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At least 235 records · Page 13

Evaluation of Direct Drive Capsule Fill-Tube Assembly Survivability in Support of the 100 GBar Campaign

Capsule fill-tube target assemblies (CFTAs) for direct-drive have been demonstrated in the past for Laser for Laboratory Energetics (LLE) cryogenic layering studies, evolving and building upon successful deliveries for NIF. The current 100 GigaBar (GBar) campaign requires increased tolerances over prior CFTA work in terms of robustness, cleanliness, reduced fill tube diameter and glue size. To tackle these challenges, GA and LLE are developing a direct drive CFTA that survives all fabrication activities, from assembly, qualification testing and transport to cryogenic layering and target chamber insertion at the OMEGA laser facility. Approximately 55 CFTAs of two main designs have been constructed and tested to date, building off the current LLE cryogenic layering study CFTA design (typically 870 µm diameter x 25 µm thick wall capsule). Variations of glass fill tubes sizes from 30, 20 and 10 µm diameter, which are inserted and glued into the capsule. Testing protocols were developed to enable comparison of different designs against one another and evaluate their robustness at room temperature. The testing protocols include pressure checks, resonant vibration mode sweeps, runout and vibration testing to a power spectral density (PSD) input. In this paper we will compare the different design tradeoffs, measurements and results including glue fillets, sag of the fill tubes under gravity, runout and hysteresis, ringdown response, X-ray imaging of the pipette wall thicknesses, and scanning electron microscope (SEM) images taken of failed fill tubes and glue joints. Assessment of the modal vibration modeling for the designs will be compared against the vibration data. Lastly, a design recommendation is put forth meeting the design constraints, which consists of a polymicro composite tube and 10 µm fill tube, ensuring survivability at cryogenic temperatue, a higher first mode resonance and smaller fuel volume.

100 GBar↗

Stress Analysis and Structural Optimization of a Three-Layer Composite Cladding Tube Under Thermo-Mechanical Loads

A general solution for the stress and strain fields in a three-layer composite tube subjected to internal and external pressures and temperature changes is first derived using thermo-elasticity. The material in each layer is treated as orthotropic, and the composite tube is regarded to be in a generalized plane strain state. A three-layer ZRY4-SiCf/SiCSiC composite cladding tube under a combined pressure and thermal loading is then analyzed and optimized by applying the general solution. The effects of temperature changes, applied pressures, and layer thickness on the mechanical behavior of the tube are quantitatively studied. The von Mises failure criterion for isotropic materials and the Tsai-Wu's failure theory for composites are used, respectively, to predict the failure behavior of the monolithic ZRY4 (i.e., Zircaloy-4) inner layer and SiC outer layer and the composite SiCf/SiC core layer of the three-layer tube. The numerical results reveal that the maximum radial and circumferential stresses in each layer always occur on the bonding surfaces. By adjusting the thickness of each layer, the effective stress in the three-layer cladding tube under the prescribed thermal-mechanical loading can be changed, thereby making it possible to optimally design the cladding tube.

36 MATERIALS SCIENCE↗

Experimental Investigation of the Heat Transfer between Finned Tubes and a Bubbling Fluidized Bed with Horizontal Sand Mass Flow

The sandTES technology utilizes a fluidized bed counter current heat exchanger for thermal energy storage applications. Its main feature is an imposed horizontal flow of sand (SiO2) particles fluidized by a vertical air flow across a heat exchanger consisting of several horizontal rows of tubes. Past international research on heat transfer in dense fluidized beds has focused on stationary (stirred tank) systems, and there is little to no information available on the impact of longitudinal or helical fins. Previous pilot plant scale experiments at TU Wien led to the conclusion that the currently available correlations for predicting the heat transfer coefficient between the tube surface and the surrounding fluidized bed are insufficient for the horizontal sand flow imposed by the sandTES technology. Therefore, several smaller test rigs were designed in this study to investigate the influence of different tube arrangements and flow conditions on the external convective heat transfer coefficient and possible improvements by using finned tubes. It could be shown that helically finned tubes in a transversal arrangement, where the horizontal sand flow is perpendicular to the tube axes, allows an increase in the heat transfer coefficient per tube length (i.e., the virtual heat transfer coefficient) by a factor of 3.5 to about 1250 W/m2K at ambient temperature. Based on the literature, this heat transfer coefficient is expected to increase at higher temperatures. The new design criteria allow the design of compact, low-cost heat exchangers for thermal energy storage applications, in particular electro-thermal energy storage.

25 ENERGY STORAGE↗

Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle

In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.

42 ENGINEERING↗

Benchmarking gyrokinetic simulations in a toroidal flux-tube

A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v{sub ||}-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fabrication of fine-grain tantalum diffusion barrier tube for Nb{sub 3}Sn conductors

Diffusion barriers used in Nb{sub 3}Sn wire are often fabricated by wrapping Ta sheet into a tube with an overlap seam. A common result of such practice is non-uniform deformation in the Ta sheet as it thins by wire drawing because of non-uniform grain size and texture in the original Ta sheet. Seamless Ta tube with a fine-grain and uniform microstructure would be much better for the diffusion barrier application, but such material is expensive and difficult to manufacture. This report presents results on a new fabrication strategy for Ta tube that shows promise for manufacture of less costly tube with an improved microstructure. The fabrication method begins with seam-welded tube but gives a fine-grain uniform microstructure with little difference between the longitudinal seam weld region and the parent metal after post-weld processing. Severe plastic deformation processing (SPD) applied by area reduction extrusion and tube equal channel angular extrusion (tECAE) are used to refine and homogenize the microstructure. Microstructure and mechanical property results are presented for Ta tubes fabricated by this new processing strategy.

36 MATERIALS SCIENCE↗

Feasibility of cooling positrons via conduction in conductive micro-tubes

A first order perturbation with respect to velocity has been employed to find the frictional damping force imposed on a single moving charge inside a conductive cylindrical micro-tube. The tensorial relationship between the force and velocity is derived and numerically estimated. Our results asymptotically match that of a flat geometry presented in the literature. Using the single particle analysis the cooling is formulated for an arbitrary density ensemble. It is shown that no further cooling via conduction occurs in the well-established non-neutral plasma equilibrium state. Also, the cooling rate for a weakly interacting ensemble is estimated. It is shown micro-tubes can be employed to cool down low density positron ensembles and/or to improve the beam emittance. A pack of tens of thousands of individual micro-tubes, each cooling only tens of positrons, is capable of cooling hundreds of thousands of particles in each cooling cycle. For example, with tens of particles per micro-tube in a 5 cm long micro-tube stack with the resistivity of 0.46 Ωm and the tubes of radius 50 μm, hundreds of thousands of positrons can be cooled down with a time constant of 103 μs in longitudinal and 7 μs in perpendicular direction. However, it must be noted that the cooling does not guarantee long term storage of particles in micro-tubes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Explosively driven air blast in a conical shock tube

Explosively driven shock tubes present challenges in terms of safety concerns and expensive upkeep of test facilities but provide more realistic approximations to the air blast resulting from free-field detonations than those provided by gas-driven shock tubes. Likewise, the geometry of conical shock tubes can naturally approximate a sector cut from a spherically symmetric blast, leading to a better agreement with the blast profiles of free-field detonations when compared to those provided by shock tubes employing constant cross sections. The work presented in this article documents the design, fabrication, and testing of an explosively driven conical shock tube whose goal was to closely replicate the blast profile seen from a larger, free-field detonation. By constraining the blast through a finite area, large blasts (which can add significant damage and safety constraints) can be simulated using smaller explosive charges. The experimental data presented herein show that a close approximation to the free-field air blast profile due to a 1.5 lb charge of C4 at 76 in. can be achieved by using a 0.032 lb charge in a 76-in.-long conical shock tube (which translates to an amplification factor of nearly 50). Modeling and simulation tools were used extensively in designing this shock tube to minimize expensive fabrication costs.

42 ENGINEERING↗

A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit

In this paper, we employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a “microscopic absolute yielding” event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. Finally, we qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

Visualization of R410A Flow Boiling Inside Horizontal Smooth Tubes under Diabatic Conditions

This article presents a novel approach to visualize the flow boiling in round tubes under “diabatic conditions”. In the visualization test section, a 3D printed round tube is placed inside a glass tube with secondary fluid at a higher temperature flowing in the annulus between the two tubes thus providing diabatic conditions. Experimental work was conducted for evaporating R410A flow in a horizontal smooth round tube with the inner diameter of 6.3 mm. Compared to the traditional adiabatic visualization technique, the more realistic evaporative condition is simulated and the developing evaporation process is captured. New insights for the flow behavior at low vapor quality are brought by this diabatic method. The vapor plug occurs at very low vapor quality, and this is attributed to the coalescence of bubbles generated on the heated tube wall. For the intermittent flow, liquid slug triggered by Kelvin–Helmholtz instability affects the nucleation on the tube wall. It brings the fresh liquid to rewet the dry surface and activate the nucleation sites. Finally, heat flux condition affects the heat transfer mechanisms during the flow boiling, and the heat transfer through the nucleate boiling mechanism increases as the heat flux increases.

3D printed↗

TH-C-18A-10: The Influence of Tube Current On X-Ray Focal Spot Size for 70 KV CT Imaging

Purpose: Focal spot blooming is an increase in the focal spot size at increased tube current and/or decreased tube potential. In this work, we evaluated the influence of tube current on the focal spot size at low kV for two CT systems, one of which used a tube designed to reduce blooming effects. Methods: A slit camera (10 micron slit) was used to measure focal spot size on two CT scanners from the same manufacturer (Siemens Somatom Force and Definition Flash) at 70 kV and low, medium and maximum tube currents, according to the capabilities of each system (Force: 100, 800 and 1300 mA; Flash: 100, 200 and 500 mA). Exposures were made with a stationary tube in service mode using a raised stand without table movement or flying focal spot technique. Focal spot size, nominally 0.8 and 1.2 mm, respectively, was measured parallel and perpendicular to the cathode-anode axis by calculating the full-width-at-half-maximum of the slit profile recording using computed radiographic plates. Results: Focal spot sizes perpendicular to the anode-cathode axis increased at the maximum mA by 5.7% on the Force and 39.1% on the Flash relative to that at the minimal mA, even though the mA was increased 13-fold on the Force and only 5- fold on the Flash. Focal spot size increased parallel to the anode-cathode axis by 70.4% on Force and 40.9% on Flash. Conclusion: For CT protocols using low kV, high mA is typically required. These protocols are relevant in children and smaller adults, and for dual-energy scanning. Technical measures to limit focal spot blooming are important in these settings to avoid reduced spatial resolution. The x-ray tube on a recently-introduced scanner appears to greatly reduce blooming effects, even at very high mA values. CHM has research support from Siemens Healthcare.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Electrostatic focal spot correction for x-ray tubes operating in strong magnetic fields

Purpose: A close proximity hybrid x-ray/magnetic resonance (XMR) imaging system offers several critical advantages over current XMR system installations that have large separation distances (∼5 m) between the imaging fields of view. The two imaging systems can be placed in close proximity to each other if an x-ray tube can be designed to be immune to the magnetic fringe fields outside of the MR bore. One of the major obstacles to robust x-ray tube design is correcting for the effects of the MR fringe field on the x-ray tube focal spot. Any fringe field component orthogonal to the x-ray tube electric field leads to electron drift altering the path of the electron trajectories. Methods: The method proposed in this study to correct for the electron drift utilizes an external electric field in the direction of the drift. The electric field is created using two electrodes that are positioned adjacent to the cathode. These electrodes are biased with positive and negative potential differences relative to the cathode. The design of the focusing cup assembly is constrained primarily by the strength of the MR fringe field and high voltage standoff distances between the anode, cathode, and the bias electrodes. From these constraints, a focusing cup design suitable for the close proximity XMR system geometry is derived, and a finite element model of this focusing cup geometry is simulated to demonstrate efficacy. A Monte Carlo simulation is performed to determine any effects of the modified focusing cup design on the output x-ray energy spectrum. Results: An orthogonal fringe field magnitude of 65 mT can be compensated for using bias voltages of +15 and −20 kV. These bias voltages are not sufficient to completely correct for larger orthogonal field magnitudes. Using active shielding coils in combination with the bias electrodes provides complete correction at an orthogonal field magnitude of 88.1 mT. Introducing small fields (<10 mT) parallel to the x-ray tube electric field in addition to the orthogonal field does not affect the electrostatic correction technique. However, rotation of the x-ray tube by 30° toward the MR bore increases the parallel magnetic field magnitude (∼72 mT). The presence of this larger parallel field along with the orthogonal field leads to incomplete correction. Monte Carlo simulations demonstrate that the mean energy of the x-ray spectrum is not noticeably affected by the electrostatic correction, but the output flux is reduced by 7.5%. Conclusions: The maximum orthogonal magnetic field magnitude that can be compensated for using the proposed design is 65 mT. Larger orthogonal field magnitudes cannot be completely compensated for because a pure electrostatic approach is limited by the dielectric strength of the vacuum inside the x-ray tube insert. The electrostatic approach also suffers from limitations when there are strong magnetic fields in both the orthogonal and parallel directions because the electrons prefer to stay aligned with the parallel magnetic field. These challenging field conditions can be addressed by using a hybrid correction approach that utilizes both active shielding coils and biasing electrodes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Optimizing Facility Configurations and Operating Conditions for Improved Performance in the NASA Ames 24 Inch Shock Tube

The Ames Electric Arc Shock Tube (EAST) is a shock tube wherein the driver gas can be heated by an electric arc discharge. The electrical energy is stored in a 1.2 MJ capacitor bank. Four inch and 24 inch diameter driven tubes are available. The facility is described and the need for testing in the 24 inch tube to better simulate low density NASA mission profiles is discussed. Three test entries, 53, 53B and 59, are discussed. Tests are done with air or Mars gas (95.7% CO2/2.7% N2/1.6% Ar) at pressures of 0.01 to 0.14 Torr. Velocities spanned 6.3-9.2 km/s, with a nominal center of 7 km/s. Many facility configurations are studied in an effort to improve data quality. Various driver and driven tube configurations and the use of a buffer section between the driver and the driven tube are studied. Diagnostics include test times, time histories of the shock light pulses and tilts of the shock wave off the plane normal to the tube axis. The report will detail the results of the various trials, give the best configuration/operating conditions found to date and provide recommendations for further improvements. Finally, diaphragm performance is discussed.

Shock Tube↗

Restoration of Dehiscent Pancreaticojejunostomy Causing a Major Postoperative Pancreatic Fistula by Reinsertion of a Pancreatic Duct Tube Using the Rendezvous Technique

Introduction: A postoperative clinically relevant pancreatic fistula can cause severe sequelae. We aimed to describe our minimally invasive procedure (rendezvous technique) for the treatment of a pancreatic fistula resulting from pancreaticojejunal anastomosis dehiscence involving a dislodged main pancreatic duct tube. Methods: In our rendezvous technique, a guidewire is advanced into the jejunal lumen from the access site of the drainage tube and is caught by a snare catheter, which is used to replace the dislodged main pancreatic duct tube. Then, the guidewire is passed from the access site of the drainage tube to the site of the dislodged main pancreatic duct tube. A sheath is inserted along the route of the dislodged main pancreatic duct tube and is placed across the pancreaticojejunal anastomosis over the guidewire. Another guidewire is advanced into the main pancreatic duct via the sheath, and a new main pancreatic duct tube is inserted into the main pancreatic duct over the second wire. This technique was performed in two patients with a pancreatic fistula. Results: Our rendezvous technique was successfully performed in a 73-year-old man with an intractable clinically relevant pancreatic fistula and large discharge from the drain and a 74-year-old woman with a pancreatic fistula and fluid collection between the elevated jejunum and remnant pancreas. Discharge from the drain and fluid collection decreased after the procedure. Conclusion: Our rendezvous technique is an effective minimally invasive approach for a pancreatic fistula resulting from pancreaticojejunal anastomosis dehiscence.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Mechanical Properties, Microstructural Evolution, and the Effect of Friction on the Plastic Flow of the AISI 321 Austenitic Stainless Steel Tube During Cold Pilgering: An Experimental and Simulation Analysis

The mechanical properties, microstructural evolution, and the effect of friction on the plastic flow of the AISI 321 austenitic stainless steel (ASS) tube were investigated during the cold pilger process. The elastic–plastic behavior of as-received tube was simulated by the Johnson-cook model. The model parameters were obtained by the compression and tensile tests. The mechanical properties of the material were examined by the tensile and microhardness tests. Based on the ring compression test results, three different situations for friction conditions were considered. The stress and strain states at these conditions were examined for the outer and inner surfaces of the tube. Numerical evaluation of plastic shearing due to the cold pilgering of the AISI321 tube was performed. The X-ray diffraction, ferrite scope tests, and optical microscope were also used for the microstructure evaluation and verification of the simulation results, respectively. The Latham-Cockcraft damage was calculated for different conditions by introducing the new subroutine, showing that it was strongly dependent on the friction conditions and the shear strain, ε{sub zr}, respectively. It was shown that the friction coefficient of 0.3 resulted in the minimum damage of the tube and the different friction conditions between the two surfaces of the tube enhanced the damage function. Also, the strain induced ά-martensite increased the work-hardening capacity and affected the ductility of the tube.

36 MATERIALS SCIENCE↗

Microstructure Characteristic and Mechanical Properties of High-Strength Mg-Nd-Zn-Zr Alloy Seamless Tube Produced by Integrated Extrusion

Large size seamless tubes of Mg-3.0Nd-0.4Zn-0.4Zr alloy (NZ30K, in weight percent) were prepared by integrating backward extrusion with forward extrusion. Microstructure, mechanical properties, aging behavior and texture of the tubes were investigated. The microstructure of as-extruded tube is characterized by the blend of considerably elongated grains and fine equiaxed grains. The maximum values of yield strength and ultimate tensile strength, i.e., 191 and 245 MPa, were obtained in the as-extruded tubes, and these values were increased to 212 and 267 MPa in the peak-aged tubes (T5), implying an increasing ratio of 9 and 11%, respectively. The peak value of the Vickers’ micro-hardness of the NZ30K tubes extruded at 673, 723 and 753 K are 66, 64 and 60 (kilogram-force per square millimeter), respectively. The texture of NZ30K tube is weak, the primary mechanism behind which is suggested to be the particle-induced nucleation responsible for the promotion of recrystallization.

36 MATERIALS SCIENCE↗

Effect of tube processing methods on microstructure, mechanical properties and irradiation response of 14YWT nanostructured ferritic alloys

In this research, innovative thermal spray deposition (Process I) and conventional hot extrusion processing (Process II) methods have been used to produce thin walled tubing (~0.5 mm wall thickness) out of 14YWT, a nanostructured ferritic alloy. The effects of processing methods on the microstructure, mechanical properties and irradiation response have been investigated by using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and, micro- and nano-hardness techniques. It has been found that these two processes have a significant effect on the microstructure and mechanical properties of the as-fabricated 14YWT tubes. Even though both processing methods yield the formation of various size Y-Ti-O particles, the conventional hot extrusion method results in a microstructure with smaller, homogenously distributed nano-oxides (NOs, Y-Ti-O particles < 5 nm) with higher density. Therefore, Process II tubes exhibit twice the hardness of Process I tubes. It has also been found that these two tremendously different initial microstructures strongly affect irradiation response in these tubes under extremely high dose ion irradiations up to 1100 peak dpa at 450 °C. The finer, denser and homogenously distributed NOs in the Process II tube result in a reduction in swelling by two orders of magnitude. On the other hand, inhomogeneity of the initial microstructure in the Process I tube leads to large variations in both swelling and irradiation induced hardening. Moreover, hardening mechanisms before and after irradiation were measured and compared with detailed calculations. In conclusion, this study clearly indicates the crucial effect of initial microstructure on radiation response of 14YWT alloys.

36 MATERIALS SCIENCE↗

CFD Analysis Of Particle Transport In Axi-Symmetric Tubes Under The Influence Of Thermophoretic Force

In this study, we developed two frameworks to investigate the thermophoretic particulate deposition in non-isothermal tube flows conveying particles ranging from 10 to 300 nm; a one dimensional model where the variables are assumed to be uniform in each cross section perpendicular to the tube axis and an axi-symmetric model where the aforementioned assumption is relaxed. In the one dimensional model, the rate of mass deposition along the inner surface of the tube is computed based on the local thermophoretic velocity of the particulate phase at the wall. This velocity is proportional to the radial gradient of the temperature at the wall and is calculated via some empirical correlations for heat transfer in tube flows. In the axi-symmetric model, the rate of deposition is computed through the Fick s law after solving the species transport equation for the solid phase. We included the formation of the soot layer through moving the gas solid interface in both models. The tube effectiveness (the ratio of actual heat transfer to the maximum possible heat transfer) decreases due to the formation of the layer. Model outputs including deposited mass along the tube wall and the tube effectiveness drop have been compared against experiments. While the computed results through both models agree with the trend of experimental data, the axi-symmetric results are closer to the experiments in most cases. The calculated deposited mass is smaller (and closer to experiments) for the axi-symmetric model compared to the one dimensional model in all cases. This indicates that the axi-symmetric model estimates the deposited mass more accurately.

Abarham, Mehdi↗