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At least 181 records · Page 10

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Groves, Curtis E.↗

CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences

This report documents the results of a study to address the long range, strategic planning required by NASA's Revolutionary Computational Aerosciences (RCA) program in the area of computational fluid dynamics (CFD), including future software and hardware requirements for High Performance Computing (HPC). Specifically, the "Vision 2030" CFD study is to provide a knowledge-based forecast of the future computational capabilities required for turbulent, transitional, and reacting flow simulations across a broad Mach number regime, and to lay the foundation for the development of a future framework and/or environment where physics-based, accurate predictions of complex turbulent flows, including flow separation, can be accomplished routinely and efficiently in cooperation with other physics-based simulations to enable multi-physics analysis and design. Specific technical requirements from the aerospace industrial and scientific communities were obtained to determine critical capability gaps, anticipated technical challenges, and impediments to achieving the target CFD capability in 2030. A preliminary development plan and roadmap were created to help focus investments in technology development to help achieve the CFD vision in 2030.

Jeffrey P Slotnick↗

Understanding the Flow Physics of Shock Boundary-Layer Interactions Using CFD and Numerical Analyses

Computational fluid dynamic (CFD) analyses of the University of Michigan (UM) Shock/Boundary-Layer Interaction (SBLI) experiments were performed as an extension of the CFD SBLI Workshop held at the 48th AIAA Aerospace Sciences Meeting in 2010. In particular, the UM Mach 2.75 Glass Tunnel with a semi-spanning 7.75deg wedge was analyzed in attempts to explore key physics pertinent to SBLI's, including thermodynamic and viscous boundary conditions as well as turbulence modeling. Most of the analyses were 3D CFD simulations using the OVERFLOW flow solver, with additional quasi-1D simulations performed with an in house MATLAB code interfacing with the NIST REFPROP code to explore perfect verses non-ideal air. A fundamental exploration pertaining to the effects of particle image velocimetry (PIV) on post-processing data is also shown. Results from the CFD simulations showed an improvement in agreement with experimental data with key contributions including adding a laminar zone upstream of the wedge and the necessity of mimicking PIV particle lag for comparisons. Results from the quasi-1D simulation showed that there was little difference between perfect and non-ideal air for the configuration presented.

Friedlander, David J.↗

Experimental Database with Baseline CFD Solutions: 2-D and Axisymmetric Hypersonic Shock-Wave/Turbulent-Boundary-Layer Interactions

A database compilation of hypersonic shock-wave/turbulent boundary layer experiments is provided. The experiments selected for the database are either 2D or axisymmetric, and include both compression corner and impinging type SWTBL interactions. The strength of the interactions range from attached to incipient separation to fully separated flows. The experiments were chosen based on criterion to ensure quality of the datasets, to be relevant to NASA's missions and to be useful for validation and uncertainty assessment of CFD Navier-Stokes predictive methods, both now and in the future. An emphasis on datasets selected was on surface pressures and surface heating throughout the interaction, but include some wall shear stress distributions and flowfield profiles. Included, for selected cases, are example CFD grids and setup information, along with surface pressure and wall heating results from simulations using current NASA real-gas Navier-Stokes codes by which future CFD investigators can compare and evaluate physics modeling improvements and validation and uncertainty assessments of future CFD code developments. The experimental database is presented tabulated in the Appendices describing each experiment. The database is also provided in computer-readable ASCII files located on a companion DVD.

Database↗

Development of an Aerodynamic Analysis Method and Database for the SLS Service Module Panel Jettison Event Utilizing Inviscid CFD and MATLAB

This paper describes the development, testing, and utilization of an aerodynamic force and moment database for the Space Launch System (SLS) Service Module (SM) panel jettison event. The database is a combination of inviscid Computational Fluid Dynamic (CFD) data and MATLAB code written to query the data at input values of vehicle/SM panel parameters and return the aerodynamic force and moment coefficients of the panels as they are jettisoned from the vehicle. The database encompasses over 5000 CFD simulations with the panels either in the initial stages of separation where they are hinged to the vehicle, in close proximity to the vehicle, or far enough from the vehicle that body interference effects are neglected. A series of viscous CFD check cases were performed to assess the accuracy of the Euler solutions for this class of problem and good agreement was obtained. The ultimate goal of the panel jettison database was to create a tool that could be coupled with any 6-Degree-Of-Freedom (DOF) dynamics model to rapidly predict SM panel separation from the SLS vehicle in a quasi-unsteady manner. Results are presented for panel jettison simulations that utilize the database at various SLS flight conditions. These results compare favorably to an approach that directly couples a 6-DOF model with the Cart3D Euler flow solver and obtains solutions for the panels at exact locations. This paper demonstrates a method of using inviscid CFD simulations coupled with a 6-DOF model that provides adequate fidelity to capture the physics of this complex multiple moving-body panel separation event.

Applebaum, Michael P.↗

NASA ERA Integrated CFD for Wind Tunnel Testing of Hybrid Wing-Body Configuration

The NASA Environmentally Responsible Aviation (ERA) Project explored enabling technologies to reduce impact of aviation on the environment. One project research challenge area was the study of advanced airframe and engine integration concepts to reduce community noise and fuel burn. To address this challenge, complex wind tunnel experiments at both the NASA Langley Research Center's (LaRC) 14'x22' and the Ames Research Center's 40'x80' low-speed wind tunnel facilities were conducted on a BOEING Hybrid Wing Body (HWB) configuration. These wind tunnel tests entailed various entries to evaluate the propulsion-airframe interference effects, including aerodynamic performance and aeroacoustics. In order to assist these tests in producing high quality data with minimal hardware interference, extensive Computational Fluid Dynamic (CFD) simulations were performed for everything from sting design and placement for both the wing body and powered ejector nacelle systems to the placement of aeroacoustic arrays to minimize its impact on vehicle aerodynamics. This paper presents a high-level summary of the CFD simulations that NASA performed in support of the model integration hardware design as well as the development of some CFD simulation guidelines based on post-test aerodynamic data. In addition, the paper includes details on how multiple CFD codes (OVERFLOW, STAR-CCM+, USM3D, and FUN3D) were efficiently used to provide timely insight into the wind tunnel experimental setup and execution.

Computational Fluid Dynamics↗

A CFD Case Study of a Fan Stage with Split Flow Path Subject to Total Pressure Distortion Inflow

This report is the documentation of the work performed under the Hypersonic Project of the NASA's Fundamental Aeronautics Program. It was funded through Task Number NNC10E444T under GESS-2 Contract NNC06BA07B. The objective of the task is to develop advanced computational tools for the simulation of multi-stage turbomachinery in support of aeropropulsion. This includes work elements in extending the TURBO code and validating the multi-stage URANS (Unsteady Reynolds Averaged Navier Stokes) simulation results with the experimental data. The unsteady CFD (Computation Fluid Dynamics) calculations were performed in full wheel mode with and without screen generated total pressure distortion at the computational inflow boundary, as well as in single passage phase lag mode for uniform inflow. The experimental data were provided by NASA from the single stage RTA (Revolutionary Turbine Accelerator) fan test program.Significant non-uniform flow condition at the fan-face of the aeropropulsion system is frequentlyencountered in many of the advanced aerospace vehicles. These propulsion systems can be eithera podded or an embedded design employed in HWB (Hybrid Wing Body) airframe concept. It isalso a topic of interest in military applications, in which advanced air vehicles have already deployedsome form of embedded propulsion systems in their design because of the requirementsof compact and low observable inlets. Even in the conventional airframe/engine design, the fancould operate under such condition when the air vehicle is undergoing rapid maneuvering action.It is believed that a better understanding of the fan’s aerodynamic and aeromechanical responseto this type of operating condition or off design operation would be beneficial to designing distortiontolerant blades for improved engine operability.The objective for this research is to assess the capability of turbomachinery code as an analysistool in understanding the effects and evaluating the impact of flow distortion on the aerodynamicand aeromechanical performance of the fan in advanced propulsion systems. Results from thetesting of an advanced fan stage released by NASA are available and will be used here for CFDcode validation. The experiment was performed at NASA’s high speed compressor facility aspart of the RTA (Revolutionary Turbine Accelerator) demonstration project, a joint effort ofNASA Glenn Research Center and GE Aircraft Engines in developing an advanced Mach 4TBCC (Turbine Based Combined Cycle) turbofan/ramjet engine for access to space. Part of thetest was to assess the aerodynamic performance and operability of the fan stage under nonuniforminflow condition. Various flow distortion patterns were created at the fan-face by manipulatingsets of screens placed upstream of the wind tunnel. Measurements at the fan-face willprovide the necessary distortion flow information as the inflow boundary condition for the CFDin a full wheel simulation. Therefore the purpose of this work is to demonstrate the NASA supportedmulti-stage turbomachinery code, TURBO [1-5], in the aerodynamic performance analysisof a modern fan design operating under off design condition, and in particular to validate theCFD results with the RTA fan test data.A brief description of the RTA fan rig configuration is given in the next section, explaining onhow flow distortion were measured in the test and constructed for the CFD at the fan-face. It isfollowed by a section summarizing previous CFD work performed at NASA relevant to the currentfan configuration. A short description of the TURBO code is given next, followed by detailsin the computational model of the fan rig, the required computing resources, and the numericalprocedure for the simulations. The CFD results are presented in the discussion section and finallyconcluding remarks are summarized.

Fan Stage↗

PIV and Rotational Raman-Based Temperature Measurements for CFD Validation in a Single Injector Cooling Flow

NASA's Turbulent Heat Flux (THX) task under the Transformational Tools & Technologies project is focused on acquiring benchmark temperature and velocity data in turbulent shear layers for validation of computational fluid dynamics (CFD) codes. Standard CFD turbulence models lack the ability to accurately calculate a number of fundamental flow phenomena, including the turbulent transport of heat. In nearly all production class Reynolds-averaged Navier-Stokes (RANS) CFD codes, a gradient-diffusion approximation is used whereby a constant turbulent Prantdl number, Prt, is used to relate an eddy viscosity calculated for the momentum terms, to the turbulent heat flux terms. The default in most CFD codes is Prt = 0.9, however this is not representative of all flows. As discussed in Yoder et al. (2015) and Reynolds (1974), Prt = 0.7 is felt to be more appropriate for jets. Recent work, as discussed in Yoder (2016a), has explored more complex formulations including variable turbulent Prantdl number models. PARTICLE IMAGE VELOCIMETRY; TEMPERATURE MEASURING INSTRUMENTS; FILM COOLING; HIGH TEMPERATURE GASES; COMPUTATIONAL FLUID DYNAMICS; PREDICTION ANALYSIS TECHNIQUES; TURBULENCE MODELS; RAMAN SPECTRA; VELOCITY; MACH NUMBER; GAS TURBINE ENGINES; NOZZLE FLOW; THERMOCOUPLES; LASER INDUCED FLUORESCENCE; COOLING FLOWS (ASTROPHYSICS); RAMAN SPECTROSCOPY; HEAT FLUX

Wernet, Mark P.↗

Sketch-To-Solution: An Exploration of Viscous CFD with Automatic Grids

Numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations has become a critical tool for the design of aerospace vehicles. However, the issues that affect the grid convergence of three dimensional RANS solutions are not completely understood, as documented in the AIAA Drag Prediction Workshop series. Grid adaption methods have the potential for increasing the automation and discretization error control of RANS solutions to impact the aerospace design and certification process. The realization of the CFD Vision 2030 Study includes automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification by using analysis without demonstration in flight test (i.e., certification or qualification by analysis). For example, the Cart3D inviscid analysis package has automated Cartesian cut-cell gridding with output-based error control. Fueled by recent advances in the fields of anisotropic grid adaptation, error estimation, and geometry modeling, a similar work flow is explored for viscous CFD simulations; where a CFD application engineer provides geometry, boundary conditions, and flow parameters, and the sketch-to-solution process yields a CFD simulation through automatic, error-based, grid adaptation.

Kleb, William L.↗

Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports

A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.

low-boom supersonic transports↗

CFD-Assisted Nodal Modeling of Sloshing in a Cryogenic Propellant Tank

During autogenous pressurization, tank sloshing causes a significant increase in pressurant consumption to maintain constant ullage pressure during draining of the tank. This increase in pressurant consumption is caused by a significant increase in condensation at the liquid-vapor interface. Sloshing strongly affects the liquid side heat transfer coefficient and thereby the condensation rate. Traditionally, sloshing is modeled by CFD code using the VOF (Volume of Fluid) method to track the liquid vapor interface during sloshing. CFD calculations require a very fine grid to accurately compute the heat and mass transfer at the interface. Therefore, computations are time consuming and prohibit performing many parametric studies often needed during the design of a new system. This paper describes an alternative approach by developing a CFD-assisted nodal model to predict system parameters more economically with reasonable accuracy. In this approach, a multi-node model of tank pressurization was developed using GFSSP. A multi-node model was needed to account for stratification. The model computes heat and mass transfer at the interface to calculate the condensation rate. The liquid side heat transfer is computed using the parameters of sloshing dynamics such as frequency, wave amplitude, and interface area. The parameters of sloshing dynamics are computed by the CFD code LOCI-Stream. The model predictions were compared with test data for several cases.

Cryogenic Tank Sloshing↗

CFD-trained ANN Model for Approximating Near-occupant Condition in Real-time Simulations

The main drawback of Computational Fluid Dynamics (CFD) simulations has been the time and resource consuming nature which is not suitable for real-time applications. In this work, we first generated numerous CFD models of a given indoor space to obtain airspeed, temperature, and mean radiant temperature near an occupant as training data. Several artificial neural networks (ANN) models were trained using this CFD simulated data to approximate near real-time environmental conditions for a given occupant. This trained ANN model approach is a part of a real-time simulation of building operations using a combination of software and real hardware (HVAC equipment) approaches. The preliminary results suggest that the CFD- generated training data and the trained ANN model can accurately approximate such conditions in a real-time application, a method that has great potential in building simulation and building digital twin areas of research.

Zhang, Yun↗

Small-scale validation tests for MFIX-Exa CFD-DEM

This report describes several bench-scale fluidization experiments that can be used to validate the CFD-DEM method as encapsulated in the MFIX-Exa code. The five cases considered are the cold-flow fluidized beds of Müller et al., Link et al. (spout-fluid), and Goldschmidt et al. (bi-disperse), the hot fluidized bed of Patil et al., and the adsorbing fluidized bed of Li et al. and Janssen. In most cases, MFIX-Exa with “standard” or “typical” CFD-DEM settings, the Gidaspow drag model, and the Gunn heat transfer provide a relatively good prediction of the quantities considered: mean void fraction profiles, mean velocity profiles, fluctuating velocity profiles, mean particle temperature and segregation index. These results, with other verification and validation tests reported elsewhere, contribute to a body of work providing confidence and credibility in CFD predictions from the MFIX-Exa code.

97 MATHEMATICS AND COMPUTING↗

Attitude Reconstruction of Free-Flight CFD Generated Trajectories Using Non-Linear Pitch Damping Coefficient Curves

Attitude history reconstruction of Free-flight CFD generated trajectories with non-linear pitch damping coefficient curves is investigated. Free-flight CFD simulations of the capsule shape used for the Genesis sample return mission and the upcoming Dragonfly mission to Titan are conducted for 1-, 2-, and 3-degree-of-freedom cases. Two different data reduction methodologies are employed to derive a pitch damping curve as a function of instantaneous angle of attack. These curves are then used to reconstruct the attitude history of the body which is compared to the raw simulation results. While both data reduction methods produce pitch damping curves that can generally reconstruct the motion seen in the Free-flight simulations, it is found that optimization of the pitch damping curve using an inverse estimation process yields superior and more generalizable results. Further refinement of this technique could allow pitch damping curves derived using CFD to serve as a capability complementary to existing techniques for dynamic stability characterization.

entry↗

A hybrid porous model for full reactor core scale CFD investigation of a prismatic HTGR

Three-dimensional (3-D) Computational Fluid Dynamics (CFD) analysis of a whole nuclear reactor core is a tremendous challenge due to the large geometric volume and complex structures. Here, this research presents a hybrid porous (HP) model to simplify a prismatic High Temperature Gas-cooled Reactor (HTGR) core, so 3-D CFD investigation can be performed on a full reactor core scale. In the HP model, the prototypic small coolant channels in the nuclear fuel blocks are lumped together to form multiple equivalent large coolant channels, and then the porous medium flow model is applied to each of them. Therefore, heat transfer in fuel blocks is computed by a hybrid combination of solid energy and porous flow energy equations. The similarity between the HP model and prototypic model is achieved by deriving the porous flow permeability, inertial resistance factor, and artificial thermophysical properties. Compared with the widely used whole porous (WP) flow model, the HP model preserves more realistic geometric structures, and therefore more accurate physical processes. The General Atomics' Modular High Temperature Gas-cooled Reactor (MHTGR) design was chosen as a prototype to demonstrate the methodology. Simulations were performed using the prototypic CFD model and HP model at steady-state forced circulation, steady-state natural circulation, and transient conditions that correspond to normal operation, extended period of pressurized cool down, and short-term transients after reactor shutdown, respectively. The comparison shows good agreement between the HP model and prototypic model in the maximum fuel temperature, average solid temperature, and helium flow rate, which demonstrates the potential applicability of the HP model for a full reactor core scale simulation in the future. As a benefit, the HP model reduces the mesh quantity by a factor of 50 from a prototypic model. Correspondingly, the computation time was reduced by a factor of at least 30.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

CFD modeling of natural circulation in LiCl-KCl molten salt closed loop

Characterizing flow within a molten salt closed-loop system is crucial for assessing system requirements, evaluating performance, and identifying potential flaws. Direct flow measurement using instrumentation is challenging due to extreme environmental conditions and the limitations associated with measuring molten salt flow under natural convection. Here, this study aims to provide comprehensive insights into the thermal-hydraulic behavior of a closed loop, with a particular focus on temperature distribution and velocity prediction. The Computational Fluid Dynamics (CFD) model demonstrated the capability to effectively simulate and predict both temperature distributions and flow velocities within the molten salt loop. The CFD model's predictive capability was validated by its ability to replicate temperature measurements under varying boundary conditions. The analysis revealed that the CFD model tends to underpredict temperatures in the cold leg and overpredict them in the hot leg, highlighting the need for continuous model refinement and acknowledging the limitations of using a steady-state approach. Furthermore, the potential of using external temperature measurements to estimate internal molten salt temperatures and predict flow velocity was explored, revealing that this approach could introduce up to a 5.5% error in flow velocity calculations. Line probes mapping temperature distributions across the tube's cross-section and molten salt provided valuable insights into temperature gradients, emphasizing the need for a thermal conductivity equation for molten salt with lower uncertainty to achieve more accurate temperature predictions of the system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

CFD-DEM and PR-DNS studies of low-temperature densely packed beds

Over the past few decades, granular media is gaining attention as a viable option for heat transfer fluids (HTFs). Several research efforts are studying the use of particle-based heat transfer fluids in a wide variety of applications. With this motivation, the current work focusses on analyzing the different heat transfer mechanisms in low-temperature mono-sized densely packed granular media. To study the heat transfer behavior of granular media at different scales, the current work employs a two-way coupled computational strategy. The motion of particles is solved using the Discrete Element Method (DEM) and the interstitial air is solved using a Finite-Volume (CFD) approach. The Open-Source library CFDEM Coupling® is used in the current study to join the Finite Volume PISO solver of OpenFOAM® and the DEM solver of LIGGGHTS®. Typically, particle-particle contact conduction and particle-air convection are the most popular closure models. But recent research identified a different heat transfer phenomenon in packed beds that cannot be identified by conduction or convection models. While closure models were developed to implement this on a CFD-DEM framework, they did not capture the effect of intra-particulate thermal gradients on this phenomenon. Hence the current work also employs Particle-Resolved Direct Numerical Simulations (PR-DNS) to gain valuable insights allowing for the modification of existing models. A new closure model is then proposed here and is implemented in the CFD-DEM framework. This model provides key insights into the different heat transfer mechanism of packed beds.

42 ENGINEERING↗

Validation of a Hybrid Domain Overlapping Coupling Between SAM and CFD Against the TALL-3D Transients

The System Thermal Hydraulics (STH) code SAM has been coupled to the Computational Fluid Dynamics (CFD) code Simcenter STAR-CCM+ utilizing a hybrid domain overlapping method with an explicit coupling in time. The coupling aims to extend the STH code’s applicability to scenarios where local momentum and energy transfers are important yet difficult for STH codes to capture, such as three-dimensional (3D) mixing. The coupling method’s numerical stability was verified in the past against two closed-loop configurations, and it was validated against a double T-junction experiment with 3D scalar mixing. In the present work, the coupling method is validated against the TALL-3D STH/CFD coupling benchmark facility. TALL-3D is a three-legged, liquid-metal facility with a large, pool-type enclosure (test section) that exhibits 3D flow effects to be modeled by a CFD code. The rest of the system exhibits approximately 1D behavior well-predicted by an STH code. First, the present STAR-CCM+ CFD model of the 3D test section is validated against experimental data. Then, the SAM-STARCCM+ coupled model is validated against six different TALL-3D steady states, including SAM standalone model results for comparison. Lastly, the SAM-STARCCM+ coupled model is validated against two TALL-3D transients, one exhibiting flow reversal in the test section and one exhibiting nonlinear, Limit Cycle Oscillations (LCO). For the first transient, the SAM-STARCCM+ coupled model properly predicts an increase in the test section’s inlet temperature during flow reversal, and this is not predicted by the SAM standalone model. Following flow reversal, the SAM-STARCCM+ coupled model better-predicts the initial flow recovery and following oscillations as the system approaches a final natural circulation state. For the second transient, no true final steady state is observed due to LCO. Neither the SAM-STARCCM+ coupled model nor the SAM standalone model can perfectly capture the experiment’s changing oscillation frequency during the transient. However, the SAM-STARCCM+ coupled model does reproduce the oscillatory feedback observed in the system. This is a significant achievement as the SAM-STARCCM+ coupled model only uses an explicit coupling in time, as opposed to a semi-implicit coupling. In comparison, previous STH/CFD coupling efforts of the TALL-3D facility required semi-implicit coupling to obtain similar results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗