Structure of thermal boundary layers in turbulent Rayleigh–Bénard convection

2007 ◽  
Vol 572 ◽  
pp. 231-254 ◽  
Author(s):  
R. DU PUITS ◽  
C. RESAGK ◽  
A. TILGNER ◽  
F. H. BUSSE ◽  
A. THESS
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Temperature Difference ◽  
Temperature Fluctuation ◽  
Scaling Exponent ◽  
Data Set ◽  
Cooling Plate ◽  
Mean Temperature ◽  
The Mean ◽  
Rayleigh Benard

We report high-resolution local-temperature measurements in the upper boundary layer of turbulent Rayleigh–Bénard (RB) convection with variable Rayleigh number Ra and aspect ratio Γ. The primary purpose of the work is to create a comprehensive data set of temperature profiles against which various phenomenological theories and numerical simulations can be tested. We performed two series of measurements for air (Pr = 0.7) in a cylindrical container, which cover a range from Ra≈109 to Ra≈1012 and from Γ≈1 to Γ≈10. In the first series Γ was varied while the temperature difference was kept constant, whereas in the second series the aspect ratio was set to its lowest possible value, Γ=1.13, and Ra was varied by changing the temperature difference. We present the profiles of the mean temperature, root-mean-square (r.m.s.) temperature fluctuation, skewness and kurtosis as functions of the vertical distance z from the cooling plate. Outside the (very short) linear part of the thermal boundary layer the non-dimensional mean temperature Θ is found to scale as Θ(z)∼zα, the exponent α≈0.5 depending only weakly on Ra and Γ. This result supports neither Prandtl's one-third law nor a logarithmic scaling law for the mean temperature. The r.m.s. temperature fluctuation σ is found to decay with increasing distance from the cooling plate according to σ(z)∼zβ, where the value of β is in the range -0.30>β>-0.42 and depends on both Ra and Γ. Priestley's β=−1/3 law is consistent with this finding but cannot explain the variation in the scaling exponent. In addition to profiles we also present and discuss boundary-layer thicknesses, Nusselt numbers and their scaling with Ra and Γ.

scholarly journals The airglow layer emission altitude cannot be determined unambiguously from temperature comparison with lidars

2018 ◽  
Vol 18 (9) ◽  
pp. 6691-6697 ◽  
Author(s):  
Tim Dunker
Keyword(s):  
Temperature Difference ◽  
Minimum Temperature ◽  
Rotational Temperature ◽  
Half Maximum ◽  
Data Set ◽  
Gaussian Distributions ◽  
Northern Norway ◽  
Mean Temperature ◽  
The Mean ◽  
Emission Height

Abstract. I investigate the nightly mean emission height and width of the OH* (3–1) layer by comparing nightly mean temperatures measured by the ground-based spectrometer GRIPS 9 and the Na lidar at ALOMAR. The data set contains 42 coincident measurements taken between November 2010 and February 2014, when GRIPS 9 was in operation at the ALOMAR observatory (69.3∘ N, 16.0∘ E) in northern Norway. To closely resemble the mean temperature measured by GRIPS 9, I weight each nightly mean temperature profile measured by the lidar using Gaussian distributions with 40 different centre altitudes and 40 different full widths at half maximum. In principle, one can thus determine the altitude and width of an airglow layer by finding the minimum temperature difference between the two instruments. On most nights, several combinations of centre altitude and width yield a temperature difference of ±2 K. The generally assumed altitude of 87 km and width of 8 km is never an unambiguous, good solution for any of the measurements. Even for a fixed width of ∼ 8.4 km, one can sometimes find several centre altitudes that yield equally good temperature agreement. Weighted temperatures measured by lidar are not suitable to unambiguously determine the emission height and width of an airglow layer. However, when actual altitude and width data are lacking, a comparison with lidars can provide an estimate of how representative a measured rotational temperature is of an assumed altitude and width. I found the rotational temperature to represent the temperature at the commonly assumed altitude of 87.4 km and width of 8.4 km to within ±16 K, on average. This is not a measurement uncertainty.

scholarly journals The OH<sup>*</sup>(3–1) layer emission altitude cannot be determined unambiguously from temperature comparison with lidars

2017 ◽  
Author(s):  
Tim Dunker
Keyword(s):  
Temperature Difference ◽  
Minimum Temperature ◽  
Rotational Temperature ◽  
Half Maximum ◽  
Data Set ◽  
Gaussian Distributions ◽  
Northern Norway ◽  
Mean Temperature ◽  
The Mean ◽  
Emission Height

Abstract. I investigate the nightly mean emission height and width of the OH*(3–1) layer by comparing nightly mean temperatures measured by the ground–based spectrometer GRIPS 9 and the Na lidar at ALOMAR. The data set contains 42 coincident measurements between November 2010 and February 2014, when GRIPS 9 was in operation at the ALOMAR observatory (69.3° N, 16.0° E) in northern Norway. To closely resemble the mean temperature measured by GRIPS 9, I weighted each nightly mean temperature profile measured by the lidar using Gaussian distributions with 40 different centre altitudes and 40 different full widths at half maximum. In principle, one can thus determine the altitude and width of the OH*(3–1) layer by finding the minimum temperature difference between the two instruments. On most nights, several combinations of centre altitude and width yield a temperature difference of ±2 K. The generally assumed altitude of 87 km and width of 8 km is never an unambiguous, good solution for any of the measurements. Even for a fixed width of ∼ 8.4 km, one can sometimes find several centre altitudes that yield equally good temperature agreement. Weighted temperatures measured by lidar are not suitable to determine unambiguously the emission height and width of an OH* layer. If the OH*(3–1) rotational temperature is used as a proxy for the temperature at an altitude of 87 km with a width of 8.4 km, this proxy is representative to within ±16 K.

Data Analysis Methods for Stereo PIV of a High Aspect Ratio Flexible Cylinder

2007 ◽  
Author(s):  
D. Furey ◽  
P. Atsavapranee ◽  
K. Cipolla
Keyword(s):  
Boundary Layer ◽  
Data Analysis ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Particle Image Velocimetry Data ◽  
Flow Fields ◽  
Mean Flow ◽  
Boundary Flow ◽  
The Mean ◽  
Cylinder Flow

Stereo Particle Image velocimetry data was collected over high aspect ratio flexible cylinders (L/a = 1.5 to 3 × 105) to evaluate the axial development of the turbulent boundary layer where the boundary layer thickness becomes significantly larger than the cylinder diameter (δ/a&gt;&gt;1). The flexible cylinders are approximately neutrally buoyant and have an initial length of 152 m and radii of 0.45 mm and 1.25 mm. The cylinders were towed at speeds ranging from 3.8 to 15.4 m/sec in the David Taylor Model Basin. The analysis of the SPIV data required a several step procedure to evaluate the cylinder boundary flow. First, the characterization of the flow field from the towing strut is required. This evaluation provides the residual mean velocities and turbulence levels caused by the towing hardware at each speed and axial location. These values, called tare values, are necessary for comparing to the cylinder flow results. Second, the cylinder flow fields are averaged together and the averaged tare fields are subtracted out to remove strut-induced ambient flow effects. Prior to averaging, the cylinder flow fields are shifted to collocate the cylinder within the field. Since the boundary layer develops slowly, all planes of data occurring within each 10 meter increment of the cylinder length are averaged together to produce the mean boundary layer flow. Corresponding fields from multiple runs executed using the same experimental parameters are also averaged. This flow is analyzed to evaluate the level of axisymmetry in the data and determine if small changes in cylinder angle affect the mean flow development. With axisymmetry verified, the boundary flow is further averaged azimuthally around the cylinder to produce mean boundary layer profiles. Finally, the fluctuating velocity levels are evaluated for the flow with the cylinder and compared to the fluctuating velocity levels in the tare data. This paper will first discuss the data analysis techniques for the tare data and the averaging methods implemented. Second, the data analysis considerations will be presented for the cylinder data and the averaging and cylinder tracking techniques. These results are used to extract relevant boundary layer parameters including δ, δ* and θ. Combining these results with wall shear and momentum thickness values extracted from averaged cylinder drag data, the boundary layer can be well characterized.

Mean Temperature Difference Charts for Air Coolers

1983 ◽  
Vol 105 (3) ◽  
pp. 592-597 ◽  
Author(s):  
A. Pignotti ◽  
G. O. Cordero
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Temperature Difference ◽  
Optimization Technique ◽  
Independent Variables ◽  
Mean Temperature ◽  
Air Cooler ◽  
The Mean ◽  
The One ◽  
Water Ratio

Computer generated graphs are presented for the mean temperature difference in typical air cooler configurations, covering the combinations of numbers of passes and rows per pass of industrial interest. Two sets of independent variables are included in the graphs: the conventional one (heat capacity water ratio and cold fluid effectiveness), and the one required in an optimization technique of widespread use (hot fluid effectiveness and the number of heat transfer units). Flow arrangements with side-by-side and over-and-under passes, frequently found in actual practice, are discussed through examples.

scholarly journals VI.—The Body-Temperature of Fishes and other Marine Animals.

1908 ◽  
Vol 28 ◽  
pp. 66-84 ◽  
Author(s):  
Sutherland Simpson
Keyword(s):  
Body Temperature ◽  
Temperature Difference ◽  
Great Majority ◽  
The Body ◽  
Shore Crab ◽  
First Year ◽  
Marine Animals ◽  
Mean Temperature ◽  
The Mean ◽  
Image Position

SUMMARYThe body-temperature of the following fishes, crustaceans, and echinoderms has been examined and compared with the temperature of the water in which they live:—Cod-fish (Gadus morrhua), ling (Molva vulgaris), torsk (Brosmius brosme), coal-fish or saithe (Gadus virens), haddock (Gadus œgelfinus), flounder (Pleuronectes flesus), smelt (Osmerus eperlanus), dog-fish (Scyllium catulus), shore crab (Carcinus mœnas), edible crab (Cancer pagurus), lobster (Homarus vulgaris), sea-urchin (Echinus esculentus), and starfish (Asterias rubens). The minimum, maximum, and mean temperature difference for each species are given in the following table:—The excess of temperature is most evident in the larger specimens. This is well shown in the case of the coal-fish, where in the adult it was 0°·7 C., and in the great majority (11 out of 12) of the young of the first year, 0°·0 C. The body-weight and the conditions under which the fish are captured probably form the most important factors in determining the temperature difference.In 14 codfish, where the rectal, blood, and muscle temperatures were recorded in the same individual, it was found to be highest in the muscle and lowest in the rectum, the mean temperature difference being 0°·46 C. for the muscle, 0°·41 C for the blood, and 0°·36 C. for the rectum.

scholarly journals Effectiveness of Tympanic Thermometry for diagnosing Acute Otitis Media

2019 ◽  
Vol 8 (2) ◽  
pp. 74-78
Author(s):  
Muhammad Zubair ◽  
Ghulam Saqulain ◽  
Arfat Jawaid
Keyword(s):  
Tympanic Membrane ◽  
Otitis Media ◽  
Temperature Difference ◽  
Acute Otitis Media ◽  
P Value ◽  
Upper Respiratory Tract ◽  
Mean Temperature ◽  
Ear Wax ◽  
The Mean ◽  
Group B

Background: Acute Otitis Media (AOM) is a common upper respiratory tract infection (URTI) in children and usually presents with fever and otalgia. AOM is characterized by congested tympanic membrane and possible increase in temperature, which might be picked up by infrared tympanic thermometry. The objective of this study was to compare the temperature difference of tympanic membrane of affected ear with the unaffected ear and axilla in unilateral acute otitis media, and compare it with the control group.Material and Methods: This case control study comprised of 200 cases of both genders, aged up to 5 years. They were divided into two groups; Group A included 100 clinically diagnosed cases of acute otitis media (AOM), who reported in the ENT Outpatient Department (OPD) and Group B included 100 controls who presented in General Filter Clinic with no ear complaints. Cases with chronic ear disease, ear discharge, and use of local drugs including ear drops, impacted ear wax, tragal tenderness and congenital malformations of the ear were excluded by taking a detailed history. Clinical examination including otoscopy by an expert was done before subjecting patients to axillary and tympanic thermometry measurements and data recording. Data was collected and tabulated using Microsoft Excel Worksheet and analyzed by SPSS 16. Qualitative data like gender were presented as percentage and ratio, while means and standard deviation were calculated for the quantitative data. Difference between the means of experimental and control groups were analyzed by independent sample t-test and P value of less than or equal to 0.05 was taken as significant.Results: This study included 100 cases of unilateral AOM and 100 normal controls without AOM. In patients with AOM, the mean temperature difference between the affected ear and axilla was 1.41ºF as compared to 0.075ºF in controls (p=0.026). While the mean temperature difference between the affected ear and other ear was 0.65ºF as compared to 0.19ºF in controls (p=0.069).Conclusion: In acute otitis media, the temperature of affected ear is significantly higher than axilla but was not significantly higher than the other ear. The finding may help establish thermometry as a diagnostic tool in clinics manned by doctors not competent to do otoscopy.

scholarly journals Bounds for convection between rough boundaries

2016 ◽  
Vol 804 ◽  
pp. 370-386 ◽  
Author(s):  
David Goluskin ◽  
Charles R. Doering
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Temperature Difference ◽  
Upper Bound ◽  
Bottom Boundary ◽  
Leading Term ◽  
The Mean ◽  
Rough Boundaries ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We consider Rayleigh–Bénard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background method to derive an upper bound on the mean heat flux across the layer for all admissible boundary geometries. This flux, normalized by the temperature difference between the boundaries, can grow with the Rayleigh number ($Ra$) no faster than $O(Ra^{1/2})$ as $Ra\rightarrow \infty$. Our analysis yields a family of similar bounds, depending on how various estimates are tuned, but every version depends explicitly on the boundary geometry. In one version the coefficient of the $O(Ra^{1/2})$ leading term is $0.242+2.925\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$, where $\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$ is the mean squared magnitude of the boundary height gradients. Application to a particular geometry is illustrated for sinusoidal boundaries.

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