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At least 469 records · Page 26

Counterrotating-Shoulder Mechanism for Friction Stir Welding

A counterrotating-shoulder mechanism has been proposed as an alternative to the mechanism and fixtures used in conventional friction stir welding. The mechanism would internally react most or all of the forces and torques exerted on the workpiece, making it unnecessary to react the forces and torques through massive external fixtures. In conventional friction stir welding, a rotating pin tool is inserted into, and moved along, a weld seam. As the pin tool moves, it stirs together material from the opposite sides of the seam to form the weld. A large axial plunge force must be exerted upon the workpiece through and by the pin tool and a shoulder attached above the pin tool in order to maintain the pressure necessary for the process. The workpiece is secured on top of an anvil, which supports the workpiece against the axial plunge force and against the torque exerted by the pin tool and shoulder. The anvil and associated fixtures must be made heavy (and, therefore, are expensive) to keep the workpiece stationary. In addition, workpiece geometries must be limited to those that can be accommodated by the fixtures. The predecessor of the proposed counterrotating-shoulder mechanism is a second-generation, self-reacting tool, resembling a bobbin, that makes it possible to dispense with the heavy anvil. This tool consists essentially of a rotating pin tool with opposing shoulders. Although the opposing shoulders maintain the necessary pressure without need to externally apply or react a large plunge force, the torque exerted on the workpiece remains unreacted in the absence of a substantial external fixture. Depending on the RPM and the thickness of the workpiece, the torque can be large. The proposed mechanism (see figure) would include a spindle attached to a pin tool with a lower shoulder. The spindle would be coupled via splines to the upper one of three bevel gears in a differential drive. The middle bevel gear would be the power-input gear and would be coupled to the upper and lower bevel gears. The lower bevel gear would be attached to the upper shoulder and would slide and rotate freely over the spindle. The spindle would be fastened by its threaded upper end to an external submechanism that would exert axial tension on the spindle to load the workpiece in compression between the shoulders. By reducing or eliminating (relative to the use of a self reacting tool) the torque that must be reacted externally, the use of the proposed tool would reduce the tendency toward distortion or slippage of the workpiece. To begin a weld, the spindle would be inserted through a hole in the workpiece or run-on tab at the beginning of the seam and fastened to the loading submechanism. Rotation and axial loading would be increased gradually from zero and, after a time to be determined by trial and error, translation along the weld seam would be increased gradually from zero to a steady weld speed. The weld would be ended by running the mechanism off the workpiece or, if the lower shoulder were detachable, by detaching the lower shoulder from the spindle and pulling the pin tool out.

Nunes, Arthur C., Jr.↗

Experimental study of combustion in a turbulent free shear layer formed at a rearward facing step

A premixed propane-air flame is stabilized in a turbulent free shear layer formed at a rearward facing step. The mean and rms averages of the turbulent velocity flow field are determined by LDV for both reacting (equivalence ratio 0.57) and nonreacting flows (Reynolds number 15,000-37,000 based on step height). The effect of combustion is to shift the layer toward the recirculation zone and reduce the flame spread. For reacting flow, the growth rate is unchanged except very near the step. The probability density function of the velocity is bimodial near the origin of the reacting layer and single-peaked but often skewed elsewhere. Large-scale structures dominate the reacting shear layer. Measurements of their passing frequency from LDV are consistent with high-speed Schlieren movies of the reacting layer and indicate that the coalescence rate of the eddies in the shear layer is reduced by combustion.

Pitz, R. W.↗

Combustion in a turbulent mixing layer formed at a rearward-facing step

A premixed propane/air flame was stabilized in a turbulent mixing layer formed at a rearward-facing step. The mean and rms averages of the turbulent velocity flowfield were determined by laser velocimetry for both reacting (phi = 0.57) and nonreacting flows (Re = 15,000-37,000 based on step height). The reacting-flow was visualized by high-speed schlieren photography. Large-scale structures dominate the reacting mixing layer. The growth of the large-scale structures was tied to the propagation of the flame. The linear growth rate of the reacting mixing layer defined by the mean velocity profiles was unchanged by combustion but the virtual origin moves downstream. The reacting mixing layer boundaries based on the mean velocity profiles were shifted toward the recirculation zone and reattachment lengths were shortened by 30 percent. The edge of the flame controlled by the large-scale structure development propagated faster into the incoming reactants than the boundary of the mixing layer given by the mean velocity flowfield. Thus, the region of high velocity gradient did not coincide with the region of high reaction and heat transfer.

Pitz, R. W.↗

Amorphous metallic films in silicon metallization systems

The general objective was to determine the potential of amorphous metallic thin films as a means of improving the stability of metallic contacts to a silicon substrate. The specific objective pursued was to determine the role of nitrogen in the formation and the resulting properties of amorphous thin-film diffusion barriers. Amorphous metallic films are attractive as diffusion barriers because of the low atomic diffusivity in these materials. Previous investigations revealed that in meeting this condition alone, good diffusion barriers are not necessarily obtained, because amorphous films can react with an adjacent medium (e.g., Si, Al) before they recrystallize. In the case of a silicon single-crystalline substrate, correlation exists between the temperature at which an amorphous metallic binary thin film reacts and the temperatures at which the films made of the same two metallic elements react individually. Amorphous binary films made of Zr and W were investigated. Both react with Si individually only at elevated temperatures. It was confirmed that such films react with Si only above 700 C when annealed in vacuum for 30 min. Amorphous W-N films were also investigated. They are more stable as barriers between Al and Si than polycrystalline W. Nitrogen effectively prevents the W-Al reaction that sets in at 500 C with polycrystalline W.

Nicolet, M. A.↗

The combustion program at CTR

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct numerical simulation (DNS) appears to be one of the most attractive tools to use in addressing this problem. The general objective of DNS of reacting flows is to improve our knowledge of turbulent combustion but also to use this information for turbulent combustion models. For the foreseeable future, numerical simulation of the full three-dimensional governing partial differential equations with variable density and transport properties as well as complex chemistry will remain intractable; thus, various levels of simplification will remain necessary. On one hand, the requirement to simplify is not necessarily a handicap: numerical simulations allow the researcher a degree of control in isolating specific physical phenomena that is inaccessible in experiments. CTR has pursued an intensive research program in the field of DNS for turbulent reacting flows since 1987. DNS of reacting flows is quite different from DNS of non-reacting flows: without reaction, the equations to solve are clearly the five conservation equations of the Navier Stokes system for compressible situations (four for incompressible cases), and the limitation of the approach is the Reynolds number (or in other words the number of points in the computation). For reacting flows, the choice of the equations, the species (each species will require one additional conservation equation), the chemical scheme, and the configuration itself is more complex.

Poinsot, Thierry J.↗

Influence of Geometry and Flow Variations on NO Formation in the Quick Mixer of a Staged Combustor

Staged combustion, such as Rich-Burn/Quick-Mix/Lean-Burn (RQL), is a viable strategy to meet nitric oxide (NO) emission goals for both stationary and propulsion gas turbine engines. A critical element of the design is the quick mixer section where the potential for NO production is high. While numerical calculations of the quick mixer under reacting conditions have been conducted, the hostile environment and lack of appropriate diagnostics have, to date, precluded experimental probing of the reacting case. As an alternative to understanding the effect of geometry and flow variations on the production of NO in the quick mixer, the present paper presents (1) a series of non-reacting parametric studies, and (2) a computational method to extrapolate the results of the non-reacting experiments to reacting conditions. The results show that the rate of NO production is highest in the immediate vicinity of the injection plane. For a given momentum flux ratio between the jets and mainstream, the most effective mixing geometry is that which mixes effectively in both (1) the plane of injection, and (2) the wall regions downstream of the plan of injection. The tailoring of the mixing is key to minimize the NO formed. As a result, the best overall mixer with respect to the minimization of NO production may depend on the system specific characteristics of the particular application.

Hatch, M. S.↗

Association reactions at low pressure. 5: The CH3(+)/HCN system. A final word?

The reaction of the methyl cation with hydrogen cyanide is revisited. We have confidence that we have resolved a long standing apparent contradiction of experimental results. A literature history is presented along with one new experiment and a re-examination of an old experiment. In this present work it is shown that all of the previous studies had made consistent observations. Yet, each of the previous studies failed to observe all of the information present. The methyl cation does react with HCN by radiative association, a fact which had been in doubt. The product ions formed in the two-body and three-body processes react differently with HCN. The collisionally stabilized association product formed by a three-body mechanism, does not react with HCN and is readily detected in the experiments. The radiatively stabilized association product, formed by a slow two-body reaction, is not detected because it reacts with HCN by a fast proton transfer reaction forming the protonated HCN ion. Previous studies either 'lost' this product in the extremely large protonated HCN signal that is always present when HCN is used, or discounted it for various reasons. We have been able to show by ion cyclotron resonance (ICR) techniques (both FT-ICR and tandem ICR-dempster-ICR) that the radiative association product does react with the HCN to form the protonated HCN ion.

Anicich, Vincent G.↗

Minimizing Load Effects on NA4 Gear Vibration Diagnostic Parameter

NA4 is a vibration diagnostic parameter, developed by researchers at NASA Glenn Research Center, for health monitoring of gears in helicopter transmissions. The NA4 reacts to the onset of gear pitting damage and continues to react to the damage as it spreads. This research also indicates NA4 reacts similarly to load variations. The sensitivity of NA4 to load changes will substantially affect its performance on a helicopter gearbox that experiences continuously changing load throughout its flight regimes. The parameter NA4 has been used to monitor gear fatigue tests at constant load. At constant load, NA4 effectively detects the onset of pitting damage and tracks damage severity. Previous research also shows that NA4 reacts to changes in load applied to the gears in the same way it reacts to the onset of pitting damage. The method used to calculate NA4 was modified to minimize these load effects. The modified NA4 parameter was applied to four sets of experimental data. Results indicate the modified NA4 is no longer sensitive to load changes, but remains sensitive to pitting damage.

Dempsey, Paula J.↗

Gimballed Shoulders for Friction Stir Welding

In a proposed improvement of tooling for friction stir welding, gimballed shoulders would supplant shoulders that, heretofore, have been fixedly aligned with pins. The proposal is especially relevant to self-reacting friction stir welding. Some definitions of terms, recapitulated from related prior NASA Tech Briefs articles, are prerequisite to a meaningful description of the proposed improvement. In friction stir welding, one uses a tool that includes (1) a rotating shoulder on top (or front) of the workpiece and (2) a pin that rotates with the shoulder and protrudes from the shoulder into the depth of the workpiece. In conventional friction stir welding, the main axial force exerted by the tool on the workpiece is reacted through a ridged backing anvil under (behind) the workpiece. When conventional friction stir welding is augmented with an auto-adjustable pin-tool (APT) capability, the depth of penetration of the pin into the workpiece is varied in real time by a position- or forcecontrol system that extends or retracts the pin as needed to obtain the desired effect. In self-reacting (also known as self-reacted) friction stir welding as practiced heretofore, there are two shoulders: one on top (or front) and one on the bottom (or back) of the workpiece. In this case, a threaded shaft protrudes from the tip of the pin to beyond the back surface of the workpiece. The back shoulder is held axially in place against tension by a nut on the threaded shaft. Both shoulders rotate with the pin and remain aligned coaxially with the pin. The main axial force exerted on the workpiece by the tool and front shoulder is reacted through the back shoulder and the threaded shaft into the friction-stir-welding machine head, so that a backing anvil is no longer needed. A key transmits torque between the bottom shoulder and the threaded shaft, so that the bottom shoulder rotates with the shaft. This concludes the prerequisite definitions of terms.

Carter, Robert↗

Monte Carlo Computational Modeling of Atomic Oxygen Interactions

Computational modeling of the erosion of polymers caused by atomic oxygen in low Earth orbit (LEO) is useful for determining areas of concern for spacecraft environment durability. Successful modeling requires that the characteristics of the environment such as atomic oxygen energy distribution, flux, and angular distribution be properly represented in the model. Thus whether the atomic oxygen is arriving normal to or inclined to a surface and whether it arrives in a consistent direction or is sweeping across the surface such as in the case of polymeric solar array blankets is important to determine durability. When atomic oxygen impacts a polymer surface it can react removing a certain volume per incident atom (called the erosion yield), recombine, or be ejected as an active oxygen atom to potentially either react with other polymer atoms or exit into space. Scattered atoms can also have a lower energy as a result of partial or total thermal accommodation. Many solutions to polymer durability in LEO involve protective thin films of metal oxides such as SiO2 to prevent atomic oxygen erosion. Such protective films also have their own interaction characteristics. A Monte Carlo computational model has been developed which takes into account the various types of atomic oxygen arrival and how it reacts with a representative polymer (polyimide Kapton H) and how it reacts at defect sites in an oxide protective coating, such as SiO2 on that polymer. Although this model was initially intended to determine atomic oxygen erosion behavior at defect sites for the International Space Station solar arrays, it has been used to predict atomic oxygen erosion or oxidation behavior on many other spacecraft components including erosion of polymeric joints, durability of solar array blanket box covers, and scattering of atomic oxygen into telescopes and microwave cavities where oxidation of critical component surfaces can take place. The computational model is a two dimensional model which has the capability to tune the interactions of how the atomic oxygen reacts, scatters, or recombines on polymer or nonreactive surfaces. In addition to the specification of atomic oxygen arrival details, a total of 15 atomic oxygen interaction parameters have been identified as necessary to properly simulate observed interactions and resulting polymer erosion that have been observed in LEO. The tuning of the Monte Carlo model has been accomplished by adjusting interaction parameters so the erosion patterns produced by the model match those from several actual LEO space experiments. Surface texturing in LEO can also be predicted by the model. Such comparison of space tests with ground laboratory experiments have enabled confidence in ground laboratory lifetime prediction of protected polymers. Results of Monte Carlo tuning, examples of surface texturing and undercutting erosion prediction, and several examples of how the model can be used to predict other LEO and Mars orbital space results are presented.

Monte Carlo Modeling↗

Monte Carlo Computational Modeling of Atomic Oxygen Interactions

Computational modeling of the erosion of polymers caused by atomic oxygen in low Earth orbit (LEO) is useful for determining areas of concern for spacecraft environment durability. Successful modeling requires that the characteristics of the environment such as atomic oxygen energy distribution, flux, and angular distribution be properly represented in the model. Thus whether the atomic oxygen is arriving normal to or inclined to a surface and whether it arrives in a consistent direction or is sweeping across the surface such as in the case of polymeric solar array blankets is important to determine durability. When atomic oxygen impacts a polymer surface it can react removing a certain volume per incident atom (called the erosion yield), recombine, or be ejected as an active oxygen atom to potentially either react with other polymer atoms or exit into space. Scattered atoms can also have a lower energy as a result of partial or total thermal accommodation. Many solutions to polymer durability in LEO involve protective thin films of metal oxides such as SiO2 to prevent atomic oxygen erosion. Such protective films also have their own interaction characteristics. A Monte Carlo computational model has been developed which takes into account the various types of atomic oxygen arrival and how it reacts with a representative polymer (polyimide Kapton H) and how it reacts at defect sites in an oxide protective coating, such as SiO2 on that polymer. Although this model was initially intended to determine atomic oxygen erosion behavior at defect sites for the International Space Station solar arrays, it has been used to predict atomic oxygen erosion or oxidation behavior on many other spacecraft components including erosion of polymeric joints, durability of solar array blanket box covers, and scattering of atomic oxygen into telescopes and microwave cavities where oxidation of critical component surfaces can take place. The computational model is a two dimensional model which has the capability to tune the interactions of how the atomic oxygen reacts, scatters, or recombines on polymer or nonreactive surfaces. In addition to the specification of atomic oxygen arrival details, a total of 15 atomic oxygen interaction parameters have been identified as necessary to properly simulate observed interactions and resulting polymer erosion that have been observed in LEO. The tuning of the Monte Carlo model has been accomplished by adjusting interaction parameters so the erosion patterns produced by the model match those from several actual LEO space experiments. Surface texturing in LEO can also be predicted by the model. Such comparison of space tests with ground laboratory experiments have enabled confidence in ground laboratory lifetime prediction of protected polymers. Results of Monte Carlo tuning, examples of surface texturing and undercutting erosion prediction, and several examples of how the model can be used to predict other LEO and Mars orbital space results are presented.

Atomic Oxygen↗

A Computational Study of Plume Modeling for Space Launch System Abort Scenarios

A series of viscous CFD simulations depicting Space Launch System (SLS) post Mode-1abort scenarios are conducted and analyzed. The primary purpose of these simulations is to study the effect of launch abort vehicle attitude control motor (ACM) and abort motor(AM) plume modeling fidelity on the drag of the aborted core stage. The simulations are first conducted with a fully-coupled, multi-species and chemically reacting model for the freestream gases and the solid rocket abort motor combustion products. Following this, equivalent species are created for the ACM and AM exhaust gases. These equivalent species aim to provide near the same results for core stage drag as the chemically reacting model at a significantly lower computational cost. Finally, the exhaust gases are modeled as calorically perfect air. It was concluded that under most scenarios, both the equivalent species and the perfect air models predict the drag of the aborted core stage sufficiently close to that predicted by the chemically reacting simulations. In these cases, the flow and geometry conditions did not induce significant changes in the composition of the ‘true’ exhaust gas via afterburning of the combustion products. For cases where this was not the case, the properties of the essentially frozen equivalent species and perfect air models deviated from the true mixture, yielding unsatisfactory results. Finally, the accuracy improvements by using the chemically reacting model are weighed against the significant increase in associated computational costs. It was found that the simplified exhaust gas models are at least 4 times less expensive than the chemically reacting model. This may justify the judicious use of these simple models in future work.

CFD↗

A Computational Study of Plume Modeling for Space Launch System Abort Scenarios

A series of viscous CFD simulations depicting Space Launch System (SLS) post Mode-1abort scenarios are conducted and analyzed. The primary purpose of these simulations is to study the effect of launch abort vehicle attitude control motor (ACM) and abort motor(AM) plume modeling fidelity on the drag of the aborted core stage. The simulations are first conducted with a fully-coupled, multi-species and chemically reacting model for the freestream gases and the solid rocket abort motor combustion products. Following this, equivalent species are created for the ACM and AM exhaust gases. These equivalent species aim to provide near the same results for core stage drag as the chemically reacting model at a significantly lower computational cost. Finally, the exhaust gases are modeled as calorically perfect air. It was concluded that under most scenarios, both the equivalent species and the perfect air models predict the drag of the aborted core stage sufficiently close to that predicted by the chemically reacting simulations. In these cases, the flow and geometry conditions did not induce significant changes in the composition of the ‘true’ exhaust gas via afterburning of the combustion products. For cases where this was not the case, the properties of the essentially frozen equivalent species and perfect air models deviated from the true mixture, yielding unsatisfactory results. Finally, the accuracy improvements by using the chemically reacting model are weighed against the significant increase in associated computational costs. It was found that the simplified exhaust gas models are at least 4 times less expensive than the chemically reacting model. This may justify the judicious use of these simple models in future work.

CFD↗

A computational investigation of flow losses in a supersonic combustor

This computational investigation provides a detailed comparative study of both non-reacting and reacting supersonic combustor flow-fields and attendant flow losses. Three different injection configurations in the same combustor are examined; a swept-sided ramp with base hydrogen injection, a straight ramp with base hydrogen injection and a thirty-degree downstream directed wall jet. Detailed comparisons are made with available reacting experimental data for the swept and the unswept ramps. A seven reaction, seven species reaction model as well as a global (one reaction) model are used for all three reacting cases. Relative performance (as measured by thrust) of all cases are described. Details of the flow, mixing, and combustion processes are discussed.

Riggins, David W.↗

Nonequilibrium effects on the aerothermodynamics of transatmospheric and aerobraking vehicles

A 3D CFD algorithm is used to study the effect of thermal and chemical nonequilibrium on slender and blunt body aerothermodynamics. Both perfect gas and reacting gas air models are used to compute the flow over a generic transatmospheric vehicle and a proposed lunar transfer vehicle. The reacting air is characterized by a translational-rotational temperature and a vibrational-electron-electronic temperature and includes eight chemical species. The effects of chemical reaction, vibrational excitation, and ionization on lift-to-drag ratio and trim angle are investigated. Results for the NASA Ames All-body Configuration show a significant difference in center of gravity location for a reacting gas flight case when compared to a perfect gas wind tunnel case at the same Mach number, Reynolds number, and angle of attack. For the same center of gravity location, the wind tunnel model trims at lower angle of attack than the full-scale flight case. Nonionized and ionized results for a proposed lunar transfer vehicle compare well to computational results obtained from a previously validated reacting gas algorithm. Under the conditions investigated, effects of weak ionization on the heat transfer and aerodynamic coefficients were minimal.

Hassan, Basil↗

Reaction of Ta thin film with single crystalline (001) beta-SiC

The reaction between a sputtered-deposited Ta film (320 nm thick) and a single crystalline (001) beta-SiC substrate induced by vacuum annealing at temperatures of 600-1200 C for 1 h (30 min at 1100 C) is investigated by 3 MeV He(+2) backscattering spectrometry, x-ray diffraction, secondary ion mass spectrometry, and transmission and scanning electron microscopies. No significant reaction is observed at 800 C or at lower tempertures. At 900 C, the main product phases are Ta2C and carbon-stabilized Ta5Si3. A minor amount of unreacted Ta is also present. After annealing at 1000 C, all the tantalum has reacted; the reaction zone possesses a multilayered structure of beta-SiC/TaC/carbon-stabilized Ta5Si3/alpha-Ta5Si3/Ta2C. The diffusion path at 1000 C is plotted on the isothermal section of the Ta-Si-C phase diagram. At 1100 C, the reacted layer has an interface with the SiC substrate that is still quite flat but has a rough surface due to the formation of macroscopic voids within the reacted layer. The equilibrium products predicted by the phase diagram are TaC and TaSi2. This final state is reached by annealing at 1200 C for 1 h. At that point, the reacted layer has a latterally very uneven structure and morphology.

Chen, J. S.↗

Influence of Geometry and Flow Variation on Jet Mixing and NO Formation in a Model Staged Combustor Mixer with Eight Orifices

A series of non-reacting parametric experiments was conducted to investigate the effect of geometric and flow variations on mixing of cold jets in an axis-symmetric, heated cross flow. The confined, cylindrical geometries tested represent the quick mix region of a Rich-Burn/Quick-Mix/Lean-Burn (RQL) combustor. The experiments show that orifice geometry and jet to mainstream momentum-flux ratio significantly impact the mixing characteristic of jets in a cylindrical cross stream. A computational code was used to extrapolate the results of the non-reacting experiments to reacting conditions in order to examine the nitric oxide (NO) formation potential of the configurations examined. The results show that the rate of NO formation is highest immediately downstream of the injection plane. For a given momentum-flux ratio, the orifice geometry that mixes effectively in both the immediate vicinity of the injection plane, and in the wall regions at downstream locations, has the potential to produce the lowest NO emissions. The results suggest that further study may not necessarily lead to a universal guideline for designing a low NO mixer. Instead, an assessment of each application may be required to determine the optimum combination of momentum-flux ratio and orifice geometry to minimize NO formation. Experiments at reacting conditions are needed to verify the present results.

Samuelsen, G. S.↗

The Deontic Transaction Model in Multi-Agent Normative Systems

In the area of multi-agent systems, much research is devoted to the coordination of the agents. There exist several issues, two of which are summarized. The first is that, although agents are said to be autonomous, they always react in a predictable way to each message, and they cannot decide to violate the conventions that are hard-wired into the protocol. In fact, there might be circumstances in which the agent violates a convention in order to realize a private goal that it considers to be more important. Another issue is that, if the protocols that agents use to react to the environment are fixed, they have no way to respond to changes. However, an important characteristic of agents is that they eon react to a changing environment. Although transaction models ([BOH92], [GR93]) evolved from the database domain, they establish a general execution paradigm that ideally covers all the subsystems invoked in a sequence of transactions. So transaction models apply to multi-agent systems. Recently, some research has been devoted to overcoming the limitations of the traditional transaction models which are suitable for conventional systems and focus on system integrity, e,g., [SJ97]. Here we solve above issues by turning to a deontic concept: obligation. In multi-agent systems, agents interact with each other according to norms, We use deontic logic ([And58], [Aqv84], [B C96], [JS94], [MW93]) to model norms. Here the norms prescribe how the agents ought to behave, but-- and this is essential-- they do not exclude the possibility of "bad" behavior (i.e., the actual behavior may deviate from the ideal), and so they also prescribe what should be done in circumstances of norm violation. Thus, we propose a new approach --- a deontic transaction model for multi-agent normative systems. Our approach improves the protocol of "abort/commit" of traditional transaction models to a protocol of "abort/exception/commit". In multi-agent normative systems, we can see the violation of a norm as an exception and how the other agents react to the violation as exception handling. This paper concentrates on our formal model.

Huang, Yonghua↗