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Flow disturbances and side forces in supersonic rocket nozzle due to gaseous secondary injection analyzed by semiempirical models
Computations are based on mean-diameter flow properties. For any given turbine, all stages, except the first, are specified to have same shape velocity diagram. First stage inlet flow is axial.
An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.
A basic problem, which is of considerable interest in geoastrophysical applications of magnetogasdynamics, is the nonlinear interaction of a fast shock (S sub f) with a tangential discontinuity (T). The problem is treated for an arbitrary S sub f interacting with an arbitrary T under the assumption that in the frame of reference in which S sub f and T are at rest, the flow is superfast on both sides of T, and that a steady flow develops. As a result of the nonlinear analysis a flow pattern is obtained consisting of the incident discontinuities S sub f 1 and T2 and a transmitted fast shock S sub f 3, the modified tangential discontinuity T4 and a reflected fast shock S sub f 5 or fast rarefaction wave R sub f 5. The results are discussed in terms of seven significant similarity parameters. In addition special cases like changes in magnetic field direction only, changes in desnity or velocity shear only etc. are discussed.
It has been found that, in general, the local potential cannot be employed to obtain approximate solutions for the various correlations of turbulent properties which appear in the time averaged form of the conservation equations. Although the method of local potential is equivalent to the Galerkin method when the self-consistent condition is applied, the local potential can also be applied as an iterative algorithm in place of using the selfconsistent condition. This procedure offers an alternative to the Galerkin method and may be useful in obtaining approximate solutions for the total turbulent velocity. In addition, for certain simple turbulent shear flows the iterative algorithm may permit approximate, but non-empirical, solutions by modeling only the mean velocity and the Reynolds stress.
An analytical procedure based on Navier-Stokes equations was developed for representing unsteady flow patterns around oscillating obstacles. A variational formulation of the Helmholtz vorticity equation was discretized in finite element form and integrated numerically. At each step of the numerical integration the velocity field around the obstacle was determined from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints at each time step of the numerical integration. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.
A reacting shear layer program for a complete second-order closure of turbulent reacting flows is developed. The program uses a typical eddy box model and many of the fluid mechanical turbulence models developed in earlier studies. The computer program actually solves a total of 30 equations, where the numerical integration of the equations is performed by a forward-time-centered space quasi-implicit upwind finite-difference scheme. Results for nonreacting and simple isothermal reacting flows are presented along with preliminary results for propane-air flames. It is shown that the program predictions for simple nonreacting flows are in good agreement with available data. The calculations for isothermal reacting flows demonstrate the importance of including a mixedness correlation in finite rate chemistry calculations, where significant errors in the flowfield properties can result from neglect of the interaction between turbulence and the chemistry. Results for propane-air diffusion flames further support this conclusion.
A laser velocimeter operating in the backscatter mode was used to survey the flow above a stalled wing. Polarization was used to separate the two orthogonal velocity components of the fringe-type laser velocimeter, and digital counters were used for data processing. The velocities of the kerosene seed particles were measured with less than 2 percent uncertainty. The particle velocity measurements were collected into histograms. The flow field survey was carried out above an aspect-ratio-8 stalled wing with an NACA 0012 section. The angle of attack was 19.5 deg, the Mach number was 0.49, and the Reynolds number was 1,400,000. The flow field was characterized by the periodic shedding of discrete vortices from near the crest of the airfoil.
A computer program was used to solve the governing of the potential flow in the cross sectional planes of a radial inflow turbine scroll. A list of the main program, the subroutines, and typical output example are included.
Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.
A computational method with which to obtain a physical understanding of the turbulent field of two coaxial jets entering an axisymmetric chamber is developed. Even the laminar field of this flow is quite complicated. This is due to the many different domains which exist in the field especially in the entrance region. Physically, three regions may be identified: the wall region, the initial region near the axis of symmetry and the mixing region. Advancing downstream, these regions change relative size with the ratio of the two jets' mass fluxes as the main parameter. The turbulent field of these flows is much more complicated due to the difference in the effective transport coefficients and turbulence level from region to region. However, being aware beforehand of the complications and the different regions of this field, the appropriate turbulence model and numerical scheme can be adjusted to treat the problem.
Attention is given to hypersonic laminar flow over a quilted surface configuration that simulates an array of Space Shuttle Thermal Protection System panels bowed in a spherical shape as a result of thermal gradient through the panel thickness. Pressure and heating loads to the surface are determined. The flow field over the configuration was mathematically modeled by means of time-dependent, three-dimensional conservation of mass, momentum, and energy equations. A boundary mapping technique was then used to obtain a rectangular, parallel piped computational domain, and an explicit MacCormack (1972) explicit time-split predictor corrector finite difference algorithm was used to obtain steady state solutions. Total integrated heating loads vary linearly with bowed height when this value does not exceed the local boundary layer thickness.
Attention is given to hypersonic laminar flow over a quilted surface configuration that simulates an array of Space Shuttle Thermal Protection System panels bowed in a spherical shape as a result of thermal gradients through the panel thickness. Pressure and heating loads to the surface are determined. The flow field over the configuration was mathematically modeled by means of time-dependent, three-dimensional conservation of mass, momentum, and energy equations. A boundary mapping technique was then used to obtain a rectangular, parallelepiped computational domain, and an explicit MacCormack (1972) explicit time-split predictor-corrector finite difference algorithm was used to obtain steady state solutions. Total integrated heating loads vary linearly with bowed height when this value does not exceed the local boundary layer thickness.
The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution, for both subsonic and supersonic external flow, and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data taken at flight Reynolds numbers for like-flow conditions. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive-grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular point boundary conditions are used for similar purposes, and are especially effective for highly under-expanded jets. For all cases considered, except one with a very large base-to-nozzle-exit-diameter ratio, the agreement with experimental measurements is excellent. For geometries with large base regions, enhancements in the turbulence transport model are necessary to support improvements in the flow-field simulation.
Computer program, IMPOUT 2, developed using newly-established "limit formulas" to prevent lubricant non-impingement on pinion. Program used to analyze impingement depth on gear teeth for oil jet located at out-of-mesh position with arbitrary offset and inclination angles and with arbitrary addendum and center-distance modification. IMPOUT 2 program written in ANSI FORTRAN IV for use on CDC 750.
The three-dimensional inviscid DENTON code is used to analyze flow through a radial-inflow turbine rotor. Experimental data from the rotor are compared with analytical results obtained by using the code. The experimental data available for comparison are the radial distributions of circumferentially averaged values of absolute flow angle and total pressure downstream of the rotor exit. The computed rotor-exit flow angles are generally underturned relative to the experimental values, which reflect the boundary-layer separation at the trailing edge and the development of wakes downstream of the rotor. The experimental rotor is designed for a higher-than-optimum work factor of 1.126 resulting in a nonoptimum positive incidence and causing a region of rapid flow adjustment and large velocity gradients. For this experimental rotor, the computed radial distribution of rotor-exit to turbine-inlet total pressure ratios are underpredicted due to the errors in the finite-difference approximations in the regions of rapid flow adjustment, and due to using the relatively coarser grids in the middle of the blade region where the flow passage is highly three-dimensional. Additional results obtained from the three-dimensional inviscid computation are also presented, but without comparison due to the lack of experimental data. These include quasi-secondary velocity vectors on cross-channel surfaces, velocity components on the meridional and blade-to-blade surfaces, and blade surface loading diagrams. Computed results show the evolution of a passage vortex and large streamline deviations from the computational streamwise grid lines. Experience gained from applying the code to a radial turbine geometry is also discussed.
Research is aimed at the fundamental understanding of the interactions of heat and mass transport and fluid mechanics in crystal growth from the melt, especially in how it pertains to experiments supported by the Microgravity Science and Applications program. Emphasis has been on studies of the vertical Bridgman system, on small-scale floating zone systems proposed for space flight, and on quantitative prediction of nonlinear transitions in melt/solid interface morphologies leading to the formation of dendrites in directional solidification. The analysis of vertical Bridgman growth has lead to the complete numerical analysis of transport phenomena in directional solidification and to a detailed comparison of calculations to the GaGe growth experiments of Wang and Witt. Calculations show the central role of the ampoule material in determining the radial temperature gradients in the melt and thus, the intensity of convection. Results indicate that diffusion-controlled growth can not be achieved on Earth with conventional growth systems, but are feasible in microgravity
A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.