Fluctuating Thermal Field in the Near-Hole Region for Film Cooling Flows

1998 ◽  
Vol 120 (1) ◽  
pp. 86-91 ◽  
Author(s):  
A. Kohli ◽  
D. G. Bogard
Keyword(s):  
Probability Density ◽  
Film Cooling ◽  
Thermal Field ◽  
Density Ratio ◽  
Flux Ratio ◽  
Probability Density Functions ◽  
Intermittent Flow ◽  
Density Functions ◽  
High Frequency Response ◽  
Cooling Flow

The film cooling flow field is the result of a highly complex interaction between the film cooling jets and the mainstream. Understanding this interaction is important in order to explain the physical mechanisms involved in the rapid decrease of effectiveness, which occurs close to the hole exit. Not surprisingly, it is this region that is not modeled satisfactorily with current film cooling models. This study uses a high-frequency-response temperature sensor, which provides new information about the film cooling flow in terms of actual turbulence levels and probability density functions of the thermal field. Mean and rms temperature results are presented for 35 deg round holes at a momentum flux ratio of I = 0.16, at a density ratio of DR = 1.05. Probability density functions of the temperature indicate penetration of the mainstream into the coolant core, and ejection of coolant into the mainstream. Extreme excursions in the fluctuating temperature measurements suggest existence of strong intermittent flow structures responsible for dilution and dispersion of the coolant jets.

Fluctuating Thermal Field in the Near Hole Region for Film Cooling Flows

1996 ◽  
Author(s):  
Atul Kohli ◽  
David G. Bogard
Keyword(s):  
Probability Density ◽  
Film Cooling ◽  
Thermal Field ◽  
Density Ratio ◽  
Flux Ratio ◽  
Probability Density Functions ◽  
Intermittent Flow ◽  
Density Functions ◽  
High Frequency Response ◽  
Cooling Flow

The film cooling flow field is the result of a highly complex interaction between the film cooling jets and the mainstream, Understanding this interaction is important in order to explain the physical mechanisms involved in the rapid decrease of effectiveness which occurs close to the hole exit. Not surprisingly, it is this region which is not modeled satisfactorily with current film cooling models. This study uses a high frequency response temperature sensor which provides new information about the film cooling flow in terms of actual turbulence levels and probability density functions of the thermal field. Mean and rms temperature results are presented for 35° round holes at a momentum flux ratio of I = 0.16, at a density ratio of DR = 1.05. Probability density functions of the temperature indicate penetration of the mainstream into the coolant core, and ejection of coolant into the mainstream. Extreme excursions in the fluctuating temperature measurements suggests existence of strong intermittent flow structures responsible for dilution and dispersion of the coolant jets.

Adiabatic Effectiveness, Thermal Fields, and Velocity Fields for Film Cooling With Large Angle Injection

1997 ◽  
Vol 119 (2) ◽  
pp. 352-358 ◽  
Author(s):  
A. Kohli ◽  
D. G. Bogard
Keyword(s):  
Film Cooling ◽  
Momentum Flux ◽  
Thermal Field ◽  
Density Ratio ◽  
Large Angle ◽  
Flux Ratio ◽  
Cryogenic Cooling ◽  
Round Hole ◽  
Mean Velocity ◽  
Injection Angle

The film cooling performance and velocity field were investigated for discrete round holes inclined at an injection angle of 55 deg. Results are compared to typical round film cooling holes, with an injection angle of 35 deg. All experiments in this study were performed at a density ratio of DR = 1.6, using cryogenic cooling of the injected air. Centerline and lateral distributions of effectiveness were obtained for a range of momentum flux ratios. Thermal field and two component mean velocity and turbulence intensity measurements were made at a momentum flux ratio that was within the range of maximum spatially averaged effectiveness. Compared to round holes with 35 deg injection angle, the 55 deg holes showed only a slight degradation in centerline effectiveness for low momentum flux ratios, while a significant reduction in effectiveness was seen at high momentum flux ratios. The thermal field for the 55 deg round holes indicated a faster decay of cooling capacity for the 55 deg round holes. The high turbulence levels for the 55 deg round hole coincided with the sharp velocity gradients between the jet and free stream, and the decay of turbulence levels with downstream distance was found to be similar to those for a 35 deg hole.

Effects of Very High Free-Stream Turbulence on the Jet–Mainstream Interaction in a Film Cooling Flow

1998 ◽  
Vol 120 (4) ◽  
pp. 785-790 ◽  
Author(s):  
A. Kohli ◽  
D. G. Bogard
Keyword(s):  
High Frequency ◽  
Film Cooling ◽  
Thermal Field ◽  
Free Stream ◽  
Complex Interaction ◽  
Free Stream Turbulence ◽  
High Frequency Response ◽  
Cooling Flow ◽  
The Mean ◽  
Very High

Dispersion of coolant jets in a film cooling flow field is the result of a highly complex interaction between the film cooling jets and the mainstream. Understanding this complex interaction, particularly near the injection location, is critical for improving the predictive capabilities of existing film cooling models, especially when very high free-stream turbulence levels exist. This study uses a high-Frequency-response temperature sensor to investigate the mean and fluctuating thermal field of a film cooling flow for two vastly different free-stream turbulence levels (0.5 and 20 percent). The high-frequency-response temperature sensor provides new information about the film cooling flow in terms of actual rms levels (Θ′), probability density functions (pdf’s), and frequency spectra of the thermal field. Results are presented for both free-stream conditions using round hosed inclined at 35 deg, at a momentum flux ration of I = 0.156 and density ratio of DR = 1.05. The mean thermal field results show severe degradation of the film cooling jet occurs with very high free-stream turbulence levels. Temperature rms results indicate levels as high as Θ′ = 0.25 exist at the jet-mainstream interface. More information is provided by the temperature pdf’s, which are able to identify differences in the jet-mainstream interaction for the two free stream conditions. With small free-stream turbulence, strong intermittent flow structures generated at the jet-mainstream interface disperse the jet by moving hot main stream fluid into the coolant core, and ejecting coolant fluid into the mainstream. When the free stream has large scales and very high turbulence levels, the jet-mainstream interface is obliterated by large-scale turbulent structures originating from the free stream, which completely penetrate the coolant jet, causing very rapid dispersion of the film cooling jet.

scholarly journals Adiabatic Effectiveness, Thermal Fields, and Velocity Fields for Film Cooling With Large Angle Injection

1995 ◽  
Author(s):  
Atul Kohli ◽  
David G. Bogard
Keyword(s):  
Film Cooling ◽  
Momentum Flux ◽  
Thermal Field ◽  
Density Ratio ◽  
Large Angle ◽  
Flux Ratio ◽  
Cryogenic Cooling ◽  
Round Hole ◽  
Mean Velocity ◽  
Injection Angle

The film cooling performance and velocity field were investigated for discrete round holes inclined at an injection angle of 55°. Results are compared to typical round film cooling holes, with an injection angle of 35°. All experiments in this study were performed at a density ratio of DR = 1.6, using cryogenic cooling of the injected air. Centerline and lateral distributions of effectiveness, were obtained for a range of momentum flux ratios. Thermal field and two component mean velocity and turbulence intensity measurements were made at a momentum flux ratio which was within the range of maximum spatially averaged effectiveness. Compared to round holes with 35° injection angle, the 55° holes showed only a slight degradation in centerline effectiveness for low momentum flux ratios, while a significant reduction in effectiveness was seen at high momentum flux ratios. The thermal field for the 55° round holes indicated a faster decay of cooling capacity for the 55° round holes. The high turbulence levels for the 55° round hole coincided with the sharp velocity gradients between the jet and freestream, and the decay of turbulence levels with downstream distance was found to be similar to those for a 35° hole.

scholarly journals Effects of Very High Free-Stream Turbulence on the Jet-Mainstream Interaction in a Film Cooling Flow

1997 ◽  
Author(s):  
Atul Kohli ◽  
David G. Bogard
Keyword(s):  
High Frequency ◽  
Film Cooling ◽  
Thermal Field ◽  
Free Stream ◽  
Complex Interaction ◽  
Free Stream Turbulence ◽  
High Frequency Response ◽  
Cooling Flow ◽  
The Mean ◽  
Very High

Dispersion of coolant jets in a film cooling flow field is the result of a highly complex interaction between the film cooling jets and the mainstream. Understanding this complex interaction, particularly near the injection location, is critical for improving the predictive capabilities of existing film cooling models, especially when very high free-stream turbulence levels exist. This study uses a high frequency response temperature sensor to investigate the mean and fluctuating thermal field of a film cooling flow for two vastly different free-stream turbulence levels (0.5% and 20%). The high frequency response temperature sensor provides new information about the film cooling flow in terms of actual rms levels (Θ′), probability density functions (pdf’s), and frequency spectra of the thermal field. Results are presented for both free-stream conditions using round holes inclined at 35°, at a momentum flux ratio of I = 0.156 and density ratio of DR = 1.05. The mean thermal field results show severe degradation of the film cooling jet occurs with very high free-stream turbulence levels. Temperature rms results indicate levels as high as Θ′ = 0.25 exist at the jet-mainstream interface. More information is provided by the temperature pdf’s which are able to identify differences in the jet-mainstream interaction for the two free-stream conditions. With small free-stream turbulence, strong intermittent flow structures generated at the jet-mainstream interface disperse the jet by moving hot mainstream fluid into the coolant core, and ejecting coolant fluid into the mainstream. When the free-stream has large scales and very high turbulence levels, the jet-mainstream interface is obliterated by large scale turbulent structures originating from the free-stream which completely penetrate the coolant jet causing very rapid dispersion of the film cooling jet.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars
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