Transition scenario of a sphere freely falling in a vertical tube

2012 ◽  
Vol 711 ◽  
pp. 40-60 ◽  
Author(s):  
Thibaut Deloze ◽  
Yannick Hoarau ◽  
Jan Dušek
Keyword(s):  
Density Ratio ◽  
Vertical Tube ◽  
Falling Sphere ◽  
Unsteady Wake ◽  
Planar Trajectory ◽  
Freely Moving ◽  
Wall Interaction ◽  
Density Ratios ◽  
Two Stages ◽  
Transition Scenario

AbstractThe paper presents the results of direct numerical simulations of the fall of a single freely moving sphere in a vertical circular tube. Most results are obtained for the solid–fluid density ratio ${\rho }_{s} / \rho = 2$. The parametric investigation is carried out depending on the Galileo number defined in Jenny, Dušek & Bouchet J. Fluid Mech., vol. 508, 2004, pp. 201–239. A qualitatively new scenario is found, as compared to that of an unconfined sphere. The primary bifurcation making the sphere deviate from a vertical fall along the tube axis at a constant velocity is of Hopf type. It sets in at a Galileo number (between 155 and 160) similar to that for an unconfined sphere. We find evidence for two stages of the primary regime: a planar trajectory at $G= 160$ and a helical one (at $G= 165$ and 170). At these Galileo numbers, the regime is perfectly periodic, with a slow period corresponding to a Strouhal number only slightly above 0.01. The dynamics is identified as a periodic wake–wall interaction. The helical regime is found to give way directly to chaos between $G= 170$ and $G= 180$. This transition is associated with the onset of vortex shedding in the wake of the falling sphere and with a complex interaction between the unsteady wake and the wall marked by intermittent wake extinction. The effect of density ratio is partly investigated at $G= 250$ by considering three density ratios: 2, 3 and 5. A significant change of behaviour is found between the ratios 3 and 5.

Equation of State’s Crossover Enhancement of Pseudopotential Lattice Boltzmann Modeling of CO2 Flow in Homogeneous Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 434
Author(s):  
Assetbek Ashirbekov ◽  
Bagdagul Kabdenova ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Equations Of State ◽  
Density Ratio ◽  
Narrow Channel ◽  
Lattice Boltzmann Model ◽  
High Density Ratio ◽  
Homogeneous Porous Medium ◽  
Density Ratios

The original Shan-Chen’s pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile.

A Numerical Study of Flow and Heat Transfer in Rotating Rectangular Channels AR=4 With 45 deg Rib Turbulators by Reynolds Stress Turbulence Model

2003 ◽  
Vol 125 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Mohammad Al-Qahtani ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Density Ratio ◽  
Convective Transport ◽  
High Density ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Rectangular Channels ◽  
Density Ratios

Computations were performed to study three-dimensional turbulent flow and heat transfer in stationary and rotating 45 deg ribbed rectangular channels for which experimental heat transfer data were available. The channel aspect ratio (AR) is 4:1, the rib height-to-hydraulic diameter ratio e/Dh is 0.078 and the rib-pitch-to-height ratio P/e is 10. The rotation number and inlet coolant-to-wall density ratios, Δρ/ρ, were varied from 0.0 to 0.28 and from 0.122 to 0.40, respectively, while the Reynolds number was fixed at 10,000. Also, two channel orientations (β=90deg and 135 deg from the rotation direction) were investigated with focus on the high rotation and high density ratios effects on the heat transfer characteristics of the 135 deg orientation. These results show that, for high rotation and high density ratio, the rotation induced secondary flow overpowered the rib induced secondary flow and thus change significantly the heat transfer characteristics compared to the low rotation low density ratio case. A multi-block Reynolds-Averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure. In the present method, the convective transport equations for momentum, energy, and turbulence quantities are solved in curvilinear, body-fitted coordinates using the finite-analytic method.

Film Cooling of the Gas Turbine Endwall by Discrete-Hole Injection

1996 ◽  
Vol 118 (2) ◽  
pp. 278-284 ◽  
Author(s):  
M. Y. Jabbari ◽  
K. C. Marston ◽  
E. R. G. Eckert ◽  
R. J. Goldstein
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Hole Injection ◽  
Qualitative Information ◽  
Cooling Effectiveness ◽  
Cooling Performance ◽  
Film Cooling Effectiveness ◽  
Density Ratios

Film cooling performance for injection through discrete holes in the endwall of a turbine blade is investigated. The effectiveness is measured at 60 locations in the region covered by injection. Three nominal blowing rates, two density ratios, and two approaching flow Reynolds numbers are examined. Analysis of the data reveals that even 60 locations are insufficient for the determination of the field of film cooling effectiveness with its strong local variations. Visualization of the traces of the coolant jets on the endwall surface, using ammonium-diazo-paper, provides useful qualitative information for the interpretation of the measurements, revealing the paths and interaction of the jets, which change with blowing rate and density ratio.

Effect of Density Ratio on Film-Cooling Effectiveness Distribution and Its Uniformity for Several Hole Geometries on a Flat Plate

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Jiaxu Yao ◽  
Jin Xu ◽  
Ke Zhang ◽  
Jiang Lei ◽  
Lesley M. Wright
Keyword(s):  
Flat Plate ◽  
Film Cooling ◽  
Density Ratio ◽  
Lateral Spread ◽  
Spanwise Direction ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Cylindrical Holes ◽  
Density Ratios ◽  
Compound Angle

The film cooling effectiveness distribution and its uniformity downstream of a row of film cooling holes on a flat plate are investigated by pressure sensitive paint (PSP) under different density ratios. Several hole geometries are studied, including streamwise cylindrical holes, compound-angled cylindrical holes, streamwise fan-shape holes, compound-angled fan-shape holes, and double-jet film-cooling (DJFC) holes. All of them have an inclination angle (θ) of 35 deg. The compound angle (β) is 45 deg. The fan-shape holes have a 10 deg expansion in the spanwise direction. For a fair comparison, the pitch is kept as 4d for the cylindrical and the fan-shape holes, and 8d for the DJFC holes. The uniformity of effectiveness distribution is described by a new parameter (Lateral-Uniformity, LU) defined in this paper. The effects of density ratios (DR = 1.0, 1.5 and 2.5) on the film-cooling effectiveness and its uniformity are focused. Differences among geometries and effects of blowing ratios (M = 0.5, 1.0, 1.5, and 2.0) are also considered. The results show that at higher density ratios, the lateral spread of the discrete-hole geometries (i.e., the cylindrical and the fan-shape holes) is enhanced, while the DJFC holes is more advantageous in film-cooling effectiveness. Mostly, a higher lateral-uniformity is obtained at DR = 2.5 due to better coolant coverage and enhanced lateral spread, but the effects of the density ratio on the lateral-uniformity are not monotonic in some cases. Utilizing the compound angle configuration leads to an increased lateral-uniformity due to a stronger spanwise motion of the jet. Generally, with a higher blowing ratio, the lateral-uniformity of the discrete-hole geometries decreases due to narrower traces, while that of the DJFC holes increases due to a stronger spanwise movement.

Unsteady Wake Effect on Film Effectiveness and Heat Transfer Coefficient From a Turbine Blade With One Row of Air and CO2 Film Injection

1994 ◽  
Vol 116 (4) ◽  
pp. 921-928 ◽  
Author(s):  
S. Ou ◽  
J. C. Han
Keyword(s):  
Heat Transfer ◽  
Strouhal Number ◽  
Turbine Blade ◽  
Density Ratio ◽  
Transfer Coefficients ◽  
Suction Surface ◽  
Wake Effect ◽  
Pressure Surface ◽  
Heat Transfer Coefficients ◽  
Unsteady Wake

The effect of unsteady wake and film injection on heat transfer coefficients and film effectiveness from a gas turbine blade was found experimentally. A spoked wheel type wake generator produced the unsteady flow. Experiments were done with a five airfoil linear cascades in a low-speed wind tunnel at a chord Reynolds number of 3 × 105, two wake Strouhal numbers of 0.1 and 0.3, and a no-wake case. A model turbine blade injected air or CO2 through one row of film holes each on the pressure and suction surfaces. The results show that the large-density injectant (CO2) causes higher heat transfer coefficients on the suction surface and lower heat transfer coefficients on the pressure surface. At the higher blowing ratios of 1.0 and 1.5, the film effectiveness increases with increasing injectant-to-mainstream density ratio at a given Strouhal number. However, the density ratio effect on film effectiveness is reversed at the lowest blowing ratio of 0.5. Higher wake Strouhal numbers enhance the heat transfer coefficients but reduce film effectiveness for both density ratio injectants at all three blowing ratios. The effect of the wake Strouhal number on the heat transfer coefficients on the suction surface is greater than that on the pressure surface.

Comprehensive studies on hot compaction and vibration assisted compaction tests of aluminum powder

2020 ◽  
pp. 1-20 ◽  
Author(s):  
Qiang Zhou ◽  
Shutao Song ◽  
Quanfang Chen ◽  
Yuanli Bai
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Finite Element Model ◽  
Density Ratio ◽  
Element Model ◽  
Powder Compaction ◽  
Compression Pressure ◽  
Cold Compaction ◽  
Hot Compaction ◽  
Density Ratios

Abstract Aluminum powder compaction was studied using both test and simulation. Cold compaction, hot compaction and vibration assisted (cold) compaction tests were conducted to achieve different density ratios. Firstly, hot compaction test (at 300°C, compression pressure 140MPa) improved about 6% compared with cold compaction under the same compression pressure. Secondly, although the relative density ratio doesn’t obviously improve at vibration assisted (cold) compaction, the strength of the specimens made under vibration loading is much better than those of cold compaction. Additionally, finite element models with well calibrated Drucker Prager Cap (DPC) material constitutive model were built in Abaqus/standard to simulate the powder compaction process. The results of finite element model have very good correlations with test results up to the tested range, and this finite element model further predicts the loading conditions needed to achieve the higher density ratios. Two exponential equations of the predicted density ratio were obtained by combining the test data and the simulation results. A new analytical solution was developed to predict the axial pressure versus the density ratio for the powder compaction according to DPC material model. The results between the analytical solution and the simulation model have a very good match.

Turbine Vane Endwall Film Cooling Effectiveness of Different Purge Slot Configurations in a Linear Cascade

2019 ◽  
Author(s):  
Gunther Müller ◽  
Christian Landfester ◽  
Martin Böhle ◽  
Robert Krewinkel
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Region Of Interest ◽  
Experimental Tests ◽  
Secondary Flows ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Turbine Vane ◽  
Density Ratios ◽  
Endwall Film Cooling

Abstract This study is concerned with the film cooling effectiveness of the flow issuing from the gap between the NGV and the transition duct on the NGV endwall, i.e. the purge slot. Different slot widths, positions and injection angles were examined in order to represent changes due to thermal expansion as well as design modifications. Apart from these geometric variations, different blowing ratios (BR) and density ratios (DR) were realized to investigate the effects of the interaction between secondary flow and film cooling effectiveness. The experimental tests were performed in a linear scale-1 cascade equipped with four highly loaded turbine vanes at the Institute of Fluid Mechanics and Fluid Machinery of the University of Kaiserslautern. The mainstream flow parameters were, with a Reynolds number of 300,000 and a Mach number (outlet) of 0.6, set to meet real engine conditions. By using various flow conditioners, periodic flow was obtained in the region of interest (ROI). The adiabatic film cooling effectiveness was determined by using the Pressure Sensitive Paint (PSP) technique. In this context, nitrogen and carbon dioxide were used as tracer gases realizing two different density ratios DR = 1.0 and 1.6. The investigation was conducted for a broad range of blowing ratios with 0.25 ≤ BR ≤ 1.50. In combination with 10 geometry variations and the aforementioned blowing and density ratio variations 100 single operating points were investigated. For a better understanding of the coolant distribution, the secondary flows on the endwall were visualized by oil dye. The measurement results will be discussed based on the areal distribution of film cooling effectiveness, its lateral spanwise as well as its area average. The results will provide a better insight into various parametric effects of gap variations on turbine vane endwall film cooling performance — notably under realistic engine conditions.

Film Cooling of the Gas Turbine Endwall by Discrete-Hole Injection

1994 ◽  
Author(s):  
M. Y. Jabbari ◽  
K. C. Marston ◽  
E. R. G. Eckert ◽  
R. J. Goldstein
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Hole Injection ◽  
Qualitative Information ◽  
Cooling Effectiveness ◽  
Cooling Performance ◽  
Film Cooling Effectiveness ◽  
Density Ratios

Film cooling performance for injection through discrete holes in the endwall of a turbine blade is investigated. The effectiveness is measured at sixty locations in the region covered by injection. Three nominal blowing rates, two density ratios, and two approaching flow Reynolds numbers are examined. Analysis of the data reveals that even sixty locations are insufficient for the determination of the field of film cooling effectiveness with its strong local variations. Visualization of the traces of the coolant jets on the endwall surface, using ammonium-diazo-paper, provides useful qualitative information for the interpretation of the measurements, revealing the paths and interaction of the jets which change with blowing rate and density ratio.

Latticework (Vortex) Cooling Effectiveness: Part 2 — Rotating Channel Experiments

2004 ◽  
Author(s):  
S. Acharya ◽  
Fuguo Zhou ◽  
Jonathan Lagrone ◽  
Gazi Mahmood ◽  
Ronald S. Bunker
Keyword(s):  
Heat Transfer ◽  
Thermal Performance ◽  
Density Ratio ◽  
Transfer Coefficients ◽  
Performance Factors ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Smooth Channel ◽  
Rib Turbulators ◽  
Density Ratios

The heat transfer and pressure drop characteristics of latticework coolant blade passages have been investigated experimentally under conditions of rotation. Stationary studies with the latticework configuration have shown potential advantages including spatially-uniform streamwise distributions of the heat transfer coefficient, greater blade strength, and enhancement levels comparable to conventional rib turbulators. In the present study, a latticework coolant passage, with orthogonal-ribs, is studied in a rotating heat transfer test-rig for a range of Reynolds numbers (Res), Rotation numbers (Ros), and density ratios. Measurements indicate that for Res≥20,000, the latticework coolant passage provides very uniform streamwise distributions of the Nusselt number (Nus) with enhancement levels (relative to smooth-channel values) in the range of 2.0 to 2.5. No significant dependence of Nus on Ros and density ratio is observed except at lower Res values (≤10,000). Nusselt numbers are highest immediately downstream of a turn indicating that bend-effects play a major role in enhancing heat transfer. Friction factors are relatively insensitive to Ros, and thermal performance factors at higher Res values appear to be comparable to those obtained with conventional rib-turbulators. The present study indicates that latticework cooling geometry can provide comparable heat transfer enhancements and thermal performance factors as conventional rib-turbulators, with potential benefits of streamwise uniformity in the heat transfer coefficients and added blade strength.

Unsteady Wake and Coolant Density Effects on Turbine Blade Film Cooling Using PSP Technique

2010 ◽  
Author(s):  
Akhilesh P. Rallabandi ◽  
Shiou-Jiuan Li ◽  
Je-Chin Han
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Leading Edge ◽  
Suction Side ◽  
Suction Surface ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Unsteady Wake ◽  
Lift Off ◽  
Film Cooling Holes

The effect of an unsteady stator wake (simulated by wake rods mounted on a spoke wheel wake generator) on the modeled rotor blade is studied using the Pressure Sensitive Paint (PSP) mass transfer analogy method. Emphasis of the current study is on the mid-span region of the blade. The flow is in the low Mach number (incompressible) regime. The suction (convex) side has simple angled cylindrical film-cooling holes; the pressure (concave) side has compound angled cylindrical film cooling holes. The blade also has radial shower-head leading edge film cooling holes. Strouhal numbers studied range from 0 to 0.36; the exit Reynolds Number based on the axial chord is 530,000. Blowing ratios range from 0.5 to 2.0 on the suction side; 0.5 to 4.0 on the pressure side. Density ratios studied range from 1.0 to 2.5, to simulate actual engine conditions. The convex suction surface experiences film-cooling jet lift-off at higher blowing ratios, resulting in low effectiveness values. The film coolant is found to reattach downstream on the concave pressure surface, increasing effectiveness at higher blowing ratios. Results show deterioration in film cooling effectiveness due to increased local turbulence caused by the unsteady wake, especially on the suction side. Results also show a monotonic increase in film-cooling effectiveness on increasing the coolant to mainstream density ratio.

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