This paper presents a study of the flow of an incompressible second-order fluid past a stretching sheet. The problem has a bearing on some polymer processing application such as the continuous extrusion of a polymer sheet from a die.

/pdf/flow-of-a-viscoelastic-fluid-over-a-stretching-sheet-37oecwznqc.pdf

Flow of a viscoelastic fluid over a stretching sheet

Viscous flow and heat transfer over a nonlinearly stretching sheet

Viscous flow over a nonlinearly stretching sheet

Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet

Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation

A thin-layer Navier-Stokes code has been used to compute the turbulent flow over two axisymmetric bodies at transonic speeds. A critical element of calculating such flows is the turbulence model. Numerical computations have been made with an algebraic eddy viscosity model and the k — e two-equation model. The k — e equations are developed in a general spatial coordinate system and incorporated into the thin-layer, compressible, time-dependent Navier-Stokes code. The same implicit algorithm that simultaneously solves the Reynolds-averaged mean flow equations is extended to solve the turbulence field equations using block tridiagonal matrix inversions. Calculations with the k — e model are extended up to the wall. Numerical solutions have been obtained for two transonic flow situations to determine the accuracy of the k — e model. First, the attached flow over an axisymmetric projectile has been investigated. The second flow situation considered is the transonic separated flow over an axisymmetric bump model. Furthermore, the accuracy and applicability of the k — e model are determined by comparing the computed results with experimental data.

Navier-Stokes computations of transonic flows with a two-equation turbulence model

Experimental measurements of the mean profile characteristics of the supersonic turbulent boundary layer in a region of moderate adverse pressure gradient along the curved surface of an isentropic ramp model are reported. Detailed surveys of impact pressure, static pressure and total temperature were made through the boundary layer and local values of wall shear stress were obtained using the Preston tube technique. The measurements were made for a nominal tunnel nozzle setting of Mach 3.5, closely adiabatic wall, and momentum thickness Reynolds number of 1.9 to 4.2 x 10. In addition to the mean profile data, fluctuation data were obtained using constant temperature hot wire anemometry at one station in the region of zero pressure gradient and at one station in the region of adverse pressure gradient.

Supersonic Turbulent Boundary Layer in Adverse Pressure Gradient. Part I: The Experiment

: The transonic flow field about a secant-ogive-cylinder-boattail with a turbulent boundary layer has been studied. A joint theoretical and experimental effort is presented which compares the results of a generalized axisymmetric Navier-Stokes code, a composite inviscid boundary-layer/shock interaction solution method, and experiment. The experimental longitudinal pressure distribution at M= 0.94, and 0.97 for alpha = 0.0 degree are generally well predicted by both theoretical techniques although the Navier-Stokes solutions are shown to be superior in describing the detail, such as, upstream effects of expansion corners and the position and magnitude of minimum pressure regions. Both theoretical solutions predict the boundary layer velocity profiles very well in all cases with the largest differences occurring just downstream of the boattail corner. Comparisons of displacement thickness and skin friction distributions are also presented.

A Theoretical and Experimental Investigation of a Transonic Projectile Flow Field

it may be recognized that the closer a plate deflection comes to a sine wave, the smaller the edge effect error and thus the greater the accuracy achieved. This is borne out by the results of Table 1 where it may be seen that the larger discrepancies occur for the compressive forces, where the plate deflection tends to deviate from a sine wave, than for tensile forces, where the plate tends to behave more and more like a membrane, the exact shape for which is a pure sine wave. Figure 1, which shows the variation in frequency with in-plane load for the isotropic plate (computed using the edge effect method and the series solution), further illustrates this trend. For completeness, Table 2 shows the buckling loads obtained using the edge effect method for the various cases of orthotropy and, in the case of the isotropic plate, shows the accurate value presented by Taylor. The accuracy of the method for buckling problems is somewhat poorer than that for natural frequency calculations for plates subject to zero or tensile in-plane forces. But, since the method is believed to always yield a lower bound for single plates (which is not necessarily the case for plate systems), the results still have utility. ASME, Journal of Applied Mechanics, Vol. 38, No. 3, Sept. 1971 pp. 699-700. 5 Taylor, G. I., "The Buckling Load for a Rectangular Plate with Four Clamped Edges," Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 13, 1933, p. 147.

Separation-Like Similarity Solutions on Two-Dimensional Moving Walls

References 1 Koosinlin, M. L., Launder, B. E., and Sharma, B. I., "Prediction of Momentum, Heat and Mass Transfer in Swirling, Turbulent Boundary Layers," Journal of Heat Transfer, Vol. 96, May 1974, pp. 204209. Furuya, Y., Nakamura, L, and Kavachi, H., "The Experiments on the Skewed Boundary Layer on a Rotating Body," Japan Society of Mechanical Engineers, Vol. 9, 1966, p. 702. 3 Parr, V. O., "Untersuchungen der dreidimensionalen Grenzschicht an rotierenden Drehkorpern bei Axialer Anstrmung," Ingenieur Archives, Vol. 32, 1963, p. 393. Jones, W. P. and Launder, B. E., "The Calculation of Low Reynolds Number Phenomena with a Two-Equation Model of Turbulence," International Journal of Heat and Mass Transfer, Vol. 16, June 1973,p.1119. Launder, B. E., Priddin, C. H., and Sharma, B. I., "The Calculation of Turbulent Boundary Layers on Spinning and Curved Surfaces," Journal of Fluids Engineering, Paper number 493-FMW (in press), 1976. Patankar, S. V. and Spalding, D. B., Heat and Mass Transfer in Boundary Layers, Intertext Books, London, 1970.

Boundary-layer separation on moving walls using an integral theory

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