The Influence of Pressure Gradient on Desinent Cavitation From Isolated Surface Protrusions

1986 ◽  
Vol 108 (2) ◽  
pp. 254-260 ◽  
Author(s):  
J. William Holl ◽  
Michael L. Billet ◽  
Masaru Tada ◽  
David R. Stinebring
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shape Factor ◽  
Cavitation Number ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Relative Height ◽  
Velocity Range ◽  
Circular Arc ◽  
Air Content

An experimental investigation was conducted to study the desinent cavitation characteristics of various sizes of two-dimensional triangular and circular arc protrusions in a turbulent boundary layer for favorable, zero, and unfavorable pressure gradients. The roughness height (h) varied from 0.025 cm (0.01 in.) to 0.762 cm (0.30 in.) and the relative height (h/δ) varied from 0.026 to 2.53. Desinent cavitation numbers (σd) were obtained visually over a velocity range of 9.1 mps (30 fps) to 18.3 mps (60 fps) at an average total air content of 3.8 ppm (mole basis). The data for zero pressure gradient were in fair agreement with data obtained for the same protrusion shapes by Holl (1958). The cavitation number (σd) was correlated with relative height (h/δ), Reynolds number (Uδ/ν) and Clauser’s (1954) equilibrium boundary layer shape factor (G) which includes the effect of pressure gradient. The data show that σd increases with pressure gradient. This result was not expected since it appears to contradict the trends implied by the so-called characteristic velocity theory developed by Holl (1958).

Modification of Turbulence in Boundary Layers by Mean and Fluctuating Pressure Gradients

2012 ◽  
Author(s):  
Pranav Joshi ◽  
Xiaofeng Liu ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Wall Region ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Time Resolved ◽  
Freestream Velocity ◽  
Vortical Structures ◽  
Fluctuating Pressure ◽  
Near Wall

In this study we focus on the effect of mean and fluctuating pressure gradients on the structure of boundary layer turbulence. Two dimensional, time-resolved PIV measurements have been performed upstream of and inside an accelerating sink flow for inlet Reynolds number of Reθ = 3071, and acceleration parameter of K=1.1×10−6. The time-resolved data enables us to calculate the planer projection of pressure gradient by integrating the in-plane components of the material acceleration of the fluid (neglecting out-of-plane contribution). We use it to study the effect of boundary layer scale fluctuating pressure gradients ∂p′~/∂x, which are expected to be mostly two-dimensional, on the flow structure. Due to the imposed mean favorable pressure gradient (FPG) within the sink flow, the Reynolds stresses normalized by the local freestream velocity decrease over the entire boundary layer. However, when scaled by the inlet freestream velocity, the stresses increase close to the wall and decrease in the outer part of the boundary layer. This trend is caused by the confinement of the newly generated vortical structures in the near-wall region of the accelerating flow due to combined effects of downward mean flow, and stretching by velocity gradients. Within both the zero pressure gradient (ZPG) and FPG boundary layers, sweeping motions mostly occur during positive fluctuating pressure gradients ∂p′~/∂x>0 as the fluid moving towards the wall is decelerated by the presence of the wall. Vorticity is depleted in the near-wall region, as the wall absorbs −ω′ from the flow by viscous diffusion. On the other hand, ejections occur mostly during periods of favorable fluctuating pressure gradients ∂p′~/∂x<0. During these periods, there is more viscous flux of vorticity −ω′ into the flow, since ∂−ω′/∂y<0 at the wall. Large scale ejection motions associated with ∂p′~/∂x<0 are more likely to transport smaller scale turbulence to the outer region of the boundary layer, while turbulence remains largely confined close to the wall due to the sweeping motions accompanying ∂p′~/∂x>0. During periods of ∂p′~/∂x>0 in the ZPG boundary layer, sweeps tend to increase the momentum in the near-wall region, whereas the adverse pressure gradient decelerates the fluid. These competing effects result in an unstable ω′<0 shear layer which rolls up into coherent vortical structures and increases ω′ω′ near the wall as compared to periods of ∂p′~/∂x<0. Due to the strong mean acceleration of the flow and weaker sweeps in the FPG boundary layer, the formation of an unstable shear layer, and hence vortical structures, is suppressed, decreasing the enstrophy close to the wall as compared to periods of ∂p′~/∂x<0.

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

1993 ◽  
Vol 246 ◽  
pp. 503-527 ◽  
Author(s):  
Promode R. Bandyopadhyay ◽  
Anwar Ahmed
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
The Other ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Internal Layers ◽  
Vortex Systems ◽  
Corner Vortex

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2003 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number (Rex≅900,000). An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy (2St/cf). Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

An Accurate Calculation Method for Two-dimensional Incompressible Laminar Boundary Layers, Including Cases with Regions of Sharp Pressure Gradient

1977 ◽  
Vol 28 (3) ◽  
pp. 149-162 ◽  
Author(s):  
N Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Calculation Method ◽  
Boundary Layer Separation ◽  
Pressure Gradients ◽  
Accurate Calculation ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Type Boundary

SummaryThe paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

scholarly journals Influence of two-dimensional roughness element on boundary layer structure in the favourable pressure gradient region of the swept wing

2019 ◽  
Vol 234 (1) ◽  
pp. 20-27
Author(s):  
Stepan Tolkachev ◽  
Victor Kozlov ◽  
Valeriya Kaprilevskaya
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Layer Structure ◽  
Roughness Element ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Frequency Range ◽  
Swept Wing ◽  
Boundary Layer Structure ◽  
Roughness Elements

In this article, the results of research about stationary and secondary disturbances development behind the localized and two-dimensional roughness elements are presented. It is shown that the two-dimensional roughness element has a destabilizing effect on the disturbances induced by the three-dimensional roughness element lying upstream. In this case, the two-dimensional roughness element causes the appearance of stationary structures, and then secondary perturbations, whose frequency range lies lower than in the case of the stationary vortices excited by a three-dimensional roughness element.

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