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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle

An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6-DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has a significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to the conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

Yang, H. Q.↗
NASA NTRS2017

A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle

An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6-DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has a significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to the conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

Yang, H. Q.↗
NASA NTRS2017

Semi-Supervised Learning of Lift Optimization of Multi-Element Three-Segment Variable Camber Airfoil

This chapter describes a new intelligent platform for learning optimal designs of morphing wings based on Variable Camber Continuous Trailing Edge Flaps (VCCTEF) in conjunction with a leading edge flap called the Variable Camber Krueger (VCK). The new platform consists of a Computational Fluid Dynamics (CFD) methodology coupled with a semi-supervised learning methodology. The CFD component of the intelligent platform comprises of a full Navier-Stokes solution capability (NASA OVERFLOW solver with Spalart-Allmaras turbulence model) that computes flow over a tri-element inboard NASA Generic Transport Model (GTM) wing section. Various VCCTEF/VCK settings and configurations were considered to explore optimal design for high-lift flight during take-off and landing. To determine globally optimal design of such a system, an extremely large set of CFD simulations is needed. This is not feasible to achieve in practice. To alleviate this problem, a recourse was taken to a semi-supervised learning (SSL) methodology, which is based on manifold regularization techniques. A reasonable space of CFD solutions was populated and then the SSL methodology was used to fit this manifold in its entirety, including the gaps in the manifold where there were no CFD solutions available. The SSL methodology in conjunction with an elastodynamic solver (FiDDLE) was demonstrated in an earlier study involving structural health monitoring. These CFD-SSL methodologies define the new intelligent platform that forms the basis for our search for optimal design of wings. Although the present platform can be used in various other design and operational problems in engineering, this chapter focuses on the high-lift study of the VCK-VCCTEF system. Top few candidate design configurations were identified by solving the CFD problem in a small subset of the design space. The SSL component was trained on the design space, and was then used in a predictive mode to populate a selected set of test points outside of the given design space. The new design test space thus populated was evaluated by using the CFD component by determining the error between the SSL predictions and the true (CFD) solutions, which was found to be small. This demonstrates the proposed CFD-SSL methodologies for isolating the best design of the VCK-VCCTEF system, and it holds promise for quantitatively identifying best designs of flight systems, in general.

Intelligent Systems↗
NASA NTRS2018

A Physics-Based Approach to Urban Air Mobility

High-fidelity Computational Fluid Dynamics (CFD) simulations for multi-rotor vehicles have been carried out. The three-dimensional unsteady Navier-Stokes equations are solved on overset grids employing high order accurate schemes, dual-time stepping, and a hybrid turbulence model using NASA's CFD code Over- flow. The vehicles studied consist of small to medium sized drones, and bigger vehicles for future Urban Air Mobility (UAM) applications. The performances for different configurations and rotor mounting are calculated in hover and in forward flight. Understanding the complex flows and the interactions between rotors and with other elements will help design the future multi-rotor vehicles to be quieter, safer, and more efficient.

Urban↗
NASA NTRS2018

Rotor CFD Analysis at Terrestrial and Martian Atmospheric Densities

Much effort has been made to enhance exploration on Mars. In addition to a rover and Mars-orbiting satellites, a Mars helicopter (MH) was proposed in order to augment planetary research. Computational Fluid Dynamics (CFD) simulations have been performed to have a better understanding of the behavior and performance of vertical lift Planetary Aerial Vehicles (PAV). Due to the large differences in atmospheric conditions between Mars and Earth, predicting and testing rotorcraft performance is a complex task. The goal of this project is to understand the capability of the mid-fidelity CFD software RotCFD to predict rotor performance in terms of thrust at 1013.25 milibar and 14 milibar corresponding to Terrestrial and Martian conditions, respectively. Also, in order to characterize the wind tunnel wall effects free field and wind tunnel simulations were performed, analyzed and compared. Different analytical tools have been used in order to aid with the design process for the future vertical lift planetary aerial vehicles. One of them includes experimental tests performed on a rotor in the Aeolian Wind Tunnel (AWT) facility at NASA Ames Research Center under different pressure conditions ranging from Terrestrial to Martian atmospheric conditions. Other software was used as well in order to capture the aerodynamic coefficients of the corresponding rotor sections based on the Mach and Reynolds numbers used for the experimental tests. The aerodynamic coefficients were input into RotCFD, and various simulations were performed under Terrestrial and Martian conditions in order to mimic the experimental test. Then, the obtained results from RotCFD were compared with the AWT collected data.

Atmospheric Pressures↗
NASA NTRS2023

Application of Thermal Loads to a Numerical Model

A detailed aerothermal model requires the application of the heat flux profile over all exposed aerodynamic surfaces. These loads are created using both engineering methods (e.g., FORTRAN codes implementing correlations) and CFD simulations (e.g., solutions to Navier-Stokes equations). The goal is to define the spatial and temporal dependency of the heat flux upon the model.

cfd↗
NASA NTRS2011

Noise of Embedded High Aspect Ratio Nozzles

A family of high aspect ratio nozzles were designed to provide a parametric database of canonical embedded propulsion concepts. Nozzle throat geometries with aspect ratios of 2:1, 4:1, and 8:1 were chosen, all with convergent nozzle areas. The transition from the typical round duct to the rectangular nozzle was designed very carefully to produce a flow at the nozzle exit that was uniform and free from swirl. Once the basic rectangular nozzles were designed, external features common to embedded propulsion systems were added: extended lower lip (a.k.a. bevel, aft deck), differing sidewalls, and chevrons. For the latter detailed Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) simulations were made to predict the thrust performance and to optimize parameters such as bevel length, and chevron penetration and azimuthal curvature. Seventeen of these nozzles were fabricated at a scale providing a 2.13 inch diameter equivalent area throat." ! The seventeen nozzles were tested for far-field noise and a few data were presented here on the effect of aspect ratio, bevel length, and chevron count and penetration. The sound field of the 2:1 aspect ratio rectangular jet was very nearly axisymmetric, but the 4:1 and 8:1 were not, the noise on their minor axes being louder than the major axes. Adding bevel length increased the noise of these nozzles, especially on their minor axes, both toward the long and short sides of the beveled nozzle. Chevrons were only added to the 2:1 rectangular jet. Adding 4 chevrons per wide side produced some decrease at aft angles, but increased the high frequency noise at right angles to the jet flow. This trend increased with increasing chevron penetration. Doubling the number of chevrons while maintaining their penetration decreased these effects. Empirical models of the parametric effect of these nozzles were constructed and quantify the trends stated above." Because it is the objective of the Supersonics Project that future design work be done more by physics-based computations and less by experiments, several codes under development were evaluated against these test cases. Preliminary results show that the RANS-based code JeNo predicts the spectral directivity of the low aspect ratio jets well, but has no capability to predict the non-axisymmetry. An effort to address this limitations, used in the RANS-based code of Leib and Goldstein, overpredicted the impact of aspect ratio. The broadband shock noise code RISN, also limited to axisymmetric assumptions, did a good job of predicting the spectral directivity of underexpanded 2:1 cold jet case but was not as successful on high aspect ratio jets, particularly when they are hot. All results are preliminary because the underlying CFD has not been validated yet. An effort using a Large Eddy Simulation code by Stanford University predicted noise that agreed with experiments to within a few dB.

Bridges, James E.↗
NASA NTRS2001

Development and Validation of High Performance Unshrouded Centrifugal Impeller

The feasibility of using a two-stage unshrouded impeller turbopump to replace the current three-stage reusable launch vehicle engine shrouded impeller hydrogen pump has been evaluated from the standpoint of turbopump weight reduction and overall payload improvement. These advantages are a by-product of the higher tip speeds that an unshrouded impeller can sustain. The issues associated with the effect of unshrouded impeller tip clearance on pump efficiency and head have been evaluated with one-dimensional tools and full three-dimensional rotordynamic fluid reaction forces and coefficients have been established through time dependent computational fluid dynamics (CFD) simulation of the whole 360 degree impeller with different rotor eccentricities and whirling ratios. Unlike the shrouded impeller, the unshrouded impeller forces are evaluated as the sum of the pressure forces on the blade and the pressure forces on the hub using the CFD results. The turbopump axial thrust control has been optimized by adjusting the first stage impeller backend wear ring seal diameter and diverting the second stage backend balance piston flow to the proper location. The structural integrity associated with the high tip speed has been checked by analyzing a 3D-Finite Element Model at maximum design conditions (6% higher than the design speed). This impeller was fabricated and tested in the NASA Marshall Space Flight Center water-test rig. The experimental data will be compared with the analytical predictions and presented in another paper. The experimental data provides validation data for the numerical design and analysis methodology. The validated numerical methodology can be used to help design different unshrouded impeller configurations.

Chen, Wei-Chung↗
NASA NTRS2016

Computational Evaluation of Inlet Distortion on an Ejector Powered Hybrid Wing Body at Takeoff and Landing Conditions

Due to the aft, upper surface engine location on the Hybrid Wing Body (HWB) planform, there is potential to shed vorticity and separated wakes into the engine when the vehicle is operated at off-design conditions and corners of the envelope required for engine and airplane certification. CFD simulations were performed of the full-scale reference propulsion system, operating at a range of inlet flow rates, flight speeds, altitudes, angles of attack, and angles of sideslip to identify the conditions which produce the largest distortion and lowest pressure recovery. Pretest CFD was performed by NASA and Boeing, using multiple CFD codes, with various turbulence models. These data were used to make decisions regarding model integration, characterize inlet flow distortion patterns, and help define the wind tunnel test matrix. CFD was also performed post-test; when compared with test data, it was possible to make comparisons between measured model-scale and predicted full-scale distortion levels. This paper summarizes these CFD analyses.

Wind Tunnel Testing↗
NASA NTRSDate not supplied

Gas Phase Effects on Slosh Dynamics

Gas phase effects on slosh dynamics were quantified using computational fluid dynamics (CFD) simulation for a range of propellant and gas combinations. Historical slosh modeling using potential flow solutions typically neglects gas phase effects. Regardless, the results have been shown to compare well with slosh ground tests typically performed with water and air at standard temperature and pressure. CFD analysis reveals that as the liquid-to-gas density ratio decreases, slosh dynamics change due to the relative increase in gas inertia and thus influence on liquid motion. The result is a profound impact on slosh dynamics over certain parameter spaces particularly for liquid hydrogen. Gas phase effects on slosh dynamics should be considered in slosh models especially for liquid hydrogen propellant tanks.

Jacob M Brodnick↗
NASA NTRSDate not supplied

Gas Phase Effects on Slosh Dynamics

Gas phase effects on slosh dynamics were quantified using computational fluid dynamics (CFD) simulation for a range of propellant and gas combinations. Historical slosh modeling using potential flow solutions typically neglects gas phase effects. Regardless, the results have been shown to compare well with slosh ground tests typically performed with water and air at standard temperature and pressure. CFD analysis reveals that as the liquid-to-gas density ratio decreases, slosh dynamics change due to the relative increase in gas inertia and thus influence on liquid motion. The result is a profound impact on slosh dynamics over certain parameter spaces particularly for liquid hydrogen. Gas phase effects on slosh dynamics should be considered in slosh models especially for liquid hydrogen propellant tanks.

Jacob M Brodnick↗
NASA NTRSDate not supplied

Comparing Methods to Extract Sectional Angle of Attack From Blade-Resolved Rotor Simulations

The angle of attack is widely used to describe the aerodynamics of rotor blades. Models based on lifting lines, actuator lines, and actuator disks use it as a primary variable, assuming the aerodynamics can be represented by the flow around a collection of equivalent 2D airfoils. This paper evaluates the accuracy of existing methods that extract the angle of attack from blade-resolved CFD simulations, towards enabling a direct comparison of angle of attack between blade-resolved and blade-modeled simulations. Results are compared for a 2D airfoil for which the angle of attack is known by definition. The hovering rotor case is also considered, where we look at two different rotor blades. We discuss the factors that impact the accuracy of the 2D predictions. For the 3D rotors, we show that three-dimensional effects in the root and tip regions lead to large discrepancies between methods. This suggests that the very definition of angle of attack is unable to accurately represent the flow in these regions. Finally, based on guidelines that we establish, we propose an alternate method that uses local velocities sampled on a contour located 0.25 chord, or less, away from the airfoil surface and generally yields improved accuracy compared to most existing techniques.

ARMD↗
NASA NTRS2016

Dynamic Stall Suppression Using Combustion-Powered Actuation (COMPACT)

Retreating blade stall is a well-known phenomenon that limits rotorcraft speed, maneuverability, and efficiency. Airfoil dynamic stall is a simpler problem, which demonstrates many of the same flow phenomena. Combustion Powered Actuation (COMPACT) is an active flow control technology, which at the outset of this work, had been shown to mitigate static and dynamic stall at low Mach numbers. The attributes of this technology suggested strong potential for success at higher Mach numbers, but such experiments had never been conducted. The work detailed in this report documents a 3-year effort focused on assessing the effectiveness of COMPACT for dynamic stall suppression at freestream conditions up to Mach 0.5. The work done has focused on implementing COMPACT on a high-lift rotorcraft airfoil: the VR-12. This selection was made in order to ensure that any measured benefits are over and above the capabilities of state-of-the-art high-lift rotorcraft airfoils. The detailed Computational Fluid Dynamics (CFD) simulations, wind-tunnel experiments, and system-level modeling conducted have shown the following: (1) COMPACT, in its current state of development, is capable of reducing the adverse effects of deep dynamic stall at Mach numbers up to 0.4; (2) The two-dimensional (2D) CFD results trend well compared to the experiments; and (3) Implementation of the CFD results into a system-level model suggest that significant rotor-level benefits are possible.

Matalanis, Claude G.↗
NASA NTRSDate not supplied

Gas Phase Effects on Slosh Dynamics

Gas phase effects on slosh dynamics were quantified using computational fluid dynamics (CFD) simulation for a range of propellant and ullage gas combinations. Historical slosh modeling using potential flow solutions typically neglects gas phase effects. Regardless, the results have been shown to compare well with slosh ground tests typically performed with water and air at standard temperature and pressure. CFD analysis reveals that as the liquid-to-gas density ratio decreases, slosh dynamics change due to the relative increase in gas inertia and thus influence on liquid motion. The result is a profound impact on slosh dynamics over certain parameter spaces particularly for liquid hydrogen. Gas phase effects on slosh dynamics should be considered in slosh models especially for liquid hydrogen propellant tanks.

Jacob M Brodnick↗
NASA NTRSDate not supplied

Numerical Investigation of Film Coefficient Engineering Methodology for Dissociated, Chemically Reacting Boundary Layers

Aerothermal analysis of spacecraft planetary entry is heavily dependent on heritage engineering models. The film coefficient heat transfer model examined in this paper estimates the convective heating to the vehicle for a laminar, dissociated, chemically reacting boundary layer for an Earth atmosphere. This model requires information about the vehicle and flow field for a given trajectory point and estimates a proportional relationship between enthalpy potential and convective heat flux. In practice it is the aerothermal engineer who must decide which assumptions are appropriate for their application. This work looks at numerous CFD simulations for an arbitrary, axisymmetric flight vehicle to analyze the relative importance of both the mass and energy constraints imposed at the wall boundary, as well as the effect of various diffusion models. The sensitivity of the engineering model is assessed based on the impact of the CFD assumptions as an effort to make it available to design engineers across industry.

numerical boundary layer↗
NASA NTRSDate not supplied

Aerodynamic loss generation in a low-pressure turbine stage with high lift blading

The present work aims to investigate the loss generation mechanisms in a highly loaded low-pressure turbine (LPT) stage. The turbine employs high-lift airfoils to reduce the number of blades and therefore the overall engine weight. Large Eddy Simulation (LES) is applied to study the detailed flow fields at two representative Reynolds numbers (150,000 and 40,000). The calculated flow fields are compared with available measured data. LES calculates the measured aerodynamic performance of the current turbine stage well. Both the measurements and the CFD simulations indicate that most of the aerodynamic loss is generated by the development of secondary flows near the rotor hub. An area of low momentum and high aerodynamic loss forms at roughly 25 % span above the hub downstream of the rotor. Formation and migration of a vortex system near the hub is the primary source of the loss generation. The hub wall vortex system in this highly loaded turbine stage is quite different from the horse-shoe vortex system in a typical stationary turbine cascade. Calculated instantaneous and time-averaged flow fields at two Reynolds numbers are examined in detail to study Reynolds number effects on the turbine stage performance. Steady and unsteady flow separation on the rotor suction side is calculated at both high and low Reynolds numbers. At the lower Reynolds number of 40,000, thicker blade boundary layers increase the area of flow separation on the rotor suction side, resulting in a 1.9 % increase in aerodynamic loss compared to the higher Reynolds number case.

low pressure turbine↗
NASA NTRS2021

Anti-Phase Vortex Reduction Control for Rotor Noise Suppression

An investigation is conducted in 2019 under the NASA Ames Center Innovation Funds (CIF) project entitled “Anti-Phase Vortex Reduction Control for Rotor Noise Suppression“ to experimentally validate an anti-phase rotor noise suppression concept. The first objective of the investigation is to conduct computational fluid dynamics (CFD) simulations to investigate the noise characteristics of several anti-phase rotor designs. The second objective is to conduct a series of acoustic tests of anti-phase rotors in an anechoic chamber at Pennsylvania State University (PSU) to evaluate the merit of the anti-phase rotor concept. The CFD investigation seeks to optimize the anti-phase alternating trailing edge patterns for rotor noise suppression. The design objective is to maximize the noise reduction while maintaining the aerodynamic thrust. The investigation is performed using a three-dimensional (3D) Unsteady Reynolds-Averaged Navier-Stokes (URANS) commercial solver STAR-CCM+ together with the Ffowcs-Williams and Hawkings (FW-H) formula to obtain the aerodynamic thrust and far-field noise level. An acoustic study is conducted for 13 anti-phase design candidates based on a proprietary rotor design. The CAD geometry of the rotor is furnished by PSU. These design candidates include different alternating trailing edge (TE) waveforms, TE segment lengths, TE deflection amplitudes, and transition characteristics. The best design candidate among those explored is an anti-phase rotor that has a four-period TE waveform which results in a reduction in far-field noise level of 2.1 dB in the hover condition and a reduction of 1.1 dB in the forward flight condition at 9.7 m/s. A further acoustic study is conducted for a different rotor manufactured by APC. Five APC rotor design candidates are simulated. The best anti-phase design candidate for the APC rotor results in a reduction in far-field noise level of 4.0 dB in the hover condition. An in-phase design candidate is also studied. This in-phase design provides a noise reduction of 2.5 dB. A series of acoustic experiments in the PSU anechoic chamber have been conducted in July 2019 and October 2019. Both anti-phase and in-phase rotors fabricated for the left-hand and right-hand rotations are tested. In the hover condition, all the rotors do not provide sufficient evidence of improved acoustic performance. However, the experimental data in the hover condition are deemed to be inconclusive due to the flow recirculation in the anechoic chamber caused by the rotor downwash. In the forward flight condition at 9.7 m/s, the anti-phase right-hand rotor produces a noise reduction by as much as 6.5 dB in the frequency range of 2000-4000 Hz, while the in-phase right-hand rotor produces a noise reduction by as much as 5 dB in the same frequency range. Both the anti-phase and in-phase left hand rotors offer no evidence of noise reduction. The difference in the acoustic performance of the left-hand and right-hand rotors could be explained by the location of the microphone array which is placed to the left side of the rotors. This microphone array location could create a bias in the sound pressure level in favor of the right-hand rotor. Using the average noise reduction values, the anti-phase 4H rotor could offer a noise reduction by as much as 3.25 dB while the in-phase 4I rotor could produce up to a 2.5 dB noise reduction. Both the computational and experimental results have provided sufficient evidence to support the noise suppression capability of the proposed anti-phase rotor concepts.

Rotor noise↗
NASA NTRS2005

Advanced Turbulence Modeling Concepts

The ZCET program developed at NASA Glenn Research Center is to study hydrogen/air injection concepts for aircraft gas turbine engines that meet conventional gas turbine performance levels and provide low levels of harmful NOx emissions. A CFD study for ZCET program has been successfully carried out. It uses the most recently enhanced National combustion code (NCC) to perform CFD simulations for two configurations of hydrogen fuel injectors (GRC- and Sandia-injector). The results can be used to assist experimental studies to provide quick mixing, low emission and high performance fuel injector designs. The work started with the configuration of the single-hole injector. The computational models were taken from the experimental designs. For example, the GRC single-hole injector consists of one air tube (0.78 inches long and 0.265 inches in diameter) and two hydrogen tubes (0.3 inches long and 0.0226 inches in diameter opposed at 180 degree). The hydrogen tubes are located 0.3 inches upstream from the exit of the air element (the inlet location for the combustor). To do the simulation, the single-hole injector is connected to a combustor model (8.16 inches long and 0.5 inches in diameter). The inlet conditions for air and hydrogen elements are defined according to actual experimental designs. Two crossing jets of hydrogen/air are simulated in detail in the injector. The cold flow, reacting flow, flame temperature, combustor pressure and possible flashback phenomena are studied. Two grid resolutions of the numerical model have been adopted. The first computational grid contains 0.52 million elements, the second one contains over 1.3 million elements. The CFD results have shown only about 5% difference between the two grid resolutions. Therefore, the CFD result obtained from the model of 1.3-million grid resolution can be considered as a grid independent numerical solution. Turbulence models built in NCC are consolidated and well tested. They can handle both coarse and fine grids near the wall. They can model the effect of anisotropy of turbulent stresses and the effect of swirling. The chemical reactions of Magnusson model and ILDM method were both used in this study.

Shih, Tsan-Hsing↗