Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows
Previously announced in STAR as N81-32875
SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Previously announced in STAR as N81-32875
A nonlinear aerodynamic prediction technique which solves the conservative full potential equation has been applied to the analysis of three waverider configurations. This technique was selected based on its capability to analyze the off-design characteristics of the waveriders. Very good correlations were achieved with surface pressure data for both the Mach 4 elliptic cone waverider and the Mach 6 caret-wing derivative. Off-design Mach number and angle-of-attack pressure correlations were very good for the elliptic cone waverider. The range of correlation with data exceeded that expected based on the theory limitations. A surface pressure integration routine was demonstrated and agreement between predicted aerodynamic forces and experimental force data for the Mach 4 waverider was excellent. Analysis of a nonconical waverider configuration was initiated where a discrete input option is used to achieve the computational gridding. Preliminary analysis of this configuration indicates the correct shock location will be predicted.
Previously cited in issue 18, p. 2839, Accession no. A82-37173
Previously cited in issue 15, p. 2347, Accession no. A82-31961
Explore the source record for details and available documents.
Explore the source record for details and available documents.
The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.
Wall static pressure distributions, surface flow patterns, pitot pressures, and yaw angle profiles were measured in a skewed three-dimensional shock wave/turbulent boundary layer interaction region. The test section was axisymmetric with a constant diameter. The nominal freestream Mach number was 4. Upstream of the interaction, the boundary layer thickness was 0.31 in. (0.787 cm). The three-dimensional flow was produced by azimuthal pressure gradients which were generated by an 8-degree cone aligned with the primary flow direction, but with the cone axis displaced 0.3 in. (0.76 cm) from the channel centerline. The yaw angle was found to be a function of both the azimuthal angle and the distance from the beginning of the interaction. It was observed that yaw angle increased substantially near the wall. The maximum yaw angle for the whole flow field was obtained in the 90 degree azimuthal plane.
Explore the source record for details and available documents.
Polystyrene latex particles have been successfully used as laser velocimetry seed material for flows in the Ames High Reynolds Channels (HR) 1 and 2, the pilot channel, and the one-foot low speed tunnel. These facilities provide test flows with Mach numbers from 0.1 to 3.0 and test section sizes from 4 inches by 6 inches to 18 inches by 24 inches. Tunnel mass flow in the HR-2 channel can approach 1000 lb/sec. The latex particles have the following favorable characteristics: size of 0.35 to 0.55 microns diameter; spherical shape; specific gravity of 1.05; excellent flow trackability; low toxicity; and low cost. they have the disadvantage of being packaged as an aqueous suspension which must be diluted and introduced into the test flow as an atomized mist. This must occur sufficiently far upstream of the test section to minimize flow disturbances and permit the liquid mist to evaporate before reaching the model. Several techniques which have been developed to accomplish satisfactory seeding will be described.
An optical technique is presented for combined, spatially resolved measurements of two-dimensional velocity and pressure fields in compressible flows. The single-mode frequency of an argon laser is fixed in the wing of an absorption line of iodine molecules, seeded in an underexpanded round jet of nitrogen gas. The emitted fluorescence, being proportional to the amount of absorbed radiation and hence the absorption line-shape function, is detected with an intensified 100 x 100 photodiode array camera. A single-microchannel-plate image intensifier is fiber-optically coupled to the array in order to improve time resolution and SNR. Three components of the velocity vector in a cross-sectional plane are sequentially probed with four laser sheets from three different directions. By shifting the laser frequency in one of the sheets with a piezo-tuned intra-cavity etalon, the slope of the absorption line can be measured in situ in order to provide the required scaling factor for the velocity measurement. With its short measurement times of less than 250 ms, this method is well suited for blow-down wind tunnel experiments.
A comparison of transition on wavy-wall and smooth-wall cones in a Mach 3.5 wind tunnel is made under conditions of either low freestream noise (quiet flow) or high freestream noise (noisy flow). The noisy flow compares to that found in conventional wind tunnels while the quiet flow gives transitional Reynolds numbers on smooth sharp cones comparable to those found in flight. The waves were found to have a much smaller effect on transition than similar sized trip wires. A satisfatory correlating parameter for the effect of waves on transition was simply the wave height-to-length ratio. A given value of this ratio was found to cause the same percentage change in transition location in quiet and noisy flows.
The Schiff-Steger parabolized Navier-Stokes (PNS) code has been modified to allow computation of conical flowfields around cones at high incidence. The improved algorithm of Degani and Schiff has been incorporated with the PNS code. This algorithm adds the cross derivative and circumferential viscous terms to the original PNS code and modifies the algebraic eddy viscosity turbulence model to take into account regions of so called cross-flow separation. Assuming the flowfield is conical (but not necessarily symmetric) a marching stepback procedure is used: the solution is marched one step downstream using improved PNS code and the flow variables are then scaled to place the solution back to the original station. The process is repeated until no change in the flow variables is observed with further marching. The flow variables are then constant along rays of the flowfield. The experiments obtained by Bannik and Nebbeling were chosen as a test case. In these experiments a cone of 7.5 deg. half angle at Mach number 2.94 and Reynolds number 1.372 x 10(7) was tested up 34 deg. angle of attack. At high angle of attack nonconical asymmetric leeward side vortex patterns were observed. In the first set of computations, using an earlier obtained solution of the above cone for angle of attack of 22.6 deg. and at station x=0.5 as a starting solution, the angle of attack was gradually increased up to 34 deg. During this procedure the grid was carfully adjusted to capture the bow shock. A stable, converged symmetric solution was obtained. Since the numerical code converged to a symmetric solution which is not the physical one, the stability was tested by a random perturbation at each point. The possible effect of surface roughness or non perfect body shape was also investigated. It was concluded that although the assumption of conical viscous flows can be very useful for certain cases, it can not be used for the present case. Thus the second part of the investigation attempted to obtain a marching (in space) solution with the PNS method using the conical solution as initial data. Finally, the solution of the full Navier-Stokes equations was carried out.
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.
Two- and three-dimensional separated flows around cylindrical sections and a body-of-revolution at angles of attack from -10 deg to +20 deg are computed. The blunt-nose-cylinders chosen for the analyses have different configurations, and one of them has a boat-tail. The freestream Mach numbers are 1.5 and 1.6, the unit Reynolds number and the total temperature are 2 million/ft, and 585 R, respectively. Among the possible areas of application for this study are the aerodynamics of separating stores and missiles. The Reynolds-averaged Navier-Stokes equations are solved by an approximately-factored, implicit, upwind-biased, finite-volume algorithm. The convergence to steady state was accelerated using a multigrid strategy. The results helped understanding the structure of the flowfield with varying incidence and configuration, and the suitability of the computational algorithm used for this class of flows. A two-layer algebraic eddy viscosity model is used for the two-dimensional turbulent flows. Laminar three-dimensional calculations are benchmarked through comparisons with wind tunnel test results.
Three-dimensional, viscous, and separated flows over a blunt-nose-cylinder at 20, 32, and 44-deg attack angles were computed. The approaching freestream was at a Mach number of 1.6 and a unit Reynolds number of 2 x 10 to the 6th/ft with a total temperature of 585 R. The cylinder used for the computations had a length-to-diameter ratio of 6.67 with a base diameter of 3 in. The flowfield was dominated by large-scale and multiple vortices generated by crossflow separation. The effect of turbulence on the flow structure of one case was modeled algebraically with modifications to correct the length and velocity scales in the regions of separation. The mass averaged Navier-Stokes equations were solved by an approximately factored, upwind-biased, implicit, finite volume scheme. The initialization of the flows was enhanced by a mesh sequencing strategy applied to the diagonalized form of the discretized equations. The convergence to steady-state was accelerated by a multigrid algorithm and using the block inversions for the discretized equations. Calculations were compared with experimental results.