Entropy Generation in the Viscous Parts of Turbulent Boundary Layers

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Donald M. McEligot ◽  
Edmond J. Walsh ◽  
Eckart Laurien ◽  
Philippe R. Spalart
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Turbulent Boundary Layers ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Unit Surface Area ◽  
Pressure Gradients ◽  
Viscous Layer ◽  
Flat Plates

The local (pointwise) entropy generation rate per unit volume S‴ is a key to improving many energy processes and applications. Consequently, in the present study, the objectives are to examine the effects of Reynolds number and favorable streamwise pressure gradients on entropy generation rates across turbulent boundary layers on flat plates and—secondarily—to assess a popular approximate technique for their evaluation. About two-thirds or more of the entropy generation occurs in the viscous part, known as the viscous layer. Fundamental new results for entropy generation in turbulent boundary layers are provided by extending available direct numerical simulations. It was found that, with negligible pressure gradients, results presented in wall coordinates are predicted to be near “universal” in the viscous layer. This apparent universality disappears when a significant pressure gradient is applied; increasing the pressure gradient decreases the entropy generation rate. Within the viscous layer, the approximate evaluation of S‴ differs significantly from the “proper” value but its integral, the entropy generation rate per unit surface area Sap″, agrees within 5% at its edge.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally-sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the non-dimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally-sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Vol 129 (3) ◽  
pp. 512-517 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time-averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the nondimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time-averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements, a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

An Entropic Minimization Technique for Turbine Blade Profiles

2002 ◽  
Author(s):  
Ed Walsh ◽  
Mark Davies ◽  
Roy Myose
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Incompressible Flows ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimization Technique ◽  
Boundary Layer Edge

The optimization of the boundary layer edge velocity distribution may hold the key to the minimization of entropy generation in the boundary layers of turbomachinery blades. A preliminary optimization analysis in the laminar region of a non film cooled turbine blade is presented, which demonstrates the concept of how the entropy generation rate may be reduced by varying the boundary layer edge velocity distribution along the suction surface, whilst holding the work done by the blade constant. In the laminar region the analytical technique developed by Pohlhausen and others to predict the boundary layer momentum thickness in the presence of pressure gradients has been adopted to predict the entropy generated as described in other papers by the same authors. The result gives an expression for the entropy generation rate in terms of the boundary layer edge velocity distribution for incompressible flows. The boundary layer edge velocity distribution may then be represented as a polynomial with undefined variables. This allows a minimization technique to be used to minimize the entropy generation rate on these variables. Constraints are included to keep the work output constant and the diffusion low to avoid separation. In this analysis it is only the laminar region that is considered for minimization, thus it is necessary to ensure that the modified boundary layer edge velocity distribution does not undergo transition earlier than the baseline boundary layer edge velocity distribution. This is accomplished by considering transition and separation criteria available in the literature. The result of this analysis indicates that the entropy generation rate may be reduced in the laminar boundary layers by using this technique.

Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients

1978 ◽  
Vol 89 (2) ◽  
pp. 305-342 ◽  
Author(s):  
B. A. Kader ◽  
A. M. Yaglom
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Local Equilibrium ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Experimental Information ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Pressure Gradients

Dimensional analysis is applied to the velocity profile U(y) of turbulent boundary layers subjected to adverse pressure gradients. It is assumed that the boundary layer is in moving or local equilibrium in the sense that the free-stream velocity U∞ and kinematic pressure gradient α = ρ−1dP/dx vary only slowly with the co-ordinate x. This assumption implies a rather complicated general equation for the velocity gradient dU/dy which may be considerably simplified for several specific regions of the flow. A general family of velocity profiles is derived from the simplified equations supplemented by some experimental information. This family agrees well with almost all existing data on velocity profiles in adverse-pressure-gradient turbulent boundary layers. It may be used for the derivation of a skin-friction law which predicts satisfactorily the values of the wall shear stress at any non-negative value of the pressure gradient. The variation of the boundary-layer thickness with x is also predicted by dimensional considerations.

Structures in turbulent boundary layers subjected to adverse pressure gradients

2009 ◽  
Vol 639 ◽  
pp. 101-131 ◽  
Author(s):  
JOUNG-HO LEE ◽  
HYUNG JIN SUNG
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stochastic Estimation ◽  
Pressure Gradients ◽  
Linear Stochastic Estimation ◽  
Mean Width ◽  
The Mean

The effects of adverse pressure gradients on turbulent structures were investigated by carrying out direct numerical simulations of turbulent boundary layers subjected to adverse and zero pressure gradients. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution U∞ ~ xm. Two-point correlations of velocity fluctuations were used to show that the spanwise spacing between near-wall streaks is affected significantly by a strong adverse pressure gradient. Low-momentum regions are dominant in the middle of the boundary layer as well as in the log layer. Linear stochastic estimation was used to provide evidence for the presence of low-momentum regions and to determine their statistical properties. The mean width of such large-scale structures is closely associated with the size of the hairpin-like vortices in the outer layer. The conditionally averaged flow fields around events producing Reynolds stress show that hairpin-like vortices are the structures associated with the production of outer turbulence. The shapes of the vortices beyond the log layer were found to be similar when their length scales were normalized according to the boundary layer thickness. Estimates of the conditionally averaged velocity fields associated with the spanwise vortical motion were obtained by using linear stochastic estimation. These results confirm that the outer region of the adverse pressure gradient boundary layer is populated with streamwise-aligned vortex organizations, which are similar to those of the vortex packet model proposed by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54). The adverse pressure gradient augments the inclination angles of the packets and the mean streamwise spacing of the vortex heads in the packets.

scholarly journals Influence of pressure gradients on wall pressure beneath a turbulent boundary layer

2018 ◽  
Vol 838 ◽  
pp. 715-758 ◽  
Author(s):  
Elie Cohen ◽  
Xavier Gloerfelt
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Scaling Law ◽  
Pressure Fluctuations ◽  
Turbulent Boundary Layers ◽  
Wall Pressure ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
Significant Difference

This study investigates the effects of a pressure gradient on the wall pressure beneath equilibrium turbulent boundary layers. Excitation of the walls of a vehicle by turbulent boundary layers indeed constitutes a major source of interior noise and it is necessary to take into account the presence of a pressure gradient to represent the effect of the curvature of the walls. With this aim, large-eddy simulations of turbulent boundary layers in the presence of both mild adverse and mild favourable pressure gradients are carried out by solving the compressible Navier–Stokes equations. This method provides both the aeroacoustic contribution and the hydrodynamic wall-pressure fluctuations. A critical comparison with existing databases, including recent measurements, is conducted to assess the influence of a free stream pressure gradient. The analyses of wall-pressure spectral densities show an increase in the low-frequency content from adverse to favourable conditions, yielding higher integrated levels of pressure fluctuations scaled by the wall shear stress. This is accompanied by a steeper decay rate in the medium-frequency portion for adverse pressure gradients. No significant difference is found for the mean convection velocity. Frequency–wavenumber spectra including the subconvective region are presented for the first time in the presence of a pressure gradient. A scaling law for the convective ridge is proposed, and the acoustic domain is captured by the simulations. Direct acoustic emissions have similar features in all gradient cases, even if slightly higher levels are noted for boundary layers subjected to an adverse gradient.

Scaling of adverse-pressure-gradient turbulent boundary layers

1992 ◽  
Vol 238 ◽  
pp. 699-722 ◽  
Author(s):  
P. A. Durbin ◽  
S. E. Belcher
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Wall Layer ◽  
Small Range ◽  
Surface Shear Stress ◽  
Pressure Gradients ◽  
Mean Flow ◽  
The Mean

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y½ behaviour in the overlap layer between the wall and transition regions.The analysis is done in the context of eddy viscosity closure modelling. It is found that k-ε-type models are suitable to the wall region, and have a power-law solution in the y½ layer. The outer-region scaling precludes the usual ε-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.

Entropy Generation for Bypass Transitional Boundary Layers

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Richard S. Skifton ◽  
Ralph S. Budwig ◽  
John C. Crepeau ◽  
Tao Xing
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Entropy Generation ◽  
Boundary Layer Flow ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Transitional Region ◽  
Bypass Transition ◽  
Layer Flow

The principal purpose of this study is to understand the entropy generation rate in bypass, transitional, boundary-layer flow better. The experimental work utilized particle image velocimetry (PIV) and particle tracking velocimetry (PTV) to measure flow along a flat plate. The flow past the flat plate was under the influence of a negligible “zero” pressure gradient, followed by the installation of an adverse pressure gradient. Further, the boundary layer flow was artificially tripped to turbulence (called “bypass” transition) by means of elevated freestream turbulence. The entropy generation rate was seen to behave similar to that of published computational fluid dynamics (CFD) and direct numerical simulation (DNS) results. The observations from this work show the relative decrease of viscous contributions to entropy generation rate through the transition process, while the turbulent contributions of entropy generation rate greatly increase through the same transitional flow. A basic understanding of entropy generation rate over a flat plate is that a large majority of the contributions come within a wall coordinate less than 30. However, within the transitional region of the boundary layer, a tradeoff between viscous and turbulent dissipation begins to take place where a significant amount of the entropy generation rate is seen out toward the boundary layer edge.

Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers

2008 ◽  
Vol 615 ◽  
pp. 445-475 ◽  
Author(s):  
SHIVSAI AJIT DIXIT ◽  
O. N. RAMESH
Keyword(s):  
Differential Equations ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Mean Velocity ◽  
Wide Range ◽  
Gradient Parameter ◽  
The Mean

Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp=(ν/ρU3τ)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws.

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