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At least 217 records · Page 12

The distribution of cD galaxy peculiar velocities

A modified version of a cluster evolution computer code first described in Richstone and Malumuth (1983) and Malumuth and Richstone (1984) to investigate the distributon of cD galaxy peculiar velocities and positions relative to the center, for a sample of cDs formed through mergers in a virialized cluster. This distribution is compared to an observed distribution of 19 cD galaxies to test whether cD galaxies with large peculiar velocities could have been formed in virialized clusters. At the time of their formation the cD galaxies have a distribution of peculiar velocities similar to that of the observed cD galaxies. By the end of the simulations the cD galaxies were dragged to the center of the cluster by dynamical friction, and the distribution of peculiar velocities is inconsistent with the observed distribution. The typical cD galaxy has nine mergers and is 5 solar luminosities. This is in comparison with the observed luminosity of Morgan poor clusters of 7 solar luminosities.

Malumuth, Eliot M.↗

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Cho, Soo-Yong↗

Navier-Stokes analysis of turbine flowfield and external heat transfer

An explicit 2D Navier-Stokes code has been modified and used to analyze the aerodynamics and heat transfer of a transonic turbine cascade. This code is based on a four-stage Runge-Kutta scheme. An algebraic Reynolds stress model (ARSM) and two versions of low Reynolds number (LRN) two-equation turbulence models, Chien's (1982) LRN k-epsilon model and Coakley's (1983) LRN q-omega model, have been employed in the computations. The surface pressure distributions and wake profiles are predicted well by all the models. The k-epsilon model and the k-epsilon/ARSM model yield better predictions of heat transfer than the q-omega model. The k-epsilon/ARSM solutions show some significant, though not dramatic, differences in the predicted skin friction coefficients, heat transfer rates, and performance parameters, as compared to the k-epsilon model. The predicted semiwake width is consistent with the measurement and correlation.

Luo, J.↗

Three-dimensional compressible laminar boundary layers on sharp and blunt circular cones at angle of attack

A method for solving the three-dimensional compressible laminar boundary layer equations for the case of a circular cone and a sphere-cone body at an angle of attack is presented. The governing equations are modified by a similarity type transformation and then transformed into a Crocco-type form. The resulting set of equations is solved simultaneously by an iterative method using an implicit finite difference scheme by means of an efficient algorithm for equations of tridiagonal form. The effects of streamline swallowing on a sharp cone are included by introducing the true inviscid edge conditions at the distance from the wall equal to the boundary layer thickness. The validity of the approach was established by comparison of the computational results with similar results by other methods and with experimental data. It was concluded that at sufficiently high Mach number and moderate to large angles of attack, the streamline swallowing effects on a sharp cone result in higher values of skin friction and heat transfer as compared with the classical results for constant entropy.

Popinski, Z.↗

Study of Critical Heat Flux and Two-Phase Pressure Drop Under Reduced Gravity

The design of the two-phase flow systems which are anticipated to be utilized in future spacecraft thermal management systems requires a knowledge of two-phase flow and heat transfer phenomena in reduced gravities. This program was funded by NASA headquarters in response to NRA-91-OSSA-17 and was managed by Lewis Research Center. The main objective of this program was to design and construct a two-phase test loop, and perform a series of normal gravity and aircraft trajectory experiments to study the effect of gravity on the Critical Heat Flux (CHF) and onset of instability. The test loop was packaged on two aircraft racks and was also instrumented to generate data for two-phase pressure drop. The normal gravity tests were performed with vertical up and downflow configurations to bound the effect of gravity on the test parameters. One set of aircraft trajectory tests was performed aboard the NASA DC-9 aircraft. These tests were mainly intended to evaluate the test loop and its operational performance under actual reduced gravity conditions, and to produce preliminary data for the test parameters. The test results were used to demonstrate the applicability of the normal gravity models for prediction of the two-phase friction pressure drop. It was shown that the two-phase friction multipliers for vertical upflow and reduced gravity conditions can be successfully predicted by the appropriate normal gravity models. Limited critical heat flux data showed that the measured CHF under reduced gravities are of the same order of magnitude as the test results with vertical upflow configuration. A simplified correlation was only successful in predicting the measured CHF for low flow rates. Instability tests with vertical upflow showed that flow becomes unstable and critical heat flux occurs at smaller powers when a parallel flow path exists. However, downflow tests and a single reduced gravity instability experiment indicated that the system actually became more stable with a parallel single-phase flow path. Several design modifications have been identified which will improve the system performance for generating reduced gravity data. The modified test loop can provide two-phase flow data for a range of operating conditions and can serve as a test bed for component evaluation.

Abdollahian, Davood↗

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗

High-Strain-Rate Compression Testing of Ice

In the present study a modified split Hopkinson pressure bar (SHPB) was employed to study the effect of strain rate on the dynamic material response of ice. Disk-shaped ice specimens with flat, parallel end faces were either provided by Dartmouth College (Hanover, NH) or grown at Case Western Reserve University (Cleveland, OH). The SHPB was adapted to perform tests at high strain rates in the range 60 to 1400/s at test temperatures of -10 and -30 C. Experimental results showed that the strength of ice increases with increasing strain rates and this occurs over a change in strain rate of five orders of magnitude. Under these strain rate conditions the ice microstructure has a slight influence on the strength, but it is much less than the influence it has under quasi-static loading conditions. End constraint and frictional effects do not influence the compression tests like they do at slower strain rates, and therefore the diameter/thickness ratio of the samples is not as critical. The strength of ice at high strain rates was found to increase with decreasing test temperatures. Ice has been identified as a potential source of debris to impact the shuttle; data presented in this report can be used to validate and/or develop material models for ice impact analyses for shuttle Return to Flight efforts.

Shazly, Mostafa↗

Experimental Investigation of Subsonic Turbulent Boundary Layer Flow Over a Wall-Mounted Axisymmetric Hill

An important goal for modern fluid mechanics experiments is to provide datasets which present a challenge for Computational Fluid Dynamics simulations to reproduce. Such "CFD validation experiments" should be well-characterized and well-documented, and should investigate flows which are difficult for CFD to calculate. It is also often convenient for the experiment to be challenging for CFD in some aspects while simple in others. This report is part of the continuing documentation of a series of experiments conducted to characterize the flow around an axisymmetric, modified-cosine-shaped, wall-mounted hill named "FAITH" (Fundamental Aero Investigates The Hill). Computation of this flow is easy in some ways - subsonic flow over a simple shape - while being complex in others - separated flow and boundary layer interactions. The primary set of experiments were performed on a 15.2 cm high, 45.7 cm base diameter machined aluminum model that was tested at mean speeds of 50 m/s (Reynolds Number based on height = 500,000). The ratio of model height to boundary later height was approximately 3. The flow was characterized using surface oil flow visualization, Cobra probe to determine point-wise steady and unsteady 3D velocities, Particle Image Velocimetry (PIV) to determine 3D velocities and turbulence statistics along specified planes, Pressure Sensitive Paint (PSP) to determine mean surface pressures, and Fringe Imaging Skin Friction (FISF) to determine surface skin friction magnitude and direction. A set of pathfinder experiments were also performed in a water channel on a smaller scale (5.1 cm high, 15.2 cm base diameter) sintered nylon model. The water channel test was conducted at a mean test section speed of 3 cm/s (Reynolds Number of 1500), but at the same ratio of model height to boundary layer thickness. Dye injection from both the model and an upstream rake was used to visualize the flow. This report summarizes the experimental set-up, techniques used, and data acquired. It also describes some details of the dataset that is being constructed for use by other researchers, especially the CFD community.

fluid machanics cfd validation wind tunnel↗

MSFC cryogenic turbopump bearing tester results and analysis

A full scale High Pressure Oxidizer Turbopump (HPOTP) bearing tester has been developed, and an existing test stand modified, to simulate turbopump operating conditions for Space Shuttle Main Engine HPOTP design. Following a description of test facilities and procedures, design certification and calibration tests, and tests at a moderate axial load, are discussed. Results show that a bearing life of about 4500 seconds is comparable to the life experienced in the engine pump at nominal high power level operating conditions, and that although increased coolant flow increased fluid viscous work and bearing loads, a net decrease in bearing temperature was noted. Increased coolant flow is found to improve bearing cooling for marginal conditions, and bearing temperatures are shown to become more sensitive to coolant flow as shaft speed is increased. For the 6.4 lbs/s test conditions, the heat generated in a bearing pair is determined to be about 67 percent viscous work and 33 percent contact friction.

Dolan, F. J.↗

Numerical study to assess sulfur hexafluoride as a medium for testing multielement airfoils

A methodology is described for computing viscous flows of air and sulfur hexafluoride (SF6). The basis is an existing flow solver that calculates turbulent flows in two dimensions on unstructured triangular meshes. The solver has been modified to incorporate the thermodynamic model for SF6 and used to calculate the viscous flow over two multielement airfoils that have been tested in a wind tunnel with air as the test medium. Flows of both air and SF6 at a free-stream Mach number of 0.2 and a Reynolds number of 9 x 10(exp 6) are computed for a range of angles of attack corresponding to the wind-tunnel test. The computations are used to investigate the suitability of SF6 as a test medium in wind tunnels and are a follow-on to previous computations for single-element airfoils. Surface-pressure, lift, and drag coefficients are compared with experimental data. The effects of heavy gas on the details of the flow are investigated based on computed boundary-layer and skin-friction data. In general, the predictions in SF6 vary little from those in air. Within the limitations of the computational method, the results presented are sufficiently encouraging to warrant further experiments.

Bonhaus, Daryl L.↗

Tuning Neural Network Models for Improved Prediction of Boundary Layer Transition

Boundary layer transition can strongly impact flight vehicle performance as it influences surface skin friction and aerodynamic heating, making accurate transition prediction a key to designing next generation aircraft. Artificial neural networks (ANNs) have shown promise toward predicting laminar-turbulent transition based on linear stability correlations. The computational efficiency of ANNs and the substantially reduced user involvement in relation to direct computations based on the linear stability theory (LST) makes them an attractive methodology for integrating the LST based correlations in computational fluid dynamics codes. Tollmien-Schlichting (TS) waves correspond to the dominant transition mechanism in 2D or weakly 3D subsonic boundary layers, such as those encountered in general aviation applications. Improvements to neural network model accuracy in predicting the amplification rates of TS instability waves have been investigated by leveraging recent machine learning developments in conjunction with surrogate optimization techniques and via suitable augmentation of the data used to train the networks. The optimized models trained on the modified dataset reduced the average transition location errors on different airfoils at several flow conditions by 51% of the original manually-tuned network’s errors on the same flow cases. The actual transition locations were derived from the Langley Stability and Transition Analysis Code (LASTRAC).

Machine Learning↗

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Carlson, John R.↗

The Improvement of Ion Plated Ag and Au Film Adherence to Si3N4 and SiC Surfaces for Increased Tribological Performance

A modified dc-diode plating system, utilizing a metallic screen cage as a cathode and referred as SCREEN CAGE ION PLATING (SCIP), is used to deposit Ag and Au lubricating films on Si3N4 and SiC surfaces. When deposition is performed in Ar or N2, glow discharge, the surface displays poor adhesive strength (less than 5 MPa). A dramatic increase in adhesive strength (less than 80 MPa) is achieved when plating is performed in a reactive 50% 02 + 50% Ar glow discharge. The excited/ionized oxygen species (O2(+)/O(+) in the glow discharge contribute to the oxidation of the Si3N4 or SiC surfaces as determined by X-ray Photoelectron Spectroscopy (XTS) depth profiling. The reactively sputter-oxidized S3N4 or SiC surfaces and the activated-oxidized-metastable Ag or Au species formed in the plasma cooperatively contribute to the increased adherence. As a result, the linear thermal expansion coefficient mismatch at the interface is reduced. These lubricating Ag and Au films under sliding conditions reduce the friction coefficient by a factor of 2-1/2 to 4.

Spalvins, Talivaldis↗

Affect of Brush Seals on Wave Rotor Performance Assessed

The NASA Lewis Research Center's experimental and theoretical research shows that wave rotor topping can significantly enhance gas turbine engine performance levels. Engine-specific fuel consumption and specific power are potentially enhanced by 15 and 20 percent, respectively, in small (e.g., 400 to 700 hp) and intermediate (e.g., 3000 to 5000 hp) turboshaft engines. Furthermore, there is potential for a 3- to 6-percent specific fuel consumption enhancement in large (e.g., 80,000 to 100,000 lbf) turbofan engines. This wave-rotor-enhanced engine performance is accomplished within current material-limited temperature constraints. The completed first phase of experimental testing involved a three-port wave rotor cycle in which medium total pressure inlet air was divided into two outlet streams, one of higher total pressure and one of lower total pressure. The experiment successfully provided the data needed to characterize viscous, partial admission, and leakage loss mechanisms. Statistical analysis indicated that wave rotor product efficiency decreases linearly with the rotor to end-wall gap, the square of the friction factor, and the square of the passage of nondimensional opening time. Brush seals were installed to further minimize rotor passage-to-cavity leakage. The graph shows the effect of brush seals on wave rotor product efficiency. For the second-phase experiment, which involves a four-port wave rotor cycle in which heat is added to the Brayton cycle in an external burner, a one-dimensional design/analysis code is used in conjunction with a wave rotor performance optimization scheme and a two-dimensional Navier-Stokes code. The purpose of the four-port experiment is to demonstrate and validate the numerically predicted four-port pressure ratio versus temperature ratio at pressures and temperatures lower than those that would be encountered in a future wave rotor/demonstrator engine test. Lewis and the Allison Engine Company are collaborating to investigate wave rotor integration in an existing turboshaft engine. Recent theoretical efforts include simulating wave rotor dynamics (e.g., startup and load-change transient analysis), modifying the one-dimensional wave rotor code to simulate combustion internal to the wave rotor, and developing an analytical wave rotor design/analysis tool based on macroscopic balances for parametric wave rotor/engine analysis.

Source record↗

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

Surface and Flow Field Measurements on the FAITH Hill Model

A series of experimental tests, using both qualitative and quantitative techniques, were conducted to characterize both surface and off-surface flow characteristics of an axisymmetric, modified-cosine-shaped, wall-mounted hill named "FAITH" (Fundamental Aero Investigates The Hill). Two separate models were employed: a 6" high, 18" base diameter machined aluminum model that was used for wind tunnel tests and a smaller scale (2" high, 6" base diameter) sintered nylon version that was used in the water channel facility. Wind tunnel and water channel tests were conducted at mean test section speeds of 165 fps (Reynolds Number based on height = 500,000) and 0.1 fps (Reynolds Number of 1000), respectively. The ratio of model height to boundary later height was approximately 3 for both tests. Qualitative techniques that were employed to characterize the complex flow included surface oil flow visualization for the wind tunnel tests, and dye injection for the water channel tests. Quantitative techniques that were employed to characterize the flow included Cobra Probe to determine point-wise steady and unsteady 3D velocities, Particle Image Velocimetry (PIV) to determine 3D velocities and turbulence statistics along specified planes, Pressure Sensitive Paint (PSP) to determine mean surface pressures, and Fringe Imaging Skin Friction (FISF) to determine surface skin friction (magnitude and direction). This initial report summarizes the experimental set-up, techniques used, data acquired and describes some details of the dataset that is being constructed for use by other researchers, especially the CFD community. Subsequent reports will discuss the data and their interpretation in more detail

Bell, James H.↗

The Effect of Composition on the Surface Finish of PS400: A New High Temperature Solid Lubricant Coating

A new composite, multi-constituent, solid lubricant coating, NASA PS400, developed for high temperature tribological applications, exhibits a smoother surface finish after grinding and polishing than its predecessors PS200 and PS300. In this paper, the baseline composition of PS400 is modified to investigate each individual constituent s role on the achievable surface finish through a series of coating deposition, grinding, and polishing experiments. Furthermore, to explore the limits of compositional tailoring for improved tribological performance, several PS400 coatings were doped with additional solid lubricants (graphite, MoS2 and BN) and tribologically tested. The test results clearly showed that, compared to PS300 coatings, PS400 achieves a smoother surface finish via a reduced lubricant content. Coatings prepared with higher than the baseline level (10 wt%) of lubricants exhibited higher final surface roughness than the earlier generation PS300 coatings. Reducing or eliminating the one or both lubricants (fluorides or silver) did not further improve the surface finish suggesting that the current composition of PS400 is near optimal with respect to surface finish. Lastly, attempts to improve the poor initial room temperature tribological behavior of PS400 via the addition of traditional solid lubricants were unsuccessful. Based upon this work and earlier results it is expected that future research will concentrate on developing methods to produce a lubricious glaze on the rubbing surface during break in to ensure that low friction and wear are rapidly achieved.

DellaCorte, Christopher↗

Mechanistic Models of Friction Stir Welding

Friction stir welding is a welding process developed at The Welding Institute (TWI) in England. The method uses very large strain plastic deformation of the material to join two pieces of metal together. The material is deformed using a tool which is forced between the two pieces which rotates causing a bond. Beyond this, very little is actually known although many people working in the field are willing to speculate on the detailed mechanisms involved. Some measurements made using sacrificial thermocouples at the weld joint indicate that the maximum temperature during the weld process is on the order of 370C - well below the melting temperature of the material. However, at this temperature, the material properties are highly temperature dependent, and the yield stress is approximately an order of magnitude less at this temperature than it is at room temperature. As expected, there are many interpretations of the physical mechanisms occurring during the weld process. Although there is very little published concerned with FSW, some of the anecdotal theories will be described. One describes the primary mechanism as frictional heating at the front of the tool caused by slip between the tool and the material. At elevated temperatures, the weld material becomes soft and deforms around the tool but not essentially altered by the tool rotation, similar to an extrusion. As the material meets again at the rear of the tool, the temperatures and pressures are sufficient to cause the material to bond. All other structures seen are secondary and unimportant. Another theory examined last summer at NASA's Marshall Space Flight Center (MSFC) was that there was no slip between the tool and the material resulting in a rotating mass of plastic weld material traveling at a variety of angular velocities - the greatest at the tool surface diminishing to zero at the outer edge of the plastic mass surrounding the tool. This conceptual model was followed by simplified calculations which showed that the balance of moments through the weld plug was not possible under steady state conditions and realistic temperature profiles. This led to some consideration of a quasi-steady oscillating process. Later when force measurements became available some models were modified and new ones were proposed.

Stewart, Michael B.↗