Similarity Parameters for Comparing Erosive Particle Trajectories in Hot Air and Cold Air Radial Inflow Turbines

1974 ◽  
Vol 96 (4) ◽  
pp. 358-364 ◽  
Author(s):  
W. B. Clevenger ◽  
W. Tabakoff
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Gas Flows ◽  
Particle Trajectories ◽  
Cold Air ◽  
Hot Gas ◽  
Hot Air ◽  
Radial Turbine ◽  
Cold Gas

The similarity parameters that can be used to relate erosive particle trajectories in hot gas and equivalent cold gas flows are derived from the equations of motion. The flow in a radial turbine is used as the basis for studying the range of applicability of these similarity parameters. The study includes the vortex and rotor regions of the radial turbine and indicates the ranges of Reynolds number within which these parameters can be used. In addition, the study shows that when general trends of particle trajectories are to be considered, and precise trajectories are not necessary, one of the similarity parameters can be used for Reynolds numbers that are not within the limits indicated for precisely similar trajectories.

Flow about a fluid sphere at low to moderate Reynolds numbers

1987 ◽  
Vol 177 ◽  
pp. 1-18 ◽  
Author(s):  
D. L. R. Oliver ◽  
J. N. Chung
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Solid Sphere ◽  
Fluid Sphere ◽  
State Equations ◽  
Drag Coefficients ◽  
Low Reynolds Number Flows ◽  
Analytical Series ◽  
Reynolds Number Flows

The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 107 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

An almost-inviscid geostrophic flow

1962 ◽  
Vol 12 (1) ◽  
pp. 129-134 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Rigid Rotation ◽  
Velocity Variation ◽  
Geostrophic Flow ◽  
The Difference ◽  
Streaming Motion

An almost rigid rotation of a viscous fluid is produced by dividing the containing cylinder into two sections and rotating them at slightly different speeds. The fluid velocity can be separated into two parts, a swirl about the axis and a streaming motion in the axial planes. When the difference in the speeds of rotation of the two sections is small, the equations of motion can be linearized. The solution is found for large Reynolds numbers and provides an illustration of the way in which the conditions of geostrophic flow (no velocity variation in the axial direction and an inability to insist on undistrubed flow at infinity) are approached as the Reynolds number tends to infinity.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

Experiments on the Resistance Law for Non-Darcy Compressible Gas Flows in Porous Media

1974 ◽  
Vol 96 (4) ◽  
pp. 353-357 ◽  
Author(s):  
B. A. Masha ◽  
G. S. Beavers ◽  
E. M. Sparrow
Keyword(s):  
Reynolds Number ◽  
Porous Material ◽  
Incompressible Flow ◽  
Gas Flow ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Gas Flows ◽  
Pressure Distributions ◽  
Flow Through ◽  
Compressible Gas

Experiments were performed to examine the resistance law for non-Darcy compressible gas flow through a porous material. A particular objective of the investigation was to determine whether a resistance law deduced from incompressible flow experiments could be applied to flows with significant density changes. To this end, the coefficients appearing in the Forchheimer resistance law were first determined from experiments in the incompressible flow regime. These values were then used in an analytical model employing the Forchheimer resistance law to predict streamwise pressure distributions for subsonic compressible flow through the porous material. Corresponding experimental pressure distributions were measured for flow Reynolds numbers up to 81.6. At the highest Reynolds number of the tests the density changed by about a factor of two along the length of the porous medium. The greatest discrepancy between experimental and predicted pressures at any Reynolds number was 2 percent. This agreement lends strong support to the validity of using the incompressible Forchheimer resistance law for subsonic flows in which density changes are significant.

scholarly journals Temporal stability of free liquid threads with surface viscoelasticity

2018 ◽  
Vol 846 ◽  
pp. 877-901 ◽  
Author(s):  
A. Martínez-Calvo ◽  
A. Sevilla
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Temporal Stability ◽  
Reynolds Numbers ◽  
Elasticity Parameter ◽  
Insoluble Surfactant ◽  
Stress Boundary Conditions ◽  
Stress Boundary ◽  
Maximum Amplification ◽  
Effect Of Surface

We analyse the effect of surface viscoelasticity on the temporal stability of a free cylindrical liquid jet coated with insoluble surfactant, extending the results of Timmermans & Lister (J. Fluid Mech., vol. 459, 2002, pp. 289–306). Our development requires, in particular, deriving the correct expressions for the normal and tangential stress boundary conditions at a general axisymmetric interface when surface viscosity is modelled with the Boussinesq–Scriven constitutive equation. These stress conditions are applied to obtain a new dispersion relation for the liquid thread, which is solved to describe its temporal stability as a function of four governing parameters, namely the capillary Reynolds number, the elasticity parameter, and the shear and dilatational Boussinesq numbers. It is shown that both surface viscosities have a stabilising influence for all values of the capillary Reynolds number and elasticity parameter, the effect being more pronounced at low capillary Reynolds numbers. The wavenumber of maximum amplification depends non-monotonically on the Boussinesq numbers, especially for very viscous threads at low values of the elasticity parameter. Finally, two different lubrication approximations of the equations of motion are derived. While the validity of the leading-order model is limited to small enough values of the elasticity parameter and of the Boussinesq numbers, a higher-order parabolic model is able to accurately capture the linearised behaviour for the whole range of values of the four control parameters.

scholarly journals Hot Gas in Galactic Haloes and Winds

1980 ◽  
Vol 5 ◽  
pp. 411-417
Author(s):  
Lennox L. Cowie
Keyword(s):  
Spiral Galaxies ◽  
Elliptical Galaxies ◽  
Solar Neighborhood ◽  
Gas Flows ◽  
Hot Gas ◽  
Upper Limits ◽  
Alternative Suggestion ◽  
Emission Studies ◽  
Galactic Haloes ◽  
Cold Gas

At this time we have no direct evidence for the presence of hot gaseous haloes or winds associated with galaxies. We do know that hot gas exists in conjunction with cold gas in the disks of the spirals and that this gas is hot enough to form a substantial corona. There are also a number of indirect observations which would suggest that hot gas flows and possibly bound hot gas occur in both elliptical and spiral galaxies.In the case of elliptical galaxies the expected accumulated mass loss from the stars is not observed. Typical upper limits to the mass of cold gas at less than 1040K are around 108 M based on 21cm emission studies of the galaxies (reviewed by Van Woerden 1977). We would expect almost two orders of magnitude more material than this to have been ejected from the stars. Burke (1968), Johnson and Axford (1971) and Mathews and Baker (1971) postulated the existance of a hot galactic wind with temperatures of a few times 1060K powered by supernovae, in order to clear material from these galaxies. The evidence for hot galactic haloes around spiral galaxies is even more indirect and is based on the existance of high latitude cold clouds in our own galaxy. The velocities and number of these clouds imply that they almost certainly lie high above the galactic cold gas which extends only to a height of 130 Fc in the solar neighborhood. Spitzer therefore suggested in 1956 that an intercloud gas would have to exist to keep these clouds confined, and that to have such a large scaleheight it would have to be hot with temperatures of around 1060K. (An alternative suggestion by Pickelner (1955) was that the halo was cold but supported by turbulent velocities of around 70 km s-1.) The Spitzer Halo was assumed to be maintained by energetic particles from SN in the plane.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

Performance Characteristics of a Microscale Ranque–Hilsch Vortex Tube

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
A. F. Hamoudi ◽  
A. Fartaj ◽  
G. W. Rankin
Keyword(s):  
Reynolds Number ◽  
Vortex Tube ◽  
Reynolds Numbers ◽  
Performance Characteristics ◽  
Energy Separation ◽  
Dimensionless Temperature ◽  
Inlet Temperature ◽  
Separation Performance ◽  
Air Mass ◽  
Cold Air

The results of an experimental investigation of the energy separation performance of a microscale Ranque–Hilsch vortex tube are presented. The supply channel Reynolds number of a microscale Ranque–Hilsch vortex tube is varied over a considerable range, which extends into the laminar flow regime in order to determine the minimum conditions for cooling. Experiments are conducted for a fixed geometry and control valve setting. At low Reynolds numbers based on the inlet tube hydraulic diameter and average velocity, the results exhibit an increase in dimensionless temperature in both the hot and cold outlets as the Reynolds number is increased from zero, reaching maximum values below 500 and 1000, respectively. The hot outlet dimensionless temperature decreases after reaching its maximum and achieves a minimum value at a Reynolds number below 1500. It then increases steadily with further increases in Reynolds number. The cold outlet dimensionless temperature decreases steadily after the maximum to become negative at a Reynolds number of approximately 1800. This implies that the cooling effect occurs at Reynolds numbers consistent with turbulent flow. The performance characteristics of the microscale vortex tube operating at higher inlet pressures of 200kPa, 300kPa, and 400kPa with an average inlet temperature of 293.6K are also presented for cold air mass ratio values over the range of 0.05–0.95. An increase in the inlet pressure causes the values of the dimensionless cold temperature difference to increase over the whole range of the cold air mass fraction. An unstable operation is observed at a length to diameter ratio of approximately 10, causing radial mixing between the cold and hot flow streams and a dramatic change in the cold mass flow fraction plot.

Design and CFD Analysis of a Novel Compact Mixing Chamber in Blast Furnace Ironmaking

2021 ◽  
pp. 1-22
Author(s):  
Tanmay Dutta
Keyword(s):  
Blast Furnace ◽  
Carbon Dioxide Emission ◽  
Cfd Analysis ◽  
Efficient Design ◽  
Efficient Operation ◽  
Cold Air ◽  
Hot Air ◽  
Mixing Chamber ◽  
Hot Blast ◽  
Cold Gas

Abstract Homogeneous mixing of hot air from the hot blast stove with suitable quantity of cold air in a mixing chamber is very essential to maintain uniform temperature of hot air at all tuyers of a blast furnace. Proper design of the mixing chamber is very important for stable and efficient operation of blast furnace, lower energy consumption, and lower carbon dioxide emission. Comprehensive understanding of the physics of the mixing process is very essential for efficient design of the mixing chamber. In this paper CFD simulations are conducted to analyze the mixing of hot and cold air in a tangential cold gas inlet type and in a radial cold gas inlet type mixing chambers, which are commonly used in the industry. Results show that both types of mixing chamber produce very non-homogeneous mixture of cold and hot air despite having large mixing length in the long hot blast main. Also, design of a novel compact mixing chamber is presented and CFD analysis of this mixing chamber is conducted. The new mixing chamber is found to produce almost homogeneously mixed air stream within a very short length due to very high turbulence of the intensely swirling air flow. Also, the new mixing chamber is found to save large amount of high quality thermal energy, which is wasted in the other two designs through the wall of the long hot blast main.

Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers

1969 ◽  
Vol 37 (1) ◽  
pp. 95-114 ◽  
Author(s):  
Robert Leigh Underwood
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Number Range ◽  
Flow Parameters ◽  
Flow Past

The steady, two-dimensional, incompressible flow past a circular cylinder is calculated for Reynolds numbers up to ten. An accurate description of the flow field is found by employing the semi-analytical method of series truncation to reduce the governing partial differential equations of motion to a system of ordinary differential equations which can be integrated numerically. Results are given for Reynolds numbers between 0.4 and 10.0 (based on diameter). The Reynolds number at which separation first occurs behind the cylinder is found to be 5.75. Over the entire Reynolds number range investigated, characteristic flow parameters such as the drag coefficient, pressure coefficient, standing eddy length, and streamline pattern compare favourably with available experimental data and numerical solution results.

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