Effects of a Source-Type Hypersonic Free Stream on the Flow Field about an Axisymmetric Cone

1966 ◽  
Vol 17 (2) ◽  
pp. 161-176
Author(s):  
Stuart B. Savage
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Layer Thickness ◽  
Surface Pressure ◽  
Shock Layer ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Inviscid Flow ◽  
Source Type ◽  
Displacement Thickness

SummaryMost hypervelocity tunnels presently make use of conical or wedge type nozzles which produce source-type flow non-uniformities in the test section. The present paper considers the effects of such free-stream non-uniformities on the flow fields about slender axisymmetric cones. The inviscid flow is considered within the framework of the Newtonian expansion procedure of Cole and simple expressions are obtained for the flow field properties in the shock layer. This inviscid analysis predicts that a free-stream gradient of a magnitude typical of present hypervelocity test facilities can cause sizeable reductions in surface pressure and increased shock-layer thickness at the aft end of long slender conical models. The cone pressure, accounting for the viscous-inviscid interaction, is obtained by applying the inviscid analysis in tangent-cone fashion to the effective body (i.e. physical cone plus boundary-layer displacement thickness). Cheng’s simple equation is used to approximate the hypersonic boundary-layer development. Large increases in the boundary-layer thickness at the aft end of the model are predicted as a consequence of the source flow effects. The analyses agree well with experimental measurements of surface pressure and boundary-layer thickness made on a 5° half-angle cone tested in the Republic 24 inch Longshot I hypervelocity shock tunnel.

Influence of Chord Length and Inlet Boundary Layer on the Secondary Losses of Turbine Blades

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Helmut Sauer ◽  
Robin Schmidt ◽  
Konrad Vogeler
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Main Flow ◽  
Chord Length ◽  
Displacement Thickness ◽  
Wide Range ◽  
Main Flow Direction

In this paper, results concerning the influence of chord length and inlet boundary layer thickness on the endwall loss of a linear turbine cascade are discussed. The investigations were performed in a low speed cascade tunnel using the turbine profile T40. The turning of 90 deg and 70 deg, the velocity ratio in the cascade from 1.0 to 3.5 as well as the chord length of 100 mm, 200 mm, and 300 mm were specified. In a measurement distance of one chord behind the cascade in main flow direction, an approximate proportionality of endwall loss and chord was observed in a wide range of velocity ratios. At small measurement distances (e.g., s2/l=0.4), this proportionality does not exist. If a part of the flow path within the cascade is approximately incorporated, a proportionality to the chord at small measurement distances can be obtained, too. Then, the magnitude of the endwall loss mainly depends on the distance in main flow direction. At velocity ratios near 1.0, the influence of the chord decreases rapidly, while at a velocity ratio of 1.0, the endwall loss is independent of the chord. By varying the inlet boundary layer thickness, no correlation of displacement thickness and endwall loss was achieved. A calculation method according to the modified integral equation by van Driest delivers the wall shear stress. Its influence on the endwall loss was analyzed.

Subsonic Flow Over Open Cavities: Part 1 — Analytical Models and Numerical Investigations

2016 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Feedback Loop ◽  
Subsonic Flow ◽  
Free Stream ◽  
Open Cavities ◽  
Free Stream Mach Number

The aeroacoustical oscillation and acoustic field generated by subsonic flow grazing over open cavities has been investigated analytically and numerically. The tone generation mechanism is elucidated with an analytical model based on the coupling between shear layer instabilities and acoustic feedback loop. The near field turbulent flow is obtained using two-dimensional Large Eddy Simulation (LES). A special mesh is used to absorb propagating disturbances and prevent spurious numerical reflections. Comparisons with available experimental data demonstrate good agreement in both the frequency and amplitude of the aeroacoustical oscillation. The physical phenomenon of the noise generated by the feedback loop is discussed. The correlation analysis of primitive variables is also made to clarify the characteristics of wave propagation in space and time. The effects of free-stream Mach number and boundary layer thickness on pressure fluctuations within the cavity and the nature of the noise radiated to the far field are examined in detail. As free-stream Mach number increases velocity fluctuations and mass flux into the cavity increase, but the resonant Strouhal numbers slightly decrease. Both the resonant Strouhal numbers and sound pressure levels decrease with the increase of boundary layer thickness. Results indicate that the instability of the shear layer dominates both the frequency and amplitude of the aeroacoustical oscillation.

Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685

2000 ◽  
Vol 420 ◽  
pp. 47-83 ◽  
Author(s):  
NIKOLAUS A. ADAMS
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Shear Stresses ◽  
Numerical Representation ◽  
Computational Domain ◽  
The Mean ◽  
Compression Ramp

The turbulent boundary layer along a compression ramp with a deflection angle of 18° at a free-stream Mach number of M = 3 and a Reynolds number of Reθ = 1685 with respect to free-stream quantities and mean momentum thickness at inflow is studied by direct numerical simulation. The conservation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact- finite-difference-ENO scheme for the spatial discretization of the convective fluxes and 6th-order central compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge–Kutta scheme is used. The computational domain is discretized with about 15 × 106 grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statistical analysis, the flow is sampled 600 times over about 385 characteristic timescales δ0/U∞, defined by the mean boundary-layer thickness at inflow and the free-stream velocity. Diagnostics show that the numerical representation of the flow field is sufficiently well resolved.Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of similar magnitude to the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly amplified owing to the shock–boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently, resulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations involving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between velocity and temperature fluctuations is found to be invalid in the interaction area.

Effect of Mainstream Variables on Jets Issuing from a Row of Inclined Round Holes

1979 ◽  
Vol 101 (2) ◽  
pp. 298-304 ◽  
Author(s):  
K. Kadotani ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Film Cooling ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Source Model ◽  
Mean Velocity ◽  
Film Cooling Effectiveness ◽  
Free Stream Turbulence ◽  
Eddy Diffusivities

The effects of boundary layer thickness, Reynolds number and free stream turbulence intensity on jets issuing from a row of inclined holes are investigated from the viewpoint of film cooling. The local film cooling effectiveness and mean velocity and mean temperature distributions are measured. The turbulent eddy diffusivities are evaluated from calculations based on a heat source model. The boundary layer thickness and the free stream turbulence significantly influence the jet-mainstream interaction process and consequently the film cooling performance.

Streakline Flow Visualization of Discrete Hole Film Cooling for Gas Turbine Applications

1976 ◽  
Vol 98 (2) ◽  
pp. 245-250 ◽  
Author(s):  
R. S. Colladay ◽  
L. M. Russell
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Field ◽  
Gas Turbine ◽  
Layer Thickness ◽  
Turbulent Mixing ◽  
Film Cooling ◽  
Boundary Layer Thickness ◽  
Hole Diameter ◽  
Neutrally Buoyant

Film injection from discrete holes in a three row staggered array with 5-dia spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the mainstream, and (3) slanted 30 deg to the surface and 45 deg laterally to the mainstream. The ratio of the boundary layer thickness-to-hole diameter and the Reynolds number were typical of gas turbine film cooling applications. Results from two different injection locations are presented to show the effect of boundary layer thickness on film penetration and mixing. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally-buoyant helium filled “soap” bubbles which follow the flow field. Unlike smoke, which diffuses rapidly in the high turbulent mixing region associated with discrete hole blowing, the bubble streaklines passing downstream injection locations are clearly identifiable and can be traced back to their point of ejection.

The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity

2009 ◽  
Vol 638 ◽  
pp. 267-303 ◽  
Author(s):  
PIERRE RICCO
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Matched Asymptotic Expansion ◽  
Two Dimensional ◽  
Mean Flow ◽  
Flow Distortion ◽  
The Mean

The response of the Blasius boundary layer to free-stream vortical disturbances of the convected gust type is studied. The vorticity signature of the boundary layer is computed through the boundary-region equations, which are the rigorous asymptotic limit of the Navier–Stokes equations for low-frequency disturbances. The method of matched asymptotic expansion is employed to obtain the initial and outer boundary conditions. For the case of forcing by a two-dimensional gust, the effect of a wall-normal wavelength comparable with the boundary-layer thickness is taken into account. The gust viscous dissipation and upward displacement due to the mean boundary layer produce significant changes on the fluctuations within the viscous region. The same analysis also proves useful for computing to second-order accuracy the boundary-layer response induced by a three-dimensional gust with spanwise wavelength comparable with the boundary-layer thickness. It also follows that the boundary-layer fluctuations of the streamwise velocity match the corresponding free-stream velocity component. The velocity profiles are compared with experimental data, and good agreement is attained.The generation of Tollmien–Schlichting waves by the nonlinear mixing between the two-dimensional unsteady vorticity fluctuations and the mean flow distortion induced by localized wall roughness and suction is also investigated. Gusts with small wall-normal wavelengths generate significantly different amplitudes of the instability waves for a selected range of forcing frequencies. This is primarily due to the disparity between the streamwise velocity fluctuations in the free stream and within the boundary layer.

The modified Myers boundary condition for swirling flow

2018 ◽  
Vol 847 ◽  
pp. 868-906 ◽  
Author(s):  
James R. Mathews ◽  
Vianney Masson ◽  
Stéphane Moreau ◽  
Hélène Posson
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Azimuthal Velocity ◽  
Inviscid Flow ◽  
Layer Model ◽  
Quadratic Error ◽  
The Time Domain

This paper gives a modified Myers boundary condition in swirling inviscid flow, which differs from the standard Myers boundary condition by assuming a small but non-zero boundary layer thickness. The new boundary condition is derived and is shown to have the correct quadratic error behaviour with boundary layer thickness and also to agree with previous results when the swirl is set to zero. The boundary condition is initially derived for swirling flow with constant azimuthal velocity, but easily extends to radially varying swirling flow, with terms depending on the boundary layer model. The modified Myers boundary condition is then given in the time domain rather than in the frequency domain. The effect of the boundary layer profile is then considered, and shown to be small compared to the boundary layer thickness. The boundary condition is then used to analyse the eigenmodes and Green’s function in a realistic flow. Modelling the thickness of the boundary layer properly is shown to be essential in order to get accurate results.

Characteristics of the Flow Past a Wall-Mounted Finite-Length Square Cylinder at Low Reynolds Number With Varying Boundary Layer Thickness

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Sachidananda Behera ◽  
Arun K. Saha
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Field ◽  
Layer Thickness ◽  
Finite Length ◽  
Boundary Layer Thickness ◽  
Square Cylinder ◽  
Near Wake ◽  
Wall Boundary Layer ◽  
Wall Boundary

Direct numerical simulation (DNS) is performed to investigate the modes of shedding of the wake of a wall-mounted finite-length square cylinder with an aspect ratio (AR) of 7 for six different boundary layer thicknesses (0.0–0.30) at a Reynolds number of 250. For all the cases of wall boundary layer considered in this study, two modes of shedding, namely, anti-symmetric and symmetric modes of shedding, were found to coexist in the cylinder wake with symmetric one occurring intermittently for smaller time duration. The phase-averaged flow field revealed that the symmetric modes of shedding occur only during instances when the near wake experiences the maximum strength of upwash/downwash flow. The boundary layer thickness seems to have a significant effect on the area of dominance of both downwash and upwash flow in instantaneous and time-averaged flow field. It is observed that the near-wake topology and the total drag force acting on the cylinder are significantly affected by the bottom-wall boundary layer thickness. The overall drag coefficient is found to decrease with thickening of the wall boundary layer thickness.

Influence of Chord Length and Inlet Boundary Layer on the Secondary Losses of Turbine Blades

2010 ◽  
Author(s):  
Helmut Sauer ◽  
Robin Schmidt ◽  
Konrad Vogeler
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Turbine Blades ◽  
Flow Path ◽  
Chord Length ◽  
Displacement Thickness ◽  
Wide Range

In the present paper results concerning the influence of chord length and inlet boundary layer thickness on the endwall losses are discussed. The investigations were performed in a low speed cascade tunnel using the turbine profile T40. The deflection of 90 and 70 deg, the velocity ratio in the cascade from 1.0 to 3.5 as well as the chord length of 100,200 and 300 mm were predetermined. In a measurement distance behind the cascade of s2/l = 1, an approximate proportionality of endwall losses and chord length was observed in a wide range of velocity ratios. At small measurement distances (e.g. s2/l = 0.4), this proportionality does not exist. If aside from the flow path behind the cascade the flow path in the cascade is approximately incorporated, a proportionality to the chord length at small measurement distances can be obtained, too. Then to a large extent, the magnitude of the endwall losses is dependent on the length in main flow direction. At velocity ratios near 1.0, the influence of the chord length decreases rapidly, while at a velocity ratio of 1.0, the endwall losses are independent of chord length. By varying the inlet boundary layer thickness no correlation of displacement thickness and endwall losses was achieved. With a calculation method according to the modified integral equation by van Driest, the velocity gradient on the wall, the wall shear stress and the local friction coefficient were determined and their influence on the endwall losses analyzed.

Effect of Free-Stream Velocity Definition on Boundary Layer Thickness and Losses in Centrifugal Compressors

2017 ◽  
Author(s):  
Jonna Tiainen ◽  
Ahti Jaatinen-Värri ◽  
Aki Grönman ◽  
Teemu Turunen-Saaresti ◽  
Jari Backman
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Centrifugal Compressor ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Compressor Blade ◽  
Free Stream Velocity ◽  
Wake Flow ◽  
Stream Velocity ◽  
Centrifugal Compressors

The estimation of boundary layer losses requires the accurate specification of the free-stream velocity, which is not straightforward in centrifugal compressor blade passages. This challenge stems from the jet-wake flow structure, where the free-stream velocity between the blades cannot be clearly specified. In addition, the relative velocity decreases due to adverse pressure gradient. Therefore, the common assumption of a single free-stream velocity over the blade surface might not be valid in centrifugal compressors. Generally in turbomachinery, the losses in the blade cascade boundary layers are estimated e.g. with different loss co-efficients, but they often rely on the assumption of a uniform flow field between the blades. To give guidelines for the estimation of the mentioned losses in highly distorted centrifugal compressor flow fields, this paper discusses the difficulties in the calculation of the boundary layer thickness in the compressor blade passages, compares different free-stream velocity definitions, and demonstrates their effect on estimated boundary layer losses. Additionally, a hybrid method is proposed to overcome the challenges of defining a boundary layer in centrifugal compressors.

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