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Laminarization of turbulent boundary layer observed from heat transfer and boundary layer measurements in conical nozzles
Boundary layer and heat transfer measurements for turbulent boundary layer laminarizing in conical nozzle flow with wall cooling
Reducing differential equations of viscous shock layer to boundary layer equations
Mathematical model of nonsimilar laminar or turbulent boundary layer, including entropy layer and turbulence effects, solved by Newton-Raphson iteration
An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.
A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.
The effects of distributed roughness, arising from space shuttle orbiter panel joints, on boundary layer transition are investigated. The North American Rockwell 134B delta wing shuttle configuration was used for the study. Results show: (1) Premature boundary layer transition occurred in models having simulated heat shield panels with rased joints. (2) Laminar flow was maintained with slot type panel joint models to a Reynolds number twice that at which transition occurred in raised joints. (3) Significant increases in peak surface temperature and the time during which turbulent flow occurs may result from distributed roughness of heat shield panel joints. (4) Laminar and turbulent heating levels were predicted within available theories. (5) A complex interference between the wing and fuselage flow was observed in the delta wing model.
A two-dimensional differential analysis is developed to approximate the turbulent boundary layer on a compressor blade element with strong adverse pressure gradients, including the separated region with reverse flow. The predicted turbulent boundary layer thicknesses and velocity profiles are in good agreement with experimental data for a cascade blade, even in the separated region.
A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows.
The effect of the laminar/turbulent boundary layer state on the mean and rms velocities of a developing plane mixing layer was investigated. The use of commonly accepted nondimensional representations of the data confirm (at least) an approximately self-preserving condition. It is suggested that the effects of the laminar/turbulent initial condition persist in the self-preserving region.
Tabulated data from a series of experimental studies of the interaction of a shock wave with a turbulent boundary layer in axisymmetric flow configurations is presented. The studies were conducted at the walls of circular wind tunnels and on the cylindrical centerbody of an annular flow channel. Detailed pitot pressure profiles and wall static pressure profiles upstream of, within and downstream of the interaction region are given. Results are presented for flows at nominal freestream Mach Numbers of 2, 3 and 4. For studies at the tunnel sidewalls, the shock waves were produced by conical shock generators mounted on the centerline of the wind tunnel at zero angle of attack. The annular ring generator was used to produce the shock wave at the centerbody of the annular flow channel. The effects of boundary layer bleed were examined in the investigation. Both bleed rate and bleed location were studied. Most of the bleed studies were conducted with bleed holes drilled normal to the wall surface but the effects of slot suction were also examined. A summary of the principal results and conclusions is given.
The effect, of the laminar/turbulent boundary layer state on the mean and rms velocities of a developing plane mixing layer, has been investigated. The maximum Ux/nu allowed by the facility was 6.7 x 100.000; the maximum x station surveyed corresponds to approximately 2000 and 700 initial momentum thicknesses for the laminar and turbulent cases respectively. The use of commonly accepted non-dimensional representations of the data confirm (at least) an approximately self-preserving condition. They also suggest that the effects of the laminar/turbulent initial condition persist in the self-preserving region. A direct comparison of the data reveals that the persistence so observed is illusory. An interpretation of the reason for this misunderstanding is advanced.
A model for the boundary layer at the exit plane of a rocket nozzle was developed which, unlike most previous models, includes the subsonic sublayer. The equations for the flow near the nozzle exit plane are presented and the method by which the subsonic sublayer transitions to supersonic flow in the plume is described. The resulting model describes the entire boundary layer and can be used to provide a startline for method-of-characteristics calculations of plume flowfields. The model was incorporated into a method of characteristics computer program and comparisons of computed results to experimental data show good agreement. The data used in the comparisons were obtained in tests in which mass fluxes from a 22.2-N (5 lbf) thrust engine were measured at angles off the nozzle centerline of up to 150 deg. Additional comparisons were made with data obtained during tests of a 0.89-N (0.2 lbr) monopropellant thruster and from the OH-64 space shuttle heating tests. The agreement with the data indicates that the model can be used for calculating plume backflow properties.
The formulation of the planetary boundary layer (PBL) and stratocumulus parametrizations in the UCLA general circulation model (GCM) are briefly summarized, and extensive new results are presented illustrating some aspects of the simulated seasonal changes of the global distributions of PBL depth, stratocumulus cloudiness, cloud-top entrainment instability, the cumulus mass flux, and related fields. Results from three experiments designed to reveal the sensitivity of the GCM results to aspects of the PBL and stratocumulus parametrizations are presented. The GCM results show that the layer cloud instability appears to limit the extent of the marine subtropical stratocumulus regimes, and that instability frequently occurs in association with cumulus convection over land. Cumulus convection acts as a very significant sink of PBL mass throughout the tropics and over the midlatitude continents in winter.
A comparison of two viscous shock layer methods and one boundary layer method for predicting the aerodynamic heating around the Orbiter nose cap during STS-5 entry is presented. The object of the study was to compare these methods with one another and with the measured Orbiter flight data for this trajectory. The nonequilibrium, chemically reacting viscous flow fields obtained by these methods are evaluated, and effects on heating rate of wall catalycity variation with time are presented. The effects of shock slip and combined wall/shock slip are considered at high altitudes (above 300,000 ft). Using the variable wall catalycity analysis, it is shown that heating rates can be predicted within a 5.7 percent flight data band for altitudes between 175,000 ft and 265,000 ft in this trajectory.
The ability of outer-layer devices to reduce wall shear stress over a substantial streamwise distance in rough-wall turbulent boundary layers has been studied experimentally. The devices examined are a pair of thin flat ribbons placed in tandem as well as those having symmetric airfoil sections. The wall conditions examined are smooth, d- and k-type transverse-groove and sandgrain roughnesses. The wall drag is found to be reduced from the respective normal levels in all rough walls. All k-type rough walls exhibit a similar level of relative wall drag reduction which is also smaller than that in a smooth-wall. The d-type rough walls exhibit a transitional behaviour - the relative wall drag reduction drops from the smooth wall level to that of the k-type roughness with increasing roughness Reynolds number. However, the absolute reductions in the local wall shear stress are similar in both the rough and smooth walls. On the other hand, the relative reductions are lower in the rough walls because of a higher reference drag which is caused by the unique presence of a pressure component on which the devices are not as effective.
A specially designed wind tunnel was used to examine the effects of tandemly arranged parallel plate manipulators (TAPPMs) on a turbulent boundary-layer structure and the associated drag. Momentum balances, as well as measurements of the local shear stress from the velocity gradient near the wall, were used to obtain the net drag and local skin friction changes. Two TAPPMs, identical except for the thickness of their plates, were used in the study. Results with .003 inch plates were a maximum net drag reduction of 10 percent at 58 beta sub o (using a momentum balance). At 20 beta sub o, simultaneous laser sheet flow visualization and hot-wire anemometry data showed that the Reynolds stress in the large eddies was significantly reduced, as were the streamwise and normal velocity components. Using space-time correlations the reductions were again identified. Furthermore, quantitative flow visualization showed that the outward normal velocity of the inner region was also significantly decreased in the region around 20 beta sub o. However, throughout the first 130 beta sub o, the measured sublayer thickness with the TAPPMs in place was 15 to 20 percent greater. The data showed that the skin friction, as well as the structure of the turbulence, was strongly modified in the first 35 beta sub o, but that they both significantly relaxed toward unmanipulated boundary layer values by 50 beta sub o.
A one-component laser Doppler velocimeter (LDV) has been used to measure the two-dimensional periodic flow field about a double circular arc, compressor blade in cascade. Eleven boundary layer profiles were taken on both the pressure and suction surfaces of the blade, and two profiles were taken in the near wake. In this part of the study, the detailed LDV studies are described. The measurements indicate that the onset of transition occurs near 60 percent chord. The lack of a logarithmic region in the data measured at 97.9 percent chord indicates that transition is not complete. The thin laminar boundary layers near the leading edge led to some measurement problems, characterized by large turbulence intensities, in using the LDV.