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NASA NTRS1977

A length-scale model for developing turbulent flow in a rectangular duct

A three-dimensional mixing length model is proposed for modeling local Reynolds stress behavior in rectangular ducts of arbitrary aspect ratio. The model is applicable to both developing and fully-developed flows, and can be applied to other 90-degree corner flows with mild streamwise pressure gradients. Comparisons between theory and experiment show that all components of the Reynolds stress tensor are modeled reasonably well, both in the vicinity of a corner and in two-dimensional regions away from the corner.

Gessner, F. B.↗

NASA NTRS1977

Theory of viscous transonic flow over airfoils at high Reynolds number

This paper considers viscous flows with unseparated turbulent boundary layers over two-dimensional airfoils at transonic speeds. Conventional theoretical methods are based on boundary layer formulations which do not account for the effect of the curved wake and static pressure variations across the boundary layer in the trailing edge region. In this investigation an extended viscous theory is developed that accounts for both effects. The theory is based on a rational analysis of the strong turbulent interaction at airfoil trailing edges. The method of matched asymptotic expansions is employed to develop formal series solutions of the full Reynolds equations in the limit of Reynolds numbers tending to infinity. Procedures are developed for combining the local trailing edge solution with numerical methods for solving the full potential flow and boundary layer equations. Theoretical results indicate that conventional boundary layer methods account for only about 50% of the viscous effect on lift, the remaining contribution arising from wake curvature and normal pressure gradient effects.

Melnik, R. E.↗

NASA NTRS1977

Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

A theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force is presented. A diffusion flame sheet model was used to describe the combustion process. The effects of gravity on the purely force convection flow can be characterized by a dimensionless coordinate quantity, which is involved in the generation of the governing equations. A numerical solution of the zero and first order governing equations subject to the appropriate physical boundary conditions was obtained. It is shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. It is concluded that buoyancy plays an important role in boundary layer diffusion flames.

Lavid, M.↗

NASA NTRS1979

Static-pressure probe for small geometries

Contoured pressure probe with static orifices located near tip is more effective than conventional probes in taking measurements in small high-Reynolds number geometries such as nozzles or flow inlets. Probe is less sensitive to pressure gradients and off axis variations in flow directions over short distances.

Pinckney, S. Z.↗

NASA NTRS1977

Reducing secondary losses by blowing cold air in a turbine

Local blowing on the profile suction side of the turbine guide wheel blades can be effective in preventing the propagation of secondary flows that is, the transport of casing and hub boundary layers by pressure gradients. Some preliminary results on how the blowing should be accomplished in order to influence the secondary flows in the desired manner are given. The effectiveness of blowing is demonstrated. Blowing is also seen to be more effective than using boundary layer slots as far as diminishing losses in the rim zones is concerned.

Koschel, W.↗

NASA NTRS1977

Investigation of compressible vortex flow characteristics

The nature of intense air vortices was studied and the factors which determine the intensity and rate of decay of both single and pairs of vortices were investigated. Vortex parameters of axial pressure differential, circulation, outflow rates, separation distance and directions of rotation were varied. Unconfined vortices, generated by a single rotating cage, were intensified by an increasing axial pressure gradient. Breakdown occurred when the axial gradient became negligible. The core radius was a function of the axial gradient. Dual vortices, generated by two counterrotating cages, rotated opposite to the attached cages. With minimum spacing only one vortex was formed which rotated in a direction opposite to the attached cage. When one cage rotated at half the speed of the other cage, one vortex formed at the higher speed cage rotating in the cage direction.

Muirhead, V. U.↗

NASA NTRS1977

Injection of coal by screw feed

The use of the screw feeder for injecting solids through a 20 to 30 psi barrier is common practice in the cement making industry. An analytical extrapolation of that design, accounting for pressure holding characteristics of a column of solids, shows that coal can be fed to zones at several hundred psi with minimal or no loss of gas. A series of curves showing the calculated pressure gradient through a moving column of solids is presented. Mean particle size, solids velocity, and column length are parameters. Further study of this system to evaluate practicality is recommended.

Fisher, R.↗

NASA NTRS1977

Calculation of three-dimensional compressible turbulent boundary layers

From comparisons of high speed data with low speed closure procedures using variable mean density, there does not appear to be any appreciable influence of compressibility upon turbulent shear stress modeling in compressible turbulent boundary layers, even for extreme cases such as Mach 14 to 20 with a change in density across the layer of up to a factor of 100. Other evidence of apparent lack of compressibility caused new physics which may alter the shear stress for the compressible boundary layer cases including: (1) fluctuation Mach number was generally less than 1; (2) the shear stress distribution through the boundary layer was not a function of Mach number for zero pressure gradient flows; (3) the Morkovin hypothesis was valid up to Mach 5 (based on fluctuation data); (4) profile N power was not a function of Mach number, at least up to Mach 10; and (5) the nondimensional burst period was approximately the same as that for low speed.

Source record↗

NASA NTRS1977

Atmospheric model development in support of SEASAT. Volume 3: Prediction models

As part of the SEASAT program of NASA, a set of four hemispheric, atmospheric models are developed. The four models use a polar stereographic grid in the horizontal and a sigma coordinate in the vertical. Conservation forms of the difference equations are integrated using either a fifteen or four minute time step on a 381 km or 127 km grid (at 60 deg N) for the 63 x 63 or 187 x 187 models respectively. A nonlinear pressure smoother is used along with momentum and temperature diffusion to help control computational noise. The horizontal boundary conditions are insulated slippery walls. Centered time differencing with time averaging of the pressure gradient force term in the momentum equations is used. Robert time filtering on of the temperature and moisture solutions is used for computational stability. The moisture and heat source/sink terms are modeled. Terms representing evaporation and large scale condensation, sensible heat exchange, parameterized cumulus convection and precipitation, and solar and terrestrial radiation are included. Initialization of the models is based on a pattern conservation technique to obtain objective analysis of the state parameter structure from the surface to 50 mb.

Wellck, R. E.↗

NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗

NASA NTRS1978

Turbulent-flow separation criteria for overexpanded supersonic nozzles

A comprehensive compilation of available turbulent flow separation data for overexpanded supersonic nozzles is presented with a discussion of correlation techniques, and prediction methods. Data are grouped by nozzle types: conical, contoured, and two dimensional wedge. Correlation of conical nozzle separation is found to be independent of nozzle divergence half-angle above the 9 deg, whereas the contoured nozzle data follow a different correlation curve. Zero pressure gradient prediction techniques are shown to predict adequately the higher divergence angle conical separation data, and an empirical equation is given for the contoured nozzle data correlation. Flow conditions for which the correlations are invalid are discussed and bounded. A nozzle boundary layer transition criterion is presented which can be used to show that much of the noncorrelating data in the literature are concerned with nonturbulent separation and which explains the previously reported external flow effects on nozzle separation.

Morrisette, E. L.↗

NASA NTRS1978

Experimental analysis and computation of the onset and development of the boundary layer transition

The transition of an incompressible boundary layer, with zero pressure gradient and low free-stream turbulence is studied. Mean velocity, turbulence and Reynolds shear stress profiles are presented. The development of the Tollmien-Schlichting waves is clearly shown until the turbulent spots appear. The intermittency phenomenon is studied by conditional sampling of the hotwire signal. The comparison with calculation results obtained by resolution of a set of transport equations shows a good agreement for the mean characteristics of the flow; discrepancies observed for the turbulent quantities evolution are due to the intermittency phenomenon.

Arnal, D.↗

NASA NTRS1977

Experimental determination of sound and high-speed flow interaction

An experimental facility for measuring the attenuation of sound at various frequencies and modes in a finite duct with high-speed flow (with or without an axial pressure gradient) is described. The facility consists of an anechoic chamber transonic compressor with inlets of different area variations (or axial gradients); sound of selected frequencies and modes is produced with eight circumferential acoustic drivers. The experimental results indicate that high Mach number inlets can increase noise propagation. In addition, an inlet with a constant axial gradient is found to have a better acoustic and aerodynamic performance than inlets of the same area ratio with steep gradients near the throat or exit.

Lumsdaine, E.↗

NASA NTRS1978

An interaction solution algorithm for viscous aerodynamic performance prediction

A weak-interaction solution algorithm is established for aerodynamic flow field prediction about an isolated airfoil. It requires numerical solution of differential equations governing potential flow, viscous and turbulent boundary layer flow, and the turbulent wake flow downstream of a trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. These in turn alter the viscous flow through imposed pressure gradients. Closure for turbulence is accomplished using a second order model. Numerical evaluations assess factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems as solved using a finite element algorithm.

Baker, A. J.↗

NASA NTRS1978

Effect of wall temperature on a supersonic turbulent boundary layer

Measurement of mean flow profiles in a fully developed Mach 3 turbulent boundary layer with negligible pressure gradient is reported. Data were acquired at several streamwise locations for wall-to-total temperature ratios of 0.94, 0.71, and 0.54. The results demonstrate that the velocity defect formulation of the law-of-the-wake, which successfully correlates compressible, adiabatic boundary layers, is also valid for nonadiabatic flows. It is also shown that for adiabatic walls, the linear Crocco relation between total temperature and velocity does not provide a valid test of the nature of the boundary-layer flow for practical cases where the Prandtl number departs from unity. Finally, the turbulent shear stress, mixing length, and eddy viscosity were extracted from the 'time-averaged' conservation equations using the measured mean flow profiles and found to be insensitive to wall temperature. In particular, the latter properties are in good agreement with earlier compressible, adiabatic correlations of turbulent transport properties.

Laderman, A. J.↗

NASA NTRS1978

Bi-directional, buried-wire skin-friction gage

A compact, nonobtrusive, bi-directional, skin-friction gage was developed to measure the mean shear stress beneath a three-dimensional boundary layer. The gage works by measuring the heat flux from two orthogonal wires embedded in the surface. Such a gage was constructed and its characteristics were determined for different angles of yaw in a calibration experiment in subsonic flow with a Preston tube used as a standard. Sample gages were then used in a fully three-dimensional turbulent boundary layer on a circular cone at high relative incidence, where there were regimes of favorable and adverse pressure gradients and three-dimensional separation. Both the direction and magnitude of skin friction were then obtained on the cone surface.

Higuchi, H.↗

NASA NTRS1979

A theoretical investigation of forebody shapes designed for natural laminar boundary-layer flow

The design of forebody shapes for natural laminar flow is discussed. For subsonic flow, computed results for three shapes of different fineness ratios indicate that laminar flow can be attained under conditions that approximate those on the forebody of a cruise missile flying at a low altitude at a high subsonic Mach number. For supersonic (Mach 2.00) design, a one-parameter family of hyperbolic arcs was used to generate forebody shapes having a favorable pressure gradient over the forebody length. Computed results for these shapes indicated laminar and transitional flow over the range of Reynolds numbers considered.

Barger, R. L.↗

NASA NTRS1978

Operational physical models of the ionosphere

Global models of the neutral constituents are considered relevant to ion density models and improved knowledge of the ion chemistry. Information provided on the pressure gradients that control the wind system and the electric field systems due to balloon, satellite, and incoherent scatter measurements is discussed along with the implication of these results to the development of global ionospheric models. The current state of knowledge of the factors controlling the large day to day variations in the ionosphere and possible approaches for operational models are reviewed.

Nisbet, J. S.↗