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An improved joint is described for reducing the peak shear stress in adhesive bonds when adhesives are used to bond two materials which are in a lapped relationship and which differ in value of modulus of elasticity. An insert placed between the adhesive and one of the two materials acts to cushion the discontinuity of material stiffness thereby reducing the peak shear stress in the adhesive bond.
A shortcut is presented to the classical Hertzian solution for local stress and deformation of two elastic bodies in contact, which employs simplified forms for the ellipticity and for the complete elliptic integrals of the first and second kinds as a function of the geometry. Unlike previously proposed simplified formulas whose range of applicability was limited to ellipticities equal to, or greater than one, the present method extends the range of validity to include ellipticities less than one; in which the semimajor axis in the elliptical contact lies in a direction parallel to the rolling, rather than being perpendicular, as in previous studies. An auxiliary shear stress parameter is also expressed in simplified form as a function of the geometry, permitting a shortcut calculation to be made for the location and magnitude of the maximum subsurface shear stress.
Among the information presented are included displacement, momentum, and kinetic energy thicknesses, shearing stress distributions across boundary layer, and surface friction coefficients. The Gruschwitz method and its modifications are examined and tested. An energy theorem for the turbulent boundary layer is introduced and discussed but does not lead to a method for the prediction of the behavior of the turbulent boundary layer because relations for the shearing stress and the surface friction are lacking.
The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.
Endothelial cells alter their morphology, growth rate, and metabolism in response to fluid shear stress. To study rapid flow-induced responses in the 3D endothelial cell morphology and calcium distribution, coupled fluorescence microscopy with optical sectioning, digital imaging, and numerical deconvolution techniques have been utilized. Results demonstrate that within the first minutes of flow application nuclear calcium is increasing. In the same time frame whole cell height and nuclear height are reduced by about 1 microm. Whole cell height changes may facilitate reduction of shear stress gradients on the luminal surface, whereas nuclear structural changes may be important for modulating endothelial growth rate and metabolism. To study the role of the cytoskeleton in these responses, endothelial cells have been treated with specific disrupters (acrylamide, cytochalasin D, and colchicine) of each of the cytoskeleton elements (intermediate filaments, microfilaments, and microtubules, respectively). None of these compounds had any effect on the shear-induced calcium response. Cytochalasin D and acrylamide did not affect the shear-induced nuclear morphology changes. Colchicine, however, completely abrogated the response, indicating that microtubules may be implicated in force transmission from the plasma membrane to the nucleus. A pedagogical model based on tensegrity theory principles is presented that is consistent with the results on the 3D endothelial morphology.
The effects of secondary end-wall corner flows on near wall flow parameters in turbomachinary are studied. Important near wall flow parameters such as the wall shear stress vector, the mean wall pressure, the wall pressure fluctuations, and the correlation of the wall pressure fluctuation with the velocity fluctuation in three-dimensional turbulent flows are first experimentally investigated. The blade end-wall corner region is simulated by mounting airfoil section of symmetric blades on both sides of the flat plate with semicircular leading edge. Observed changes in the maximum values of the wall shear stress and its location from the corner line could be associated with the streching and attenuation of the horseshoe vortex. The values of wall pressure fluctuation intensity in the blade end-wall corner region are found to be influenced by the changes of the strength of the horseshoe vortex. The correlation of the wall pressure fluctuation with the velocity fluctuation indicated higher values of correlation coefficient in the inner region as compared to the outer region of the shear layer. The values of wall pressure-velocity correlation coefficient in the blade end-wall corner region also decrease in the streamwise direction while increasing in the presence of favorable and adverse pressure gradients.
Shear stress transmission to solid boundary of turbulent shear flow by thin laminar sublayer governed by pressure fluctuations
Turbulent intensity and Reynolds shear stress measurements are presented for two nonadiabatic hypersonic shock-wave boundary-layer interaction flows, one with and one without separation. These measurements were obtained using a new hot-wire probe specially designed for heated flows. Comparison of the separated and attached flows shows a significant increase above equilibrium values in the turbulent intensity and shear stress downstream of the interaction region for the attached case, while for the separated case, the turbulent fluxes remain close to equilibrium values. This effect results in substantial differences in turbulence lifetimes for the two flows. It is proposed that these differences are due to a coupling between the turbulent energy and separation bubble unsteadiness, a hypothesis supported by the statistical properties of the turbulent fluctuations.
Turbulent intensity and Reynolds shear stress measurements are presented for two nonadiabatic hypersonic shock-wave boundary-layer interaction flows, one with and one without separation. These measurements were obtained using a new hot-wire probe specially designed for heated flows. Comparison of the separated and attached flows shows a significant increase above equilibrium values in the turbulent intensity and shear stress downstream of the interaction region for the attached case, while for the separated case, the turbulent fluxes remain close to equilibrium values. This effect results in substantial differences in turbulence lifetime for the two flows. We propose that these differences are due to a coupling between the turbulent energy and separation bubble unsteadiness, a hypothesis supported by the statistical properties of the turbulent fluctuations.
Hot-wire measurements in an incompressible rectangular jet, issuing into a quiet environment at ambient conditions, are presented. A blow-down-type air supply system was used to provide the airflow to a cylindrical settling chamber 1.75 m in length and 0.6 m in diameter. The measurements were made with constant-temperature anemometers in conjunction with linearizers. The two signals from the linearizers were sent through a sum and difference unit which was calibrated from dc to 100 kHz. The distributions of mean velocity and the turbulence shear stresses were measured in the two central planes of the jet stations up to 115 widths downstream of the nozzle exit. Three distinct regions characterized the jet flow field: a potential core origin, a two-dimensional-type region, and an axisymmetric type region. The onset of the second region appeared to be at a location where the shear layers separated by the short dimension of the nozzle meet; and the third region occurred at a downstream location where the two shear layers from the short edges of the nozzle meet. In the central plane, similarity was found both in the mean velocity and shear stress profiles beyond 30 widths downstream of the nozzle exit; profiles of rms velocity showed similarity in the second, but not the third region.
The roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million was studied with an emphasis on suction side and near wake measurements. The research was conducted in a 32 in. x 48 in. low-speed wind tunnel. The half-wing model had a semi-span of 36 in. a chord of 48 in. and a rounded tip. Seven-hole pressure probe measurements of the velocity field surrounding the wingtip showed that a large axial velocity of up to 1.77 U(sub infinity) developed in the vortex core. This level of axial velocity has not been previously measured. Triple-wire probes have been used to measure all components of the Reynolds stress tensor. It was determined from correlation measurements that meandering of the vortex was small and did not appreciably contribute to the turbulence measurements. The flow was found to be turbulent in the near-field (as high as 24 percent RMS w - velocity on the edge of the core) and the turbulence decayed quickly with streamwise distance because of the nearly solid body rotation of the vortex core mean flow. A streamwise variation of the location of peak levels of turbulence, relative to the core centerline, was also found. Close to the trailing edge of the wing, the peak shear stress levels were found at the edge of the vortex core, whereas in the most downstream wake planes they occurred at a radius roughly equal to one-third of the vortex core radius. The Reynolds shear stresses were not aligned with the mean strain rate, indicating that an isotropic-eddy-viscosity based prediction method cannot accurately model the turbulence in the cortex. In cylindrical coordinates, with the origin at the vortex centerline, the radial normal stress was found to be larger than the circumferential.
Experimental results, including surveys of the mean and fluctuating flow, and measurements of surface pressure, skin friction, and separation length, are compared with solutions to the Navier-Stokes equations utilizing various algebraic eddy viscosity models to describe the Reynolds shear stresses. The experimental data, obtained at a free-stream Mach number of 1.5 and Reynolds numbers between 10 million and 80 million, show that a separated zone forms near the foot of the shock and that its length is proportional to the initial boundary-layer thickness; that a supersonic region forms downstream of the shock; and that the shear stress increases significantly through the interaction and subsequently decays downstream. The computations adequately represent the qualitative features of the flow field throughout the interaction but quantitatively underpredict the extent of separation and the downstream level of skin friction.
A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zeropressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation SpalartAllmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient cold wall flat plate case.
A detailed anaylsis and examples are presented that show how to enrich the kinematics of classical Kirchhoff plate theory by appending them with a set of continuous piecewise-cubic functions. This analysis is used to obtain functions that contain the effects of laminate heterogeneity and asymmetry on the variations of the inplane displacements and transverse shearing stresses, for use with a {3, 0} plate theory in which these distributions are specified apriori. The functions used for the enrichment are based on the improved zig-zag plate theory presented recently by Tessler, Di Scuva, and Gherlone. With the approach presented herein, the inplane displacements are represented by a set of continuous piecewise-cubic functions, and the transverse shearing stresses and strains are represented by a set of piecewise-quadratic functions that are discontinuous at the ply interfaces.
A coupled thermomechanical subsolidus model of the oceanic lithosphere and asthenosphere is developed which includes vertical heat conduction, a temperature-dependent thermal conductivity, heat advection by a horizontal and vertical mass flow that depends on depth and age, contributions of viscous dissipation or shear heating, a linear or nonlinear deformation law relating shear stress and strain rate, as well as a temperature- and pressure-dependent viscosity. The model requires a constant horizontal velocity and temperature at the surface, but zero horizontal velocity and constant temperature at great depths. The depth- and age-dependent temperature, horizontal and vertical velocities, and viscosity structure of the lithosphere and asthenosphere are determined along with the age-dependent shear stress in those two zones. The ocean-floor topography, oceanic heat flow, and lithosphere thickness are deduced as functions of ocean-floor age; seismic velocity profiles which exhibit a marked low-velocity zone are constructed from the age-dependent geotherms and assumed values of the elastic parameters. It is found that simple boundary-layer cooling determines the thermal structure at young ages, while effects of viscous dissipation become more important at older ages.
A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zero-pressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient flat plate case.
Analytical and experimental investigation of the characteristics of a three-dimensional turbulent boundary layer in a rotating helical channel. Expressions are developed for the velocity profiles in the inner layer, where viscous effects dominate, and the outer layer, where viscous effects are small. The velocity profiles, wall shear stress, and limiting streamline angles are measured inside the passages of a flat-plate inducer at various radial and chordwise locations using rotating probes. Flow near the blade tip is found to be highly complex, due to interaction of blade boundary layers and annulus wall, resulting in appreciable radial inward flow, as well as a defect in mainstream velocity near the mid-passage. A wall shear stress correlation, which includes the effect of both Reynolds number and rotation parameter, is derived from the measured data.
Reynolds-averaged Navier-Stokes computations of a shock-wave/boundary-layer interaction (SWBLI) created by a Mach 2.85 flow over an axisymmetric 30-degree compression corner were carried out. The objectives were to evaluate four turbulence models commonly used in industry, for SWBLIs, and to evaluate the suitability of this test case for use in further turbulence model benchmarking. The Spalart-Allmaras model, Menter's Baseline and Shear Stress Transport models, and a low-Reynolds number k- model were evaluated. Results indicate that the models do not accurately predict the separation location; with the SST model predicting the separation onset too early and the other models predicting the onset too late. Overall the Spalart-Allmaras model did the best job in matching the experimental data. However there is significant room for improvement, most notably in the prediction of the turbulent shear stress. Density data showed that the simulations did not accurately predict the thermal boundary layer upstream of the SWBLI. The effect of turbulent Prandtl number and wall temperature were studied in an attempt to improve this prediction and understand their effects on the interaction. The data showed that both parameters can significantly affect the separation size and location, but did not improve the agreement with the experiment. This case proved challenging to compute and should provide a good test for future turbulence modeling work.