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A procedure for designing ducts for subsonic and transonic speeds is described. Examples discussed are a wind-tunnel contraction cone, a supersonic nozzle, and a diffuser. A listing of the computer program is included. The streamline curvature equations represent a form of the exact, compressible, inviscid flow equations. The method is applicable from low subsonic to supersonic speeds.
A computer program (program LEE) has been developed to calculate the fully coupled solution of the radiating viscous stagnation streamline flow with strong blowing. The report describes the digital computer program, including FORTRAN IV listing, flow charts, instructions for the user, and a test case with input and output. Program LEE is available through COSMIC.
A FORTRAN-IV computer program, MERIDL, has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables can vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.
An airfoil design procedure, applicable to both subcritical and supercritical airfoils, is described. The method is based on the streamline curvature velocity equation. Several examples illustrating this method are presented and discussed.
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Streamline patterns calculated from transonic flow solutions which were generated using a nonconservative finite difference scheme showed a net streamtube area increase far downstream of the disturbance indicating that the global mass balance was destroyed. Similar calculations using a conservative finite difference scheme did not show this defect. Comparative calculations were made at several free-stream Mach numbers for nonlifting flow over a 10% parabolic arc airfoil. In a transonic internal flow, this nonconservation of mass may be of greater concern than in an unconfined external flow.
A method has been developed for accurately computing the imaginary flow fields outside a flexible walled test section, applicable to lifting and non-lifting models. The tolerances in the setting of the flexible walls introduce only small levels of aerodynamic interference at the model. While it is not possible to apply corrections for the interference effects, they may be reduced by improving the setting accuracy of the portions of wall immediately above and below the model. Interference effects of the truncation of the length of the streamlined portion of a test section are brought to an acceptably small level by the use of a suitably long test section with the model placed centrally.
Exact inviscid flow-field codes are used together with a quasi-three-dimensional boundary-layer analysis to provide estimates of the windward surface heating and streamline patterns of the shuttle orbiter vehicle. The accuracy and limitations of the methods are established by comparison with available wind-tunnel experiments and with more exact numerical solutions for simple flows. Flight predictions are presented showing the effects of finite-rate (nonequilibrium) chemical reactions, and the effects of varying boundary-layer edge conditions due to the growth of the boundary-layer into the inviscid flow (entropy layer swallowing). Differences between flow-field predictions at wind-tunnel and nominal flight conditions are discussed.
A computer program recently developed by South and Brandt (1976) which contained the Murman (1973) conservative finite-difference scheme is easily modified to use the Garabedian and Korn (1971) nonconservative finite difference scheme. This program solves the transonic small disturbance equation for only symmetric flow, but incorporates several iterative solution techniques. Results are presented for the case where the equally spaced computational grid extended to infinity in both the streamwise and normal directions. Streamline shapes are obtained along several grid lines by a streamwise integration of the normal component of the perturbation velocity. Comparison cases are run for a 10% thick parabolic arc airfoil at zero incidence for freestream Mach numbers of 0, 0.70, 0.84, and 0.95. It is shown that the use of a nonconservative finite-difference scheme in transonic flow calculations destroys the global mass balance when shocks are present. This lack of mass balance may prove to be more crucial in the case of an unconfined external flow.
A FORTRAN 4 computer program was developed that obtains a detailed subsonic or shock-free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface as well as approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference, stream-function solution. Transonic solutions are obtained by a velocity-gradient method that uses information from a finite-difference, stream-function solution at a reduced mass flow.
A FORTRAN IV computer program has been developed that obtains a detailed subsonic or shock free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provisions are made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface and approximate blade surface velocities.
An analytical procedure is discussed for designing wall shapes for streamlined, nonporous, two-dimensional, transonic wind tunnels. It is based upon currently available 2-D inviscid transonic and boundary layer analysis computer programs. Predicted wall shapes are compared with experimental data obtained from the NASA Langley 6 by 19 inch Transonic Tunnel where the slotted walls were replaced by flexible nonporous walls. Comparisons are presented for the empty tunnel operating at a Mach number of 0.9 and for a supercritical test of an NACA 0012 airfoil at zero lift. Satisfactory agreement is obtained between the analytically and experimentally determined wall shapes.
It has been shown that turbulent flows are greatly affected by streamline curvature. In spite of this and the fact that curved shear flows are frequently encountered in engineering applications, the predictions of such flows are relatively less developed than the predictions of two-dimensional plane flows. Recently, various attempts were made by different investigators; however, their methods are only successful when the product of the boundary layer thickness to the local surface curvature is approximately 0.05. The present paper investigates the more general case where this product is in the range from 0.1 to 0.5. Results show that the calculated boundary-layer characteristics for arbitrary free stream conditions are in good agreement with measurements.
Testing in the low speed flexible walled tunnel in an effort to explain the reasons for data discrepancies at high angles of attack are presented. Automated transonic test sections were developed. The flexible walled tunnel was used in a new operating mode to a generated curved flow around the airfoil, allowing the extraction of purely rotary derivatives. Some straight wall, low speed pressure data, for wall and model, which is used for checking interference correction methods were reported. Computer software which includes an old streamlining algorithm and a prediction algorithm was examined.
An existing axial compressor streamline analysis computer program to allow input of measured radial pressure and temperature profiles obtained from engine or cascade data is described. The proposed modifications increase the input flexibility and are accomplished without changing the computer program's input format.
Streamline separation bubbles on aircraft profiles and fuselages were investigated. The additional drag was examined in relation to increased angle of incidence and unusually high wall sheer stress. A reduction of the separation bubble and a decrease in drag is obtained with pneumatic turbulators that blow ram air out of 0.6mm pilot tubes at a distance of 16 mm. The pneumatic models are implemented at various positions and are found to be effective after the position of separation.
The experimental verification of an inviscid, incompressible through-flow analysis method is presented. The primary component of this method is an axisymmetric streamline curvature technique which is used to compute the hub-to-tip flow field of a given turbomachine. To analyze the flow field in the blade-to-blade plane of the machine, the potential flow solution of an infinite cascade of airfoils is also computed using a source model technique. To verify the accuracy of such an analysis method an extensive experimental verification investigation was conducted using an axial flow research fan. Detailed surveys of the blade-free regions of the machine along with intra-blade surveys using rotating pressure sensing probes and blade surface static pressure taps provide a one-to-one relationship between measured and predicted data. The results of this investigation indicate the ability of this inviscid analysis method to predict the design flow field of the axial flow fan test rotor to within a few percent of the measured values.
Matrix of ink dots covers matte surface of polyester drafting film. Film placed against wind-tunnel wall. Layer of methyl salicylate (oil of wintergreen) sprayed over dotted area. Ink dot streaklines show several characteristics of flow, including primary saddle point of separations, primary horseshoe vortex and smaller vortex at cylinder/ endwall junction. Surface streamline flow visualization technique suitable for use in low-speed windtunnels or other low-speed gas flows.