Steady flows in rectangular cavities

1967 ◽  
Vol 28 (4) ◽  
pp. 643-655 ◽  
Author(s):  
Frank Pan ◽  
Andreas Acrivos
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Creeping Flow ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Viscous Effects ◽  
Number Range ◽  
Infinite Depth ◽  
Aspect Ratios ◽  
High Reynolds

This paper deals with the steady flow in a rectangular cavity where the motion is driven by the uniform translation of the top wall. Creeping flow solutions for cavities having aspect ratios from ¼ to 5 were obtained numerically by a relaxation technique and were shown to compare favourably with Dean & Montagnon's (1949) similarity solution, as extended by Moffatt (1964), in the region near the bottom corners of a square cavity as well as throughout the major portion of a cavity with aspect ratio equal to 5. In addition, for a Reynolds number range from 20 to 4000, flow patterns were determined experimentally by means of a photographic technique for finite cavities, as well as for cavities of effectively infinite depth. These experimental results suggest that, within finite cavities, the high Reynolds number steady flow should consist essentially of a single inviscid core of uniform vorticity with viscous effects being confined to thin shear layers near the boundaries, while, for cavities of infinite depth, the viscous and inertia forces should remain of comparable magnitude throughout the whole domain even in the limit of very large Reynolds number R.

Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

2013 ◽  
Author(s):  
Matthew A. Smith ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Internal Cooling ◽  
Number Range ◽  
Aspect Ratios ◽  
Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

Row Removal Heat Transfer Study for Pin Fin Arrays

2014 ◽  
Author(s):  
Kathryn L. Kirsch ◽  
Jason K. Ostanek ◽  
Karen A. Thole ◽  
Eleanor Kaufman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Pin Fin ◽  
Heat Transfer Augmentation ◽  
Aspect Ratios ◽  
Pin Fins ◽  
High Reynolds ◽  
Pin Fin Arrays ◽  
Transfer Study

Arrays of variably-spaced pin fins are used as a conventional means to conduct and convect heat from internal turbine surfaces. The most common pin shape for this purpose is a circular cylinder. Literature has shown that beyond the first few rows of pin fins, the heat transfer augmentation in the array levels off and slightly decreases. This paper provides experimental results from two studies seeking to understand the effects of gaps in pin spacing (row removals) and alternative pin geometries placed in these gaps. The alternative pin geometries included large cylindrical pins and oblong pins with different aspect ratios. Results from the row removal study at high Reynolds number showed that when rows four through eight were removed, the flow returned to a fully-developed channel flow in the gap between pin rows. When larger alternative geometries replaced the fourth row, heat transfer increased further downstream into the array.

Experimental Results of Flow Nozzle Based on PTC 6 for High Reynolds Number

2014 ◽  
Author(s):  
Noriyuki Furuichi ◽  
Kar-Hooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Discharge Coefficient ◽  
Experimental Results ◽  
Flow Conditions ◽  
Number Range ◽  
Discharge Coefficients ◽  
Reynolds Number Range ◽  
Lower Reynolds Number ◽  
High Reynolds

Discharge coefficients for three flow nozzles based on ASME PTC 6 are measured under many flow conditions at AIST, NMIJ and PTB. The uncertainty of the measurements is from 0.04% to 0.1% and the Reynolds number range is from 1.3×105 to 1.4×107. The discharge coefficients obtained by these experiments is not exactly consistent to one given by PTC 6 for all examined Reynolds number range. The discharge coefficient is influenced by the size of tap diameter even if at the lower Reynolds number region. Experimental results for the tap of 5 mm and 6 mm diameter do not satisfy the requirements based on the validation procedures and the criteria given by PTC 6. The limit of the size of tap diameter determined in PTC 6 is inconsistent with the validation check procedures of the calibration result. An enhanced methodology including the term of the tap diameter is recommended. Otherwise, it is recommended that the calibration test should be performed at as high Reynolds number as possible and the size of tap diameter is desirable to be as small as possible to obtain the discharge coefficient with high accuracy.

Further Investigation of Discharge Coefficient for PTC 6 Flow Nozzle in High Reynolds Number

2015 ◽  
Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
High Reynolds Number ◽  
Discharge Coefficient ◽  
Flow Region ◽  
Number Range ◽  
Discharge Coefficients ◽  
Reynolds Number Range ◽  
High Reynolds

The discharge coefficients of the throat tap flow nozzle based on ASME PTC 6 are measured in wide Reynolds number range from Red=5.8×104 to Red=1.4×107. The nominal discharge coefficient (the discharge coefficient without tap) is determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. Finally, by combing the nominal discharge coefficient and the tap effect determined in three flow regions, that is, laminar, transitional and turbulent flow region, the new equations of the discharge coefficient are proposed in three flow regions.

On the continuum theory for the large Reynolds number spherical expansion into a near vacuum

1975 ◽  
Vol 68 (4) ◽  
pp. 625-638 ◽  
Author(s):  
N. C. Freeman ◽  
R. S. Johnson ◽  
S. Kumar ◽  
W. B. Bush
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Continuum Theory ◽  
Large Reynolds Number ◽  
Heat Conducting ◽  
Sonic Point ◽  
Spherical Expansion ◽  
High Reynolds ◽  
Background Gas ◽  
Very High

The steady, spherically symmetric flow of a compressible gas is considered. The gas is both viscous and heat-conducting. In the limit of very high Reynolds number (= α−1, α → 0) and correspondingly low pressure at infinity, the structure of the whole flow field is discussed. The five regions that arise by virtue of the limit α → 0 are briefly considered. Special care is given to the matching across the overlap domains and the first region (close to, but outside, the sonic point) and the fifth (where the pressure adjusts to its ambient value) are carefully examined. It is argued that the application of appropriate matching principles, together with judicious use of numerical solutions, allows an arbitrary pressure and temperature to be assigned to the background gas.

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