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This analysis computes for a predetermined airfoil and given Reynolds Number the course of the "displacement thickness," i.e., the course of the layer by which the streamlines of the potential flow are pushed away from the wing through the frictional layer. The result is, to a certain extent, a new wing contour.
We report the results of measurements of the disturbance velocity field generated in a boundary layer by a shallow three-dimensional bump oscillating at a very low frequency on the surface of a flat plate. Profiles of the mean velocity, the disturbance velocity at the fundamental frequency and at the first harmonic are presented. These profiles were measured both upstream and downstream of the oscillating bump. Measurements of the disturbance velocity were also made at various spanwise and downstream locations at a fixed distance from the boundary of one displacement thickness. Finally, the spanwise spectrum of the disturbances at three locations downstream of the bump are presented.
Wind tunnel tests have been conducted on a NASA GA(W)-2 airfoil section at Reynolds number of 2.2 x 10(exp 6) and Mach number of 0.13. Detailed measurements of flow fields associated with turbulent boundary layers have been obtained at angles of attack of 10.3, 14.4, and 18.3 deg. Pre- and post-separated velocity and pressure survey results over the airfoil and in the associated wake are presented. Extensive force, pressure, tuft survey, hot-film survey, local skin friction, and boundary layer data are also included. Pressure distributions and separation point locations show good agreement with theory for the two lower angles of attack. Boundary layer displacement thickness, momentum thickness, and shape factor agree well with theory up to the point of separation. There is considerable disparity between extent of flow reversal in the wake as measured by pressure and hot-film probes. The difference is attributed to the intermittent nature of the flow reversal.
Wind tunnel tests have been conducted on an NACA 2412 airfoil section at Reynolds number of 2.2 x 10(exp 6) and Mach number of 0.13. Detailed measurements of flow fields associated with turbulent boundary layers have been obtained at angles of attack of 12.4 degrees, 14.4 degrees, and 16.4 degrees. Pre- and post-separated velocity and pressure survey results over the airfoil and in the associated wake are presented. Extensive force, pressure, tuft survey, hot-film survey, local skin friction, and boundary layer data are also included. Pressure distributions and separation point locations show good agreement with theory for the two layer angles of attack. Boundary layer displacement thickness, momentum thickness, and shape factor agree well with theory up to the point of separation. There is considerable disparity between extent of flow reversal in the wake as measured by pressure and hot-film probes. The difference is attributed to the intermittent nature of the flow reversal.
Conventional procedures for designing nozzles involve the design of an inviscid contour (using the method of characteristics) that is corrected with a displacement thickness calculated from boundary-layer theory. However, nozzles designed using this classical procedure have been shown to exhibit poor flow quality at Mach numbers characteristic of hypersonic applications. The nozzle to be designed will be a part of the NASA HYPULSE facility which is being used for hypervelocity flight research. Thus, the flow quality of the nozzle is a critical question that needs to be addressed. Design of nozzles for hypersonic applications requires a proper assessment of the effects of the thick boundary layer on the inviscid flowfield. Since the flow field is largely supersonic, the parabolized form of the Navier-Stokes (PNS) equations can be used. The requirement of a uniform flow at the exit plane of the nozzle can be used to define an objective function as part of an optimization procedure. The design procedure used in this study involves the coupling of a nonlinear (least-squares) optimization algorithm with an efficient, explicit PNS solver. The thick boundary layers growing on the walls of the nozzle limit the extent of the usable core region (region with uniform flow) for testing models (especially rectangular). In order to maximize the region of uniform flow, it was decided to have the exit plane of this nozzle to be (nearly) rectangular. Thus, an additional constraint on the nozzle shape resulted, namely the nozzle will have a shape transitioning from a circular one at the inlet to that of a rectangle at the exit. In order to provide for a smooth shape transition, the cross sectional contour of the nozzle is defined by a superellipse. The nozzle is taken to be a meter in length. The axial variations of the major and minor radii of the superellipse are governed by cubic splines. The design parameters are the coefficients of the splines associated with the local nozzle wall slopes. Extensive calculations have been made (with a three-dimensional Euler code) to understand the effects of various parameters such as location of the knot points of the spline function, different ways of characterizing the uniformity of the flow in the exit plane, as well as the effect of constraining the area of the nozzle to be invariant. Turbulent flow (measurements indicate that the flow at the nozzle inlet is turbulent) calculations are now being performed (with the inviscidly designed nozzle contours) to assess the flow quality.
An algebraic eddy-viscosity model is derived from the renormalization group (RNG) theory of turbulence. A new length scale, based on boundary layer characteristics (displacement thickness, shape factor), is proposed. The model was applied to transitional boundary layer flow over a flat plate. Integral characteristics, such as the total skin friction coefficient, and mean velocity profile across the boundary layer, are found to be in good agreement with experimental data.
Large-eddy simulations of a turbulent boundary layer with Reynolds number based on displacement thickness equal to 3500 were performed with two grid resolutions. The computations were continued for sufficient time to obtain frequency spectra with resolved frequencies that correspond to the most important structural frequencies on an aircraft fuselage. The turbulent stresses were adequately resolved with both resolutions. Detailed quantitative analysis of a variety of statistical quantities associated with the wall-pressure fluctuations revealed similar behavior for both simulations. The primary differences were associated with the lack of resolution of the high-frequency data in the coarse-grid calculation and the increased jitter (due to the lack of multiple realizations for averaging purposes) in the fine-grid calculation. A new curve fit was introduced to represent the spanwise coherence of the cross-spectral density.
A computational investigation was conducted to support the development of a semi-span model test capability in the NASA LaRC's National Transonic Facility. This capability is required for the testing of high-lift systems at flight Reynolds numbers. A three-dimensional Navier-Stokes solver was used to compute the low-speed flow over both a full-span configuration and a semi-span configuration. The computational results were found to be in good agreement with the experimental data. The computational results indicate that the stand-off height has a strong influence on the flow over a semi-span model. The semi-span model adequately replicates the aerodynamic characteristics of the full-span configuration when a small stand-off height, approximately twice the tunnel empty sidewall boundary layer displacement thickness, is used. Several active sidewall boundary layer control techniques were examined including: upstream blowing, local jet blowing, and sidewall suction. Both upstream tangential blowing, and sidewall suction were found to minimize the separation of the sidewall boundary layer ahead of the semi-span model. The required mass flow rates are found to be practicable for testing in the NTF. For the configuration examined, the active sidewall boundary layer control techniques were found to be necessary only near the maximum lift conditions.
Results of an experimental investigation are presented in which the use of porous and microporous honeycomb composite materials is evaluated as an alternate to perforated solid plates for boundary-layer bleed in supersonic aircraft inlets. The terms "porous" and "microporous," respectively, refer to bleed orifice diameters roughly equal to and much less than the displacement thickness of the approach boundary-layer. A Baseline porous solid plate, two porous honeycomb, and three microporous honeycomb configurations are evaluated. The performance of the plates is characterized by the flow coefficient and relative change in boundary-layer profile parameters across the bleed region. The tests were conducted at Mach numbers of 1.27 and 1.98. The results show the porous honeycomb is not as efficient at removing mass compared to the baseline. The microporous plates were about equal to the baseline with one plate demonstrating a significantly higher efficiency. The microporous plates produced significantly fuller boundary-layer profiles downstream of the bleed region for a given mass flow removal rate than either the baseline or the porous honeycomb plates.
A methodology has been devised for the design of three-dimensional hypersonic inlets which include a rectangular to elliptical shape transition. This methodology makes extensive use of inviscid streamtracing techniques to generate a smooth shape transition from a rectangular-like capture to an elliptical throat. Highly swept leading edges and a significantly notched cowl enable use of these inlets in fixed geometry configurations. The design procedure includes a three dimensional displacement thickness calculation and uses established correlations to check for boundary layer separation due to shock wave interactions. Complete details of the design procedure are presented and the characteristics of a modular inlet with rectangular to elliptical shape transition and a design point of Mach 7.1 are examined. Comparison with a classical two-dimensional inlet optimized for maximum total pressure recovery indicates that this three-dimensional inlet demonstrates good performance even well below its design point.
Solar thermal upper stage propulsion systems currently under development utilize small low chamber pressure/high area ratio nozzles. Consequently, the resulting flow in the nozzle is highly viscous, with the boundary layer flow comprising a significant fraction of the total nozzle flow area. Conventional uncoupled flow methods which treat the nozzle boundary layer and inviscid flowfield separately by combining the two calculations via the influence of the boundary layer displacement thickness on the inviscid flowfield are not accurate enough to adequately treat highly viscous nozzles. Navier Stokes models such as VNAP2 can treat these flowfields but cannot perform a vacuum plume expansion for applications where the exhaust plume produces induced environments on adjacent structures. This study is built upon recently developed artificial intelligence methods and user interface methodologies to couple the VNAP2 model for treating viscous nozzle flowfields with a vacuum plume flowfield model (RAMP2) that is currently a part of the Plume Environment Prediction (PEP) Model. This study integrated the VNAP2 code into the PEP model to produce an accurate, practical and user friendly tool for calculating highly viscous nozzle and exhaust plume flowfields.
Solutions of the time-dependent, mass-averaged Navier-Stokes equations are compared In detail with experimental results obtained on an axisymmetric "bump" model at a transonic Mach number that produced an extensive separated now region. In addition, an inverse boundary method is evaluated for this type of flow. The Cebeci-Smith algebraic and the Wilcox-Rubesin two-equation turbulence models used in the Navier-Stokes calculations both predict the maximum boundary-layer displacement thickness generated by the interaction reasonably well, with the details of the now best described with the two-equation formulation. However, both models predict a shock location substantially farther aft on the bump than observed experimentally. This error in shock location was slightly less with the two-equation model (0.12 chord compared with 0.16 chord). In the vicinity of the shock, the calculations predict a more rapid increase in turbulent shear stress than observed in the experimental results; this more rapid increase is believed to be the cause or the poor predictions in shock position.
An investigation has been conducted at a Mach number of 3 of the effect of turbulence level and sandpaper-type roughness on transition for a flat plate. The Reynolds number varied from 0.8 x 10(exp 6) to 1.8 x 10(exp 6) per inch; the settling-chamber turbulence level varied from 0.7 percent to 35 percent; and the heat transfer between the plate and the stream was negligible. Transition locations were determined by an optical method. This method was indicative of a permanent change in the boundary-layer density distribution rather than the onset of turbulent bursts. Results showed that, when transition was influenced by roughness, it moved in a way similar to its movement on a smooth plate. That is, it gradually approached the roughness location with either an increase in unit Reynolds number or an increase in turbulence level. For roughness submerged in the linear portion of the boundary-layer velocity profile, the square root of the roughness Reynolds number and the ratio of roughness height to boundary-layer displacement thickness gave similar results as parameters for predicting the effects of roughness. A range of each of these parameters which moved transition less than 10 percent was found and this range was a function of turbulence level.
Tests were made on a 10-foot-diameter hemispherical nose at Reynolds numbers up to 10 x 10(exp 6) and at a maximum Mach number of about 0.1 to determine the effects of a highly favorable pressure gradient on boundary-layer transition caused by roughness. Both two-dimensional and three-dimensional roughness particles were used, and the transition of the boundary layer was determined by hot-wire anemometers. The roughness Reynolds number for transition R(sub k,t) caused by three-dimensional particles such as Carborundum grains, spherical particles, and rimmed craters was found. The results show that for particles immersed in the boundary layer, R(sub k,t) is independent of the particle size or position on the hemispherical nose and depends mainly on the height-to-width ratio of the particle. The values of R(sub k,t) found on the hemispherical nose compare closely with those previously found on a flat plate and on airfoils with roughness. For two-dimensional roughness, the ratio of roughness height to boundary-layer displacement thickness necessary to cause transition was found to increase appreciably as the roughness was moved forward on the nose. Also included in the investigation were studies of the spread of turbulence behind a single particle of roughness and the effect of holes such as pressure orifices.
Computational results are presented for hypersonic viscous flow past spinning sharp and blunt cones of angle of attack, obtained with a parabolic Navier-Stokes marching code. The code takes into account the asymmetries in the flowfield resulting from spinning motion and computes the asymmetric shock shape, cross-flow and streamwise shear, heat transfer, cross-flow separation, and vortex structure. The Magnus force and moments are also computed. Comparisons are made with other theoretical analyses based on boundary-layer and boundary-region equations, and an anomaly is discovered in the displacement thickness contribution to the Magnus force when compared with boundary-layer results.
Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.
Results of analyzing flight-test data of pressure-fluctuation fields in front of forward-facing steps and behind backward-facing steps are presented. The range of dimensionless step heights (normalized by boundary-layer displacement thickness) in the flight test was 0.042-0.236. The flight tests covered a mach-number range from 0.57 to 1.97. In the mach-number ranges covered by wind-tunnel tests (0.57 to 0.78 and 1.5 to 2) data agree very well with the flight data. Very importantly, the flight-test data fill in the gap previously existing for small-step pressure-fluctuations in the range of mach 0.78 to 1.5. Increased pressure-fluctuations were observed in the transonic region.
The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.