scholarly journals The Profile Drag of Yawed Wings of Infinite Span

1951 ◽  
Vol 3 (3) ◽  
pp. 211-229 ◽  
Author(s):  
A.D. Young ◽  
T.B. Booth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Drag Coefficient ◽  
Experimental Evidence ◽  
Flat Plate ◽  
Transition Point ◽  
Reynolds Numbers ◽  
External Pressure ◽  
Basic Assumptions ◽  
Angle Of Yaw

SummaryA method is developed for calculating the profile drag of a yawed wing of infinite span, based on the assumption that the form of the spanwise distribution of velocity in the boundary layer, whether laminar or turbulent, is insensitive to the chordwise pressure distribution. The form is assumed to be the same as that accepted for the boundary layer on an unyawed plate with zero external pressure gradient. Experimental evidence indicates that these assumptions are reasonable in this context. The method is applied to a flat plate and the N.A.C.A. 64-012 section at zero incidence for a range of Reynolds numbers between 106 and 108, angles of yaw up to 45°, and a range of transition point positions. It is shown that the drag coefficients of a flat plate varies with yaw as cos½ Λ (where Λ is the angle of yaw) if the boundary layer is completely laminar, and it varies as if the boundary layer is completely turbulent. The drag coefficient of the N.A.C.A. 64-012 section, however, varies closely as cos½ Λ for transition point positions between 0 and 0.5 c. Further calculations on wing sections of other shapes and thicknesses and more detailed experimental checks of the basic assumptions at higher Reynolds numbers are desirable.

scholarly journals Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer

2015 ◽  
Vol 785 ◽  
pp. 78-108 ◽  
Author(s):  
W. Cheng ◽  
D. I. Pullin ◽  
R. Samtaney
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Skin Friction ◽  
Separation Bubble ◽  
Reynolds Numbers ◽  
Wall Model ◽  
Large Eddy ◽  
Layer Flow

We present large-eddy simulations (LES) of separation and reattachment of a flat-plate turbulent boundary-layer flow. Instead of resolving the near wall region, we develop a two-dimensional virtual wall model which can calculate the time- and space-dependent skin-friction vector field at the wall, at the resolved scale. By combining the virtual-wall model with the stretched-vortex subgrid-scale (SGS) model, we construct a self-consistent framework for the LES of separating and reattaching turbulent wall-bounded flows at large Reynolds numbers. The present LES methodology is applied to two different experimental flows designed to produce separation/reattachment of a flat-plate turbulent boundary layer at medium Reynolds number $Re_{{\it\theta}}$ based on the momentum boundary-layer thickness ${\it\theta}$. Comparison with data from the first case at $Re_{{\it\theta}}=2000$ demonstrates the present capability for accurate calculation of the variation, with the streamwise co-ordinate up to separation, of the skin friction coefficient, $Re_{{\it\theta}}$, the boundary-layer shape factor and a non-dimensional pressure-gradient parameter. Additionally the main large-scale features of the separation bubble, including the mean streamwise velocity profiles, show good agreement with experiment. At the larger $Re_{{\it\theta}}=11\,000$ of the second case, the LES provides good postdiction of the measured skin-friction variation along the whole streamwise extent of the experiment, consisting of a very strong adverse pressure gradient leading to separation within the separation bubble itself, and in the recovering or reattachment region of strongly-favourable pressure gradient. Overall, the present two-dimensional wall model used in LES appears to be capable of capturing the quantitative features of a separation-reattachment turbulent boundary-layer flow at low to moderately large Reynolds numbers.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

Some Experiments on the Reattachment of a Laminar Boundary Layer Separating From a Rearward Facing Step on a Flat Plate Aerofoil

1960 ◽  
Vol 64 (599) ◽  
pp. 668-672 ◽  
Author(s):  
T. W. F. Moore
Keyword(s):  
Boundary Layer ◽  
Liquid Film ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Reverse Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Pressure Measurements ◽  
Flow Vortex

Summary:The results of experiments on the reattachment of a laminar boundary layer, separating from a rearward facing step in a flat plate aerofoil, are correlated with the properties of the short leading edge bubble which forms on thin aerofoils near the stall.The experiments, comprising pressure measurements, Pitot explorations, liquid film and smoke studies, indicate that for all Reynolds numbers above the value given by the Owen-KIanfer criterion the reattachment is turbulent behind a stationary air reverse flow vortex bubble. It is also found that the reattachment is laminar for Reynolds numbers below the critical, which further supports Crabtree's interpretation of the Owen-KIanfer criterion in terms of the condition for the growth of turbulent bursts.

An approximate theory for the streaming motion past axisymmetric bodies at Reynolds numbers of from 1 to approximately 100

1977 ◽  
Vol 82 (3) ◽  
pp. 583-604 ◽  
Author(s):  
Michael S. Kolansky ◽  
Sheldon Weinbaum ◽  
Robert Pfeffer
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Approximate Theory ◽  
Viscous Term ◽  
Number Range ◽  
Curvature Effects ◽  
Flow Past

In Weinbaum et al. (1976) a simple new pressure hypothesis is derived which enables one to take account of the displacement interaction, the geometrical change in streamline radius of curvature and centrifugal effects in the thick viscous layers surrounding two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < O(102) using conventional Prandtl boundary-layer equations. The new pressure hypothesis states that the streamwise pressure gradient as a function of distance from the forward stagnation point on the displacement body is equal to the wall pressure gradient as a function of distance along the original body. This hypothesis is shown to be equivalent to stretching the streamwise body co-ordinate in conventional first-order boundary-layer theory. The present investigation shows that the same pressure hypothesis applies for the intermediate Reynolds number flow past axisymmetric bluff bodies except that the viscous term in the conventional axisymmetric boundary-layer equation must also be modified for transverse curvature effects O(δ) in the divergence of the stress tensor. The approximate solutions presented for the location of separation and the detailed surface pressure and vorticity distribution for the flow past spheres, spheroids and paraboloids of revolution at various Reynolds numbers in the range O(1) < Re < O(102) are in good agreement with available numerical Navier–Stokes solutions.

The Effects of Small Changes of Prandtl Number and the Viscosity-Temperature Index on Skin Friction

1964 ◽  
Vol 15 (4) ◽  
pp. 392-406 ◽  
Author(s):  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Wall Temperature ◽  
External Pressure ◽  
Main Stream ◽  
Pressure Gradients ◽  
Temperature Index

SummaryThe analytic simplifications in boundary-layer analysis that result from the assumptions that the Prandtl number σ and the viscosity-temperature index ω are unity make it desirable to be able to assess the effects of the departures of the actual values of these parameters from unity. In this paper only the effects on skin friction are considered. Formulae of acceptable validity and wide application are first used to produce generalised curves for these effects for given main-stream Mach numbers and wall temperature conditions for the case of zero external pressure gradient for both laminar and turbulent boundary layers (Figs. 1 and 2).A number of calculated results for the laminar boundary layer with favourable and adverse pressure gradients is then analysed (Figs. 3, 4 and 5) and it is shown that these results are consistent with the assumption that, for a given wall temperature, the effects of small changes of σ and ω on skin friction are independent of the external gradient, so that the appropriate curves of Figs. 1 and 2 apply. Where the change of a- is associated with a change of wall temperature (e.g. if the heat transfer is specified as zero) then the interaction between pressure gradient and this temperature change can be significant in its effects on skin friction for the laminar boundary layer and can only be assessed if the effects of changes of wall temperature with constant σ and ω have been separately determined for the pressure distribution considered. It is inferred that in all cases, except with large adverse pressure gradients and imminent separation, the effects of changes of ω and σ for the turbulent boundary layer are reliably predicted by the zero pressure gradient curves of Figs. 1 and 2 and the effect of any associated change of wall temperature can then be reliably inferred from the zero pressure gradient formula (equation (15)) in the absence of more specific calculations covering a range of wall temperatures.

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