Accurate Study of Normal Pressure Distribution in Entrance Region of Channel

2005 ◽  
Author(s):  
Kensyuu Shimomukai ◽  
Hidesada Kanda
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Transport Equation ◽  
Normal Pressure ◽  
Reynolds Numbers ◽  
Entrance Region ◽  
Parallel Plates ◽  
The Difference ◽  
Vorticity Transport

There are few implicit solutions available for the pressure distribution in the y-direction. Thus, for the flow between parallel plates, the pressure distribution in the entrance region was studied, focusing on the pressure gradient in the y-direction at Reynolds numbers (Re) between 100 and 5000. In the numerical method, the vorticity transport equation is first solved and then Poisson’s equation for pressure distribution is solved without any assumptions taken for pressure distribution. Consequently, the difference in pressure between the wall and the centerline existed near the inlet and decreased as Re increased. The pressure at the wall is lower than that in the central core for Re ≤ 5000. This result shows that (i) the boundary-layer assumptions do not hold for Re ≤ 5000 and (ii) the pressure distribution is contrary to Bernoulli’s law across parallel plates, although the law does not apply to viscous flow.

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.

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.

Experiments on the Flow Around a Sphere at High Reynolds Numbers

1969 ◽  
Vol 36 (3) ◽  
pp. 598-607 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Distribution ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Layer Separation ◽  
High Reynolds Numbers ◽  
High Reynolds

Flow around a sphere for Reynolds numbers between 2 × 105 and 6 × 104 has been observed by measuring the pressure distribution around a circle of longitude under a variety of conditions. These include the effects of laminar and turbulent boundary layer separation, tunnel blockage, various boundary layer trip arrangements and inserting an object to disrupt the unsteady, recirculation region behind the sphere.

On the Momentum and Thermal Structures of Turbulent Spots in a Favorable Pressure Gradient

2005 ◽  
Vol 128 (4) ◽  
pp. 689-698 ◽  
Author(s):  
T. P. Chong ◽  
S. Zhong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Velocity Component ◽  
Thermal Boundary Layer ◽  
Temperature Fluctuations ◽  
Turbulent Spots ◽  
Zone Length ◽  
Favorable Pressure Gradient ◽  
The Difference

This paper represents the results from an experimental investigation of the flow physics behind the difference in the transition zone length indicated by the momentum boundary layer and thermal boundary layer parameters observed on the suction surfaces of gas turbine blades. The experiments were carried out on turbulent spots created artificially in an otherwise laminar boundary layer developing over a heated flat plate in a zero pressure gradient and a favorable pressure gradient. A specially designed miniature triple wire probe was used to measure the streamwise velocity component U, transverse velocity component V and temperature T simultaneously during the passage of the spots. In this paper, the general characteristics of the ensemble-averaged velocity and temperature perturbations, rms fluctuations, and the second moment turbulent quantities are discussed and the influence of favorable pressure gradient on these parameters is examined. When a favorable pressure gradient is present, unlike in the velocity boundary layer where significant velocity fluctuations and Reynolds shear stress occur both on the plane of symmetry and the spanwise periphery, high temperature fluctuations (and turbulent heat fluxes) are confined in the plane of symmetry. The difference in the levels of velocity/temperature fluctuations at these two locations gives an indication of the effectiveness of momentum/heat transfer across the span of the spots. The results of this study indicate that the heat transfer within a spot is inhibited more than that of the momentum transfer at the presence of a favorable pressure gradient. This phenomenon is expected to slow down the development of a transitional thermal boundary layer, leading to a longer transitional zone length indicated by the heat transfer parameters as reported in the literature.

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.

A supersonic turbulent boundary layer in an adverse pressure gradient

1990 ◽  
Vol 211 ◽  
pp. 285-307 ◽  
Author(s):  
Emerick M. Fernando ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Large Scale Structures ◽  
Streamline Curvature ◽  
The Mean ◽  
Scale Structures

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.

Experimental Investigation into the Effect of the Thermal Boundary Condition on Heat Transfer in the Entrance Region of a Pipe

1964 ◽  
Vol 6 (3) ◽  
pp. 250-255 ◽  
Author(s):  
W. B. Hall ◽  
S. A. Khan
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Reynolds Numbers ◽  
Entrance Region ◽  
Uniform Heat Flux ◽  
Layer Formation ◽  
Uniform Temperature ◽  
Significant Difference ◽  
The Difference ◽  
Boundary Layer Formation

Experimental results are presented for forced convection in the entrance region of a pipe; the results were obtained using both the boundary condition of uniform heat flux and that of uniform temperature. A significant difference which is attributable to the different boundary conditions was observed for Reynolds numbers below about 3 times 104, but at higher Reynolds numbers the difference rapidly diminishes. An approximate numerical solution for the early stages of boundary layer formation on the pipe walls gave similar differences between the two boundary conditions as were observed in the experiment.

Pressure Gradient and Leading Edge Effects on the Corner Boundary Layer

1979 ◽  
Vol 30 (3) ◽  
pp. 471-484 ◽  
Author(s):  
M. Zamir ◽  
A.D. Young
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Direction ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Small Incidence ◽  
Made In

SummaryResults are presented of velocity and pressure measurements made in the initially laminar boundary layer in a streamwise corner formed by two flat plates at 90° to each other set at various incidences. The leading edges of the plates were sharp in contrast to earlier tests with an aerofoil type leading edge. It was found impossible to obtain a steady enough flow for useful measurements to be made at zero incidence and pressure gradient, a small incidence associated with a favourable pressure gradient was necessary. This is believed to be because of the development of separation bubbles at the sharp leading edge at very small incidences due to small variations of flow direction to be expected in a wind tunnel. The profiled nose used in earlier tests afforded flow conditions much closer to the ideal theoretical model involving zero pressure gradient, but it is argued that any nose however shaped may introduce disturbances in the form of characteristic secondary flows that may well determine the downstream response of the boundary layer. In any case the corner flow is highly unstable at all but very low Reynolds numbers, and in the absence of a region of favourable pressure gradient a Reynolds number in terms of distance downstream of the leading edge greater than about 105is unlikely to be attained in practice with the flow remaining smooth and laminar.

scholarly journals Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows

2011 ◽  
Vol 673 ◽  
pp. 1-18 ◽  
Author(s):  
LIANG WEI ◽  
ANDREW POLLARD
Keyword(s):  
Pressure Gradient ◽  
Transport Equation ◽  
Turbulent Flows ◽  
Variable Viscosity ◽  
Correlation Coefficients ◽  
Channel Flows ◽  
Turbulent Channel Flows ◽  
Spanwise Vorticity ◽  
The Difference ◽  
Vorticity Flux

The interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows (TCF) are studied using direct numerical simulations (DNS). DNS of three isothermal-wall TCF for Mach number Ma = 0.2, 0.7, and 1.5, respectively are performed using a discontinuous Galerkin method (DGM). The Reynolds numbers of these three cases are ≈2800, based on the bulk velocity, bulk density, half channel width and dynamic viscosity at the wall. A high cross-correlation between density and spanwise vorticity occurs at y+≈4, which is coincident with the peak mean spanwise baroclinicity. The relationship between the spanwise baroclinicity and the correlation is analysed. The difference between the evolution of density and spanwise vorticity very near the wall is discussed. The transport equation for the mean product of density and vorticity fluctuations 〈ρ′ω′i〉 is presented and the distributions of terms in the 〈ρ′ω′z〉 transport equation indicate that the minima and maxima of the profiles are located around y+≈5. The connection between pressure gradients and vorticity fluxes for compressible turbulent flows with variable viscosity has been formulated and verified. High correlations (0.7–1.0) between pressure gradient and vorticity flux are found very close to the wall (y+<5). The correlation coefficients are significantly influenced by Ma and viscosity in this region. Turbulence advection plays an important role in destroying the high correlations between pressure gradient and vorticity flux in the region away from the wall (y+ > 5).

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