One-dimensional Numerical Analysis Research Articles

Numerical Study of Porous Cylindrical Containment for the Fuel Element of a Centrifugal Nuclear Thermal Rocket

For deep-space propulsion and interplanetary exploration, the centrifugal nuclear thermal rocket (CNTR) has the ability to achieve a very high specific impulse (Isp) metric beyond that of conventional chemical rockets or solid-core nuclear thermal propulsion systems. The high Isp allows the rocket to use less propellant or achieve a higher velocity for shorter transit times. However, the cylindrical containment structure of a CNTR fuel element encounters extreme conditions, as it houses molten uranium at temperatures exceeding 1408 K, leading to challenges such as dissolution, chemical reactions, and thermal stresses that conventional materials struggle to withstand. This study aims to address this issue by analyzing appropriate materials for constructing the cylindrical containment component. The operating conditions of the annular porous medium that confines the liquid uranium in the centrifugal fuel element are simulated by conducting a comprehensive one-dimensional numerical analysis using a range of candidate porous materials, including Mo, W, zirconium carbide, and silicon carbide. The porous structure facilitates the flow of the hydrogen propellant into the internal molten uranium section, where it gains significant thermal energy while simultaneously cooling the cylinder. The containment cylinder has an internal temperature of 1478.1 K, exceeding the melting point of uranium, while the external gas temperature of the hydrogen propellant is much lower. This temperature difference induces significant thermal stresses in the cylinder. The porous containment cylinder made from molybdenum was able to maintain elastic deformation throughout the thickness of the cylinder, showcasing its ability to handle these extreme thermal stress conditions. Tungsten, on the other hand, experienced plastic deformation at the cylinder’s edges and elastic deformation through the middle radial locations. In contrast, the stresses experienced by the ceramic materials far exceeded their failure stress values, leading to brittle failure. These findings will help with the refinement of the CNTR design, edging it closer to practical implementation.

Convection-effect-enhanced micro thermoelectric module directly heated by catalytic combustion

A novel micro thermoelectric power generation module directly heated with localized catalytic combustion has been proposed. Arrays of high-temperature plate-type thermoelectric generator (TEG) elements, of which the hot junction is directly heated by exothermic catalytic oxidation of hydrocarbon fuel, are designed. Heat losses caused by heat conduction through the TEG element are recovered by the convection effect with unburned mixture flows. Catalyst layers were prepared by impregnating Pd or Pt catalyst on porous Al2O3 supports coated by using the suspension plasma spray. A series of one-dimensional numerical analyses considering the catalytic combustion in addition to the conductive and convective heat transfer were made to examine the temperature field of the TEG module and to investigate how various parameters affect the convection effect. A model combustor using quartz plates was developed, which mimics the temperature fields of the SiGe TEG module. It is found that, with the aid of the convection effect, temperature differences over 700 °C between the hot/cold junctions can be achieved, while the unreacted fuel concentration is less than 10%. Finally, 40 mm-long Ni-based alloy TEG elements have been fabricated using laser cutting and spot welding techniques, which ensure high operating temperatures and reliability. In a power generation demonstration using butane as a fuel, an open circuit voltage of 0.64 V has been obtained from a single TEG module with a peak output power and a power generation density as high as 10.1 mW and 10.8 kW/m3, respectively.

One-dimensional transient numerical model and characteristic analysis for a double helix tube of conical J-T cryocooler

An open cycle miniature J-T cryocooler can provide a clear advantage over other cryocoolers in terms of the smaller size, faster cooling down, and no moving parts. In recent years, some experimental research has shown that the progress of heat exchanger technology promotes the application of miniature J-T cryocoolers in the field of infrared detection. Especially micro-finned double helix tube heat exchangers provide good performance for a conical J-T cryocooler. In order to study its rapid cooling mechanism, a one-dimensional numerical model is established for analyzing this unique flow and heat transfer characteristics in such a conical heat exchanger of J-T cryocooler, and the model algorithm is proved to be effective and efficient by the experiments for rapidly calculating entire J-T cryocooler. The simulated results show that the application of double layers conical helix tubes not only enhances heat transfer areas at the same mass flow rate but also optimizes the thermal mass distribution in the heat exchanger such that this part of thermal mass near the evaporator is reduced. Thus, the high-pressure working fluid can be cooled rapidly and throttled to a two-phase state, improving the heat transfer efficiency of the impact jet flow. On the other hand, excessively high vessel pressure will affect the saturation pressure in the evaporator, resulting in a cooling rate reduction. An appropriate vessel pressure can be found for a fast cooling rate by optimal evaporator pressure. In addition, studies revealed that the temperature drop resulting from the adiabatic discharge of the pressure vessel plays an indispensable role in the fast cooling process.

Statistical calibration of two-dimensional seismic aggravation effects for homogeneous basins

Two-dimensional basin effects often play a relevant role in defining earthquake ground motion at sites with deep morphologies. The quantitative estimation of two-dimensional effects requires a numerical approach which is typically complex and computationally demanding. Due to modelling complexities, basin effects are not routinely accounted for and have not received significant attention in seismic design codes. One-dimensional seismic response can be modeled with greater ease but does not allow their confident investigation. The use of simplified approaches which allow the estimation of two-dimensional effects from one-dimensional analyses is thus warranted. Past studies have defined and investigated aggravation factors, which can be applied as multiplicative coefficients to one-dimensional ground response outputs to account for two-dimensional basin effects. This paper proposes a novel framework for estimating basin effects by assigning aggravation factors for a vast range of symmetric basins overlain by a single-layer, homogeneous soil deposit and for varying basin sizes, dynamic geotechnical properties, and seismic inputs. In the study, aggravation factors are defined with reference to pseudo-acceleration response spectrum (5% of critical damping) and are calibrated statistically using a large set of dimensionless parameters from the outputs of an extensive set of one-dimensional and two-dimensional numerical analyses. The calibration process is described along with notable observations regarding the spatial variability of the magnitude of two-dimensional aggravation along the surface of the deposit. The proposed method is amenable to current design code formats involving tabulated partial factors. In principle, aggravation factors obtained in this study can be applied to 1D response spectra developed either from the provisions of the design codes themselves or from site-specific ground response analyses. A discussion focusing on the validation of the proposed approach using experimental and empirical measurements is provided. An example application attests to the simplicity of use of the method.

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO[formula omitted] high-burnup microstructure fragmentation

In this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

One-dimensional numerical analysis for the porosity impact of open-cell metal foam on the effective thermal properties of PCMs

Metal foam has found its way in many engineering industries due to its ability to improve the heat transfer rate in thermal applications. Thermal energy storage based on phase change materials (PCMs) have significant importance as a part of renewable energy sources, and thermal management applications, However, low thermal conductivity is the essential drawback associated with the PCMs, especially the organic type of it, such as paraffin. Various experimental and numerical studies performed to test the effect of using metal foam with PCMs, in order to improve PCMs thermal conductivity. Many models suggested for evaluating the effective thermal conductivity of high porosity open cells metal foam, which immersed in base fluids of low thermal conductivity such as air, water, and PCMs. This work achieved numerically by using different models for calculating the effective thermal properties of metal foam with various range of porosities impregnate in paraffin. The study discussed the temperature distribution, which control the heat transfer rate, the behavior of temperatures versus time, and improvements in the melting front phase of the paraffin, under the effect of copper metal foam of various porosities and by applying different models, for estimating the effective thermal conductivity. The results exhibit an augmentation in the effective thermal conductivity with porosity decreasing. The outputs showed paradoxical results using the presented models and the differences between them have been discussed.

A convenient approach to tuning the local piezopotential of an extensional piezoelectric semiconductor fiber via composite structure design

It has been demonstrated that the local piezopotential property of a piezoelectric semiconductor (PS) fiber has a great influence on its piezotronic performance. However, tuning the local piezopotential of the PS fiber is quite difficult due to its small size. To solve this problem, a feasible approach, i.e., composite structure design, is proposed in this paper. A two-layer composite structure is utilized to demonstrate that the local piezopotential of a PS fiber can be tuned by axial forces applied at the two ends. Based on the one-dimensional phenomenological model, theoretical and numerical analysis are performed and the local manipulation mechanism is successfully illustrated. It shows that local potential barriers and wells will emerge as long as the piezoelectric polarization is discontinuous along the fiber. The properties of these barriers and wells, including the number, the relative heights and depths, directly depend on the material combination and geometry size of different composite components, which makes it possible to artificially design the piezotronic performance of PS fibers. It also shows that the output voltage of a PS fiber based nanogenerator is significantly improved when employing composite structures. This is because part of electrons are confined to the produced local barrier, thus reducing the number of electrons that would screen the piezopotential near the two ends. In addition, the I-V characteristic of the composite fiber is further studied and its dependence on the local potential change is revealed. Conclusions obtained in the present paper have great potential applications in piezotronic field.

Thermal properties of carbon nanofibers enhanced lightweight cementitious composite under high temperature

Foam concrete is conventionally used in non-structural applications (e.g. thermal and acoustic insulation) due to its lightweight nature and poor mechanical properties. However, interest in adopting foam concrete as structural components has increased phenomenally in recent years due to its lightweight and sustainable feature. A new type of foam concrete termed as carbon nanofibers enhanced lightweight cementitious composite (CNF-LCC) was developed by blending micro-foam bubbles with carbon nanofibers enhanced ultra-high performance concrete; it has superior mechanical properties, long-term properties and bond performance with steel bar compared with conventional foam concrete. In this paper, thermal properties of CNF-LCC during heating were investigated and compared with normal weight concrete (NWC) and lightweight aggregate concrete (LWAC). From room temperature to 800 ℃, the thermal diffusivity of CNF-LCC was lower than NWC and similar to LWAC while the specific heat and thermal conductivity of CNF-LCC was lower than both NWC and LWAC. CNF-LCC showed better structural efficiency than NWC and LWAC in combination of mechanical and thermal insulation properties. The measured thermal insulation properties under high temperature were verified by conducting one-dimensional heat transfer tests and numerical analysis on CNF-LCC blocks. Furthermore, the thermal strain of CNF-LCC during heating is lower and more stable than NWC and LWAC. Dehydration reaction at isothermal elevated temperature was characterised for the analysis of experimental results. Foam bubbles could reduce both thermal insulation and strain properties while a low dosage of CNFs had minimum effect on the thermal insulation properties but could improve the mechanical properties and decrease the thermal shrinkage. CNF-LCC showed potential for fire resistant as a structural lightweight concrete due to the excellent thermal insulation and lower thermal strain properties.

Tek tabakalı sıvılaşabilir bir zeminin saha tepki davranışı üzerine yeraltı suyu seviyesinin etkisi

This study examines the effect of groundwater level ( ) on the seismic site response behavior of a one-layered liquefiable soil using one-dimensional nonlinear numerical analyses. The response of the liquefiable soil was analyzed with the help of DeepSoil open-source software. The calibration of the numerical model was carried out using the results of a centrifuge experiment from the literature. The outcomes of the site response analyses were discussed in terms of peak horizontal acceleration, amplification ratio, excess pore pressure ratio, shear stress-strain behavior, and maximum lateral displacement. Also, additional numerical analyses were performed to investigate relationships between input motion intensity- , frequency content of earthquake motion- , and layer thickness- . It is shown that the seismic site response behavior of the liquefiable soil is highly affected by changes in groundwater levels. Moreover, depending on the location of the groundwater level, the seismic behavior of the liquefiable soil may also change with the increase of the input motion intensity, frequency content, and layer thickness.

Effective Optimization-Simulation Model for Flood Control of Cascade Barrage Network

In this study, a novel simulation-optimization model for the optimal flood control of the cascade barrage network was proposed by combining a simulation-based optimization method with a one-dimensional flood numerical analysis method. The simulation-based optimization method determines the optimal operation rules of cascade barrages, including the pre-discharge stage algorithm and the main-discharge stage algorithm for the securement of flood control storage and the establishment of a minimal discharge plan. The optimal operation rules describe the detailed operation process of barrage floodgates including full and partial opening and provide the upper and downstream boundary conditions for the flood numerical analysis method, which evaluate the flood propagation in the river channel between barrages. The proposed model was applied to the flood control of the six-cascade barrage network in the Taedong River, Democratic People’s Republic of Korea, and its effectiveness was verified in comparison with a well-known PSO-optimization method. The results show that the proposed model is superior to the existing other method and practically applicable to the flood control in the rivers with cascade barrage network.

Validation of diesel engine gas flow one-dimensional numerical analysis using the method of characteristics

Validation of diesel engine gas flow one-dimensional numerical analysis using the method of characteristics

Refrigerant circulation system for cooling a HTS coil

When using the superconducting technology industrially, it is not always possible to install a refrigerator near a high temperature superconducting coil for cooling it. In the method using heat conduction cooling, cooling result as expected cannot be obtained due to temperature difference between a refrigerator and a superconducting coil via a heat transfer plate when the distance of the refrigerator and the coil is long. Therefore, a method of cooling a superconducting coil by circulating helium gas has been proposed. Helium gas discharged by a compressor at room temperature is cooled by a pre-cooling heat exchanger, thereafter cooled by a GM refrigerator. The cold helium gas cools the coil and current leads. In this study, the helium circulation cooling system was investigated by using one-dimensional numerical analysis and experiment at different helium gas mass flows.

Numerical Thermal Analysis and 2-D CFD Evaluation Model for An Ideal Cryogenic Regenerator.

Regenerative cryocoolers such as Stirling, Gifford–McMahon, and pulse tube cryocoolers possess great merits such as small size, low cost, high reliability, and good cooling capacity. These merits led them to meet many IR and superconducting based application requirements. The regenerator is a vital element in these closed-cycle cryocoolers, but the overall performance depends strongly on the effectiveness of the regenerator. This paper presents a one-dimensional numerical analysis for the idealized thermal equations of the matrix and the working gas inside the regenerator. The algorithm predicts the temperature profiles for the gas during the heating and cooling periods, along with the matrix nodal temperatures. It examines the effect of the regenerator’s length and diameter, the matrix’s geometric parameters, the number of heat transfer units, and the volumetric flow rate, on the performance of an ideal regenerator. This paper proposes a 2D axisymmetric CFD model to evaluate the ideal regenerator model and to validate its findings.

Influence of Motion Energy and Soil Characteristics on Seismic Ground Response of Layered Soil

The present study focuses on assessing local site effects (especially large-scale soil heterogeneity) and motion characteristics on seismic ground response using nonlinear one-dimensional numerical analysis. All nonlinear and curve-fitting parameters used for soil models were verified using the Class C1 prediction of centrifuge test results available in the literature. The comparison demonstrates that the available MKZ (pressure dependent Modified Kondner Zelesko) formulation with non-Masing hysteresis loading and unloading rule can reliably compute the 1-D ground response of cohesionless soil. Horizontal soil layers with different relative densities were considered next in various hypothetical models to assess the effect of subsurface properties on responses. One novel aspect of this study is that 51 different ground motions with a wide range of variation in their spectral accelerations, frequency contents, and duration characteristics were used to evaluate the effect of ground motion characteristics on the soil response. The results reveal that layering conditions play a significant role in modifying the seismic ground response of heterogeneous soil, especially when the loose liquefiable sand layer is sandwiched between two non-liquefiable soil layers. Relations were obtained to quantify the effect of different seismic inputs and varying site conditions on seismic ground response. The best correlation was obtained between the maximum excess pore water pressure (EPWP) development and the damage potential (Arias intensity) of an input ground motion. These relations can be used for estimating seismic ground response of an identical soil profile to that used in the present study for known design motion characteristics.

Influence of Grid Resolution on One-Dimensional Numerical Analysis of Laser Supported Detonation

Influence of Grid Resolution on One-Dimensional Numerical Analysis of Laser Supported Detonation

One-dimensional modelling of pile jacking installation based on CPT tests in sand

The load-transfer (t–z or q–z) curve method has been widely used for prediction of the load–settlement relationship of piles subject to axial loads because of its simplicity and good convergence. However, few studies have focused on the pile installation and friction fatigue. With this consideration, the present study develops a large-displacement t–z curve which describes the degradation of shaft friction as a function of accumulated displacement. A one-dimensional numerical analysis technique using a q–z spring and a series of t–z soil springs is proposed for simulation of the jacking installation process of a large-displacement pile. The q–z curve and the parameters of the t–z curve can be obtained by cone penetration tests. The t–z spring of each soil layer can be broken away from the lower pile node beyond the layer range and reconnected to the upper pile node with the displacement of the springs accumulated continuously. Two case studies are presented to validate the applicability of the jacked pile model. Results show that the developed model can satisfactorily simulate the axial load and shaft friction of the pile during jacked installation. It can be concluded that the amount of cyclic displacement resulting from the unloading has a significant effect on the installation resistance, which is ignored by the existing design method.

Water flow in unsaturated soils subjected to multiple infiltration events

In this paper, water flow in a 4 m height column with an unsaturated soil that is subjected to multiple infiltration events for a 62 day period is investigated. One-dimensional (1D) numerical analysis is also undertaken to analyze the flow, extending the seepage theory for unsaturated soils. Results highlight the formation of two wetting fronts; namely, wetting front I and wetting front II that are induced by the first and subsequent infiltration events, respectively. There is a stable zone where the water content is approximately constant; it forms between the two fronts. A conceptual model of the suction profile is proposed for interpreting in situ water flow by dividing the unsaturated zone into four distinct zones; namely, active, steady, transition, and capillary fringe zones. This division is helpful for providing a rational explanation of water flow in different zones. Novel contributions from this study include a relationship between the hydraulic properties in the steady zone and the flow velocity, which is determined by an average influx rate. In addition, the rate of groundwater recharge can also be estimated using the average influx rate. Results of the present study are useful to understand and interpret the relationship between water infiltration and suction or water content profile in the unsaturated zone as well as variation of groundwater table level.

Pressure-driven gas flow in viscously deformable porous media: application to lava domes

The behaviour of low-viscosity, pressure-driven compressible pore fluid flows in viscously deformable porous media is studied here with specific application to gas flow in lava domes. The combined flow of gas and lava is shown to be governed by a two-equation set of nonlinear mixed hyperbolic–parabolic type partial differential equations describing the evolution of gas pore pressure and lava porosity. Steady state solution of this system is achieved when the gas pore pressure is magmastatic and the porosity profile accommodates the magmastatic pressure condition by increased compaction of the medium with depth. A one-dimensional (vertical) numerical linear stability analysis (LSA) is presented here. As a consequence of the pore-fluid compressibility and the presence of gravitation compaction, the gradients present in the steady-state solution cause variable coefficients in the linearized equations which generate instability in the LSA despite the diffusion-like and dissipative terms in the original system. The onset of this instability is shown to be strongly controlled by the thickness of the flow and the maximum porosity, itself a function of the mass flow rate of gas. Numerical solutions of the fully nonlinear system are also presented and exhibit nonlinear wave propagation features such as shock formation. As applied to gas flow within lava domes, the details of this dynamics help explain observations of cyclic lava dome extrusion and explosion episodes. Because the instability is stronger in thicker flows, the continued extrusion and thickening of a lava dome constitutes an increasing likelihood of instability onset, pressure wave growth and ultimately explosion.

Optical Measurement of Fluid Motion in Semi-Valveless Pulse Detonation Combustor with High-Frequency Operation

ABSTRACTThe purge layer of a semi-valveless pulse detonation cycle (PDC) needs to be minimized for operating at a gas-dynamic upper frequency limit. Therefore, it is essential to better understand the process of burned gas backflow for minimizing the purge layer thickness. The flow field of the semi-valveless PDC was visualized to illustrate the movement of burned gas. A combustor of length of 95 mm with a 10-mm-square cross section was used. Supercritical ethylene and oxygen gas were used as fuel and oxidizer, respectively, and the operation frequency was 604 Hz. The unsteady refilling process of the detonable mixture was modeled by an isentropic flow. In addition, the detailed burned gas blowdown process with deflagration-to-detonation transition (DDT) and the backflow were captured. It was shown that the retonation wave generated by the DDT process was the primary trigger of the burned gas backflow. When the duration required for the DDT process was sufficiently shorter than that of the burned gas blowdown process, it was found the latter could be reproduced with approximately 90% accuracy by one-dimensional numerical analysis without the DDT process.

One-dimensional fluid and hybrid numerical analysis of the plasma properties in the discharge channel of a Hall thruster

One-dimensional fluid and hybrid fluid-kinetic numerical codes are developed and applied to the analysis of axial distributions of plasma properties in the discharge channel of a Hall-effect thruster. Within the hybrid model ions are described by the kinetic Vlasov equation, while electrons and neutral atoms are treated as fluids. The results obtained from fluid and hybrid models are compared. Different operating regimes such as damped, periodic, and aperiodic irregular oscillations about the stationary state are observed and discussed. Thrust and efficiency of the thruster for different input parameters are estimated.