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Recent advances in the development of the diagonalized alternating direction implicit multigrid method for compressible aerodynamic problems are reviewed. These include the extension of the method originally developed for the Euler equations to include viscous effects, the computation of turbulent flows and the implementation on parallel computers of the scheme on multiblock rids.
An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.
A device has been developed which measures the velocity of sound in fluids at stagnation and is especially adaptable to turbine and compressor testing for which the constituency of the working fluid may be in doubt. By utilizing the shaft frequency of a rotary compressor, the instrument can also be used to provide a direct measurement of the compressor Mach number (ratio of blade-tip velocity to inlet velocity of sound at stagnation). A Helmholtz resonator is employed in the measurement of the sound velocity. Viscous effects in the orifice of the Helmholtz resonator are shown to be important and can be taken into account with the help of a parameter obtained from Stokes solution of the flow near an oscillating wall. This parameter includes the kinematic viscosity of the fluid and the frequency of sound in the resonator. When these effects are recognized, the resonator can be calibrated to measure velocity of sound or compressor Mach number to an accuracy of better than 0.5 percent.
A mixed-flow impeller was designed to give a prescribed blade-surface velocity distribution at mean blade height for a given hub-shroud profile. The blade shape at mean blade height, which was produced by the prescribed velocity distribution, was extended by means of radial lines to form the composite blade shape from hub to shroud. The resulting blade was relatively thick; therefore, it was necessary to retain the inverse blade taper which resulted from extension of the radial lines in order to prevent merging or near merging of the separate blades near the hub. For the first test version of the impeller, designated the MFI-2A, the blade height was arbitrarily made greater than that for the basic impeller (the MFI-2) to allow for viscous effects. At design equivalent speed of 1400 feet per second the peak pressure ratio and maximum adiabatic efficiency were 3.95 and 79 percent, respectively. The adiabatic efficiency of the MFI-2A is four points lower than that for impeller model MFI-1A, but because of the higher slip factor for the MFI-2A, the pressure ratios are approximately equal. The procedures followed in the design of the MFI-1A and MFI-2A were, in general, the same; and, although the prescribed initial condition resulted in geometrical configurations that were quite dissimilar, the resulting performance characteristics compare favorably with designs for which considerable development work has been necessary.
A new procedure which unifies the best of current classical design practices, computational fluid dynamics (CFD), and optimization procedures is demonstrated for designing the aerodynamic lines of hypersonic wind-tunnel nozzles. The new procedure can be used to design hypersonic wind tunnel nozzles with thick boundary layers where the classical design procedure has been shown to break down. An efficient CFD code, which solves the parabolized Navier-Stokes (PNS) equations using an explicit upwind algorithm, is coupled to a least-squares (LS) optimization procedure. A LS problem is formulated to minimize the difference between the computed flow field and the objective function, consisting of the centerline Mach number distribution and the exit Mach number and flow angle profiles. The aerodynamic lines of the nozzle are defined using a cubic spline, the slopes of which are optimized with the design procedure. The advantages of the new procedure are that it allows full use of powerful CFD codes in the design process, solves an optimization problem to determine the new contour, can be used to design new nozzles or improve sections of existing nozzles, and automatically compensates the nozzle contour for viscous effects as part of the unified design procedure. The new procedure is demonstrated by designing two Mach 15, a Mach 12, and a Mach 18 helium nozzles. The flexibility of the procedure is demonstrated by designing the two Mach 15 nozzles using different constraints, the first nozzle for a fixed length and exit diameter and the second nozzle for a fixed length and throat diameter. The computed flow field for the Mach 15 least squares parabolized Navier-Stokes (LS/PNS) designed nozzle is compared with the classically designed nozzle and demonstrates a significant improvement in the flow expansion process and uniform core region.
In the present reporting period, the 3D version of the OVERFLOW code was used to solve the flow within the internal portion of the supersonic inlet. The internal portion of this inlet is bounded by an inflow plane containing the leading edge of the sidewalls, the sidewalls, the ramp and cowl surfaces and an outflow plane just downstream of the minimum geometric area of the inlet. Boundary layer bleed was used in the two-dimensional calculations discussed in the previous progress report and that same bleed was applied in the present study. For reference, this bleed corresponds to locations designated as R2 and R3 in the Mach 5 inlet model test. Using the GRIDGEN code, a three dimensional grid was generated that accounted for the viscous effects expected to occur on the sidewall, as well as those known to occur on the ramp and cowl surfaces. The internal flow grid size was 141 streamwise by 101 cross stream by 71 in the lateral direction between sidewalls. Since the flow entering the inlet was not symmetrical, the inlet was solved from sidewall to sidewall (without using a symmetry plane). In addition to the short sidewalls proposed in the Langley geometry database, a set of shorter sidewalls was also investigated in the present study and was shown to have beneficial effects with respect to the flow distortion exiting the supersonic inlet. In addition to these calculations, additional 3D solutions using the OVERFLOW code were obtained for the flow downstream of the throat of the supersonic inlet, including a terminal shock wave system produced by a backpressured subsonic diffuser.
Flight experiments are being conducted as part of a multiphased subsonic transport high-lift research program for correlation with wind-tunnel and computational results. The NASA Langley Transport Systems Research Vehicle (B737-100 aircraft) is used to obtain in-flight flow characteristics at full-scale Reynolds numbers to contribute to the understanding of 3-D high-lift, multi-element flows including attachment-line transition and relaminarization, confluent boundary-layer development, and flow separation characteristics. Flight test results of pressure distributions and skin friction measurements were obtained for a full-chord wing section including the slat, main-wing, and triple-slotted, Fowler flap elements. Test conditions included a range of flap deflections, chord Reynolds numbers (10 to 21 million), and Mach numbers (0.16 to 0.40). Pressure distributions were obtained at 144 chordwise locations of a wing section (53-percent wing span) using thin pressure belts over the slat, main-wing, and flap elements. Flow characteristics observed in the chordwise pressure distributions included leading-edge regions of high subsonic flows, leading-edge attachment-line locations, slat and main-wing cove-flow separation and reattachment, and trailing-edge flap separation. In addition to the pressure distributions, limited skin-friction measurements were made using Preston-tube probes. Preston-tube measurements on the slat upper surface suggested relaminarization of the turbulent flow introduced by the pressure belt on the slat leading-edge surface when the slat attachment line was laminar. Computational analysis of the in-flight pressure measurements using two-dimensional, viscous multielement methods modified with simple-sweep theory showed reasonable agreement. However, overprediction of the pressures on the flap elements suggests a need for better detailed measurements and improved modeling of confluent boundary layers as well as inclusion of three-dimensional viscous effects in the analysis.
Work continued on the improvement of 16-Inch Shock Tunnel. This comprised studies of ways of improving driver gas ignition, an improved driver gas mixing system, an axial translation system for the driver tube, improved diaphragm materials (carbon steel vs. stainless steel), a copper liner for the part of the driven tube near the nozzle, the use of a buffer gas between the driver and driven gases, the use of N2O in the driven tube, the use of a converging driven tube, operation of the facility as a non-reflected shock tunnel and expansion tube, operation with heated hydrogen or helium driver gas, the use of detonations in the driver and the construction of an enlarged test section. Maintenance and developmental work continued on the scramjet combustor continued. New software which greatly speeds up data analysis has been written and brought on line. In particular, software which provides very rapid generation of model surface heat flux profiles has been brought on line. A considerable amount of theoretical work was performed in connection with upgrading the 16 Inch Shock Tunnel Facility. A one-dimensional Godunov code for very high velocities and any equation of state is intended to add viscous effects in studying the operation of the Shock Tunnel and also of two-stage light gas guns.
A FORTRAN computer program for the semi analytic prediction of unsteady thrust augmenting ejector performance has been developed, based on a theoretical analysis for ejectors. That analysis blends classic self-similar turbulent jet descriptions with control-volume mixing region elements. Division of the ejector into an inlet, diffuser, and mixing region allowed flexibility in the modeling of the physics for each region. In particular, the inlet and diffuser analyses are simplified by a quasi-steady-analysis, justified by the assumption that pressure is the forcing function in those regions. Only the mixing region is assumed to be dominated by viscous effects. The present work provides an overview of the code structure, a description of the required input and output data file formats, and the results for a test case. Since there are limitations to the code for applications outside the bounds of the test case, the user should consider TEA as a research code (not as a production code), designed specifically as an implementation of the proposed ejector theory. Program error flags are discussed, and some diagnostic routines are presented.
A transonic compressor stage has been designed for the Naval Postgraduate School Turbopropulsion Laboratory. The design relied heavily on CFD techniques while minimizing conventional empirical design methods. The low aspect ratio (1.2) rotor has been designed for a specific head ratio of .25 and a tip relative inlet Mach number of 1.3. Overall stage pressure ratio is 1.56. The rotor was designed using an Euler code augmented by a distributed body force model to account for viscous effects. This provided a relatively quick-running design tool, and was used for both rotor and stator calculations. The initial stator sections were sized using a compressible, cascade panel code. In addition to being used as a case study for teaching purposes, the compressor stage will be used as a research stage. Detailed measurements, including non-intrusive LDV, will be compared with the design computations, and with the results of other CFD codes, as a means of assessing and improving the computational codes as design tools.
A CFD analysis of a low pressure nuclear rocket concept is presented with the use of an advanced chemical kinetics, Navier-Stokes code. The computations describe the flow field in detail, including gas dynamic, thermodynamic and chemical properties, as well as global performance quantities such as specific impulse. Computational studies of several rocket nozzle shapes are conducted in an attempt to maximize hydrogen recombination. These Navier-Stokes calculations, which include real gas and viscous effects, predict lower performance values than have been reported heretofore.
One-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a self-consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiqitous among low-mass YSOs, few constraints have until now been imposed on physical conditions in these disks. By fitting the results of time-dependent disk models to observed timescales of FU Orionis events, we estimate the magnitude of the effective viscous stress in the inner disk (r approximately less than 1 AU) to be, in accordance with an ad hoc 'alpha' prescription, the product of the local sound speed, pressure scale height, and an efficiency factor alpha of 10(exp -4) where hydrogen is neutral and 10(exp 3) where hydrogen is ionized. We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate sufficiently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass flux of dm(sub crit)/dt = 5 x 10(exp 7) solar mass/yr independent of the magnitude of alpha for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of dm(sub in)/dt = 1-10) x 10(exp -6) solar mass/yr produce observed FU Orionis timescales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propogate out to a distance of several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass flowing through the innermost disk annulus is equal to dm(sub in)/dt only in a time-averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals (approximately 1000 yr) of low-mass flux: (1-30) x 10(exp -8) solar mass/yr are punctuated by short intervals (approximately 100 yr) of high-mass flux: (1-30) x 10(exp -5) solar mass/yr. Timescales and mass fluxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems, respectively.
An experimental and computational study was carried out to investigate the parallel head-on blade-vortex interaction (BVI) and its noise generation mechanism. A shock tube, with an enlarged test section, was used to generate a compressible starting vortex which interacted with a target airfoil. The dual-pulsed holographic interferometry (DPHI) technique and airfoil surface pressure measurements were employed to obtain quantitative flow data during the BVI. A thin-layer Navier-Stokes code (BV12D), with a high-order upwind-biased scheme and a multizonal grid, was also used to simulate numerically the phenomena occurring in the head-on BVI. The detailed structure of a convecting vortex was studied through independent measurements of density and pressure distributions across the vortex center. Results indicate that, in a strong head-on BVI, the opposite pressure peaks are generated on both sides of the leading edge as the vortex approaches. Then, as soon as the vortex passes by the leading edge, the high-pressure peak suddenly moves toward the low-peak-reducing in magnitude as it moves--simultaneously giving rise to the initial sound wave. In both experiment and computation, it is shown that the viscous effect plays a significant role in head-on BVIs.
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
Performance measurements were obtained and life-limiting mechanisms were identified on a laboratory-model arcjet thruster designed to operate at a nominal power level of 300 W. The design employed a supersonic-arc-attachment concept and was operated from 200 to 400 W on hydrogen/nitrogen mixtures in ratios simulating fully decomposed hydrazine and ammonia. Power was provided by breadboard power processor. Performance was found to be a strong function of propellant flow rate. Anode losses were essentially constant for the range of mass flow rates tested. It is believed that the performance is dominated by viscous effects. Significantly improved performance was noted with simulated ammonia operation. At 300 W the specific impulse on simulated ammonia was 410 s with an efficiency of 0.34, while simulated hydrazine provided 370 s specific impulse at an efficiency of 0.27.
One of the major design tasks involved in reducing aircraft drag is the integration of the engine nacelles and airframe. With this impetus, nacelle shapes with and without the presence of a flat-plate wing nearby were optimized. This also served as a demonstration of the 3-D version of the recently developed aerodynamic design optimization methodology using sensitivity analysis, ADOS. The required flow analyses were obtained by solving the three-dimensional, compressible, thin-layer Navier-Stokes equations using an implicit, upwind-biased, finite volume scheme. The sensitivity analyses were performed using the preconditioned version of the SADD scheme (sensitivity analysis on domain decomposition). In addition to demonstrating the present method's capability for automatic optimization, the results offered some insight into two important issues related to optimizing the shapes of multicomponent configurations in close proximity. First, inclusion of the mutual interference between the components resulted in a different shape as opposed to shaping an isolated component. Secondly, exclusion of the viscous effects compromised not only the flow physics but also the optimized shapes even for isolated components.
We are interested in the study, via direct numerical simulations, of active vortex generators. Vortex generators may be used to modify the inner part of the boundary layer or to control separation thus enhancing the performance and maneuverability of aerodynamic configurations. We consider generators that consist of a surface cavity elongated in the stream direction and partially covered with a moving lid that at rest lies flush with the boundary. Streamwise vorticity is generated and ejected due to the oscillatory motion of the lid. The present simulations complement relevant experimental investigations of active vortex generators at NASA Ames and Stanford University (Saddoughi, 1994, and Jacobson and Reynolds, 1993). Jacobson and Reynolds (1993) used a piezoelectric device in water, allowing for small amplitude high frequency oscillations. They placed the lid asymmetrically on the cavity and observed a strong outward velocity at the small gap of the cavity. Saddoughi used a larger mechanically driven device in air to investigate this flow and he observed a jet emerging from the wide gap of the configuration, contrary to the findings of Jacobson and Reynolds. Our task is to simulate the flows generated by these devices and to conduct a parametric study that would help us elucidate the physical mechanisms present in the flow. Conventional computational schemes encounter difficulties when simulating flows around complex configurations undergoing arbitrary motions. Here we present a formulation that achieves this task on a purely Lagrangian frame by extending the formulation presented by Koumoutsakos, Leonard and Pepin (1994). The viscous effects are taken into account by modifying the strength of the particles, whereas fast multipole schemes employing hundreds of thousands of particles allow for high resolution simulations. The results of the present simulations would help us assess some of the effects of three-dimensionality in experiments and investigate the role of two-dimensional vortex generation due to an oscillating lid.
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.