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At least 505 records · Page 28

Cold Flow Plume Entrainment Test Final Report NTF Test Number 2456

As part of the Space Shuttle Return to Flight (RTF) program, Marshall Space Flight Center (MSFC) performed computational fluid dynamics (CFD) analysis to define the velocity flowfields around the Shuttle stack at liftoff. These CFD predicted velocity flowfields were used in debris transport analysis (DTA). High speed flows such as plumes induce or 'entrain' mass from the surrounding environment. Previous work had shown that CFD analysis over-predicts plume induced flows. Therefore, the DTA would tend to 1) predict more debris impacts, and 2) the debris velocity (and kinetic energy) of those impacts would be too high. At a November, 2004 peer-review it was recommended that the Liftoff DTA team quantify the uncertainty in the DTA caused by the CFD's over prediction of plume induced flow. To do so, the Liftoff DTA team needed benchmark quality data for plume induced flow to quantify the CFD accuracy and its effect on the DTA. MSFC's Nozzle Test Facility (NTF) conducted the "Nozzle Induced Flows test, P#2456" to obtain experimental data for plume induced flows for nozzle flow exhausting into q quiescent freestream. Planning for the test began in December, 2004 and the experimental data was obtained in February and March of 2005. The funding for this test was provided by MSFC's Space Shuttle Propulsion Systems Integration and Engineering office.

Ruf, Joseph H.↗

Space Launch System Scale Model Acoustic Test Ignition Overpressure Testing

The overpressure phenomenon is a transient fluid dynamic event occurring during rocket propulsion system ignition. This phenomenon results from fluid compression of the accelerating plume gas, subsequent rarefaction, and subsequent propagation from the exhaust trench and duct holes. The high-amplitude unsteady fluid-dynamic perturbations can adversely affect the vehicle and surrounding structure. Commonly known as ignition overpressure (IOP), this is an important design-to environment for the Space Launch System (SLS) that NASA is currently developing. Subscale testing is useful in validating and verifying the IOP environment. This was one of the objectives of the Scale Model Acoustic Test (SMAT), conducted at Marshall Space Flight Center (MSFC). The test data quantifies the effectiveness of the SLS IOP suppression system and improves the analytical models used to predict the SLS IOP environments. The reduction and analysis of the data gathered during the SMAT IOP test series requires identification and characterization of multiple dynamic events and scaling of the event waveforms to provide the most accurate comparisons to determine the effectiveness of the IOP suppression systems. The identification and characterization of the overpressure events, the waveform scaling, the computation of the IOP suppression system knockdown factors, and preliminary comparisons to the analytical models are discussed.

Nance, Donald K.↗

Simulation of Fluid Flow and Collection Efficiency for a SEA Inc. Multi-Element Probe and Ice Crystal Detector Using GlennICE

Numerical simulation results of fluid flow and collection efficiency of the Science Engineering Associates Inc. Multi-Element Probe (Multiwire) and Ice Crystal Detector (ICD) are presented. Fluid flow simulations were conducted using NASA's FUN3D while collection efficiency simulations were conducted using NASA's LEWICE3D software and GlennICE software. For both probes, 3D unsteady flow results were time averaged. Simulations were computed for freestream velocities ranging from 85 to 185 m/s and freestream total pressures of 44.8 and 93.1 kPa. Collection efficiency results were computed for four spherical particle diameter sizes of 5, 20, 50, and 100 µm. GlennICE collection efficiency results for the multiwire were compared with previously published collection efficiency values calculated using LEWICE3D. Numerical collection efficiency results for the Ice Crystal Detector are presented for the first time.

aircraft, icing, Computational Fluid Dynamics↗

Feasibility of Conducting J-2X Engine Testing at the Glenn Research Center Plum Brook Station B-2 Facility

A trade study of the feasibility of conducting J-2X testing in the Glenn Research Center (GRC) Plum Brook Station (PBS) B-2 facility was initiated in May 2006 with results available in October 2006. The Propulsion Test Integration Group (PTIG) led the study with support from Marshall Space Flight Center (MSFC) and Jacobs Sverdrup Engineering. The primary focus of the trade study was on facility design concepts and their capability to satisfy the J-2X altitude simulation test requirements. The propulsion systems tested in the B-2 facility were in the 30,000-pound (30K) thrust class. The J-2X thrust is approximately 10 times larger. Therefore, concepts significantly different from the current configuration are necessary for the diffuser, spray chamber subsystems, and cooling water. Steam exhaust condensation in the spray chamber is judged to be the key risk consideration relative to acceptable spray chamber pressure. Further assessment via computational fluid dynamics (CFD) and other simulation capabilities (e.g. methodology for anchoring predictions with actual test data and subscale testing to support investigation.

Schafer, Charles F.↗

Assessment of Hybrid RANS/LES Turbulence Models for Aeroacoustics Applications

Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroacoustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex configurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Although the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the experimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in unresolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging.

Vatsa, Veer N.↗

Novel Tilting Ducted-Fan Aerial Vehicle Configurations

There has been recent renewed interested in ducted-fan, powered-lift vertical takeoff and landing aircraft vehicles for uninhabited aerial vehicle and urban aerial mobility aerial applications. Early work was conducted in the 1950’s to the late 1980’s into ducted-fan vehicles, especially at the time for military missions. The focus of ducted-fan research began to shift to UAV’s and personal air transportation in the 2000’s. Work in the early 2000’s fostered interest into ducted-fan aerial vehicles for vertical lift planetary aerial vehicle missions, especially for missions to Titan, a moon of Saturn. For example, early work at NASA Ames conducted the first known investigation into oval ducts (with internal tandem fans) to be used for these aerial vehicles. The use of twin oval ducts (with internal tandem fans) allowed the use of quadrotor-style rotor rpm control for vehicle trim (in hover, for transition to high-speed forward flight the addition of a tilt-actuator to pitch the twin oval ducts forward to be aligned with the freestream needed to be added to the control approach. This current study explores open-rotor, single isolated ducted-fan, and full vehicle configuration aerodynamic performance for hover, transition, and cruise regimes for novel tilting ducted-fan aerial vehicle configurations. The objective of this study is to better understand the design aerodynamics trade space for noncircular tilting ducted-fans. The primary analysis tool used in this paper is the mid-fidelity computational fluid dynamics RotCFD tool. Several interesting and largely unexplored rotor-on-rotor (or fan-on-fan), duct-on-rotor, rotor- on-duct, and duct-on-airframe are examined in this paper. Many of these aerodynamic interactions are the key to overall aerial vehicle performance. Limited parametric sweeps of rotor-to-rotor spacing (and, therefore, sizing and shape of the enveloping ducts) for the various duct configurations will also be performed. The trade-offs between duct thrust augmentation in hover versus improved transition controllability versus improved cruise L/D will be discussed for various novel duct configurations. These ducted-fan configurations include oval ducts, ‘figure-eight’ ducts, and ‘B-shaped’ ducts, among others.

Ducted-Fan↗

NASA GRC Stirling Technology Development Overview

The Department of Energy, Lockheed Martin (LM), Stirling Technology Company, and NASA Glenn Research Center (GRC) are developing a high-efficiency Stirling Radioisotope Generator (SRG) for potential NASA Space Science missions. The SRG is being developed for multimission use, including providing spacecraft onboard electric power for NASA deep space missions and power for unmanned Mars rovers. NASA GRC is conducting an in- house supporting technology project to assist in developing the Stirling convertor for space qualification and mission implementation. Preparations are underway for a thermalhacuum system demonstration and unattended operation during endurance testing of the 55-We Technology Demonstration Convertors. Heater head life assessment efforts continue, including verification of the heater head brazing and heat treatment schedules and evaluation of any potential regenerator oxidation. Long-term magnet aging tests are continuing to characterize any possible aging in the strength or demagnetization resistance of the permanent magnets used in the linear alternator. Testing of the magnet/lamination epoxy bond for performance and lifetime characteristics is now underway. These efforts are expected to provide key inputs as the system integrator, LM, begins system development of the SRG. GRC is also developing advanced technology for Stirling convertors. Cleveland State University (CSU) is progressing toward a multi-dimensional Stirling computational fluid dynamics code, capable of modeling complete convertors. Validation efforts at both CSU and the University of Minnesota are complementing the code development. New efforts have been started this year on a lightweight convertor, advanced controllers, high-temperature materials, and an end-to-end system dynamics model. Performance and mass improvement goals have been established for second- and third-generation Stirling radioisotope power systems.

Thieme, Lanny G.↗

Wind Tunnel Test of a Risk-Reduction Wing/Fuselage Model to Examine Juncture-Flow Phenomena

A wing/fuselage wind-tunnel model was tested in the Langley 14- by 22-foot Subsonic Wind Tunnel in preparation for a highly-instrumented Juncture Flow Experiment to be conducted in the same facility. This test, which was sponsored by the NASA Transformational Tool and Technologies Project, is part of a comprehensive set of experimental and computational research activities to develop revolutionary, physics-based aeronautics analysis and design capability. The objectives of this particular test were to examine the surface and off-body flow on a generic wing/body combination to: 1) choose a final wing for a future, highly instrumented model, 2) use the results to facilitate unsteady pressure sensor placement on the model, 3) determine the area to be surveyed with an embedded laser-doppler velocimetry (LDV) system, 4) investigate the primary juncture corner- flow separation region using particle image velocimetry (PIV) to see if the particle seeding is adequately entrained and to examine the structure in the separated region, and 5) to determine the similarity of observed flow features with those predicted by computational fluid dynamics (CFD). This report documents the results of the above experiment that specifically address the first three goals. Multiple wing configurations were tested at a chord Reynolds number of 2.4 million. Flow patterns on the surface of the wings and in the region of the wing/fuselage juncture were examined using oil- flow visualization and infrared thermography. A limited number of unsteady pressure sensors on the fuselage around the wing leading and trailing edges were used to identify any dynamic effects of the horseshoe vortex on the flow field. The area of separated flow in the wing/fuselage juncture near the wing trailing edge was observed for all wing configurations at various angles of attack. All of the test objectives were met. The staff of the 14- by 22-foot Subsonic Wind Tunnel provided outstanding support and delivered exceptional value to the experiment, which exceeded expectations. The results of this test will directly inform the planning for the first of a series of instrumented-model tests at the same Reynolds number. These tests will be performed on a slightly larger-scale model with the selected wing, and will include off-body measurements with LDV and PIV, steady and unsteady pressure measurements, and the flow-visualization techniques that are discussed in this report.

Kegerise, Michael A.↗

Simulation of Fluid Flow and Collection Efficiency for a SEA Inc. Multi-Element Probe and Ice Crystal Detector Using GlennICE

Numerical simulation results of fluid flow and collection efficiency of the Science Engineering Associates Inc. Multi-Element Probe (Multiwire) and Ice Crystal Detector (ICD) are presented. Fluid flow simulations were conducted using NASA's FUN3D while collection efficiency simulations were conducted using NASA's LEWICE3D software and GlennICE software. For both probes, 3D unsteady flow results were time-averaged. Simulations were computed for free steam velocities ranging from 85 to 185 m/s and freestream total pressures of 44.8 and 93.1 kPa. Collection efficiency results were computed for four spherical particle diameter sizes of 5, 20, 50, and 100 µm. GlennICE collection efficiency results for the multiwire were compared with previously published collection efficiency values calculated using LEWICE3D. Numerical collection efficiency results for the Ice Crystal Detector are presented for the first time.

aircraft, icing, Computational Fluid Dynamics↗

Center for Advanced Space Propulsion (CASP)

With a mission to initiate and conduct advanced propulsion research in partnership with industry, and a goal to strengthen U.S. national capability in propulsion technology, the Center for Advanced Space Propulsion (CASP) is the only NASA Center for Commercial Development of Space (CCDS) which focuses on propulsion and associated technologies. Meetings with industrial partners and NASA Headquarters personnel provided an assessment of the constraints placed on, and opportunities afforded commercialization projects. Proprietary information, data rights, and patent rights were some of the areas where well defined information is crucial to project success and follow-on efforts. There were five initial CASP projects. At the end of the first year there are six active, two of which are approaching the ground test phase in their development. Progress in the current six projects has met all milestones and is detailed. Working closely with the industrial counterparts it was found that the endeavors in expert systems development, computational fluid dynamics, fluid management in microgravity, and electric propulsion were well received. One project with the Saturn Corporation which dealt with expert systems application in the assembly process, was placed on hold pending further direction from Saturn. The Contamination Measurment and Analysis project was not implemented since CASP was unable to identify an industrial participant. Additional propulsion and related projects were investigated during the year. A subcontract was let to a small business, MicroCraft, Inc., to study rocket engine certification standards. The study produced valuable results; however, based on a number of factors it was decided not to pursue this project further.

Source record↗

Radial Profiles of Plasma Electron Characteristics in a Low-Power Arcjet

Since 1960, the Arc Jet Complex at NASA Ames Research Center has been a source of long-duration, high-enthalpy flow for materials testing with application to the thermal protection of aerospace vehicle components. From their inception the facilities have played an integral role supporting many of NASA's space flight programs and numerous DoD projects. In recent years advancements in computational fluid dynamics (CFO) have made the resultant models a valuable tool for assessing and predicting performance, however, the inherent limitation of models to compensate for a dissociated, transitionally high temperature nonequilibrated flowfield have made further measurements necessary. The use of electrostatic probe diagnostics within similarly harsh plasma environments in previous studies have been met with much success. In this study, the use of a single Langmuir probe was implemented to characterize the plasma parameters of interest as they vary radially within a large volume of the plume. Classical Langmuir probe theory was applied to achieve first order estimates of the heavy particle temperature, the ratio T(sub i)/T(sub e), and the ionization fraction. As expected, both the electron temperature and electron density measurements show a dependence on radial distance from the plume centerline, with electron density profiles showing the largest dependence. This paper aims to validate and strengthen modeling work conducted at the NASA Ames Research Center by measuring the critical plasma parameters (electron temperature, electron density, and plasma potential) within the arc plume of a subscale arc jet. These parameters are intended to give physical insight into the flow characteristics while providing the necessary boundary conditions to validate full scale simulations.

Codron, Douglas↗

Simulations of Zero Boiloff, Densification, and Solidification in a Large-Scale Liquid Hydrogen Tank

The current research utilizes an Energy of Fluid (EOF) approach to develop a finite volume-based Computation Fluid Dynamic (CFD) model to create a benchmark simulation of the densification of liquid hydrogen (LH2) in an experimental Integrated Refrigeration and Storage (IRAS) tank at the Kennedy Space Center (KSC). The computational code will incorporate the FLUENT pressure-based model with User Defined Functions (UDF) to implement the EOF model. The enhanced model will solve the energy equation in terms of internal energy and provide temperature and pressure calculations for a given tank geometry. Specifically, a convection term will be added to an already existing code for a more accurate simulation of LH2 densification. However, currently the research focuses on utilizing User Defined Scalars (UDS) with FLUENT to show the built-in solvers are as accurate as the written UDS. This will reduce the computational time down significantly by utilizing an already built in solver for the momentum equation. A custom UDF has been written to solve transient and steady state conduction, and results obtained using the UDF agree with results obtained using the built-in FLUENT solver. Currently, a convection UDF is being added and will be verified using known solutions for solidification and validated with the experimental results from the Cryogenics Test Laboratory (CTL) at KSC for the IRAS densification process.

Colin Philip Mahony↗

Wall Modeled Large Eddy Simulations for NASA’s Jet Noise Consensus Database of Single-Flow, Round, Convergent Jets

A campaign of wall-modeled large-eddy simulations (WMLES) using structured curvilinear overlapping grids has been performed with the Launch Ascent and Vehicle Aerodynamics(LAVA) computational fluid dynamics (CFD) software to predict jet noise for single-stream axisymmetric round jets. The simulations address the new Prediction Uncertainty Reduction(PUR) technical challenge within the context of NASA’s Commercial Supersonic Technology(CST) project. The goal of PUR is to quantify and reduce uncertainties from scale-resolving simulations to assess noise characteristics of next generation quiet supersonic commercial jets during takeoff and landing conditions where the noise from the exhaust jet dominates. The focus of this effort is to generate a simulation database for single-stream axisymmetric round nozzles at several conditions both for static (no ambient co-flow), which is the focus of this article, and in-flight (flight stream co-flow) conditions, which are beyond the current scope. Nine different flow conditions ranging in jet exit Mach number from 0.38 to 1.0 with nozzle temperature ratios (NTR) from 0.84 to 2.7 have been conducted. Details of the structured overset grids, numerical discretization and wall-model are provided. Near-field comparisons to PIV data show great agreement for both velocity and normal stresses, however a systematic TKE overshoot at the nozzle exit is seen in the lip line shear-layer. A permeable Ffowcs Williams Hawkings (FWH) surface, enclosing the jet, is used to predict far-field noise from the simulated flow-field. Comparison of CFD predictions to microphone array measurements demonstrate excellent agreement within the resolved frequency range. A systematic under-prediction of far-aft observer angles larger than 150 degrees has been observed across all simulations. We achieved a cost reduction of an order of magnitude for these WMLES compared to an earlier study of this configuration due to algorithmic and software improvements. The accuracy of the results and short turnaround time demonstrate that WMLES within the LAVA framework is a cost-effective approach for jet noise predictions that could soon be incorporated into the design cycle of jet noise reduction technologies.

CST↗

Flap Edge Aeroacoustic Measurements and Predictions

An aeroacoustic model test has been conducted to investigate the mechanisms of sound generation on high-lift wing configurations. This paper presents an analysis of flap side-edge noise, which is often the most dominant source. A model of a main element wing section with a half-span flap was tested at low speeds of up to a Mach number of 0.17, corresponding to a wing chord Reynolds number of approximately 1.7 million. Results are presented for flat (or blunt), flanged, and round flap-edge geometries, with and without boundary-layer tripping, deployed at both moderate and high flap angles. The acoustic database is obtained from a Small Aperture Directional Array (SADA) of microphones, which was constructed to electronically steer to different regions of the model and to obtain farfield noise spectra and directivity from these regions. The basic flap-edge aerodynamics is established by static surface pressure data, as well as by Computational Fluid Dynamics (CFD) calculations and simplified edge flow analyses. Distributions of unsteady pressure sensors over the flap allow the noise source regions to be defined and quantified via cross-spectral diagnostics using the SADA output. It is found that shear layer instability and related pressure scatter is the primary noise mechanism. For the flat edge flap, two noise prediction methods based on unsteady-surface-pressure measurements are evaluated and compared to measured noise. One is a new causality spectral approach developed here. The other is a new application of an edge-noise scatter prediction method. The good comparisons for both approaches suggest that much of the physics is captured by the prediction models. Areas of disagreement appear to reveal when the assumed edge noise mechanism does not fully define, the noise production. For the different edge conditions, extensive spectra and directivity are presented. Significantly, for each edge configuration, the spectra for different flow speeds, flap angles, and surface roughness were successfully scaled by utilizing aerodynamic performance and boundary layer scaling method developed herein.

Brooks, Thomas F.↗

Flap Edge Aeroacoustic Measurements and Predictions

An aeroacoustic model test has been conducted to investigate the mechanisms of sound generation on high-lift wing configurations. This paper presents an analysis of flap side-edge noise, which is often the most dominant source. A model of a main element wing section with a half-span flap was tested at low speeds of up to a Mach number of 0.17, corresponding to a wing chord Reynolds number of approximately 1.7 million. Results are presented for flat (or blunt), flanged, and round flap-edge geometries, with and without boundary-layer tripping, deployed at both moderate and high flap angles. The acoustic database is obtained from a Small Aperture Directional Array (SADA) of microphones, which was constructed to electronically steer to different regions of the model and to obtain farfield noise spectra and directivity from these regions. The basic flap-edge aerodynamics is established by static surface pressure data, as well as by Computational Fluid Dynamics (CFD) calculations and simplified edge flow analyses. Distributions of unsteady pressure sensors over the flap allow the noise source regions to be defined and quantified via cross-spectral diagnostics using the SADA output. It is found that shear layer instability and related pressure scatter is the primary noise mechanism. For the flat edge flap, two noise prediction methods based on unsteady surface pressure measurements are evaluated and compared to measured noise. One is a new causality spectral approach developed here. The other is a new application of an edge-noise scatter prediction method. The good comparisons for both approaches suggest that much of the physics is captured by the prediction models. Areas of disagreement appear to reveal when the assumed edge noise mechanism does not fully define the noise production. For the different edge conditions, extensive spectra and directivity are presented. Significantly, for each edge configuration, the spectra for different flow speeds, flap angles, and surface roughness were successfully scaled by utilizing aerodynamic performance and boundary layer scaling methods developed herein.

Brooks, Thomas F.↗

Flight experiment of thermal energy storage

Thermal energy storage (TES) enables a solar dynamic system to deliver constant electric power through periods of sun and shade. Brayton and Stirling power systems under current considerations for missions in the near future require working fluid temperatures in the 1100 to 1300+ K range. TES materials that meet these requirements fall into the fluoride family of salts. These salts store energy as a heat of fusion, thereby transferring heat to the fluid at constant temperature during shade. The principal feature of fluorides that must be taken into account is the change in volume that occurs with melting and freezing. Salts shrink as they solidify, a change reaching 30 percent for some salts. The location of voids that form as result of the shrinkage is critical when the solar dynamic system reemerges into the sun. Hot spots can develop in the TES container or the container can become distorted if the melting salt cannot expand elsewhere. Analysis of the transient, two-phase phenomenon is being incorporated into a three-dimensional computer code. The code is capable of analysis under microgravity as well as 1 g. The objective of the flight program is to verify the predictions of the code, particularly of the void location and its effect on containment temperature. The four experimental packages comprising the program will be the first tests of melting and freezing conducted under microgravity. Each test package will be installed in a Getaway Special container to be carried by the shuttle. The package will be self-contained and independent of shuttle operations other than the initial opening of the container lid and the final closing of the lid. Upon the return of the test package from flight, the TES container will be radiographed and finally partitioned to examine the exact location and shape of the void. Visual inspection of the void and the temperature data during flight will constitute the bases for code verification.

Namkoong, David↗

A computational examination of directional stability for smooth and chined forebodies at high-alpha

Computational Fluid Dynamics (CFD) has been used to study aircraft forebody flowfields at low-speed, angle-of-attack conditions with sideslip. The purpose is to define forebody geometries which provide good directional stability characteristics under these conditions. The flows over the experimentally investigated F-5A forebody and chine type configuration, previously computed by the authors, were recomputed with better grid topology and resolution. The results were obtained using a modified version of CFL3D (developed at NASA Langley) to solve either the Euler equations or the Reynolds equations employing the Baldwin-Lomax turbulence model with the Degani-Schiff modification to account for massive crossflow separation. Based on the results, it is concluded that current CFD methods can be used to investigate the aerodynamic characteristics of forebodies to achieve desirable high angle-of-attack characteristics. An analytically defined generic forebody model is described, and a parametric study of various forebody shapes was then conducted to determine which shapes promote a positive contribution to directional stability at high angle-of-attack. An unconventional approach for presenting the results is used to illustrate how the positive contribution arises. Based on the results of this initial parametric study, some guidelines for aerodynamic design to promote positive directional stability are presented.

Ravi, Ramakrishnan↗

Comparison of Fire Model Predictions with Experiments Conducted in a Hangar With a 15 Meter Ceiling

The purpose of this study is to examine the predictive capabilities of fire models using the results of a series of fire experiments conducted in an aircraft hangar with a ceiling height of about 15 m. This study is designed to investigate model applicability at a ceiling height where only a limited amount of experimental data is available. This analysis deals primarily with temperature comparisons as a function of distance from the fire center and depth beneath the ceiling. Only limited velocity measurements in the ceiling jet were available but these are also compared with those models with a velocity predictive capability.

MATHEMATICAL MODELS↗