Self-preserving development within turbulent boundary layers in strong adverse pressure gradients

1965 ◽  
Vol 23 (4) ◽  
pp. 767-778 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Outer Part ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Pressure Gradients ◽  
Layer Model ◽  
Pressure Distributions ◽  
Two Layer Model ◽  
Local Parameters

The development of a turbulent boundary layer in a strong adverse pressure gradient can be described by the two-layer model proposed by Stratford (1959), in which the outer part of the flow is assumed to be unmodified by the pressure-rise and the inner part described by two local parameters, the surface stress and the pressure gradient. The description suggests that the modification of the original flow is in some sense self-preserving, and it is shown here that self-preserving development of the modification is consistent with the Reynolds equations of turbulent flow in particular pressure distributions. For these distributions, the predictions of the two-layer model are confirmed without any need to make the sharp and arbitrary distinction between the two parts of the boundary layer.

Effects of Area Ratio and Mean Rise Angle on the Aerodynamics of Interturbine Ducts

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Yanfeng Zhang ◽  
Shuzhen Hu ◽  
Ali Mahallati ◽  
Xue-Feng Zhang ◽  
Edward Vlasic
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Static Pressure ◽  
Computational Study ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Wake Flow ◽  
Height Ratio ◽  
Inlet Swirl

This work, a continuation of a series of investigations on the aerodynamics of aggressive interturbine ducts (ITD), is aimed at providing detailed understanding of the flow physics and loss mechanisms in four different ITD geometries. A systematic experimental and computational study was carried out by varying duct outlet-to-inlet area ratios (ARs) and mean rise angles while keeping the duct length-to-inlet height ratio, Reynolds number, and inlet swirl constant in all four geometries. The flow structures within the ITDs were found to be dominated by the boundary layer separation and counter-rotating vortices in both the casing and hub regions. The duct mean rise angle determined the severity of adverse pressure gradient in the casing's first bend, whereas the duct AR mainly governed the second bend's static pressure rise. The combination of upstream wake flow and the first bend's adverse pressure gradient caused the boundary layer to separate and intensify the strength of counter-rotating vortices. At high mean rise angle, the separation became stronger at the casing's first bend and moved farther upstream. At high ARs, a two-dimensional separation appeared on the casing and resulted in increased loss. Pressure loss penalties increased significantly with increasing duct mean rise angle and AR.

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.

Turbulent boundary layers in decreasing adverse pressure gradients

1966 ◽  
Vol 26 (3) ◽  
pp. 481-506 ◽  
Author(s):  
A. E. Perry
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Boundary Layer Development ◽  
Regional Similarity ◽  
Layer Development

The results of a detailed mean velocity survey of a smooth-wall turbulent boundary layer in an adverse pressure gradient are described. Close to the wall, a variety of profiles shapes were observed. Progressing in the streamwise direction, logarithmic, ½-power, linear and$\frac{3}{2}$-power distributions seemed to form, and generally each predominated at a different stage of the boundary-layer development. It is believed that the phenomenon occurred because of the nature of the pressure gradient imposed (an initially high gradient which fell to low values as the boundary layer developed) and attempts are made to describe the flow by an extension of the regional similarity hypothesis proposed by Perry, Bell & Joubert (1966). Data from other sources is limited but comparisons with the author's results are encouraging.

Backpressure propagation mode and balance property in a rectangular duct

2018 ◽  
Vol 233 (4) ◽  
pp. 1472-1489
Author(s):  
Yubao He ◽  
Hongyan Huang ◽  
Daren Yu
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Force Balance ◽  
Propagation Mode ◽  
Rectangular Duct ◽  
Local Boundary ◽  
Starting Point ◽  
Balance Property

The backpressure propagation mode accompanied by shock-train evolution is investigated numerically in a rectangular duct with an open space. On this basis, the balance mechanism and parametric effects of heat transfer and skin friction for backpressure propagation are revealed to understand the nature of force competition better. As a result, the backpressure propagation mode can be classified into two different flow processes with increased backpressure. In addition, balance property mechanism reveals that both the momentum inside the boundary layer and the shear force which transfers the momentum from the outer core flow to boundary layer are combined to resist the adverse pressure gradient. Further, parametric effect indicates that varying wall temperatures and roughness heights lead to different degrees of changes in balance property. According to quantitative results, both wall temperature and roughness height decrease the local boundary-layer momentum at the starting point of original pressure rise and thus the local adverse pressure gradient wins the force competition. In the subsequently continuous flow, the adverse pressure gradient continues to propagate upstream and then is retarded gradually by the boundary layer with a fuller velocity profile until a new force balance is generated.

Separated Turbulent Boundary Layer Under Unsteady Adverse Pressure Gradients: DNS and RANS

2014 ◽  
Author(s):  
Junshin Park
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Eddy Viscosity ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Recirculation Bubble ◽  
Rans Models

Predicitve capabilities of Reynolds Averaged Navier-Stokes (RANS) techniques have been assessed using SST k–ω model and Spalart-Allmaras model by comparing its results with direct numerical simulation (DNS) results. It has been shown that Spalart-Allmaras and SST k–ω model predict an earlier separation point and a bigger recirculation bubble as compared to the DNS result. Velocity profiles predicted by RANS for both models closely match with DNS results for the steady adverse pressure gradient case. However, the RANS fail to predict correct velocity profiles for unsteady adverse pressure gradients not only for inside the bubble but also after the reattachment zone. To provide the backgrounds for improving RANS models, these differences are explained with Reynolds stress and eddy viscosity which differ between the steady and unsteady adverse pressure gradient RANS cases.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1 — Mean Quantities

1995 ◽  
Author(s):  
Scott P. Mislevy ◽  
Ting Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Adverse Pressure Gradient ◽  
Surface Heat ◽  
Pressure Gradients ◽  
Surface Heat Transfer ◽  
Mean Temperature ◽  
The Mean

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6%. The acceleration parameter, K=vU¯∞2dU¯∞dx, was kept constant along the test section. Both surface heat transfer and boundary layer measurements were conducted. The boundary layer measurements were conducted with a three-wire probe (two velocity wires and one temperature wire) for two representative cases, K1=−0.51 × 10−6 and K2=−1.05 × 10−6. The surface heat transfer measurements were conducted for K values ranging from −0.045 × 10−6 to −1.44 × 10−6 over five divergent wall angles. The Stanton numbers of the cases with adverse pressure gradients were greater than that of the zero-pressure-gradient turbulent correlation in the low-Reynolds number turbulent flow, and the difference increased as the adverse pressure gradient was increased. The adverse pressure gradient caused earlier transition onset and shorter transition length based on Rex, Reδ*, and Reθ in comparison to zero-pressure-gradient conditions. As expected, there was a reduction in skin friction as the adverse pressure gradient increased. In the U+-Y+ coordinates, the adverse pressure gradients had a significant effect on the mean velocity profiles in the near-wall region for the late-laminar and early transition stations. The mean temperature profile was observed to precede the velocity profile in starting and ending the transition process, opposite to what occurred in favorable pressure gradient cases in previous studies. A curve fit of the turbulent temperature profile in the log-linear region for the K2 case gave a conduction layer thickness of Y+=9.8 and an average Prt=0.71. In addition, the wake region of the turbulent mean temperature profile was significantly suppressed.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1—Mean Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 717-727 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Adverse Pressure Gradient ◽  
Surface Heat ◽  
Pressure Gradients ◽  
Surface Heat Transfer ◽  
Mean Temperature ◽  
The Mean

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. The acceleration parameter, K, was kept constant along the test section. Both surface heat transfer and boundary layer measurements were conducted. The boundary layer measurements were conducted with a three-wire probe (two velocity wires and one temperature wire) for two representative cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The surface heat transfer measurements were conducted for K values ranging from −0.045 × 10−6 to −1.44 × 10−6 over five divergent wall angles. The Stanton numbers of the cases with adverse pressure gradients were greater than that of the zero-pressure-gradient turbulent correlation in the low-Reynolds-number turbulent flow, and the difference increased as the adverse pressure gradient was increased. The adverse pressure gradient caused earlier transition onset and shorter transition length based on Rex, Reδ*, and Reθ in comparison to zero-pressure-gradient conditions. As expected, there was a reduction in skin friction as the adverse pressure gradient increased. In the U+−Y+ coordinates, the adverse pressure gradients had a significant effect on the mean velocity profiles in the near-wall region for the late-laminar and early transition stations. The mean temperature profile was observed to precede the velocity profile in starting and ending the transition process, opposite to what occurred in favorable pressure gradient cases in previous studies. A curve fit of the turbulent temperature profile in the log-linear region for the K2 case gave a conduction layer thickness of Y+ = 9.8 and an average Prt = 0.71. In addition, the wake region of the turbulent mean temperature profile was significantly suppressed.

Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient

1975 ◽  
Vol 69 (2) ◽  
pp. 353-375 ◽  
Author(s):  
P. S. Andersen ◽  
W. M. Kays ◽  
R. J. Moffat
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Equation ◽  
Adverse Pressure Gradient ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Displacement Thickness

An experimental investigation of the fluid mechanics of the transpired turbulent boundary layer in zero and adverse pressure gradients was carried out on the Stanford Heat and Mass Transfer Apparatus. Profiles of (a) the mean velocity, (b) the intensities of the three components of the turbulent velocity fluctuations and (c) the Reynolds stress were obtained by hot-wire anemometry. The wall shear stress was measured by using an integrated form of the boundary-layer equation to ‘extrapolate’ the measured shear-stress profiles to the wall.The two experimental adverse pressure gradients corresponded to free-stream velocity distributions of the type u∞ ∞ xm, where m = −0·15 and −0·20, x being the streamwise co-ordinate. Equilibrium boundary layers (i.e. flows with velocity defect profile similarity) were obtained when the transpiration velocity v0 was varied such that the blowing parameter B = pv0u∞/τ0 and the Clauser pressure-gradient parameter $\beta\equiv\delta_1\tau_0^{-1}\,dp/dx $ were held constant. (τ0 is the shear stress at the wall and δ1 is the displacement thickness.)Tabular and graphical results are presented.

Effects of Area Ratio and Mean Rise Angle on the Aerodynamics of Inter-Turbine Ducts

2014 ◽  
Author(s):  
Yanfeng Zhang ◽  
Shuzhen Hu ◽  
Ali Mahallati ◽  
Xue-Feng Zhang ◽  
Edward Vlasic
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Computational Study ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Area Ratio ◽  
Wake Flow ◽  
High Area ◽  
Inlet Swirl

The present work, a continuation of a series of investigations on the aerodynamics of aggressive inter-turbine ducts (ITD), is aimed at providing detailed understanding of the flow physics and loss mechanisms in four different ITD geometries. A systematic experimental and computational study was carried out for varying duct mean rise angles and outlet-to-inlet area ratio while keeping the duct length-to-inlet height ratio, Reynolds number and inlet swirl constant in all four geometries. The flow structures within the ITDs were found to be dominated by the counter-rotating vortices and boundary layer separation in both the casing and hub regions. The duct mean rise angle determined the severity of adverse pressure gradient in the casing’s first bend whereas the duct area ratio mainly governed the second bend’s static pressure rise. The combination of upstream wake flow and the first bend’s adverse pressure gradient caused the boundary layer to separate and intensify the strength of counter-rotating vortices. At high mean rise angle, the separation became stronger at the casing’s first bend and moved farther upstream. At high area ratios, a 2-D separation appeared on the casing. Pressure loss penalties increased significantly with increasing duct mean rise angle and area ratio.

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