Search NASA⌕ Search

SEARCH · Search NASA

Results for “lumped mass”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Analysis of an electrohydraulic aircraft control surface servo and comparison with test results

An analysis of an electrohydraulic aircraft control-surface system is made in which the system is modeled as a lumped, two-mass, spring-coupled system controlled by a servo valve. Both linear and nonlinear models are developed, and the effects of hinge-moment loading are included. Transfer functions of the system and approximate literal factors of the transfer functions for several cases are presented. The damping action of dynamic pressure feedback is analyzed. Comparisons of the model responses with results from tests made on a highly resonant rudder control-surface servo indicate the adequacy of the model. The effects of variations in hinge-moment loading are illustrated.

Edwards, J. W.↗
NASA NTRS1988

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose thruster assembly as a lumped or point mass dashpot spring system at the tip. Measurements of linear acceleration at the tip are used to estimate the hose parameters (mass, stiffness, damping) and a Voigt-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations are considered to the hybrid (coupled ordinary and partial differential equations) systems; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗
NASA NTRS1992

Unsteady transonic Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented and demonstrated for 2D airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage Runge-Kutta scheme to march forward in time. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite-volume techniques. The effects of using either a lumped or consistent mass matrix are presented; the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils.

Davis, Gary A.↗
NASA NTRS2018

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Brown, Andrew M.↗
NASA NTRSDate not supplied

Soyuz Landing Risk Characterization

INTRODUCTION United States On-orbit Segment (USOS) astronauts have been returning to Earth from the International Space Station (ISS) aboard the Russian Soyuz vehicle since 2003. The energetics associated with Soyuz landings are comparable to our next generation of US space vehicles (Orion, Crew Dragon, and Starliner). Soyuz also lands crew in a similar state of spaceflight deconditioning that is anticipated using the future vehicles. A number of injuries have now been observed during these Soyuz landings. Currently it is unknown how Soyuz landing accelerations and the numbers and types of associated injuries relate to the new occupant protection requirements levied upon future space vehicles. Understanding this relationship will allow better quantification of the risk of injury for future spacecraft designs. METHODS An estimate of the occurrences of injury during Soyuz landings has been determined using data contained in NASA flight medicine databases and supplemented with data collected from crewmembers and flight surgeons. At the time of this abstract, 96 USOS astronauts have returned to Earth in the Soyuz (59 US, 31 International Partner, and 6 spaceflight participants). Of that total, data from 80 individual crew landings has been collected through this study. Injuries are classified as either contusions/abrasions, Class I (minor, no medical follow-up), Class II (moderate, medical follow-up necessary), Class III (severe), and Class IV (life threatening). Current NASA occupant protection standards are primarily based on the Multi-axial Dynamic Response Index (MDRI), which is a simple lumped-parameter spring, mass, damper model tuned to human impact responses in three orthogonal axes. RESULTS Using what is known about Soyuz landing dynamics from airborne and drop test data, the MDRI predicts essentially no Class IV or III injuries, < 1% Class II injuries, and < 5% Class I injuries. Approximately one-third of all USOS crewmembers for whom data has been gathered have suffered some sort of injury related to landing in the Soyuz vehicle. Most of these injuries fall into the contusion/abrasion category (21.3 %). Class I injuries have been sustained by 5.0% of all crew, and Class II injuries have been observed in 3.8%. No Class III or IV injuries have been sustained to date. Forty-three injuries have been documented, with some crewmembers sustaining more than one injury in a single landing. The knee was the most likely area of injury (n=9), followed by the back (n=8), and then the arm (n=7). CONCLUSION Soyuz landing dynamics are the most comparable analog environment for the anticipated loads associated with Orion and commercial crew vehicle landings. The MDRI under predicts the percentage of Class II injuries experienced during Soyuz landings. The MDRI is better at predicting Class I injury occurrences. However, if contusions/abrasions are included in the minor injury Class I category, then the MDRI also vastly under predicts those injuries as well. Given this data, it will be important to re-evaluate the expected injury rates for future vehicles, and work toward improving the predictive tools for spaceflight use. Spaceflight deconditioning may account for some of the under prediction, and work is ongoing to assess the relationship between landing injuries and impact tolerance changes due to spaceflight deconditioning.

N Newby↗
NASA NTRSDate not supplied

Soyuz Landing Risk Characterization

INTRODUCTION United States On-orbit Segment (USOS) astronauts have been returning to Earth from the International Space Station (ISS) aboard the Russian Soyuz vehicle since 2003. The energetics associated with Soyuz landings are comparable to our next generation of US space vehicles (Orion, Crew Dragon, and Starliner). Soyuz also lands crew in a similar state of spaceflight deconditioning that is anticipated using the future vehicles. A number of injuries have now been observed during these Soyuz landings. Currently it is unknown how Soyuz landing accelerations and the numbers and types of associated injuries relate to the new occupant protection requirements levied upon future space vehicles. Understanding this relationship will allow better quantification of the risk of injury for future spacecraft designs. METHODS An estimate of injury occurrence during Soyuz landings has been determined using data contained in NASA flight medicine databases and supplemented with data collected from crewmembers and flight surgeons. At the time of this abstract, 96 USOS astronauts have returned to Earth in the Soyuz (59 US, 31 International Partner, and 6 spaceflight participants). Of that total, data from 80 individual crew landings has been collected through this study as of 2021. Injuries are classified either as contusions/abrasions, Class I (minor, no medical follow-up), Class II (moderate, medical follow-up necessary), Class III (severe), or Class IV (life threatening). Current NASA occupant protection standards are primarily based on the Multi-axial Dynamic Response Index (MDRI), which is a simple lumped-parameter spring, mass, damper model tuned to human impact responses in three orthogonal axes. RESULTS Using what is known about Soyuz landing dynamics from airborne and drop test data, the MDRI predicts essentially no Class IV or III injuries, < 1% Class II injuries, and < 5% Class I injuries. Approximately one-third of all USOS crewmembers for whom data has been gathered have suffered some sort of injury related to landing in the Soyuz vehicle. Most of these injuries fall into the contusion/abrasion category (21.3 %) (n.b. This is the percent for whom contusion/abrasion was the worst injury. Those with class I or II injuries typically also received contusions/abrasions). Class I injuries have been sustained by 5.0% of all crew, and Class II injuries have been observed in 3.8%. No Class III or IV injuries have been sustained to date. Forty-three injuries have been documented, with some crewmembers sustaining more than one injury in a single landing. The knee was the most likely area of injury (n=9), followed by the back (n=8), then the arm (n=7). CONCLUSION Soyuz landing dynamics are the most comparable analog environment for the anticipated loads associated with Orion and commercial crew vehicle landings. The MDRI under predicts the percentage of Class II injuries experienced during Soyuz landings, but it is better at predicting Class I injury occurrences. However, if contusions/abrasions are included in the minor injury Class I category, then the MDRI vastly under predicts those injuries as well. Given this data, it is important to re-evaluate the expected injury rates for future vehicles and work toward improving the predictive tools for spaceflight use. Spaceflight deconditioning may account for some of the under prediction, and work is ongoing to assess the relationship between landing injuries and impact tolerance changes due to spaceflight deconditioning. Future work includes expanding this study to involve private space missions on new vehicles to better characterize the effects of time in flight, suit and seat design, and vehicle dynamics.

N Newby↗
NASA NTRSDate not supplied

Soyuz Landing Risk Characterization

INTRODUCTION United States On-orbit Segment (USOS) astronauts have been returning to Earth from the International Space Station (ISS) aboard the Russian Soyuz vehicle since 2003. The energetics associated with Soyuz landings are comparable to our next generation of US space vehicles (Orion, Crew Dragon, and Starliner). Soyuz also lands crew in a similar state of spaceflight deconditioning that is anticipated using the future vehicles. A number of injuries have now been observed during these Soyuz landings. Currently it is unknown how Soyuz landing accelerations and the numbers and types of associated injuries relate to the new occupant protection requirements levied upon future space vehicles. Understanding this relationship will allow better quantification of the risk of injury for future spacecraft designs. METHODS An estimate of injury occurrence during Soyuz landings has been determined using data contained in NASA flight medicine databases and supplemented with data collected from crew members and flight surgeons. At the time of this abstract, 96 USOS astronauts have returned to Earth in the Soyuz (59 US, 31 International Partner, and 6 spaceflight participants). Of that total, data from 80individual crew landings has been collected through this study as of September 2023. Injuries are classified either as contusions/abrasions, Class I (minor, no medical follow-up), Class II (moderate, medical follow-up necessary), Class III (severe), or Class IV (life threatening). Current NASA occupant protection standards are primarily based on the Multi-axial Dynamic Response Index (MDRI), which is a simple lumped-parameter spring, mass, damper model tuned to human impact responses in three orthogonal axes. RESULTS Using what is known about Soyuz landing dynamics from airborne and drop test data, the MDRI predicts essentially no Class IV or III injuries, < 1% Class II injuries, and < 5% Class I injuries. Approximately one-third of all USOS crewmembers for whom data has been gathered have suffered some sort of injury related to landing in the Soyuz vehicle. Most of these injuries fall into the contusion/abrasion category (21.3%) (n.b. This is the percent for whom contusion/abrasion was the worst injury. Those with class I or II injuries typically also received contusions/abrasions). Class I injuries have been sustained by 5.0% of all crew, and Class II injuries have been observed in 3.8%. No Class III or IV injuries have been sustained to date. Forty-three injuries have been documented, with some crewmembers sustaining more than one injury in a single landing. The knee was the most likely area of injury (n=9), followed by the back (n=8), then the arm (n=7). CONCLUSION Soyuz landing dynamics are the most comparable analog environment for the anticipated loads associated with Orion and commercial crew vehicle landings. The MDRI under predicts the percentage of Class II injuries experienced during Soyuz landings, but it is better at predicting Class I injury occurrences. However, if contusions/abrasions are included in the minor injury Class I category, then the MDRI vastly under predicts those injuries as well. Given this data, it is important to re-evaluate the expected injury rates for future vehicles and work toward improving the predictive tools for spaceflight use. Spaceflight deconditioning may account for some of the under prediction, and work is ongoing to assess the relationship between landing injuries and impact tolerance changes due to spaceflight deconditioning. Future work includes expanding this study to involve private space missions on new vehicles to better characterize the effects of time in flight, suit and seat design, and vehicle dynamics.

N Newby↗
NASA NTRSDate not supplied

Soyuz Landing Risk Characterization

INTRODUCTION United States On-orbit Segment (USOS) astronauts have been returning to Earth from the International Space Station (ISS) aboard the Russian Soyuz vehicle since 2003. The energetics associated with Soyuz landings are comparable to our next generation of US space vehicles (Orion, Crew Dragon, and Starliner). Soyuz also lands crew in a similar state of spaceflight deconditioning that is anticipated using the future vehicles. A number of injuries have now been observed during these Soyuz landings. Currently it is unknown how Soyuz landing accelerations and the numbers and types of associated injuries relate to the new occupant protection requirements levied upon future space vehicles. Understanding this relationship will allow better quantification of the risk of injury for future spacecraft designs. METHODS An estimate of injury occurrence during Soyuz landings has been determined using data contained in NASA flight medicine databases and supplemented with data collected from crewmembers and flight surgeons. At the time of this abstract, 96 USOS astronauts have returned to Earth in the Soyuz (59 US, 31 International Partner, and 6 spaceflight participants). Of that total, data from 80 individual crew landings has been collected through this study as of September 2023. Injuries are classified either as contusions/abrasions, Class I (minor, no medical follow-up), Class II (moderate, medical follow-up necessary), Class III (severe), or Class IV (life threatening). Current NASA occupant protection standards are primarily based on the Multi-axial Dynamic Response Index (MDRI), which is a simple lumped-parameter spring, mass, damper model tuned to human impact responses in three orthogonal axes. RESULTS Using what is known about Soyuz landing dynamics from airborne and drop test data, the MDRI predicts essentially no Class IV or III injuries, < 1% Class II injuries, and < 5% Class I injuries. Approximately one-third of all USOS crewmembers for whom data has been gathered have suffered some sort of injury related to landing in the Soyuz vehicle. Most of these injuries fall into the contusion/abrasion category (21.3 %) (n.b. This is the percent for whom contusion/abrasion was the worst injury. Those with class I or II injuries typically also received contusions/abrasions). Class I injuries have been sustained by 5.0% of all crew, and Class II injuries have been observed in 3.8%. No Class III or IV injuries have been sustained to date. Forty-three injuries have been documented, with some crewmembers sustaining more than one injury in a single landing. The knee was the most likely area of injury (n=9), followed by the back (n=8), then the arm (n=7). CONCLUSION Soyuz landing dynamics are the most comparable analog environment for the anticipated loads associated with Orion and commercial crew vehicle landings. The MDRI under predicts the percentage of Class II injuries experienced during Soyuz landings, but it is better at predicting Class I injury occurrences. However, if contusions/abrasions are included in the minor injury Class I category, then the MDRI vastly under predicts those injuries as well. Given this data, it is important to re-evaluate the expected injury rates for future vehicles and work toward improving the predictive tools for spaceflight use. Spaceflight deconditioning may account for some of the under prediction, and work is ongoing to assess the relationship between landing injuries and impact tolerance changes due to spaceflight deconditioning. Future work includes expanding this study to involve private space missions on new vehicles to better characterize the effects of time in flight, suit and seat design, and vehicle dynamics.

P Greenhalgh↗
NASA NTRS1986

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose-thruster assembly as a lumped or point mass-dashpot-spring system at the tip. Using measurements of linear acceleration at the tip, it is estimated that the parameters (mass, stiffness, damping) and a Voight-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations to the hybrid (coupled ordinary and partial differential equations) system are considered; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗
NASA NTRS1981

The influence of gyroscopic forces on the dynamic behavior of rotating blades

The question of divergent oscillatory stability of an axial turbomachine blade when the bladed rotor system is subjected to a forced precessional motion is studied by using two simplified models of the blade. The simplest (lumped) model is a point mass restrained by three orthogonal linear springs attached to the rotor. An improved distributed parameter model represents the blade by a uniform cantilever beam with bending in one plane. In both instances instability is shown to be strongly dependent upon the ratio of blade root radius to blade length and the magnitude of the rotor spin relative to the nonrotating blade natural frequency for realistic values of precession rate. Results are presented on augmented Campbell diagrams. Implications for design and operation are drawn as are the characteristics of needed future studies.

Sisto, F.↗
NASA NTRS1982

Natural frequency of rotating beams using non-rotating modes

A Lagrangian approach is formulated for predicting the rotating natural frequencies of a beam from the nonrotating modes and frequencies. Using the first two nonrotating mode shapes in one case and the first four such modes in the other case the frequencies of the rotating modes are calculated for a short tapered beam and a typical helicopter blade, respectively. In each case the beam is represented by lumped parameters. The number of mass points representing the beam and the accuracy of the calculated slopes of the nonrotating mode shapes at those points are both shown to affect the accuracy of the resulting frequencies, but the number of stations is shown to be more important.

Loewy, R. G.↗
NASA NTRS1992

Galactic disks, infall, and the global value of Omega

Stringent limits on the current rate of infall of satellite systems onto spiral galaxies are set on the basis of the thinness and coldness of Galactic disks. For infalling satellites on isotropically oriented circular orbits, it is shown that, due to scattering, the thermal energy gain of the disk exceeds the satellite energy loss from dynamical friction by a factor of 1.6, with 25 percent deposited in z motion and 75 percent in planar motions. It is found that no more than 4 percent of the Galactic mass inside the solar radius can have accreted within the last 5 billion years, or else its scale and its Toomre Q-parameter would exceed observed values. In standard cold-dark-matter-dominated models for the growth of structure with Omega sub tot of 1, the mass accreted in dark matter lumps rises faster than t exp 2/3 and would exceed 28 percent in the last 5 Gyr. It is proposed that heating from satellite infall accounts for a substantial fraction of the increase of velocity dispersion and scale height with age that is observed in the Galaxy.

Toth, G.↗
NASA NTRS1992

Structure redesign for improved dynamic response

The concepts of multivariable control design are used to redesign structures represented by lumped parameter models. When the mass is held constant, the changing of passive structural members is mathematically equivalent to an output feedback decentralized control problem. When the mass is also allowed to change, a generalization of the output feedback formulation is required. The design objective is to minimize the changes in the structure required to simultaneously satisfy inequality constraints on both the root-mean-square and absolute value of the dynamic response of each output. An alternative objective treated is to minimize the root-mean-square of the dynamic response subject to inequality constraints on the changes allowed in each structural member. Examples illustrate both procedures.

Skelton, R. E.↗
DOE OSTI2025

Understanding the Reaction of Nuclear Graphite with Molecular Oxygen

A thorough understanding of oxidation is important when considering the health and integrity of graphite components in graphite reactors. For the next generation of graphite reactors, HTGRs specifically, an unlikely air ingress has been deemed significant enough to have made its way into the licensing applications of many international licensing bodies. While a substantial body of literature exists on nuclear graphite oxidation in the presence of molecular oxygen and significant efforts have been made to characterize oxidation kinetics of various grades, the value of existing information is somewhat limited. Often, multiple competing processes, including reaction kinetics, mass transfer, and microstructural evolution, are lumped together into a single rate expression that limits the ability to translate this information to different conditions. This article reviews the reaction of graphite with molecular oxygen in terms of the reaction kinetics, gas transport, and microstructural evolution of graphite. It also presents the foundations of a model for the graphite-molecular oxygen reaction system that is kinetically independent of graphite grade, and is capable of describing both the bulk and local oxidation rates under a wide range of conditions applicable to air-ingress.

J. Kane, Joshua↗
NASA NTRS1992

Galaxies and gas in a cold dark matter universe

We use a combined gravity/hydrodynamics code to simulate the formation of structure in a random 22 Mpc cube of a cold dark matter universe. Adiabatic compression and shocks heat much of the gas to temperatures of 10 exp 6 - 10 exp 7 K, but a fraction of the gas cools radiatively to about 10 exp 4 K and condenses into discrete, highly overdense lumps. We identify these lumps with galaxies. The high-mass end of their baryonic mass function fits the form of the observed galaxy luminosity function. They retain independent identities after their dark halos merge, so gravitational clustering produces groups of galaxies embedded in relatively smooth envelopes of hot gas and dark matter. The galaxy correlation function is approximately an r exp -2.1 power law from separations of 35 kpc to 7 Mpc. Galaxy fluctuations are biased relative to dark matter fluctuations by a factor b about 1.5. We find no significant 'velocity bias' between galaxies and dark matter particles. However, virial analysis of the simulation's richest group leads to an estimated Omega of about 0.3, even though the simulation adopts Omega = 1.

Katz, Neal↗
DOE OSTI2020

A conceptual model for how to design for building envelope characteristics. Impact of thermal comfort intervals and thermal mass on commercial buildings in U.S. climates

The paper presents a simplified conceptual model for energy demand calculations based on building envelope characteristics, thermal mass and local climate. It is based on a network model and lumped analysis of the dynamic process. Characteristic parameters for the buildings are suggested; Driving temperature (DT), Driving temperature difference, (DTD), External Load Temperature (ELT), and Thermal Load Resistance (TLR). The Building Envelope Performance ( BEP 0 ), based on a controlled constant indoor temperature is introduced. Solution techniques using stable explicit forward differences based on analytical solutions are derived. The conceptual model has been used for mapping the Driving temperature difference and introduced two performance factors and . The first factor represents the effect of thermal comfort interval and thermal mass on the energy demand. The latter represents the ratio between cooling and heating energy demand. These three parameters and factors have been visualized on U.S. maps and enable a possibility to communicate the demand of energy, and cooling and the coupling to building characteristics, in a concise way.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1992

Semi-coupled flow and thermal analysis of the field joint during rapid pressurization of the redesigned solid rocket motor

A transient, semi-coupled, multi-dimensional thermal and flow analysis methodology was developed to predict the thermal/gas dynamic conditions in the field joint region of the Redesigned Solid Rocket Motor (RSRM). Transient temperature response, pressure history, and combustion gas flow rate (within the field joint region), were of principle interest, in the course of this study. The thermal environment in the field joint was modeled using SINDA, a finite difference based thermal network analyzer. The combustion gas flow boundary condition was generated using the FLAP code; this code performs a transient, lumped-parameter, control volume analysis to solve the mass, momentum, and energy conservation equations. The FLAP computer code was modified to account for erosion of the NBR insulation material, following ignition. An independent grid sensitivity study was conducted to determine an appropriate grid distribution near the wall. The predicted results, obtained using an optimum grid distribution and computer generated flow boundary condition, were compared with subscale test data.

Ghaffarian, Benny↗
NASA NTRS1981

A title-gap flow model for use in aerodynamic loads assessment of space shuttle thermal protection system: Parallel gap faces

The problem of predicting aerodynamic loads on the insulating tiles of the space shuttle thermal protection system (TPS) is discussed and seen to require a method for predicting pressure and mass flux in the gaps between tiles. A mathematical model of the tile-gap flow is developed, based upon a slow viscous (Stokes) flow analysis, and is verified against experimental data. The tile-gap pressure field is derived from a solution of the two-dimensional Laplace equation; the mass-flux vector is then calculated from the pressure gradient. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The flow model shows tile-gap mass flux to be very sensitive to the gap width indicating a need for coupling the TPS flow and tile displacement calculation. Analytical and experimental work to improve TPS flow predictions and a possible shuttle TPS hardware modification are recommended.

Dwoyer, D. L.↗