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At least 1,243 records · Page 69

Skin friction and velocity profile family for compressible turbulent boundary layers

The paper presents a general approach to constructing mean velocity profiles for compressible turbulent boundary layers with isothermal or adiabatic walls. The theory is based on a density-weighted transformation that allows the extension of the incompressible similarity laws of the wall to the compressible regions. The velocity profile family is compared to a range of experimental data, and excellent agreement is obtained. A self-consistent skin friction law, which satisfies the proposed velocity profile family, is derived and compared with the well-known Van Driest II theory for boundary layers in zero pressure gradient. The results are found to be at least as good as those obtained by using the Van Driest II transformation.

Huang, P. G.↗

The internal dynamics of slowly rotating biological systems

The structure and the dynamics of biological systems are complex. Steady gravitational forces that act on organisms cause hydrostatic pressure gradients, stress in solid components, and ordering of movable subsystems according to density. Rotation induces internal motion; it also stresses and or deforms regions of attachment and containment. The disrupted gravitationally ordered layers of movable entities are replaced by their orbital movements. New ordering geometries may arise also, especially if fluids of various densities occur. One novel result obtained concerns the application of scheduled variation of clinostat rotation rates to the management of intracellular particle trajectories. Rotation and its consequences are discussed in terms of scaling factors for parameters such as time, derived from mathematical models for simple rotating mechanical systems.

Kessler, John O.↗

A comparative study of Full Navier-Stokes and Reduced Navier-Stokes analyses for separating flows within a diffusing inlet S-duct

A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier Stokes (RNS) initial value space marching solution technique has been applied to a class of separated flow problems within a diffusing S-duct configuration characterized by vortex-liftoff. Both the FNS and the RNS solution technique were able to capture the overall flow physics of vortex lift-off, and gave remarkably similar results which agreed reasonably well with the experimental measured averaged performance parameters of engine face total pressure recovery and distortion. However, the Full Navier-Stokes and Reduced Navier-Stokes also consistently predicted separation further downstream in the M2129 inlet S-duct than was indicated by experimental data, thus compensating errors were present in the two Navier-Stokes analyses. The difficulties encountered in the Navier-Stokes separations analyses of the M2129 inlet S-duct center primarily on turbulence model issues, and these focused on two distinct but different phenomena, namely, (1) characterization of low skin friction adverse pressure gradient flows, and (2) description of the near wall behavior of flows characterized by vortex lift-off.

Anderson, B. H.↗

Dynamics of aging magnetic clouds

The dynamics of radially expanding magnetic clouds is rigorously analyzed within the framework of ideal MHD. The cloud is modelled as a cylindrically symmetric magnetic flux rope. In the force balance we include the gas pressure gradient and the Lorentz force. Interaction with the ambient solar wind due to expansion of the magnetic cloud is represented by a drag force proportional to the bulk velocity. We consider the self-similar expansion of a polytrope, and reduce the problem to an ordinary nonlinear differential equation for the evolution function. Analyzing the asymptotic behavior of the evolution function, we formulate theoretical expectations for the long-term behavior of cloud parameters. We focus on the temporal evolution of (1) the magnetic field strength; (2) the twist of the field lines; (3) the asymmetry of the total field profile; and (4) the bulk flow speed. We present data from two magnetic clouds observed at 1 AU and 2 AU, respectively, and find good agreement with theoretical expectations. For a peak magnetic field strength at 1 AU of 25 nT and a polytropic index of 0.5, we find that a magnetic cloud can be distinguished from the background interplanetary field up to a distance of about 5 AU. Taking larger magnetic fields and bigger polytropic indices this distance can double.

Osherovich, V. A.↗

Low-Reynolds-number k-epsilon model for unsteady turbulent boundary-layer flows

An assessment of the near-wall and low-Reynolds-number functions used in low-Reynolds-number k-epsilon models suggests that they are not suitable for the near-wall region of unsteady turbulent boundary layers, where the flow is characterized by rapid changes in phase. An improved low-Reynolds-number k-epsilon model is developed in this paper. The near-wall and low-Reynolds-number functions in this model are formulated as functions of the local turbulent Reynolds numbers instead of the inner variable y(+). The present model also has the correct asymptotic behavior in the near-wall region. The turbulence model has been incorporated in an unsteady boundary-layer code and validated for unsteady turbulent boundary layers with and without adverse pressure gradients. The predictions agree well with the experimental data and the theoretical analysis. For the cases tested, the present model correctly predicts the unsteady near-wall flow and the unsteady shin friction at various frequencies.

Fan, Sixin↗

Direct simulations of compressible wall-bounded turbulence

Several direct numerical simulations of high-speed turbulent Couette flow were performed with a new spectral code. Mach numbers up to three and a Reynolds number of 3000 were used. A new time-integration scheme was developed to handle Mach numbers above 1.5, which require greater accuracy and stability than lower Mach numbers. At low Mach number, the large streamwise eddies found by M. J. Lee in high incompressible Couette flow simulations were reproduced. At higher Mach numbers these structures still exist, but they become considerably less organized (although the disorganization may be a function of the spanwise box size). While the same types of vortical structures seen in the incompressible flow are observed at higher Mach numbers, a new structure involving the divergence of the velocity is also observed. This structure is generally associated with low shear areas next to the walls, but it has not been determined whether it is a cause or an effect of the low shear. A 'nonphysical' simulation was performed to determine by what mechanism the Mach number affects the flow. It appears that pressure gradient (acoustic) effects are more important than variable viscosity effects in determining the wall shear, but the size of vortical structures is determined more by the local kinematic viscosity. Low-order mean statistics are provided to help quantify these effects.

Buell, Jeffrey C.↗

Some Recent Contributions to the Study of Transition and Turbulent Boundary Layers

The first part of this paper reviews the present state of the problem of the instability of laminar boundary layers which has formed an important part of the general lectures by von Karman at the first and fourth Congresses and by Taylor at the fifth Congress. This problem may now be considered as essentially solved as the result of work completed since 1938. When the velocity fluctuations of the free-stream flow are less than 0.1 percent of the mean speed, instability occurs as described by the well-known Tollmien-Schlichting theory. The Tollmien-Schlichting waves were first observed experimentally by Schubauer and Skramstad in 1940. They devised methods of introducing controlled small disturbances and obtained measured values of frequency, damping, and wave length at various Reynolds numbers which agreed well with the theoretical results. Their experimental results were confirmed by Liepmann. Much theoretical work was done in Germany in extending the Tol1mien-Schlichting theory to other boundary conditions, in particular to flow along a porous wall to which suction is applied for removing part of the boundary layer. The second part of this paper summarizes the present state of knowledge of the mechanics of turbulent boundary layers, and of the methods now being used for fundamental studies of the turbulent fluctuations in turbulent boundary layers. A brief review is given of the semi-empirical method of approach as developed by Buri, Gruschwitz, Fediaevsky, and Kalikhman. In recent years the National Advisory.Commsittee for Aeronautics has sponsored a detailed study at the National Bureau of Standards of the turbulent fluctuations in a turbulent boundary layer under adverse pressure gradient sufficient to produce separation. The aims of this investigation and its present status are described.

Dryden, Hugh L↗

Solutions of laminar-boundary-equations which result in specific-weight-flow profiles locally exceeding free-stream values

Revised solutions of the laminar-boundary-layer equations for cases which involved cooling at the wall combined with large pressure gradients in the main stream produced specific-weight-flow profiles which locally exceeded free-stream values. Heat-transfer and friction coefficients, boundary-layer thicknesses, and velocity, temperature, and specific-weight-flow distributions resulting from the revised solutions are presented for Euler numbers of 0.5 and 1, stream-to-wall temperature ratios of 2 and 4, and cooling-air flow rates through porous walls designated by flow parameters of 0, -0.5, and -1.

HEAT TRANSFER, AERODYNAMIC↗

Effect of bluntness on transition for a cone and a hollow cylinder at Mach 3.1

Bluntness was more effective in displacing transition downstream on a cylinder than on a cone. The downstream displacement of transition is related to the formation of a shock layer within which the Reynolds and Mach numbers are reduced and to pressure gradients that exist over the forward part of the model. Round bluntness in general had a favorable effect, whereas sharp-cornered flat bluntness above a certain size had unfavorable effects on the location of the transition point.

BODIES - SHAPE VARIABLES↗

Analytical Investigation of Flow Through High-speed Mixed-flow Turbine

An analysis was made of the flow trough a high-speed mixed-flow turbine based on axially symmetric conditions. The calculated weight flow was lower than that used in the two-dimensional design. The rotor could be redesigned to increase the weight flow and a flow and alleviate undesirable pressure gradients at the expense of increased rotor blade stresses.

TURBINES - MIXED FLOW↗

Determination and Use of the Local Recovery Factor for Calculating the Effectiveness Gas Temperature for Turbine Blades / Jack B. Esgar and Alfred L. Lea

In an in experimental investigation of local recovery factors for a blade having a pressure distribution similar to that of a typical reaction-type turbine blade, it a was found that the recovery factors were essentially independent of Mach number, Reynolds number, pressure gradient, and position on the blade surface except for regions where the boundary layer was probably in the transition range from laminar to turbulent. The recommended value of local subsonic recovery factor for use in calculating the effective gas temperature for gas turbine blades was 0.89.

HEAT TRANSFER, CASCADES↗

Design and Test of Mixed-flow Impellers IV : Experimental Results for Impeller Models MFI-1 and MFI-2 with Changes in Blade Height

Modifications A and B of impeller model MFI-1 and A, B, and C of impeller model MFI-2 were investigated experimentally in an attempt to determine what allowance in blade height should be made for boundary layer and viscous losses in an impeller designed for isentropic compressible flow. A gradual increase in blade height was arbitrarily made from inlet to outlet in anticipation of a gradual build-up of boundary layer. Apparently there was a rapid build-up of boundary layer near the inlet in the experimental case rather than a gradual one. Therefore, the proper allowance for boundary layer cannot be described from the data obtained. Decreasing the pressure gradient along the shroud by reducing the blade height allowance apparently did little to increase the overall efficiency. At the design speed of 1400 feet per second, the overall adiabatic efficiency was increased from 0.83 for the MFI-1A to 0.85 for the MFI-1B with reduction in height; however, it is indicated from the theoretical velocity distribution and outlet surveys that the increase was due to a change from decelerating to accelerating flow along the hub rather than from any change along the shroud. It is further indicated that the consequences of a thickened or separated boundary layer depend not only on the design velocity gradients but also on the shape of the passage.

Hamrick, Joseph T↗

The stability of the laminar boundary layer in a compressible fluid

Report is a continuation of a theoretical investigation of the stability of the laminar boundary layer in a compressible fluid. An approximate estimate for the minimum critical Reynolds number, or stability limit, is obtained in terms of the distribution of the kinematic viscosity and the product of the mean density and mean vorticity across the boundary layer. The extension of the results of the stability analysis to laminar boundary-layer gas flows with a pressure gradient in the direction of the free stream is discussed. (author)

Lees, Lester↗

Determination of the theoretical pressure distribution for twenty airfoils

This report gives the theoretical distribution of pressure at lift coefficients of 0, 0.5, 1.0, and 1.5 for 20 airfoils, calculated on the basis of a rigorous potential theory of arbitrary airfoils. It also provides tables from which the characteristics of the airfoils for any angle of attack in 2-dimensional potential flow are readily calculable. The theoretical values of the angles of zero lift, the lift and moment coefficients, and the ideal angles of attack are listed and some comparisons with experiment are indicated. The results presented may be of value in predicting structural loads and also in a correlation of theoretical pressure gradients with profile resistance.

Garrick, I E↗

Investigation of Separation of the Turbulent Boundary Layer

An investigation was conducted on a turbulent boundary layer near a smooth surface with pressure gradients sufficient to cause flow separation. The reynolds number was high, but the speeds were entirely within the incompressible flow range. The investigation consisted of measurements of mean flow, three components of turbulence intensity, turbulent shearing stress, and correlations between two fluctuation components at a point and between the same component of different points. The results are given in the form of tables and graphs. The discussion deals first with separation and then with the more fundamental question of basic concepts of turbulent flow.

Schubauer, G B↗

Method of analysis for compressible flow through mixed-flow centrifugal impellers of arbitrary design

A method is presented for analysis of the compressible flow between the hub and the shroud of mixed-flow impellers of arbitrary design. Axial symmetry was assumed, but the forces in the meridional (hub to shroud) plane, which are derived from tangential pressure gradients, were taken into account. The method was applied to an experimental mixed-flow impeller. The analysis of the flow in the meridional plane of the impeller showed that the rotational forces, the blade curvature, and the hub-shroud profile can introduce severe velocity gradients along the hub and the shroud surfaces. Choked flow at the impeller inlet as determined by the analysis was verified by experimental results.

Hamrick, Joseph T↗

A note on secondary flow in rotating radial channels

A general vector differential equation for the vorticity component parallel to a streamline is derived for steady, nonviscous, and incompressible flow in a rotating system. This equation is then simplified by restricting it to rotating radial channels and by making further simplifying assumptions. The simplified equation is used to solve for the secondary vorticity, the vorticity component parallel to the streamline, in three special cases involving different streamtube geometries; the results are presented in a series of figures. The secondary vorticity is shown to decrease with decreased absolute angular velocity of the fluid, decreased inlet total-pressure gradient, decreased length of relative flow path, and increased relative velocity.

Kramer, James J↗

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↗