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A study is made in the physical plane of the flow properties near a conical cross flow sonic line. The shapes of the Mach lines at regular and singular sonic points are presented. Through a study of the jump conditions at a singular sonic point, the possibility of a double sonic line is discussed. The properties of bubbles of supersonic cross flow are examined. Numerical results are presented to support some of the theoretical observations.
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In order to have a high level of maneuverability, supersonic delta wings should have a cross flow that is free of embedded shock waves. The conical cross flow sonic surface differs from that of plane transonic flow in many aspects. Well-known properties such as the monotone law are not true for conical cross flow sonic surfaces. By using a local analysis of the cross flow sonic line, relevant conditions for smooth cross flow are obtained. A technique to artificially construct a smooth sonic surface and an efficient numerical method to calculate the flow field are used to obtain cones with smooth cross flow.
In order to have a high level of maneuverability, supersonic delta wings should have a cross flow that is free of embedded shock waves. The conical cross flow sonic surface differs from that of plane transonic flow in many aspects. Well-known properties such as the monotone law are not true for conical cross flow sonic surfaces. By using a local analysis of the cross flow sonic line, relevant conditions for smooth cross flow are obtained. A technique to artificially construct a smooth sonic surface and an efficient numerical method to calculate the flow field are used to obtain cones with smooth cross flow.
Turbulent boundary layer laminarization in conical nozzle flow, measuring velocity profiles and friction coefficient
Conical shock-wave angle expressions compared for axisymmetric air flow past cone with attached shock wave
Performance characteristics of conical jet nozzles were determined in an investigation covering a range of pressure ratios from 1.0 to 2.8, cone half-angles from 5 degrees to 90 degrees, and outlet-inlet diameter ratios from 0.50 to 0.91. All nozzles investigated had an inlet diameter of 5 inches. The flow coefficients of the conical nozzles investigated were dependent on the cone half-angle, outlet-inlet diameter ratio, and pressure ratio. The velocity coefficients were essentially constant at pressure ratios below the critical. For increasing pressures above critical pressure ratio, there was a small decrease in velocity coefficient that was dependent on pressure ratio and independent of cone half-angle and outlet-inlet diameter ratio. Therefore the variation in performance (air flow and thrust) of several nozzles, selected for the same performance at a particular design condition, was proportional to the ratio of their flow coefficients.
A conical Euler methodology was developed to study unsteady vortex-dominated flows about rolling highly swept delta wings undergoing either forced or free-to-roll motions. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization of the Euler equations on an unstructured grid of triangles. Results are presented for a 75-deg swept sharp-leading-edge delta wing at a freestream Mach number of 1.2 and at alpha = 10, 20, and 30 deg. At the 10 and 20 deg, forced harmonic analyses indicate that the rolling moment coefficients provide a positive damping which is verified by free-to-roll calculations. In contrast, at 30 deg, a forced harmonic analysis indicates that the rolling moment coefficient provides a negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation.
Turbulent boundary layer flow in conical supersonic nozzle, discussing convective heat transfer and adverse pressure gradient effect
Results from an experimental investigation on the flow through conical diffusers are presented. The mean and fluctuating velocity fields are compared for three diffusers with total diffusion angles of 16, 20 and 24 degrees, in the throat Mach number (M sub t) range of 0.05 to 0.95. Each of the diffusers were 14 cm long and had a 5.08 cm inlet diameter, and the flow exited into the ambient. The boundary layer at the throat was thin with the throat diameter (D sub t) to momentum thickness (O) ratio being as high as 800 at M(sub t) = 0.4. While the 16 deg diffuser flow exited with a top-hat mean velocity profile, increasing losses due to increasing separation resulted in fuller profiles for the 20 and 24 degree cases. A detailed flow field study was conducted for the 16 deg. diffuser. The u'-spectrum, measured at the exit plane, exhibited a peak apparently due to the ensuing jet column instability throughout the M(sub t) range covered. In addition, a much lower frequency spectral peak also occurred in the M(sub t) range of 0.3 to 0.7. Both of the spectral peaks were due to axisymmetric flow fluctuations. A self-sustaining flow oscillation occurred in the M(sub t) range of 0.6 to 0.85, emitting a loud tone, when the jet column instability frequency matched the resonance frequency of the diffuser. Limited data showed that artificial acoustic excitation was effective in reducing the flow fluctuations, with a resultant increase in the pressure recovery, at low M(sub t).
Results from an experimental investigation on the flow through conical diffusers are presented. The mean and fluctuating velocity fields are compared for three diffusers with total diffusion angles of 16, 20 and 24 degrees, in the throat Mach number (M sub t) range of 0.05 to 0.95. Each of the diffusers were 14 cm long and had a 5.08 cm inlet diameter, and the flow exited into the ambient. The boundary layer at the throat was thin with the throat diameter (D sub t) to momentum thickness (O) ratio being as high as 800 at M(sub t) = 0.4. While the 16 deg diffuser flow exited with a top-hat mean velocity profile, increasing losses due to increasing separation resulted in fuller profiles for the 20 and 24 degrees cases. A detailed flow field study was conducted for the 16 deg diffuser. The u'-spectrum, measured at the exit plane, exhibited a peak apparently due to the ensuing jet column instability throughout the M(sub t) range covered. In addition, a much lower frequency spectral peak also occurred in the M(sub t) range of 0.3 to 0.7. Both of the spectral peaks were due to axisymmetric flow fluctuations. A self-sustaining flow oscillation occurred in the M(sub t) range of 0.6 to 0.85, emitting a loud tone, when the jet column instability frequency matched the resonance frequency of the diffuser. Limited data showed that artificial acoustic excitation was effective in reducing the flow fluctuations, with a resultant increase in the pressure recovery, at low M(sub t).
In a variety of aeronautical applications, the flow around conical bodies at incidence is of interest. Such applications include, but are not limited to, highly maneuverable aircraft with delta wings, the aerospace plane and nose portions of spike inlets. The theoretical model used has three parts. First, the single line vortex model is used within the framework of slender body theory, to compute the outer inviscid field for specified separation lines. Next, the three dimensional boundary layer is represented by a momentum equation for the cross flow, analogous to that for a plane boundary layer; a von Karman Pohlhausen approximation is applied to solve this equation. The cross flow separation for both laminar and turbulent layers is determined by matching the pressure at the upper and lower separation points. This iterative procedure yields a unique solution for the separation lines and consequently for the position of the vortices and the vortex lift on the body. Lastly, control of separation is achieved by blowing tangentially from a slot located along a cone generator. It is found that for very small blowing coefficients, the separation can be postponed or suppressedy completely.
A quasi-three-dimensional boundary layer method for conical inviscid flows is presented. The model was developed to characterize the flow fields over slender delta wings, particularly the shed vortex sheet. A steady, incompressible, laminar boundary layer is assumed and a solution is obtained with the Smith (1966) finite difference code. Predictions are compared with oil flow patterns and surface pressure measurements for 74 and 80 deg delta wings at 0-20 deg angles of attack. The model is capable of accurately predicting the secondary separation lines. Inviscid velocities derived from panel methods lead, however, to inaccurate pressure distributions.
Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.
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Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.