Heat Transfer In Turbulent Boundary Layers Subjected to Free-Stream Turbulence—Part II: Analysis and Correlation

2003 ◽  
Vol 125 (2) ◽  
pp. 242-251 ◽  
Author(s):  
Michael J. Barrett ◽  
D. Keith Hollingsworth
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Length Scale ◽  
Free Stream Turbulence ◽  
New Correlation ◽  
Near Wall

A new heat transfer correlation for turbulent boundary layers subjected to free-stream turbulence was developed. The new correlation estimates dimensionless heat transfer coefficients without the use of conventional boundary-layer thickness measures and the associated Reynolds numbers. Using only free-stream parameters (mean velocity, turbulence intensity and length scale), the new correlation collected many authors’ elevated-turbulence, flat-plate Stanton number data to within ±11%. The level of scatter around the new correlation compared well to previous correlations that require additional flow information as input parameters. For a common subset of data, scatter using earlier correlation methods ranged from 5–10%; scatter around the new correlation varied from 6–9% over the same data subset. A length-scale dependence was identified in a Stanton number previously defined using a near-wall streamwise velocity fluctuation, St′. A new near-wall Stanton number was introduced; this parameter was regarded as a constant in a two-region boundary layer model on which the new correlation is based.

Heat Transfer in Turbulent Boundary Layers Subjected to Free-Stream Turbulence—Part I: Experimental Results

2003 ◽  
Vol 125 (2) ◽  
pp. 232-241 ◽  
Author(s):  
Michael J. Barrett ◽  
D. Keith Hollingsworth
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Small Scale ◽  
Length Scale ◽  
Momentum Thickness ◽  
Free Stream Turbulence

Turbulent boundary layers were subjected to grid-generated free-stream turbulence to study the effects of length scale and intensity on heat transfer. Relative to conventional boundary layer thickness measures, test conditions included very small-scale free-stream turbulence. The boundary layers studied ranged from 400–2700 in momentum-thickness Reynolds number and from 450–1900 in enthalpy-thickness Reynolds number. Free-stream turbulence intensities varied from 0.1–8.0%. Ratios of free-stream length scale to boundary-layer momentum thickness ranged from 4.4–32.5. The turbulent-to-viscous length-scale ratios presented are the smallest found in the heat-transfer literature; the ratios spanned from 115–1020. The turbulent-to-thermal ratios (using enthalpy thickness as the thermal scale) are also the smallest reported; the ratios ranged from 3.2–12.3. Relative to clean-free-stream expectations based on the momentum- and enthalpy-thickness Reynolds numbers, the skin friction coefficient increased by up to 16%, and the Stanton number increased by up to 46%.

scholarly journals Interactions of large-scale free-stream turbulence with turbulent boundary layers

2016 ◽  
Vol 802 ◽  
pp. 79-107 ◽  
Author(s):  
Eda Dogan ◽  
Ronald E. Hanson ◽  
Bharathram Ganapathisubramani
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Scale Interactions ◽  
Free Stream Turbulence ◽  
Small Scales ◽  
Near Wall

The scale interactions occurring within a turbulent boundary layer are investigated in the presence of free-stream turbulence. The free-stream turbulence is generated by an active grid. The free stream is monitored by a single-component hot-wire probe, while a second probe is roved across the height of the boundary layer at the same streamwise location. Large-scale structures occurring in the free stream are shown to penetrate the boundary layer and increase the streamwise velocity fluctuations throughout. It is speculated that, depending on the extent of the penetration, i.e. based on the level of free-stream turbulence, the near-wall turbulence production peaks at different wall-normal locations than the expected location of $y^{+}\approx 15$ for a canonical turbulent boundary layer. It is shown that the large scales dominating the log region have a modulating effect on the small scales in the near-wall region; this effect becomes more significant with increasing turbulence in the free stream, i.e. similarly increasing $Re_{\unicode[STIX]{x1D706}_{0}}$. This modulating interaction and its Reynolds-number trend have similarities with canonical turbulent boundary layers at high Reynolds numbers where the interaction between the large scales and the envelope of the small scales exhibits a pure amplitude modulation (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365 (1852), 2007, pp. 647–664; Mathis et al., J. Fluid Mech., vol. 628, 2009, pp. 311–337). This similarity has encouraging implications towards generalising scale interactions in turbulent boundary layers.

scholarly journals A Theory for Predicting the Turbulent-Spot Production Rate

1998 ◽  
Author(s):  
R. E. Mayle
Keyword(s):  
Boundary Layer ◽  
Production Rate ◽  
Free Stream ◽  
Length Scale ◽  
Bypass Transition ◽  
Turbulence Level ◽  
Turbulent Spot ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
New Correlation

A theory is presented for predicting the production rate of turbulent spots. The theory, based on that by Mayle-Schulz for bypass transition, leads to a new correlation for the spot production rate in boundary layer flows with a zero pressure gradient. The correlation, which agrees reasonably well with data, clearly shows the effects of both free-stream turbulence level and length scale. In addition, the theory provides an estimate for the lowest level of free-stream turbulence causing bypass transition.

A Theory for Predicting the Turbulent-Spot Production Rate

1999 ◽  
Vol 121 (3) ◽  
pp. 588-593 ◽  
Author(s):  
R. E. Mayle
Keyword(s):  
Boundary Layer ◽  
Production Rate ◽  
Free Stream ◽  
Length Scale ◽  
Bypass Transition ◽  
Turbulence Level ◽  
Turbulent Spot ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
New Correlation

A theory is presented for predicting the production rate of turbulent spots. The theory, based on that by Mayle–Schulz for bypass transition, leads to a new correlation for the spot production rate in boundary layer flows with a zero pressure gradient. The correlation, which agrees reasonably well with data, clearly shows the effects of both free-stream turbulence level and length scale. In addition, the theory provides an estimate for the lowest level of free-stream turbulence causing bypass transition.

An Aspect of Heat Transfer in Accelerating Turbulent Boundary Layers

1969 ◽  
Vol 91 (2) ◽  
pp. 229-234 ◽  
Author(s):  
B. E. Launder ◽  
F. C. Lockwood
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Stream Velocity ◽  
Velocity Boundary Layer ◽  
Positive Exponent

Theoretical consideration indicates that, in an accelerated turbulent flow, the thermal boundary layer may penetrate significantly beyond the edge of the velocity boundary layer. This effect may contribute in part to the marked decrease in Stanton number which has been reported in accelerated turbulent boundary layers. This paper presents theoretical solutions to turbulent velocity and thermal boundary layers in flow between converging planes where the wall temperature varies as the free-stream velocity raised to a positive exponent. The solutions clearly illustrate that, as the wall-temperature variation is made less rapid, the thermal boundary layer penetrates progressively further beyond the velocity boundary layer, causing the Stanton number to decrease.

Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6

2017 ◽  
Vol 822 ◽  
pp. 5-30 ◽  
Author(s):  
Chao Zhang ◽  
Lian Duan ◽  
Meelan M. Choudhari
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Pressure Fluctuation ◽  
Free Stream ◽  
Pressure Fluctuations ◽  
Turbulent Boundary Layers ◽  
Wall Pressure ◽  
Wall Region ◽  
Near Wall

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.

Development of a Large-Scale Wind Tunnel for the Simulation of Turbomachinery Airfoil Boundary Layers

1981 ◽  
Vol 103 (4) ◽  
pp. 678-687 ◽  
Author(s):  
M. F. Blair ◽  
D. A. Bailey ◽  
R. H. Schlinker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Wind Tunnel ◽  
Boundary Layers ◽  
Test Section ◽  
Large Scale ◽  
Free Stream ◽  
Two Dimensional ◽  
Transfer Data ◽  
Free Stream Turbulence

The procedures employed for the design of a closed-circuit, boundary layer wind tunnel are described. The tunnel was designed for the generation of large-scale, two-dimensional boundary layers on a heated flat surface with Reynolds numbers, pressure gradients, and free-stream turbulence levels typical of turbomachinery airfoils. The results of a series of detailed tests to evaluate the tunnel performance are also described. Testing was conducted for zero pressure gradient flow with natural boundary layer transition. Heat transfer data and boundary layer profiles are presented for a flow with 0.25 percent free-stream turbulence. The flow in the tunnel test-section was shown to be highly uniform and two-dimensional. Test boundary layer profile and convective heat transfer data were self-consistent and in excellent agreement with classic correlations. Test-section free-stream total pressure, multi-component turbulence intensity, longitudinal integral scale, and spectral distributions are presented for grid-generated turbulence levels ranging from 1 to 7 percent. The test-section free-stream turbulence was shown to be both homogeneous and nearly isotropic. Anticipated applications of the facility include studies of the heat transfer and aerodynamics for conditions typical of those existing on gas turbine airfoils.

Spectral Measurements in Transitional Boundary Layers on a Concave Wall Under High and Low Free-Stream Turbulence Conditions

1997 ◽  
Vol 122 (3) ◽  
pp. 450-457 ◽  
Author(s):  
Ralph J. Volino ◽  
Terrence W. Simon
Keyword(s):  
Boundary Layer ◽  
Transfer Function ◽  
Boundary Layers ◽  
Free Stream ◽  
Low Frequency ◽  
Turbulent Boundary Layers ◽  
Spectral Measurements ◽  
Free Stream Turbulence ◽  
Concave Wall ◽  
Frequency Fluctuations

The relationship between free-stream turbulence and boundary layer behavior has been investigated using spectral measurements. The power spectral densities of turbulence quantities in transitional and fully turbulent boundary layers were computed and compared to the power spectra of the same quantities measured in the free stream. Comparisons were made using the “transfer function.” The transfer function is the ratio of two spectra at each frequency in the spectra. Comparisons were done in flows with low (0.6 percent) and high (8 percent) free-stream turbulence intensities. Evidence was gathered that suggests that relatively low-frequency, large-scale eddies in the free stream buffet the boundary layer, causing boundary layer unsteadiness at the same low frequencies. These fluctuations are present in both transitional and fully turbulent boundary layers. They are seen under both high and low free-stream turbulence conditions, although they are stronger in the high-turbulence case. Examination of the turbulent shear stress suggests that the low-frequency fluctuations enhance transport in the boundary layer but they are not so effective in promoting eddy transport as are turbulent eddies produced and residing within the boundary layer. In the fully-turbulent boundary layer, higher-frequency fluctuations are added to the low-frequency unsteadiness. These higher-frequency fluctuations, not seen in the transitional boundary layer, are associated with turbulence production in the boundary layer and appear not to be directly related to free-stream unsteadiness. [S0889-504X(00)00403-7]

Exponential Wake Structure of Heated Turbulent Boundary Layers at Elevated Levels of Free-Stream Turbulence

1987 ◽  
Vol 109 (2) ◽  
pp. 336-344
Author(s):  
P. Sepri
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Computer Code ◽  
Turbulent Boundary Layers ◽  
Wake Region ◽  
Predictive Tool ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Computational Capability

The wake region of a turbulent boundary layer is demonstrated to exhibit simple exponential behavior at elevated levels of free-stream turbulence. As a predictive tool, the computer code STANCOOL has been modified to include FST effects in heated turbulent boundary layers. Preliminary comparisons with experimental data indicate improvements in computational capability, although further development of the code is required. From these comparisons, three new results are offered: (1) At elevated levels of FST, several statistical profiles in the boundary layer wake region decay exponentially into the free stream; (2) v′T′ decays at half the rate of the mean velocity and temperature; (3) analytical expressions are provided for u′v′ and v′T′ in this case.

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