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A procedure based on the method of similar solutions is presented by which the skin friction, heat transfer, and boundary-layer thickness in a laminar hypersonic flow with pressure gradient may be rapidly evaluated if the pressure distribution is known. This solution, which at present is. restricted to power-law variations of pressure with surface distance, is presented for a wide range of exponents in the power law corresponding to both favorable and adverse pressure gradients. This theory has been compared to results from heat-transfer experiments on blunt-nose flat plates and a hemisphere cylinder at free-stream Mach numbers of 4 and 6.8. The flat-plate experiments included tests made at a Mach number of 6.8 over a range of angle of attack of +/- 10 deg. Reasonable agreement of the experimental and theoretical heat-transfer coefficients has been obtained as well as good correlation of the experimental results over the entire range of angle of attack studied. A similar comparison of theory with experiment was not feasible for boundary-layer-thickness data; however, the hypersonic similarity theory was found to account satisfactorily for the variation in boundary-layer thickness due to local pressure distribution for several sets of measurements.
We develop numerical models of accretions disks in cataclysmic variables (CVs), including and emphasizing the boundary layer region where the accretion disk meets the accreting white dwarf. We confine ourselves to solutions where the boundary layer region is vertically optically thick, and find that these solutions share several common features. The angular and radial velocities of the accreting material drop rapidly in a dynamical boundary layer, which has a radial width approximately 1%-3% of the white dwarf radius. The energy dissipated in this region diffuses through the inner part of the disk and is radiated from the disk surface in a thermal boundary layer, which has a radial width comparable to the disk thickness, approximately 5%-15% of the white dwarf radius. We examine the dependence of the boundary layer structure on the mass accretion rate, the white dwarf mass and rotation rate, and the viscosity parameter alpha. We delineate the boundary between optically thick and optically thin boundary layer solutions as a function of these parameters and suggest that by means of a careful comparison with observations it may be possible to estimate alpha in CVs. We derive an expression for the total boundary layer luminosities as a function of the parameters and show that it agrees well with the luminosites of our numerical solutions. Finally, we calcuate simple blackbody continuum spectra of the boundary layer and disk emission for our solutions and compare these to soft X-ray, EUV, and He II emission-line observations of CVs. We show that, through such comparisons, it may be possible to determine the rotation rates of the accreting stars in CVs, and perhaps also the white dwarf masses and the accretion rates. The spectra are quite insensitive to alpha, so the uncertainty in this parameter does not affect such comparisons.
A combined experimental and analytical program was conducted to investigate the effects of boundary layer changes on the flow over high angle boattail nozzles. The tests were run on an isolated axisymmetric sting mounted model. Various boattail geometries were investigated at high subsonic speeds over a range of boundary layer thicknesses. In general, boundary layer effects were small at speeds up to Mach 0.8. However, at higher speeds significant regions of separated flow were present on the boattail. When separation was present large reductions in boattail drag resulted with increasing boundary layer thickness. The analysis predicts both of these trends.
The influence of bulk turbulence and boundary layer thickness on the secondary flow development in a square, 90 degree turning duct was investigated. A three-dimensional laser velocimetry system was utilized to measure the mean and fluctuating components of velocity at six cross-planes in the duct. The results from this investigation, with entrance boundary layer thickness of 20 percent, were compared with the thin boundary layer results documented in NASA CR-174811. The axial velocity profiles, cross-flow velocities, and turbulence intensities were compared and evaluated with regard to the influence of bulk turbulence intensity and boundary layer thickness, and the influence was significant. The results of this investigation expand the 90 degree curved duct experimental data base to higher turbulence levels and thicker entrance boundary layers. The experimental results provide a challenging benchmark data base for computational fluid dynamics code development and validation. The variation of inlet bulk turbulence intensity provides additional information to aid in turbulence model evaluation.
A combined experimental and analytical program has been conducted at the NASA Lewis Research Center, to investigate the effects of boundary layer changes on the flow over high angle boattail nozzles. The tests were run on an isolated axisymmetric sting mounted model. Various boattail geometries were investigated at high subsonic speeds over a range of boundary layer thicknesses. In general, boundary layer effects were small at speeds up to Mach 0.8. However, at higher speeds significant regions of separated flow were present on the boattail. When separation was present large reductions in boattail drag resulted with increasing boundary layer thickness. The analysis predicts both of these trends.
An investigation was conducted to determine the effect of the inlet Mach number and entrance-boundary-layer thickness on the performance of a 23 degree 21-inch conical-diffuser - tail-pipe combination with a 2:1 area ratio. The air flows used in this investigation covered an inlet Mach number range from 0.17 to 0.89 and corresponding Reynolds numbers of 1,700,000 to 7,070,000. Results are reported for two inlet-boundary-layer thicknesses. Over the entire range of flows, the mean value of the inlet displacement thickness is about 0.034 inch for the thinner inlet boundary layer and about 0.170 inch for the case of the thicker inlet boundary layer. The performance of the diffuser - tail-pipe combination is presented together with examples of longitudinal static-pressure distribution and the results of boundary-layer pressure surveys made at six points along the diffuser wall. The results indicated a progressive diminution of the static-pressure recovery and a steady increase in the total-pressure losses as the inlet Mach number was increased for both inlet-boundary-layer thicknesses. The ratio of actual static-pressure rise to that theoretically possible was much less and the total-pressure losses were greater for the case of the thicker inlet boundary layer throughout the speed range investigated. With the thinner inlet boundary layer, flow separation occurred at the diffuser exit at all inlet Mach numbers.Unseparated flow alternating with separated flow was observed near the inlet at the higher velocities. For the case of the thicker inlet boundary layer, the origin of the separated region occurred in the vicinity of the inlet-duct-diffuser junction section at all Mach numbers.
A preliminary experimental program was conducted to determine the effect of the ratio of the free-stream boundary-layer thickness to jet diameter on the secondary jet penetration and mixing rate. Tests were conducted on a flat plate in a Mach number 4.05 airflow with sonic injection of hydrogen normal to the free-stream direction from circular underexpanded injectors. The ratio of boundary-layer thickness to jet diameter ranged from 1.25 to 6.5. Previous correlations of mixing performance were modified to account for the effect of the ratio of boundary-layer thickness to jet diameter.
Inlet boundary layer thickness and structure effects on heat transfer in supersonic nozzle
Boundary layer thickness on curved walls of 20-in supersonic wind tunnel two-dimensional nozzle
The natural convection boundary layer ( δ n c ) and its influence on cathodic current in a galvanic couple under varying electrolytes as a function of concentration (1 − 5.3 M NaCl) and temperature (25 °C−45 °C) were understood. Polarization scans were obtained under quiescent conditions and at defined boundary layer thicknesses using a rotating disk electrode on platinum and stainless steel 304L (SS304L); these were combined to determine δ n c . With increasing chloride concentration and temperature, δ n c decreased. Increased mass transport (Sherwood number) results in a decrease in δ n c , providing a means to predict this important boundary. Using Finite Element Modeling, the cathodic current was calculated for an aluminum alloy/SS304L galvanic couple as a function of water layer ( WL ) thickness and cathode length. Electrolyte domains were delineated, describing (i) dominance of ohmic resistance over mass transport under thin WL , (ii) the transition from thin film to bulk conditions at δ n c , and (iii) dominance of mass transport under thick WL . With increasing chloride concentration, cathodic current decreased due to decreases in mass transport. With increasing temperature, increased cathodic current was related to increases in mass transport and solution conductivity. This study has implications for sample sizing and corrosion prediction under changing environments.
This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.
The instability of a circular jet was investigated by means of the inviscid linearized stability theory. By variation of a jet parameter which takes the ratio of jet radius to boundary layer thickness into account, the influence of axisymmetry on the spatial growth rate and disturbance phase velocity is studied. The influence of Mach number and temperature ratio is discussed. A comparison with measurements shows that the instability of a turbulent jet boundary layer may also be explained by these results.
Investigations were conducted of a 12 degree 21-inch conical diffuser of 2:l area ratio to determine the interrelation of boundary layer growth and performance characteristics. surveys were made of inlet and exit from, longitudinal static pressures were recorded, and velocity profiles were obtained through an inlet Reynolds number range, determined From mass flows and based on inlet diameter of 1.45 x 10(exp 6) to 7.45 x 10(exp 6) and a Mach number range of 0.11 to approximately choking. These investigations were made to two thicknesses of inlet boundary layer. The mean value, over the entire range of inlet velocities, of the displacement thickness of the thinner inlet boundary layer was approximately 0.035 inch and that of the thicker inlet boundary layer was approximately six times this value. The loss coefficient in the case of the thinner inlet boundary layer had a value between 2 to 3 percent of the inlet impact pressure over most of the air-flow range. The loss coefficient with the thicker inlet boundary layer was of the order of twice that of the thinner inlet boundary layer at low speeds and approximately three times at high speeds. In both cases the values were substantially less than those given in the literature for fully developed pipe flow. The static-pressure rise for the thinner inlet boundary layer was of the order of 95 percent of that theoretically possible over the entire speed range. For the thicker inlet boundary layer the static pressure rise, as a percentage of that theoretically possible, ranged from 82 percent at low speeds to 68 percent at high speeds.
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The objective of this investigation was the experimental evaluation of bulk turbulence and boundary thickness influence on the secondary flow development in a square, 90 deg turning duct. A three dimensional laser velocimetry system was utilized to measure the mean and fluctuating components of velocity in the large curved duct facility. The three dimensional development of the viscous shear layers in the curved duct has a strong influence on the complete flow field. Since ducted three dimensional flows are found in many engineering applications, including gas turbine engines, and contain high turbulence levels and high wall heat transfer rates, they present a difficult challenge to computational fluid mechanics codes. Turbulence modeling remains one of constraints to CFD advance due to inadequate physical understanding and experimental definition of turbulent shear flows. The results of this investigation expand the curved duct data base to higher turbulence levels and thicker entrance boundary layers. The experimental results provide a challenging benchmark data base for computational fluid dynamics code development and validation. The variation of inlet bulk turbulence intensity provides additional information to aid in turbulence model evaluation.
The objective of this investigation was the experimental evaluation of bulk turbulence and boundary thickness influence on the secondary flow development in a square, 90 deg turning duct. A three dimensional laser velocimetry system was utilized to measure the mean and fluctuating components of velocity in the large curved duct facility. The three dimensional development of the viscous shear layers in the curved duct has a strong influence on the complete flow field. Since ducted three dimensional flows are found in many engineering applications, including gas turbine engines, and contain high turbulence levels and high wall heat transfer rates, they present a difficult challenge to computational fluid mechanics codes. Turbulence modeling remains one of constraints to CFD advance due to inadequate physical understanding and experimental definition of turbulent shear flows. The results of this investigation expand the curved duct data base to higher turbulence levels and thicker entrance boundary layers. The experimental results provide a challenging benchmark data base for computational fluid dynamics code development and validation. The variation of inlet bulk turbulence intensity provides additional information to aid in turbulence model evaluation.
Aft-facing step base pressure flight data were obtained for three step heights for nominal transonic Mach numbers of 0.80, 0.90, and 0.95, and for supersonic Mach numbers of 2.2, 2.5, and 2.8 with a Reynolds number, based on the fuselage length ahead of the step, of about 10 to the 8th power. Surface static pressures were measured ahead of the step, behind the step, and on the step face (base), and a boundary layer rake was used to obtain boundary layer reference conditions. A comparison of the data from the present and previous experiments shows the same trend of increasing base pressure ratio (decreasing drag) with increasing values of momentum thickness to step height ratios. However, the absolute level of these data does not always agree at the supersonic Mach numbers. For momentum thickness to height ratios near 1.0, the differences in the base pressure ratios appear to be primarily a function of Reynolds number based on the momentum thickness. Thus, for Mach numbers above 2, the data analyzed show that the base pressure ratio decreases (drag increases) as Reynolds number based on momentum thickness increases for a given momentum thickness and step height.