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NASA NTRS1992

Advances in the modeling of laminated plates

The present evaluation of extant 2D theories and computational models of laminated composite plates gives attention to the classical, as well as to various shear-deformation, plate theories. A generalization of advanced theories is proposed, and computational aspects of the displacement finite-element models of these advanced theories are discussed. The 4MREDNC-R element appears to be ideally suited to use as a flat, four-noded shell element for applications in which the bending and membrane couplings are not significant.

Reddy, J. N.↗

NASA NTRS1959

Details of Exact Low Prandtl Number Boundary-Layer Solutions for Forced and For Free Convection

A detailed report is given of exact (numerical) solutions of the laminar-boundary-layer equations for the Prandtl number range appropriate to liquid metals (0.003 to 0.03). Consideration is given to the following situations: (1) forced convection over a flat plate for the conditions of uniform wall temperature and uniform wall heat flux, and (2) free convection over an isothermal vertical plate. Tabulations of the new solutions are given in detail. Results are presented for the heat-transfer and shear-stress characteristics; temperature and velocity distributions are also shown. The heat-transfer results are correlated in terms of dimensionless parameters that vary only slightly over the entire liquid-metal range. Previous analytical and experimental work on low Prandtl number boundary layers is surveyed and compared with the new exact solutions.

Sparrow, E. M.↗

NASA NTRS2004

Transitional Bubble in Periodic Flow Phase Shift

One particular characteristic observed in unsteady shear layers is the phase shift relative to the main flow. In attached boundary layers this will have an effect both on the instantaneous skin friction and heat transfer. In separation bubbles the contribution to the drag is dominated by the pressure distribution. However, the most significant effect appears to be the phase shift on the transition process. Unsteady transition behaviour may determine the bursting of the bubble resulting in an un-recoverable full separation. An early analysis of the phase shift was performed by Stokes for the incompressible boundary layer of an oscillating wall and an oscillating main flow. An amplitude overshoot within the shear layer as well as a phase shift were observed that can be attributed to the relatively slow diffusion of viscous stresses compared to the fast change of pressure. Experiments in a low speed facility with the boundary layer of a flat plate were evaluated in respect to phase shift. A pressure distribution similar to that on the suction surface of a turbomachinery aerofoil was superimposed generating a typical transitional separation bubble. A periodically unsteady main flow in the suction type wind tunnel was introduced via a rotating flap downstream of the test section. The experiments covered a range of the three similarity parameters of momentum-loss-thickness Reynolds-number of 92 to 226 and Strouhal-number (reduced frequency) of 0.0001 to 0.0004 at the separation point, and an amplitude range up to 19 %. The free stream turbulence level was less than 1% .Upstream of the separation point the phase shift in the laminar boundary layer does not appear to be affected significantly bay either of the three parameters. The trend perpendicular to the wall is similar to the Stokes analysis. The problem scales well with the wave velocity introduced by Stokes, however, the lag of the main flow near the wall is less than indicated analytically. The separation point comes closest to the Stokes analysis but the phase is still 20 degrees lower at the wall.

Talan, M.↗

NASA NTRS1975

Unified nonlinear approach to both weak and strong-interaction problems

The numerical results are obtained for heat transfer, skin-friction, and viscous interaction induced pressure for a step-wise accelerated flat plate in hypersonic flow. In the unified approach here the results are presented for both weak and strong-interaction problems without employing any linearization scheme. With the help of the numerical method used in this work an accurate prediction of wall shear can be made for the problems with plate velocity changes of 1% or larger. The obtained results indicate that the transient contribution to the induced pressure for helium is greater than that for air.

Gupta, R. N.↗

NASA NTRS1980

Flow over plates with suction through porous strips

This paper addresses the steady, incompressible, two-dimensional flow past a flat plate with suction through porous strips. Closed-form solutions for each flow quantity are developed in the context of linearized triple-deck theory using Fourier transforms. To demonstrate the validity of these closed-form solutions, we compare the wall shear stress and pressure coefficients and the streamwise velocity profiles from the linearized theory with those obtained by the numerical integration of both interacting and nonsimilar boundary-layer equations. The agreement between the linearized triple-deck and interacting boundary-layer equations is good; however, the nonsimilar boundary layers, which fail to account for upstream influence, are shown to be in poor agreement with both interacting boundary layers and the linearized triple deck. The linearized closed-form solutions will therefore be very useful in future stability calculations.

Nayfeh, A. H.↗

NASA NTRS1987

Computational fluid dynamics near the continuum limit

Two dimensional Navier-Stokes equations for a perfect gas are solved for hypersonic flow over a flat plate at Reynolds numbers ranging from continuum to the free molecule flow. In the transition flow regime, new slip boundary conditions are introduced, which reduce to the well-known slip conditions of Maxwell at small Knudsen numbers and yield the correct shear stress and heat transfer in the limiting case of free molecule flow. Comparison of the computed results with the existing experimental data and Monte Carlo calculations indicates that the continuum Navier-Stokes equations give surprisingly realistic results throughout the transition flow regime, when the new slip boundary conditions are used.

Maccormack, Robert W.↗

NASA NTRS2005

Heat Transfer on a Flat Plate with Uniform and Step Temperature Distributions

Heat transfer associated with turbulent flow on a step-heated or cooled section of a flat plate at zero angle of attack with an insulated starting section was computationally modeled using the GASP Navier-Stokes code. The algebraic eddy viscosity model of Baldwin-Lomax and the turbulent two-equation models, the K- model and the Shear Stress Turbulent model (SST), were employed. The variations from uniformity of the imposed experimental temperature profile were incorporated in the computations. The computations yielded satisfactory agreement with the experimental results for all three models. The Baldwin- Lomax model showed the closest agreement in heat transfer, whereas the SST model was higher and the K-omega model was yet higher than the experiments. In addition to the step temperature distribution case, computations were also carried out for a uniformly heated or cooled plate. The SST model showed the closest agreement with the Von Karman analogy, whereas the K-omega model was higher and the Baldwin-Lomax was lower.

Bahrami, Parviz A.↗

NASA NTRS1991

A k-epsilon modeling of near wall turbulence

A k-epsilon model is proposed for turbulent bounded flows. In this model, the turbulent velocity scale and turbulent time scale are used to define the eddy viscosity. The time scale is shown to be bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using the time scale, removing the need to introduce the pseudo-dissipation. A damping function is chosen such that the shear stress satisfies the near wall asymptotic behavior. The model constants used are the same as the model constants in the commonly used high turbulent Reynolds number k-epsilon model. Fully developed turbulent channel flows and turbulent boundary layer flows over a flat plate at various Reynolds numbers are used to validate the model. The model predictions were found to be in good agreement with the direct numerical simulation data.

Yang, Z.↗

NASA NTRS1981

Application of a Laser Interferometer Skin-Friction Meter in Complex Flows

A nonintrusive skin-friction meter has been found useful for a variety of complex wind-tunnel flows. This meter measures skin friction with a remotely located laser interferometer that monitors the thickness change of a thin oil film. Its accuracy has been proven in a low-speed flat-plate flow. The wind-tunnel flows described here include sub-sonic separated and reattached flow over a rearward-facing step, supersonic flow over a flat plate at high Reynolds numbers, and supersonic three - dimensional vortical flow over the lee of a delta wing at angle of attack. The data-reduction analysis was extended to apply to three-dimensional flows with unknown flow direction, large pressure and shear gradients, and large oil viscosity changes with time. The skin friction measurements were verified, where possible, with results from more conventional techniques and also from theoretical computations.

Monson, D. J.↗

NASA NTRS1979

Effect of transverse shear and material orthotropy in a cracked spherical cap

The elastostatic problem for a relatively thin-walled spherical cap containing a through crack is considered. The problem is formulated for a specially orthotropic material within the confines of a linearized, shallow shell theory. The theory used is equivalent to Reissner's theory of flat plates and hence permits the consideration of all five physical conditions on the shell boundaries separately. The solution of the problem is reduced to that of a pair of singular integral equations and the asymptotic stress state around the crack tips is investigated. The numerical solution of the problem is given for an isotropic shell and for two specially orthotropic shells. The results indicate that the material orthotropy as well as the shell curvature and thickness may have a considerable effect on the stress intensity factors at the crack tips.

Delale, F.↗

NASA NTRS1989

Low-speed flowfield characterization by infrared measurements of surface temperatures

An experimental program was aimed at identifying areas in low speed aerodynamic research where infrared imaging systems can make significant contributions. Implementing a new technique, a long electrically heated wire was placed across a laminar jet. By measuring the temperature distribution along the wire with the IR imaging camera, the flow behavior was identified. Furthermore, using Nusselt number correlations, the velocity distribution could be deduced. The same approach was used to survey wakes behind cylinders in a wind-tunnel. This method is suited to investigate flows with position dependent velocities, e.g., boundary layers, confined flows, jets, wakes, and shear layers. It was found that the IR imaging camera cannot accurately track high gradient temperature fields. A correlation procedure was devised to account for this limitation. Other wind-tunnel experiments included tracking the development of the laminar boundary layer over a warmed flat plate by measuring the chordwise temperature distribution. This technique was applied also to the flow downstream from a rearward facing step. Finally, the IR imaging system was used to study boundary layer behavior over an airfoil at angles of attack from zero up to separation. The results were confirmed with tufts observable both visually and with the IR imaging camera.

Gartenberg, E.↗

NASA NTRS1994

Designing Bolted Joints Between Composite Plates

Simplified methods developed for use in preliminary design and analysis of bolted joints between flat composite-material plates loaded in tension. Analysis also applicable to joints between composite and metal plates. Methods based on approximate equations for limiting stresses in single-bolt joint in five modes of failure: local-bearing-failure, net tension, wedge-type splitting, shear-out, and tension with shear-out.

Chamis, Christos C.↗

NASA NTRS1976

Shock wave-turbulent boundary layer interactions in transonic flow

The method of matched asymptotic expansions is used in analyzing the structure of the interaction region formed when a shock wave impinges on a turbulent flat plate boundary layer in transonic flow. Solutions in outer regions, governed by inviscid flow equations, lead to relations for the wall pressure distribution. Solutions in the inner regions, governed by equations in which Reynolds and/or viscous stresses are included, lead to a relation for the wall shear stress. Solutions for the wall pressure distribution are reviewed for both oblique and normal incoming shock waves. Solutions for the wall shear stress are discussed.

Adamson, T. C., Jr.↗

NASA NTRS1990

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

Librescu, L.↗

NASA NTRS2002

Near Field Trailing Edge Tone Noise Computation

Blunt trailing edges in a flow often generate tone noise due to wall-jet shear layer and vortex shedding. In this paper, the space-time conservation element (CE/SE) method is employed to numerically study the near-field noise of blunt trailing edges. Two typical cases, namely, flow past a circular cylinder (aeolian noise problem) and flow past a flat plate of finite thickness are considered. The computed frequencies compare well with experimental data. For the aeolian noise problem, comparisons with the results of other numerical approaches are also presented.

Loh, Ching Y.↗

NASA NTRS1975

Skin friction reduction in supersonic flow by injection through slots, porous sections and combinations of the two

An experimental study of skin friction reduction in a Mach 3.0 air steam with gaseous injection through a tangential slot, a porous wall section, and combinations of the two was conducted. The primary data obtained were wall shear values measured directly with a floating element balance and also inferred from Preston Tube measurements. Detailed profiles at several axial stations, wall pressure distributions and schlieren photographs are presented. The data indicate that a slot provides the greatest skin friction reduction in comparison with a reference flat plate experiment. The porous wall section arrangement suffers from an apparent roughness-induced rise in skin friction at low injection rates compared to the flat plate. The combination schemes demonstrated a potential for gain.

Schetz, J. A.↗

NASA NTRS1989

Experimental measurements of large scale structures in an incompressible turbulent boundary layer using correlated X-probes

Hot-wire anemometry measurements in an incompressible turbulent boundary-layer flow over a flat plate, at zero pressure gradient were made using two X-probes simultaneously. The over seven meters long flat plate installed within the wind tunnel generated an approximately 20-cm thick boundary layer, and R(theta) of about 4,000. The mean velocity and turbulence intensity data very close to the wall were measured with a single-wire. Space-time velocity fluctuation and shear-product correlation measurements enabled the calculation of large-scale structure convection velocity, inclination-angle to the wall, and spatial extent in space. The shear-product correlation results are reported for the first time.

Strataridakis, Constantine J.↗

NASA NTRS1986

About the coupling of turbulence closure models with averaged Navier-Stokes equations

The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.

Vandromme, D.↗