Turbulent heat and momentum transport on a rotating disk

2000 ◽  
Vol 402 ◽  
pp. 225-253 ◽  
Author(s):  
CHRISTOPHER J. ELKINS ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Boundary Layers ◽  
Outer Region ◽  
Temperature Fluctuations ◽  
Rotating Disk ◽  
Transport Processes ◽  
Turbulent Heat ◽  
Two Dimensional ◽  
The Mean

Measurements in the turbulent momentum and thermal boundary layers on a rotating disk with a uniform heat flux surface are described for Reynolds numbers up to 106. Measurements include mean velocities and temperatures, all six Reynolds stresses, turbulent temperature fluctuations, and three turbulent heat fluxes. The mean velocity profiles have no wake region, but the mean temperature profiles do. The turbulent temperature fluctuations have a large peak in the outer layer, and there is a third turbulent heat flux in the cross-flow direction. Correlation coefficients and structure parameters are not constant across the boundary layer as they are in two-dimensional boundary layers (2DBLs), and their values are lower. The turbulent Prandtl number agrees with 2DBL values in the lower part of the outer region but is reduced from the 2DBL values higher in the boundary layer. In the outer region of the boundary layer, the transport processes differ significantly from what is observed in two-dimensional turbulent boundary layers: ejections dominate the transport of momentum while both ejections and sweeps contribute to the transport of the passive scalar.

scholarly journals Effects of radiation in turbulent channel flow: analysis of coupled direct numerical simulations

2014 ◽  
Vol 753 ◽  
pp. 360-401 ◽  
Author(s):  
R. Vicquelin ◽  
Y. F. Zhang ◽  
O. Gicquel ◽  
J. Taine
Keyword(s):  
Heat Flux ◽  
Numerical Simulations ◽  
Boundary Layers ◽  
Temperature Fluctuations ◽  
Turbulent Channel Flow ◽  
Turbulent Heat Flux ◽  
Direct Numerical Simulations ◽  
Turbulent Heat Transfer ◽  
Radiative Energy ◽  
Turbulent Heat

AbstractThe role of radiative energy transfer in turbulent boundary layers is carefully analysed, focusing on the effect on temperature fluctuations and turbulent heat flux. The study is based on direct numerical simulations (DNS) of channel flows with hot and cold walls coupled to a Monte-Carlo method to compute the field of radiative power. In the conditions studied, the structure of the boundary layers is strongly modified by radiation. Temperature fluctuations and turbulent heat flux are reduced, and new radiative terms appear in their respective balance equations. It is shown that they counteract turbulence production terms. These effects are analysed under different conditions of Reynolds number and wall temperature. It is shown that collapsing of wall-scaled profiles is not efficient when radiation is considered. This drawback is corrected by the introduction of a radiation-based scaling. Finally, the significant impact of radiation on turbulent heat transfer is studied in terms of the turbulent Prandtl number. A model for this quantity, based on the new proposed scaling, is developed and validated.

Turbulence characteristics of the boundary layer on a rotating disk

1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Structural Model ◽  
Rotating Disk ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Dimensional Boundary ◽  
The Mean

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

An Explicit Algebraic Model for Turbulent Heat Transfer in Wall-Bounded Flow With Streamline Curvature

2006 ◽  
Vol 129 (4) ◽  
pp. 425-433 ◽  
Author(s):  
B. A. Younis ◽  
B. Weigand ◽  
S. Spring
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Algebraic Model ◽  
Heat Fluxes ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Streamline Curvature ◽  
Turbulent Heat Fluxes ◽  
The Mean

Fourier’s law, which forms the basis of most engineering prediction methods for the turbulent heat fluxes, is known to fail badly in capturing the effects of streamline curvature on the rate of heat transfer in turbulent shear flows. In this paper, an alternative model, which is both algebraic and explicit in the turbulent heat fluxes and which has been formulated from tensor-representation theory, is presented, and its applicability is extended by incorporating the effects of a wall on the turbulent heat transfer processes in its vicinity. The model’s equations for flows with curvature in the plane of the mean shear are derived and calculations are performed for a heated turbulent boundary layer, which develops over a flat plate before encountering a short region of high convex curvature. The results show that the new model accurately predicts the significant reduction in the wall heat transfer rates wrought by the stabilizing-curvature effects, in sharp contrast to the conventional model predictions, which are shown to seriously underestimate the same effects. Comparisons are also made with results from a complete heat-flux transport model, which involves the solution of differential transport equations for each component of the heat-flux tensor. Downstream of the bend, where the perturbed boundary layer recovers on a flat wall, the comparisons show that the algebraic model yields indistinguishable predictions from those obtained with the differential model in regions where the mean-strain field is in rapid evolution and the turbulence processes are far removed from local equilibrium.

Response of a turbulent boundary layer to a step change in surface heat flux

1977 ◽  
Vol 80 (1) ◽  
pp. 153-177 ◽  
Author(s):  
R. A. Antonia ◽  
H. Q. Danh ◽  
A. Prabhu
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Surface Heat Flux ◽  
Temperature Fluctuations ◽  
Step Change ◽  
Surface Heat ◽  
The Mean ◽  
Thermal Layer ◽  
Intermittency Factor

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

Turbulent Heat Transport in a Boundary Layer Behind a Junction of a Streamlined Cylinder and a Wall

1992 ◽  
Vol 114 (4) ◽  
pp. 840-849 ◽  
Author(s):  
D. E. Wroblewski ◽  
P. A. Eibeck
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Vortex Shedding ◽  
Turbulent Heat Flux ◽  
Temperature Fields ◽  
Turbulent Heat ◽  
Two Dimensional ◽  
Wake Region ◽  
Dimensional Boundary ◽  
Shedding Frequency

Measurements of the turbulent velocity and temperature fields were made in a heated boundary layer 14 diameters downstream of a junction of a tapered cylinder and a wall (ReD = 24,700). The boundary layer is strongly affected by the presence of large-scale unsteadiness arising from vortex shedding, which appears in the measurements as “turbulence” with a strong spectral component at the shedding frequency. The boundary layer exhibits three distinct spanwise regions: (1) the innerwake region, z/D<0.8, where vortex shedding effects are observed only in the spanwise component of the fluctuations; (2) the middle-wake region, 0.8<z/D<1.6, where strong vortex shedding is seen in all three components of the fluctuations; and (3) the outer-wake region, z/D>1.6, where the flow is approaching a two-dimensional boundary-layer flow. Cross-spectra of νθ indicate that vortex shedding increases the turbulent heat flux in the middle-wake region. However, peak values of the Stanton number and the eddy diffusivity are observed in the inner-wake region, where the cross-spectra of turbulent heat flux do not exhibit a peak near the shedding frequency, but do show an increase compared to a two-dimensional boundary layer over a much broader frequency range.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Prediction of compressible turbulent boundary layer via a symmetry-based length model

2018 ◽  
Vol 857 ◽  
pp. 449-468 ◽  
Author(s):  
Zhen-Su She ◽  
Hong-Yue Zou ◽  
Meng-Juan Xiao ◽  
Xi Chen ◽  
Fazle Hussain
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Structure ◽  
Analytic Form ◽  
Algebraic Model ◽  
Length Function ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
The Mean

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL) – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes, thus achieving a Mach number ($Ma$) invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of$Ma$from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin–Lomax and Spalart–Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our$Ma$-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.

scholarly journals Observation of sensible and latent heat flux profiles with lidar

2020 ◽  
Vol 13 (6) ◽  
pp. 3221-3233 ◽  
Author(s):  
Andreas Behrendt ◽  
Volker Wulfmeyer ◽  
Christoph Senff ◽  
Shravan Kumar Muppa ◽  
Florian Späth ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Latent Heat ◽  
Latent Heat Flux ◽  
Sensible Heat Flux ◽  
Ground Level ◽  
Sensible Heat ◽  
Flux Divergence ◽  
Convective Boundary ◽  
The Mean

Abstract. We present the first measurement of the sensible heat flux (H) profile in the convective boundary layer (CBL) derived from the covariance of collocated vertical-pointing temperature rotational Raman lidar and Doppler wind lidar measurements. The uncertainties of the H measurements due to instrumental noise and limited sampling are also derived and discussed. Simultaneous measurements of the latent heat flux profile (L) and other turbulent variables were obtained with the combination of water-vapor differential absorption lidar (WVDIAL) and Doppler lidar. The case study uses a measurement example from the HOPE (HD(CP)2 Observational Prototype Experiment) campaign, which took place in western Germany in 2013 and presents a cloud-free well-developed quasi-stationary CBL. The mean boundary layer height zi was at 1230 m above ground level. The results show – as expected – positive values of H in the middle of the CBL. A maximum of (182±32) W m−2, with the second number for the noise uncertainty, is found at 0.5 zi. At about 0.7 zi, H changes sign to negative values above. The entrainment flux was (-62±27) W m−2. The mean sensible heat flux divergence in the observed part of the CBL above 0.3 zi was −0.28 W m−3, which corresponds to a warming of 0.83 K h−1. The L profile shows a slight positive mean flux divergence of 0.12 W m−3 and an entrainment flux of (214±36) W m−2. The combination of H and L profiles in combination with variance and other turbulent parameters is very valuable for the evaluation of large-eddy simulation (LES) results and the further improvement and validation of turbulence parameterization schemes.

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