Numerical Simulation of a Particle in Air Flow Around a Turbine Blade

2020 ◽  
Author(s):  
Ippei Oshima ◽  
Mikito Furuichi
Keyword(s):  
Numerical Simulation ◽  
Theoretical Model ◽  
Turbine Blade ◽  
Gas Flow ◽  
Three Dimensional ◽  
Prediction Method ◽  
Stokes Number ◽  
Lagrangian Simulation ◽  
Background Gas ◽  
Liquid Mass Flow Rate

Abstract The Steam turbine is widely used for generating electricity, in the thermal, nuclear and geothermal power generation systems. A wet loss is known as one of the degrading factors of the performance. To reduce the amount of liquid phase generated by condensation and atomization from nozzles, the prediction of the distribution of liquid mass flow rate inside the turbine is important. However, the quantitative understanding and the prediction method of the liquid flow inside the turbine remain unclear because physics inside a turbine is consisting of complex multiscale and multiphase events. In the present study, we proposed a theoretical model predicting the motion of droplet particles in gas flow based on Stokes number whose model does not require numerical simulation. We also conducted the numerical validation test using three-dimensional Eulerian-Lagrangian simulation for the problem with turbine blade T106. The numerical simulation shows that the particle motion is characterized by the Stokes number, that is consistent with the assumption of the theoretical model and previous studies. When Stokes number is smaller than one, the particle trajectory just follows the gas flow streamline and avoids the impacts on the surface of T106. With increasing Stokes number, the particles begin to deviate from the gas flow. As a result, many particles collide with the surface of T106 when the Stokes number is approximately one. When the Stokes number is extremely larger than one, particles move straight regardless of the background gas flow. The good agreements between the theoretical predictions and numerical experiment results justify the use of our proposed theoretical model for the prediction of the particle flow around the turbine blade.

Numerical Simulation on Process of Flow and Heat Transfer in Upright Magnesium Reducing Furnace

2011 ◽  
Vol 383-390 ◽  
pp. 6657-6662 ◽  
Author(s):  
Jun Xiao Feng ◽  
Qi Bo Cheng ◽  
Si Jing Yu
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Temperature Field ◽  
Flue Gas ◽  
Gas Flow ◽  
Three Dimensional ◽  
Reaction Heat ◽  
Flow And Heat Transfer ◽  
Major Factors ◽  
High Chemical Reaction

Based on the analysis of structural characteristic superiority, the process of combustion, flue gas flow and heat transfer in the upright magnesium reducing furnace, the three dimensional mathematical model is devoloped. And numerical simulation is performed further with the commercial software FLUENT. Finally, the flow and temperature field in furnace and temperature field in reducing pot have been obtained. The results indicate that the upright magnesium reducing furnace has perfect flue gas flow field and temperature field to meet the challenge of the magnesium reducing process; the major factors that affect the magnesium reducing reaction are the low thermal conductivity of slag and the high chemical reaction heat absorption.

Discussion on Finite Element Model for Three Dimensional Rolling Process Analysis

2014 ◽  
Vol 496-500 ◽  
pp. 452-455
Author(s):  
Chi Chih Shen
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Finite Element ◽  
Theoretical Model ◽  
Process Analysis ◽  
Three Dimensional ◽  
Element Model ◽  
Rolling Process ◽  
Strip Rolling ◽  
Rigid Matrix

A three dimensional numerical simulation model of metal rolling formation is developed from the theoretical model. In this theoretical model, the two variables of element deformation and temperature variation are placed in a variable matrix. The thermal elastic plastic rigid matrix and heat transfer rigid matrix are placed in the same expansion rigid matrix. Furthermore, the numerical simulation analytical model developed in this paper was used to simulate aluminum strip rolling.

scholarly journals Influences of protoplanet-induced three-dimensional gas flow on pebble accretion

2020 ◽  
Vol 643 ◽  
pp. A21
Author(s):  
Ayumu Kuwahara ◽  
Hiroyuki Kurokawa
Keyword(s):  
Gas Flow ◽  
Planet Formation ◽  
Early Stage ◽  
Three Dimensional ◽  
Stokes Number ◽  
Flow Shear ◽  
Outer Planets ◽  
Symmetric Structure ◽  
Hydrodynamical Simulation ◽  
Hydrodynamical Simulations

Context. Pebble accretion is among the major theories of planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous work, Paper I, we focused on the shear regime of pebble accretion and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that of the unperturbed flow, particularly when St ≲ 10−3, where St is the Stokes number. Aims. Following on the findings of Paper I, we investigate the influence of planet-induced gas flow on pebble accretion. We did not consider the headwind of the gas in Paper I. Here, we extend our study to the headwind regime of pebble accretion. Methods. Assuming a nonisothermal, inviscid sub-Keplerian gas disk, we performed 3D hydrodynamical simulations on the spherical polar grid hosting a planet with the dimensionless mass, m = RBondi∕H, located at its center, where RBondi and H are the Bondi radius and the disk scale height, respectively. We then numerically integrated the equation of motion for pebbles in 3D using hydrodynamical simulation data. Results. We first divided the planet-induced gas flow into two regimes: flow-shear and flow-headwind. In the flow-shear regime, where the planet-induced gas flow has a vertically rotational symmetric structure, we find that the outcome is identical to what we obtained in Paper I. In the flow-headwind regime, the strong headwind of the gas breaks the symmetric structure of the planet-induced gas flow. In the flow-headwind regime, we find that the trajectories of pebbles with St ≲ 10−3 in the planet-induced gas flow differ significantly from those of the unperturbed flow. The recycling flow, where gas from the disk enters the gravitational sphere at low latitudes and exits at high latitudes, gathers pebbles around the planet. We derive the flow transition mass analytically, mt, flow, which discriminates between the flow-headwind and flow-shear regimes. From the relation between m, mt, flow and mt, peb, where mt, peb is the transition mass of the accretion regime of pebbles, we classify the results obtained in both Paper I and this study into four groups. In particular, only when the Stokes gas drag law is adopted and m < min(mt, peb, mt, flow), where the accretion and flow regime are both in the headwind regime, the accretion probability of pebbles with St ≲ 10−3 is enhanced in the planet-induced gas flow compared to that of the unperturbed flow. Conclusions. Combining our results with the spacial variety of turbulence strength and pebble size in a disk, we conclude that the planet-induced gas flow still allows for pebble accretion in the early stage of planet formation. The suppression of pebble accretion due to the planet-induced gas flow occurs only in the late stage of planet formation, more specifically, in the inner region of the disk. This may be helpful for explaining the distribution of exoplanets and the architecture of the Solar System, both of which have small inner and large outer planets.

scholarly journals Influences of protoplanet-induced three-dimensional gas flow on pebble accretion

2020 ◽  
Vol 633 ◽  
pp. A81 ◽  
Author(s):  
Ayumu Kuwahara ◽  
Hiroyuki Kurokawa
Keyword(s):  
Shear Flow ◽  
Gas Flow ◽  
Gravitational Interaction ◽  
Three Dimensional ◽  
Stokes Number ◽  
Thermal Mass ◽  
Hydrodynamical Simulation ◽  
Wide Range ◽  
Accretion Model ◽  
Hydrodynamical Simulations

Context. The pebble accretion model has the potential to explain the formation of various types of planets. The main difference between this and the planetesimal accretion model is that pebbles not only experience the gravitational interaction with the growing planet but also a gas drag force from the surrounding protoplanetary disk gas. Aims. A growing planet embedded in a disk induces three-dimensional (3D) gas flow, which may influence pebble accretion. However, so far the conventional pebble accretion model has only been discussed in the unperturbed (sub-)Keplerian shear flow. In this study, we investigate the influence of 3D planet-induced gas flow on pebble accretion. Methods. Assuming a nonisothermal, inviscid gas disk, we perform 3D hydrodynamical simulations on the spherical polar grid, which has a planet located at its center. We then numerically integrate the equation of motion of pebbles in 3D using hydrodynamical simulation data. Results. We find that the trajectories of pebbles in the planet-induced gas flow differ significantly from those in the unperturbed shear flow for a wide range of investigated pebble sizes (St = 10−3–100, where St is the Stokes number). The horseshoe flow and outflow of the gas alter the motion of the pebbles, which leads to a reduction of the width of the accretion window, wacc, and the accretion cross section, Aacc. On the other hand, the changes in trajectories also cause an increase in the relative velocity of pebbles to the planet, which offsets the reduction of wacc and Aacc. As a consequence, in the Stokes regime, the accretion probability of pebbles, Pacc, in the planet-induced gas flow is comparable to that in the unperturbed shear flow except when the Stokes number is small, St ~ 10−3, in 2D accretion, or when the thermal mass of the planet is small, m = 0.03, in 3D accretion. In contrast, in the Epstein regime, Pacc in the planet-induced gas flow becomes smaller than that in the shear flow in the Stokes regime in both 2D and 3D accretion, regardless of assumed St and m. Conclusions. Our results combined with the spacial variety of turbulence strength and pebble size in a disk, suggest that the 3D planet-induced gas flow may be helpful to explain the distribution of exoplanets and the architecture of the Solar System.

scholarly journals Numerical simulation of the aerobreakup of a water droplet

2017 ◽  
Vol 835 ◽  
pp. 1108-1135 ◽  
Author(s):  
Jomela C. Meng ◽  
Tim Colonius
Keyword(s):  
Numerical Simulation ◽  
Water Droplet ◽  
Gas Flow ◽  
Three Dimensional ◽  
Finite Volume Scheme ◽  
Droplet Deformation ◽  
Fourier Decomposition ◽  
Chaotic Flow ◽  
Interface Capturing ◽  
Instability Growth

We present a three-dimensional numerical simulation of the aerobreakup of a spherical water droplet in the flow behind a normal shock wave. The droplet and surrounding gas flow are simulated using the compressible multicomponent Euler equations in a finite-volume scheme with shock and interface capturing. The aerobreakup process is compared with available experimental visualizations. Features of the droplet deformation and breakup in the stripping breakup regime, as well as descriptions of the surrounding gas flow, are discussed. Analyses of observed surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in chaotic flow within the wake region.

Film Cooling of Turbine Blade Surface With Extended Exit Holes

2014 ◽  
Author(s):  
Fariborz Forghan ◽  
Omid Askari ◽  
Uichiro Narusawa ◽  
Hameed Metghalchi
Keyword(s):  
High Temperature ◽  
Turbine Blade ◽  
Film Cooling ◽  
Gas Flow ◽  
Three Dimensional ◽  
Suction Side ◽  
Ideal Gas ◽  
Coolant Flow ◽  
Blade Surface ◽  
Flow Through

The main goal of gas turbine design is the effective use of energy. Usually, the efficient high temperature first and second stage turbine blade surface is cooled by jet of coolant flow from extended exit holes (EEH). Against the prevailing hot gas flow, the flow through EEH must be designed to form a film of cool air over the blade. Computational analyses are performed to examine the cooling effectiveness of flow from EEH over the suction side of a blade by solving conservation equations (mass, momentum and energy) and the ideal gas equation of state for the three-dimensional, turbulent, compressible flow. A diverging flow through EEH is typically choked at its throat, resulting in a supersonic flow, a shock and then a subsonic flow downstream. The location of the shock relative to the high-temperature gas flow over the blade determines the temperature distribution along the blade surface; which is analyzed in detail when the coolant flow rate is varied.

scholarly journals Gas flow around a planet embedded in a protoplanetary disc

2019 ◽  
Vol 623 ◽  
pp. A179 ◽  
Author(s):  
Ayumu Kuwahara ◽  
Hiroyuki Kurokawa ◽  
Shigeru Ida
Keyword(s):  
Gas Flow ◽  
Three Dimensional ◽  
Stokes Number ◽  
Dimensional Structure ◽  
Solid Materials ◽  
Planetary Mass ◽  
Short Period ◽  
Hydrodynamical Simulations ◽  
Gas Accretion ◽  
The Hill

Context. The ubiquity of short-period super-Earths remains a mystery in planet formation, as these planets are expected to become gas giants via runaway gas accretion within the lifetime of a protoplanetary disc. The cores of super-Earths should form in the late stage of disc evolution to avoid runaway gas accretion. Aims. The three-dimensional structure of the gas flow around a planet is thought to influence the accretion of both gas and solid materials. In particular, the outflow in the midplane region may prevent the accretion of solid materials and delay the formation of the super-Earth cores. However, it is not yet understood how the nature of the flow field and outflow speed change as a function of the planetary mass. In this study, we investigate the dependence of gas flow around a planet embedded in a protoplanetary disc on the planetary mass. Methods. Assuming an isothermal, inviscid gas disc, we perform three-dimensional hydrodynamical simulations on the spherical polar grid, which has a planet located at its centre. Results. We find that gas enters the Bondi or Hill sphere at high latitudes and exits through the midplane region of the disc regardless of the assumed dimensionless planetary mass m = RBondi∕H, where RBondi and H are the Bondi radius of the planet and disc scale height, respectively. The altitude from where gas predominantly enters the envelope varies with planetary mass. The outflow speed can be expressed as |uout| = √3/2mcs (RBondi ≤ RHill) or |uout| = √3/2(m/3)1/3cs (RBondi ≥ RHill), where cs is the isothermal sound speed and RHill is the Hill radius. The outflow around a planet may reduce the accretion of dust and pebbles onto the planet when m ≳ √St, where S t is the Stokes number. Conclusions. Our results suggest that the flow around proto-cores of super-Earths may delay their growth and consequently help them to avoid runaway gas accretion within the lifetime of the gas disc.

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