A bifurcation study of mixed-convection heat transfer in horizontal ducts

1991 ◽  
Vol 231 ◽  
pp. 157-187 ◽  
Author(s):  
K. Nandakumar ◽  
H. J. Weinitschke
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Solution Structure ◽  
Primary Branch ◽  
Two Dimensional ◽  
Solution Branch ◽  
Square Duct ◽  
Grashof Number ◽  
Aspect Ratios ◽  
Asymmetric Solution

The bifurcation structure of two-dimensional, pressure-driven flows through a horizontal, rectangular duet that is heated with a uniform flux in the axial direction and a uniform temperature around the periphery is examined. The solution structure of the flow in a square duct is determined for Grashof numbers (Gr) in the range of 0 to 106 using an arclength continuation scheme. The structure is much more complicated than reported earlier by Nandakumar, Masliyah & Law (1985). The primary branch with two limit points and a hysteresis behaviour between the two-and four-cell flow structure that was computed by Nandakumar et al. is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other, and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry-breaking bifurcation points are also found for a square duct. Thus a much richer solution structure is found with up to five solutions over certain ranges of Or. A determination of linear stability indicates that all two-dimensional solutions develop some form of unstable mode by the time Gr is increased to about 220000. In particular, the four-cell becomes unstable to asymmetric perturbations. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold-following algorithm. Transcritical points are found at aspect ratios of 1.408 and 1.456 respectively for Prandtl numbers Pr = 0.73 and 5. Above these aspect ratios the four-cell solution is no longer on the primary branch. Some of the fold curves are connected in such a way as to form a tilted cusp. When the channel cross-section is tilted even slightly (1°) with respect to the gravity vector, the bifurcation points unfold and the two-cell solution evolves smoothly as the Grashof number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Grashof number increases with increasing tilt, decreasing aspect ratio and decreasing Prandtl number.

Natural Convection of Cu-Gallium Nanofluid in Enclosures

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Cong Qi ◽  
Yurong He ◽  
Yanwei Hu ◽  
Juancheng Yang ◽  
Fengchen Li ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Convection Heat Transfer ◽  
Low Velocity ◽  
Grashof Number ◽  
Aspect Ratios ◽  
Wide Range ◽  
Temperature Dependent Properties

In this work, the natural convection heat transfer of Cu-gallium nanofluid in a differentially heated enclosure is investigated. A single-phase model is employed with constant or temperature-dependent properties of the fluid. The results are shown over a wide range of Grashof numbers, volume fractions of nanoparticles, and aspect ratios. The Nusselt number is demonstrated to be sensitive to the aspect ratio. It is found that the Nusselt number is more sensitive to thermal conductivity than viscosity at a low velocity (especially for a low aspect ratio and a low Grashof number), however, it is more sensitive to the viscosity than the thermal conductivity at a high velocity (high aspect ratio and high Grashof number). In addition, the evolution of velocity vectors, isotherms, and Nusselt number for a small aspect ratio is investigated.

scholarly journals Linear biglobal analysis of Rayleigh–Bénard instabilities in binary fluids with and without throughflow

2012 ◽  
Vol 713 ◽  
pp. 216-242 ◽  
Author(s):  
Jun Hu ◽  
Daniel Henry ◽  
Xie-Yuan Yin ◽  
Hamda BenHadid
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Critical Rayleigh Number ◽  
Two Dimensional ◽  
Binary Fluids ◽  
Transverse Modes ◽  
Aspect Ratios ◽  
Rayleigh Benard ◽  
Mode A

AbstractThree-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.

Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct

1995 ◽  
Vol 117 (1) ◽  
pp. 17-23 ◽  
Author(s):  
G. Papadopoulos ◽  
M. V. O¨tu¨gen
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Three Dimensional ◽  
Side Wall ◽  
Stream Velocity ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Wall Effects ◽  
Velocity Measurements ◽  
Aspect Ratios

The incompressible turbulent flow over a backward-facing step in a rectangular duct was investigated experimentally. The side wall effects on the core flow were determined by varying the aspect ratio (defined as the step span-to-height ratio) from 1 to 28. The Reynolds number, based on the step height and the oncoming free-stream velocity, was 26,500. Detailed velocity measurements were made, including the turbulent stresses, in a region which extended past the flow reattachment zone. Wall static pressure was also measured on both the step and flat walls. In addition, surface visualizations were obtained on all four walls surrounding the separated flow to supplement near-wall velocity measurements. The results show that the aspect ratio has an influence on both the velocity and wall pressure even for relatively large aspect ratios. For example, in the redevelopment region downstream of reattachment, the recovery pressure decreases with smaller aspect ratios. The three-dimensional side wall effects tend to slow down the relaxation downstream of reattachment for smaller aspect ratios as evidenced by the evolution of the velocity field. For the two smallest aspect ratios investigated, higher centerplane streamwise and transverse velocities were obtained which indicate a three-dimensional mean flow structure along the full span of the duct.

A Method to Predict Rudder Stall Inception from Two-dimensional Airfoil Data

2014 ◽  
Vol 58 (01) ◽  
pp. 1-19
Author(s):  
Michael J. Hughes ◽  
Young T. Shen
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Stall Inception ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Flow Similarity ◽  
Naca 0015 ◽  
Naca 0012

The behavior of the force on a rudder changes significantly after the inception of stall, requiring different mathematical formulae to compute rudder forces prior-and poststall. Determining the inception angle at which stall occurs is important for predicting the rudder force on a maneuvering ship. A method to compute the inception angle of stall on a rudder is presented in this article. The theoretical formulation is based on a flow similarity approach, which relates three-dimensional rudder stall inception with two-dimensional airfoil data. Rudders are low-aspect ratio wings, and the three-dimensional lift is based on the low-aspect ratio wing theory. The two-dimensional airfoil stall data are obtained from National Advisory Committee for Aeronautics (NACA) reports. The derived theory is first validated with wind tunnel data from foils with a NACA 0015 profile of aspect ratios 1, 2, and 3. The theory is also validated with data from foils with a NACA 0012 profile and an aspect ratio of 2, 3, and 6.

scholarly journals Experimental Investigations of Three-Dimensional Effects on Cavitating Hydrofoils

1961 ◽  
Vol 5 (03) ◽  
pp. 22-43
Author(s):  
R. W. Kermeen
Keyword(s):  
Aspect Ratio ◽  
High Speed ◽  
Three Dimensional ◽  
Cavitating Flow ◽  
Experimental Investigations ◽  
Water Tunnel ◽  
Pitching Moment ◽  
Two Dimensional ◽  
Dimensional Effects ◽  
Aspect Ratios

An investigation in the high-speed water tunnel of the hydsrodynamic characteristics of a family of three-dimensional sharp-edged hydrofoils is described. Four rectangular plan-form, 6-deg wedge profiles with aspect ratios of 4.0, 2.0, 1.0 and 0.5 were tested over a range of cavitation numbers from noncavitating to fully cavitating flow. The effects of aspect ratio on the flow and cavity configurations and on the lift, drag and pitching moment are discussed. Where data were available the results have been compared with the two-dimensional case.

Granular column collapses: further experimental results

2007 ◽  
Vol 575 ◽  
pp. 177-186 ◽  
Author(s):  
ERICA L. THOMPSON ◽  
HERBERT E. HUPPERT
Keyword(s):  
Aspect Ratio ◽  
Two Dimensional ◽  
Saturated Sand ◽  
General Applicability ◽  
Initial Height ◽  
Aspect Ratios ◽  
Water Saturated ◽  
Vertical Height ◽  
Initial Geometry ◽  
Granular Column

Experimental observations of the collapse of initially static columns of sand in axisymmetric and two-dimensional geometries are presented. The experiments were carried out using cylinders and rectangular tanks 30 to 60 cm tall, and cover aspect ratios between 0.5 and 20, where the aspect ratio is defined as the ratio of the initial height to horizontal extent of the column. The final positions of sand grains from different points initially on the outer surface of the columns are mapped. For all axisymmetric columns the point of maximum runout is found to originate from a point at fractional height 0.74 ± 0.03 of the initial vertical height of the column, independent of the aspect ratio. For two-dimensional columns the corresponding point is 0.65 ± 0.07. Collapses of columns of water-saturated sand into water display a different form of flow, which leads to there being no such well-defined point. In this case, grains from all but the innermost, basal areas of the initial column can end up in the outermost region of the final deposit. For collapses in air and aspect ratios greater than 1, the detail of the initial geometry is relatively insignificant in determining the shape of the final deposit. The results of this and previous studies thus have general applicability, even to situations with less initial symmetry. Movies are available with the online version of the paper.

Experimental Study on Depositing Arch Jamming of Elliptical Disks in a Two-Dimensional Static Hopper

2016 ◽  
Vol 32 (6) ◽  
pp. 709-716 ◽  
Author(s):  
Y.-J. Lin ◽  
C. Fang
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Physical Mechanism ◽  
Force Chains ◽  
Two Dimensional ◽  
Strong Force ◽  
Aspect Ratios ◽  
Reverse Tendency ◽  
Opening Width

AbstractDepositing arch jamming of elliptical disks at the opening of a two-dimensional static hopper is studied experimentally. The hopper slope and opening width, and the aspect ratio of elliptical disks, are varied to determine their influence on the jamming probability. The jamming probability increases as the aspect ratio increases for gentle hopper slopes, while fluctuations of jamming probability appear for more steeper hopper slopes. Increasing hopper slope decreases the jamming probability in most cases. Most jamming arches result from the strong force chains along the shorter axes of elliptical disks. The disk number consisting of jamming arches decreases as the hopper slope increases. For smaller hopper openings, it decreases as the aspect ratio increases, whilst a nearly reverse tendency appears for elliptical disks with smaller aspect ratios. The study delivers a physical mechanism of jamming phenomena in depositing elliptical disks in a two- dimensional static hopper.

Experiments on Deep-Water Waves With Two-Dimensional Surface Patterns

2003 ◽  
Vol 125 (1) ◽  
pp. 48-53 ◽  
Author(s):  
Joseph L. Hammack ◽  
Diane M. Henderson
Keyword(s):  
Time Series ◽  
Aspect Ratio ◽  
Deep Water ◽  
Surface Pattern ◽  
Two Dimensional ◽  
Aspect Ratios ◽  
Wave Basin ◽  
Surface Patterns ◽  
Two Parameters ◽  
Dimensional Surface

Experiments are conducted in a three-dimensional wave basin with a wavemaker system comprising 32 side-by-side paddles for which there is precise control. Two types of wavemaker forcings are used to create two-dimensional surface patterns: (1) two symmetric carrier waves interacting at an oblique angle and (2) a single carrier wave propagating in the x-direction with a Jacobi elliptic, sn-function modulation in the y-direction. Data are presented from overhead photographs and from time series obtained by traversing a wave-gage through the patterns. Two parameters are systematically varied: the horizontal aspect ratio of the cells comprising the surface pattern and the measure of nonlinearity of the input wavefield. Unlike such waves in shallow water for which the surface pattern is made up of six-sided cells, the wave pattern for waves in deep water is made up of rectangular cells. Both the overhead photographs and the time series show that for most values of the two parameters, the wavefields evolve with significant modulations in both the x and y directions. In particular, when the aspect ratio of the cells is below about 0.4 for a fixed measure of nonlinearity, there is significant modulation in the y-direction that results in cells with smaller aspect ratios. For aspect ratio above about 0.4, the cells appear to be stable (except for viscous decay) for smaller values of nonlinearity. However, for larger values of nonlinearity even these cells modulate in the y-direction, further increasing the aspect ratio of the evolving cells. For the largest value of nonlinearity considered, the pattern evolves into one that comprises cells with aspect ratios of about 1.

Mean Wind Flow Field around Idealized Block Arrays with Various Aspect Ratios

2013 ◽  
Vol 393 ◽  
pp. 767-773 ◽  
Author(s):  
Azli Abd Razak ◽  
Aya Hagishima ◽  
Naoki Ikegaya ◽  
Mohd Faizal Mohamad ◽  
Sheikh Ahmad Zaki
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Urban Canopy ◽  
Streamwise Velocity ◽  
Area Ratio ◽  
Mean Flow ◽  
Canopy Layer ◽  
Mean Velocity ◽  
Aspect Ratios ◽  
Mean Wind Speed

This study investigates the characteristic of spatially averaged mean velocity profile and the flow pattern within urban canopy layer especially in pedestrian level using CFD technique. Large eddies simulation (LES) was used to perform a series of simulation of the flow around block arrays with staggered arrangement under various conditions of aspect ratio, αp (roof-to-frontal area ratio) from 0.33 to 3.0. The spatially-average profiles of both mean wind speed and streamwise velocity over various block arrays were compared with each other. The analysis clarified the following two facts. 1) The vertical mean flow structure inside the canyon change due to change a plan area ratio and block aspect ratio. 2) The horizontal mean flow structure around the block change if pedestrian level change form z = 0.05h to z = 0.25h. This can be translated to the effect of high-rise building to the flow around the building.

scholarly journals A Comparative Evaluation of Snowflake Particle Size and Shape Estimation Techniques used by the Precipitation Imaging Package (PIP), Multi-Angle Snowflake Camera (MASC), and Two-Dimensional Video Disdrometer (2DVD)

2022 ◽  
Author(s):  
Charles Nelson Helms ◽  
Stephen Joseph Munchak ◽  
Ali Tokay ◽  
Claire Pettersen
Keyword(s):  
Particle Size ◽  
Aspect Ratio ◽  
Two Dimensional ◽  
Shape Estimation ◽  
Shape Fitting ◽  
Size And Shape ◽  
Horizontal Extent ◽  
Aspect Ratios ◽  
Correction Technique ◽  
Particle Size And Shape

Abstract. Measurements of snowflake particle size and shape are important for studying the snow microphysics. While a number of instruments exist that are designed to measure these important parameters, this study focuses on the measurement techniques of three digital video disdrometers: the Precipitation Imaging Package (PIP), the Multi-Angle Snowflake Camera (MASC) and the Two-Dimensional Video Disdrometer (2DVD). To gain a better understanding of the relative strengths and weaknesses of these instruments and to provide a foundation upon which comparisons can be made between studies using data from different instruments, we perform a comparative analysis of the measurement algorithms employed by each of the three instruments by applying the algorithms to snowflake images captured by PIP during the ICEP-POP 2018 field campaign. Our analysis primarily focuses on the measurements of area, equivalent diameter, and aspect ratio. Our findings indicate that area and equi-area diameter measurements using the 2DVD camera setup should be the most accurate, followed by MASC, which is slightly more accurate than PIP. In terms of the precision of the area and equi-area diameter measurements, however, MASC is considerably more precise than PIP or 2DVD, which provide similar precision once the effects of the PIP image compression algorithm are taken into account. Both PIP and MASC use shape-fitting algorithms to measure aspect ratio. While our analysis of the MASC aspect ratio suggests the measurements are reliable, our findings indicate that both the ellipse and rectangle aspect ratios produced by PIP under-performed considerably due to the shortcomings of the PIP shape-fitting techniques. That said, we also demonstrate that reliable measurements of aspect ratio can be retrieved from PIP by reprocessing the PIP images using either the MASC shape-fitting technique or a tensor-based ellipse-fitting technique. Because of differences in instrument design, 2DVD produces measurements of particle horizontal and vertical extent rather than length and width. Furthermore, the 2DVD measurements of particle horizontal extent can be contaminated by horizontal particle motion. Our findings indicate that, although the correction technique used to remove the horizontal motion contamination performs remarkably well with snowflakes despite being designed for use with rain drops, the 2DVD measurements of particle horizontal extent are potentially unreliable.

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