, growth, and frequency of bubble generation are presented and a grid convergence study is performed for the two approaches. In addition to comparing the numerical results to available experimental data and observations from pilot-scale testing, the results are evaluated in relation to laboratory experiments with bubbles injected into viscous fluids, empirical correlations obtained from the published literature, and the basic laws of fluid dynamics. Furthermore, the results of this work can assist in validating waste glass melter models and provide a better understanding of the flow patterns within the WTP melters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Fuel Property Effects on Knock Propensity and Thermal Efficiency in a Direct-Injection Spark-Ignition Engine

Engine knock remains one of the major barriers to further improvement in thermal efficiency of Direct-Injection Spark-Ignition (DISI) engines. While Research Octane Number and Motor Octane Number are often used as standard rating methods for knock resistance of fuels, the impacts of other fuel properties on knock propensity in modern engines such as heat of vaporization (HoV) and laminar flame speed (LFS) require better understanding in order to co-optimize fuels and engine designs to achieve higher thermal efficiency and lower CO2 emission. In the present study, computational fluid dynamics (CFD) is used to model a boosted DISI engine with a focus on knock prediction and fuel property effects. A level-set G-equation model is employed to capture turbulent premixed combustion, and is coupled with a transported Livengood-Wu (L-W) integral approach to predict autoignition in the unburnt region. A criterion associated with the L-W integral is developed to accurately predict knock onset and knock-limited spark-advance. This model is then applied to a sensitivity analysis of HoV and LFS on knock tendency and thermal efficiency. The pressure-temperature trajectory framework is applied and extended to study the fuel effects on auto-ignition process in the engine. An existing efficiency-based merit function, which is derived from experiments for boosted SI engines, is evaluated and improved based on the current CFD results.

DISI↗

DOE OSTI2021

Symmetry-breaking in double gyroid block copolymer films by non-affine distortion

Soft-matter bicontinuous networks find a double gyroid structure from block copolymer (BCP) self-assembly. A gyroid structure composed of dissimilar blocks has proven its potential as a soft crystal capable of tuning structural periodicity and symmetry, of which the lattice dimension is variable with molecular weight of the polymer. Using an asymmetric polystyrene- b -poly(methyl methacrylate) (PS- b -PMMA), in this study we show that the self-assembled gyroid films formed via a solvent vapor annealing (SVA) process undergo unique structural distortion due to directional deformation immediately upon deswelling. During the SVA process with PS- b -PMMA films, transient cylinders developed from the as-cast morphology transform into a cubic gyroid structure in a swollen state. Rapid and spontaneous deswelling processes -the manners in which the films contract along the z-direction while retaining an enlarged lateral dimension of the cubic form -lead to triclinic gyroid structures with z-directional contraction ratios ( C z ) of 2.5 and 2.0, respectively. Our X-ray analysis reveals that the deswelling process of the swollen gyroid films produces a notable symmetry-breaking in non-affine gyroid structure that elicits several forbidden reflections such as {110} and {200} reflections. For further characterization of the symmetry-breaking, we delineate the structural features of noncubic gyroid films by computing electron-density difference maps assisted with X-ray measurements. Level-set approach is accordingly developed to quantitate the structural characteristics of the maps in terms of inversion symmetry-breaking, suggesting its possible application to optical Weyl photonic crystals.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Optimal design of fiber reinforced composite structures and their direct ink write fabrication

The majority of the current structural optimization software does not accommodate manufacturing constraints. Therefore, substantial modifications are imposed upon optimized designs to make them manufacturable and hence nonoptimal. We propose to optimize the design of composite structures that are amenable to Additive Manufacturing (AM). The printing process chosen in our study is based on Direct Ink Writing (DIW) in which short carbon fibers in a thermoset resin are extruded through a moving nozzle to build up a structure. Since the fibers are primarily aligned in the flow direction of the extrudate, the DIW printing trajectory influences the material properties of the composite structure. To accommodate this, the extrudate trajectory follows the contours of parameterized level-set functions. The parametrization allows us to prescribe the material properties and impose many DIW manufacturing constraints such as no-overlap, no-sag, minimum radius of curvature and continuity of the toolpaths. Ultimately, we obtain optimal manufacturable toolpaths that start and finish at a boundary. To minimize the fabrication time, we formulate the linking sequence of the toolpaths as a traveling salesman problem which we solve to obtain the shortest continuous toolpath per layer. Several examples illustrate the optimization procedure. Validation is also performed.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.

42 ENGINEERING↗

DOE OSTI2020

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Here, we investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

"embedded" basis↗

DOE OSTI2021

Optimal toolpath design of additive manufactured composite cylindrical structures

Structural design optimization for additive manufacturing is primarily focused on planar layer-by-layer processes and design of composite cylindrical structures does not often accommodate manufacturing constraints. In this study, we propose to optimize the toolpath trajectory of additively manufactured composite cylinders comprised of multiple thin cylindrical annuli. Additionally, our printing process is based on direct ink writing in which short carbon fibers in a thermoset resin are extruded through a moving nozzle to build up a structure. Since the fibers are primarily aligned in the flow direction of the extrudate, the printing trajectory influences the material properties of the composite structure. To accommodate this, we define the toolpaths as contours of parameterized level-set functions. This parameterization allows us to optimize the material properties and impose manufacturing constraints such as no-overlap, no-sag, minimum radius of curvature, and continuity of the toolpaths. Several examples illustrate the optimization procedure.

42 ENGINEERING↗

DOE OSTI2017

A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∊ [10, 700],Mo ∊ [1 x 10 -6 , 5 x 10 3 , and θ ∊ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R 2 = 0.97 and other available experimental data with 13.0% absolute average relative error and R 2 = 0.84 outperforming existing correlations and models.

Mechanics↗