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At least 955 records · Page 53

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NASA NTRS1956

The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

An approximate method for the calculation of the compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, based on Thwaites' correlation concept, is presented. With the definition of dimensionless shear and heat-transfer parameters and an assumed correlation of these parameters in terms of a momentum parameter, a complete system of relations for calculating skin friction and heat transfer results. Knowledge of velocity or temperature profiles is not necessary in using this calculation method. When the method is applied to a convergent-divergent, axially symmetric rocket nozzle, it shows that high rates of heat transfer are obtained at the initial stagnation point and at the throat of the nozzle. Also indicated are negative displacement thicknesses in the convergent portion of the nozzle; these occur because of the high density within the lower portions of the cooled boundary layer. (author)

Cohen, Clarence B↗

NASA NTRS1934

On the theory of laminar boundary layers involving separation

This paper presents a mathematical discussion of the laminar boundary layer, which was developed with a view of facilitating the investigation of those boundary layers in particular for which the phenomenon of separation occurs. The treatment starts with a slight modification of the form of the boundary layer equation first published by Von Mises. Two approximate solutions of this equation are found, one of which is exact at the outer edge of the boundary layer while the other is exact at the wall. The final solution is obtained by joining these two solutions at the inflection points of the velocity profiles. The final solution is given in terms of a series of universal functions for a fairly broad class of potential velocity distributions outside of the boundary layer. Detailed calculations of the boundary layer characteristics are worked out for the case in which the potential velocity is a linear function of the distance from the upstream stagnation point. Finally, the complete separation point characteristics are determined for the boundary layer associated with a potential velocity distribution made up of two linear functions of the distance from the stagnation point. It appears that extensions of the detailed calculations to more complex potential flows can be fairly easily carried out by using the explicit formulae given in the paper. (author)

Von Karman, TH↗

NASA NTRS1936

Air Flow in a Separating Laminar Boundary Layer

The speed distribution in a laminar boundary layer on the surface of an elliptic cylinder, of major and minor axes 11.78 and 3.98 inches, respectively, has been determined by means of a hot-wire anemometer. The direction of the impinging air stream was parallel to the major axis. Special attention was given to the region of separation and to the exact location of the point of separation. An approximate method, developed by K. Pohlhausen for computing the speed distribution, the thickness of the layer, and the point of separation, is described in detail; and speed-distribution curves calculated by this method are presented for comparison with experiment.

Schubauer, G B↗

NASA NTRS1943

A method for calculating heat transfer in the laminar flow region of bodies

This report has been prepared to provide a practical method for determining the chordwise distribution of the rate of heat transfer from the surface of a wing or body of revolution to air. The method is limited in use to the determination of heat transfer from the forward section of such bodies when the flow is laminar. A comparison of the calculated average heat-transfer coefficient for the nose section of the wing of a Lockheed 12-A airplane with that experimentally determined shows a satisfactory agreement. A sample calculation is appended.

Allen, H Julian↗

NASA NTRS1950

Laminar mixing of a compressible fluid

A theoretical investigation of the velocity profiles for laminar mixing of a high-velocity stream with a region of fluid at rest has been made assuming that the Prandtl number is unity. A method which involves only quadratures is presented for calculating the velocity profile in the mixing layer for an arbitrary value of the free-stream Mach number. Detailed velocity profiles have been calculated for free-stream Mach numbers of 0, 1, 2, 3, and 5. For each Mach number, velocity profiles are presented for both a linear and a 0.76-power variation of viscosity with absolute temperature. The calculations for a linear variation are much simpler than those for a 0.76-power variation. It is shown that by selecting the constant of proportionality in the liner approximation such that it gives the correct value for the viscosity in the high-temperature part of the mixing layer, the resulting velocity profiles are in excellent agreement with those calculated by a 0.76-power variation.

Chapman, Dean R↗

NASA NTRS1950

On stability of free laminar boundary layer between parallel streams

An analysis and calculations on the stability of the free laminar boundary layer between parallel streams were made for an incompressible fluid using the Tollmien-Schlichting theory of small disturbances. Because the boundary conditions are at infinity, two solutions of the Orr-Sommerfeld stability equations need not be considered, and the remaining two solutions are exponential in character at the infinite boundaries. The calculations show that the flow is unstable except for very low Reynolds numbers.

Lessen, Martin↗

NASA NTRS1953

Laminar boundary layer on cone in supersonic flow at large angle of attack

The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.

Moore, Franklin K↗

NASA NTRS1955

Theoretical and experimental investigation of heat transfer by laminar natural convection between parallel plates

Results are presented of a theoretical and experimental investigation of heat transfer involving laminar natural convection of fluids enclosed between parallel walls oriented in the direction of the body force, where one wall is heated uniformly, and the other is cooled uniformly. For the experimental work, parallel walls were simulated by using an annulus with an inner-to-outer diameter ratio near 1. The results of the theoretical investigation are presented in the form of equations for the velocity and temperature profiles and the ratio of actual temperature drop across the fluid to the temperature drop for pure conduction. No experimental measurements were made of the velocity and temperature profiles, but the experimental results are compared with theory on the basis of the ratio of the actual temperature drop to the temperature drop for pure conduction. Good agreement was obtained between theory and experiment for axial temperature gradients of 10 degrees F. per foot or larger.

Lietzke, A F↗

NASA NTRS1955

Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature

Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.

Donoughe, Patrick L↗

NASA NTRS1956

Compressible Laminar Boundary Layer over a Yawed Infinite Cylinder with Heat Transfer and Arbitrary Prandtl Number

The equations are presented for the development of the compressible laminar boundary layer over a yawed infinite cylinder. For compressible flow with a pressure gradient the chordwise and spanwise flows are not independent. Using the Stewartson transformation and a linear viscosity-temperature relation yields a set of three simultaneous ordinary differential equations in a form yielding similar solutions. These equations are solved for stagnation-line flow for surface temperatures from zero to twice the free-stream stagnation temperature and for a wide range of yaw angle and free-stream Mach number. The results indicate that the effect of yaw on the heat-transfer coefficient at the stagnation line depends markedly on the free-stream Mach number. An unusual result of the solutions is that for large yaw angles and stream Mach numbers the chordwise velocity within the boundary layer exceeds the local external chordwise velocity, even for a highly cooled wall.

Reshotko, Eli↗

NASA NTRS1990

Design of laminar flow bodies in compressible flow

An optimization method was developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary-layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(sup n)-method. A tiptank of a business jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. On the original tiptank boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 6 on the original tiptank. On the designed body shape a transition Reynolds number of 7.22 x 10 6 is predicted using compressible linear stability theory coupled with e n -method.

Simha S. Dodbele↗

NASA NTRS1993

On the combustion of a laminar spray

A spray combustor, with flow velocities in the laminar range, exhibits a unique operating mode where large amplitude, self-induced oscillations of the flame shape occur. The phenomenon, not previously encountered, only occurs when fuel is supplied in the form of fine liquid droplets and does not occur when fuel is supplied in gaseous form. Several flow mechanisms are coupled in such a fashion as to trigger and maintain the oscillatory motion of the flame. These mechanisms include heat transfer and evaporation processes, dynamics of two-phase flows, and effects of gravity (buoyancy forces). An interface volume, lying above the fuel nozzle and below the flame was found to be the most susceptible to gravity effects and postulated to be responsible for inducing the oscillatory motion. Heptane fuel was used in the majority of the tests. Tests performed with iso-octane also showed similar results.

Levy, Yeshayahou↗

NASA NTRS1993

Three-Dimensional Boundary-Layer program (BL3D) for swept subsonic or supersonic wings with application to laminar flow control

The theory, formulation, and solution of three-dimensional, compressible attached laminar flows, applied to swept wings in subsonic or supersonic flow are discussed. Several new features and modifications to an earlier general procedure described in NASA CR 4269, Jan. 1990 are incorporated. Details of interfacing the boundary-layer computation with solution of the inviscid Euler equations are discussed. A description of the computer program, complete with user's manual and example cases, is also included. Comparison of solutions with Navier-Stokes computations with or without boundary-layer suction is given. Output of solution profiles and derivatives required in boundary-layer stability analysis is provided.

Iyer, Venkit↗

NASA NTRS1993

CNSFV code development, virtual zone Navier-Stokes computations of oscillating control surfaces and computational support of the laminar flow supersonic wind tunnel

The work performed during the past year on this cooperative agreement covered two major areas and two lesser ones. The two major items included further development and validation of the Compressible Navier-Stokes Finite Volume (CNSFV) code and providing computational support for the Laminar Flow Supersonic Wind Tunnel (LFSWT). The two lesser items involve a Navier-Stokes simulation of an oscillating control surface at transonic speeds and improving the basic algorithm used in the CNSFV code for faster convergence rates and more robustness. The work done in all four areas is in support of the High Speed Research Program at NASA Ames Research Center.

Klopfer, Goetz H.↗

NASA NTRS1993

Investigation of radiative interaction in laminar flows using Monte Carlo simulation

The Monte Carlo method (MCM) is employed to study the radiative interactions in fully developed laminar flow between two parallel plates. Taking advantage of the characteristics of easy mathematical treatment of the MCM, a general numerical procedure is developed for nongray radiative interaction. The nongray model is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. To validate the Monte Carlo simulation for nongray radiation problems, the results of radiative dissipation from the MCM are compared with two available solutions for a given temperature profile between two plates. After this validation, the MCM is employed to solve the present physical problem and results for the bulk temperature are compared with available solutions. In general, good agreement is noted and reasons for some discrepancies in certain ranges of parameters are explained.

Liu, Jiwen↗

NASA NTRS1993

Studies of premixed laminar and turbulent flames at microgravity

A two and one-half year experimental and theoretical research program on the properties of laminar and turbulent premixed gas flames at microgravity was conducted. Progress during this program is identified and avenues for future studies are discussed.

Ronney, Paul D.↗

NASA NTRS1993

An analytic study of a two-phase laminar airfoil in simulated heavy rain

A mathematical model for a two-phase flow laminar airfoil in simulated heavy rain has been established. The set of non-linear partial differential equations has been converted into a set of finite difference equations; appropriate initial and boundary conditions are provided. The numerical results are compared with the experimental measurements. They show good agreement in quality.

Hsu, Yu-Kao↗